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  <front>
    <journal-meta><journal-id journal-id-type="publisher">BG</journal-id><journal-title-group>
    <journal-title>Biogeosciences</journal-title>
    <abbrev-journal-title abbrev-type="publisher">BG</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Biogeosciences</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1726-4189</issn><publisher>
    <publisher-name>Copernicus Publications</publisher-name>
    <publisher-loc>Göttingen, Germany</publisher-loc>
  </publisher></journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.5194/bg-20-1381-2023</article-id><title-group><article-title>Multi-proxy assessment of brachiopod shell calcite as a potential archive of
seawater temperature and oxygen isotope composition</article-title><alt-title>Brachiopod shells as an archive of temperature</alt-title>
      </title-group><?xmltex \runningtitle{Brachiopod shells as an archive of temperature}?><?xmltex \runningauthor{T. Letulle et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Letulle</surname><given-names>Thomas</given-names></name>
          <email>thomas.letulle@univ-lyon1.fr</email>
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Gaspard</surname><given-names>Danièle</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Daëron</surname><given-names>Mathieu</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-1210-9786</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Arnaud-Godet</surname><given-names>Florent</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Vinçon-Laugier</surname><given-names>Arnauld</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Suan</surname><given-names>Guillaume</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Lécuyer</surname><given-names>Christophe</given-names></name>
          
        </contrib>
        <aff id="aff1"><label>1</label><institution>Univ Lyon, UCBL, ENSL, UJM, CNRS, LGL-TPE, 69622 Villeurbanne,
France</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>UMR 7207, Centre de Recherche en Paléontologie, Paris
(CR2P), CNRS, MNHN, Sorbonne-Université, <?xmltex \hack{\break}?> Muséum national d'Histoire
naturelle, 8 Rue Buffon, CP 38, 75005 Paris, France</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Laboratoire des Sciences du Climat et de l'Environnement,
LSCE/IPSL, CEA-CNRS-UVSQ, <?xmltex \hack{\break}?> Université Paris-Saclay, Orme des Merisiers,
91191 Gif-sur-Yvette CEDEX, France</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Thomas Letulle (thomas.letulle@univ-lyon1.fr)</corresp></author-notes><pub-date><day>12</day><month>April</month><year>2023</year></pub-date>
      
      <volume>20</volume>
      <issue>7</issue>
      <fpage>1381</fpage><lpage>1403</lpage>
      <history>
        <date date-type="received"><day>22</day><month>October</month><year>2022</year></date>
           <date date-type="rev-request"><day>4</day><month>November</month><year>2022</year></date>
           <date date-type="rev-recd"><day>3</day><month>March</month><year>2023</year></date>
           <date date-type="accepted"><day>10</day><month>March</month><year>2023</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2023 Thomas Letulle et al.</copyright-statement>
        <copyright-year>2023</copyright-year>
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://bg.copernicus.org/articles/20/1381/2023/bg-20-1381-2023.html">This article is available from https://bg.copernicus.org/articles/20/1381/2023/bg-20-1381-2023.html</self-uri><self-uri xlink:href="https://bg.copernicus.org/articles/20/1381/2023/bg-20-1381-2023.pdf">The full text article is available as a PDF file from https://bg.copernicus.org/articles/20/1381/2023/bg-20-1381-2023.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d1e154">Most of our knowledge of past seawater temperature history is based on
<inline-formula><mml:math id="M1" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O values of calcium carbonate fossil shells. However, the
determination of past temperatures using this proxy requires the knowledge
of past seawater <inline-formula><mml:math id="M2" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O values, which is generally poorly
constrained. Other paleothermometers using carbonate archives, such as <inline-formula><mml:math id="M3" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>
ratios and clumped isotopes (<inline-formula><mml:math id="M4" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>), have been developed to allow for paleotemperatures to be estimated independently and to allow past ocean <inline-formula><mml:math id="M5" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O values to be calculated using various groups of calcifying
organisms. Articulated brachiopod shells are some of the most commonly used
archives in studies of past oceanic geochemistry and temperature. They are
abundant in the fossil record since the Cambrian, and for decades, their low
Mg–calcite mineralogy has been considered relatively resistant to diagenetic
alteration. Here, we investigate the potential of brachiopod shells as
recorders of seawater temperatures and seawater <inline-formula><mml:math id="M6" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O values
using new brachiopod shell geochemical data by testing multiple well-established or suggested paleothermometers applied to carbonate archives.</p>

      <p id="d1e225">Modern articulated brachiopod shells covering a wide range of temperatures
(<inline-formula><mml:math id="M7" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.9</mml:mn></mml:mrow></mml:math></inline-formula> to 25.5 <inline-formula><mml:math id="M8" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C), depths (5 to 3431 m) and salinities (33.4 to
37.0 PSU) were analysed for their stable isotope compositions (<inline-formula><mml:math id="M9" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>C, <inline-formula><mml:math id="M10" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O and <inline-formula><mml:math id="M11" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) and their elemental ratios
(<inline-formula><mml:math id="M12" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M13" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M14" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M15" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>). Our data allowed us to propose a revised
oxygen isotope fractionation equation between modern-brachiopod shell
calcite and seawater:
<?xmltex \hack{\newpage}?>
        <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M16" display="block"><mml:mrow><mml:mi>T</mml:mi><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5.0</mml:mn><mml:mo>(</mml:mo><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.2</mml:mn><mml:mo>)</mml:mo><mml:mo>(</mml:mo><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mi mathvariant="normal">sw</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mn mathvariant="normal">19.4</mml:mn><mml:mo>(</mml:mo><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.4</mml:mn><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
      where <inline-formula><mml:math id="M17" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M18" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:math></inline-formula> is in ‰ VPDB, <inline-formula><mml:math id="M19" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M20" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">sw</mml:mi></mml:msub></mml:math></inline-formula> is in ‰ VSMOW, and <inline-formula><mml:math id="M21" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> is in <inline-formula><mml:math id="M22" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C. Our results strongly support the use of clumped isotopes as an
alternative temperature proxy but confirm significant offsets relative to
the canonical relationship established for other biogenic and abiogenic
calcium carbonate minerals. Brachiopod shell <inline-formula><mml:math id="M23" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> ratios show no
relationship with seawater temperatures, indicating that this ratio is a
poor recorder of past changes in temperatures, an observation at variance
with several previous studies. Despite significant correlations with
brachiopod living temperature, brachiopod shell <inline-formula><mml:math id="M24" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M25" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M26" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>
values indicate the influence of environmental and biological factors
unrelated to temperature, which undermines their potential as alternative
temperature proxies. Kinetic effects (growth rates) could explain most of the
deviation of brachiopod shell calcite from expected isotopic equilibrium
with seawater and part of the distribution of <inline-formula><mml:math id="M27" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M28" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M29" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> ratios.</p>
  </abstract>
    
<funding-group>
<award-group id="gs1">
<funding-source>Agence Nationale de la Recherche</funding-source>
<award-id>ANR-18-CE31-0020</award-id>
</award-group>
</funding-group>
</article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d1e546">Oxygen isotope ratios (<inline-formula><mml:math id="M30" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O) of brachiopod shell calcite
constitute the most extensive record of marine temperatures over the
Phanerozoic eon (Prokoph et al.,
2008; Veizer and Prokoph, 2015). Nevertheless, our limited knowledge of
<inline-formula><mml:math id="M31" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O values of past seas and oceans prevents a confident
interpretation of this record, as carbonate <inline-formula><mml:math id="M32" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O values
(<inline-formula><mml:math id="M33" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M34" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:math></inline-formula>)<?pagebreak page1382?> are dependent on both shell growth temperature and
living-water <inline-formula><mml:math id="M35" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O (<inline-formula><mml:math id="M36" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M37" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">sw</mml:mi></mml:msub></mml:math></inline-formula>; Epstein
et al., 1953; Kim and O'Neil, 1997; Kim et al., 2007; Brand et al., 2013,
2019). Other paleotemperature proxies, such as trace element ratios and
clumped isotopes (<inline-formula><mml:math id="M38" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>), may be the key to building a more
confident record of Phanerozoic ocean temperatures. Owing to the
determination over the last decades of reliable oxygen isotope fractionation
equations between calcite and seawater, such independent temperature
estimates can be combined with <inline-formula><mml:math id="M39" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M40" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:math></inline-formula> measurements to
reconstruct <inline-formula><mml:math id="M41" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M42" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">sw</mml:mi></mml:msub></mml:math></inline-formula> values and hence to characterize oceanic
or local hydrography.</p>
      <p id="d1e686">Alternative carbonate archive thermometers have been developed for different
calcifying organisms and have been proposed in the literature as potentially
applicable to brachiopod shells. Element <inline-formula><mml:math id="M43" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> Ca ratios such as <inline-formula><mml:math id="M44" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M45" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math id="M46" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> are the most common in the literature. <inline-formula><mml:math id="M47" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> thermometry of
foraminiferal calcite (Nürnberg, 1995; Anand et
al., 2003) is a widely used proxy that is the basis for the reconstruction of
changes in <inline-formula><mml:math id="M48" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M49" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">sw</mml:mi></mml:msub></mml:math></inline-formula> and ice volumes over the Cenozoic era (Lear,
2000; Billups and Schrag, 2003; Miller et al., 2020). Building on the
pioneering work of Lowenstam (1961), Brand et al. (2013, 2019) documented a positive correlation between seawater temperature
and the MgCO<inline-formula><mml:math id="M50" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> content of brachiopod shells sampled at a worldwide
scale. Plus, following the conclusions of
Jiménez-López et al. (2004), Brand et
al. (2013) developed an isotopic fractionation equation that considers the
amount of Mg<inline-formula><mml:math id="M51" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> substituted for Ca<inline-formula><mml:math id="M52" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> in the crystal lattice of
the low-Mg calcitic shell which was abandoned in their more recent works
(Brand et al., 2019). The MgCO<inline-formula><mml:math id="M53" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>–temperature relationship is described by a curve named the
Global Brachiopod Mg Line (GBMgL), yet Brand et al. (2013, 2019)
acknowledge species-specific deviations from this concept that fall well above
the said line. Plus, brachiopod shell Mg content has been found to have
a strong taxonomic trend, with shells of thecideid and craniid brachiopods being made of
high-Mg calcite in contrast to the low-Mg calcite of rhynchonellide and
terebratulide brachiopod shells (Brand
et al., 2003; Ullmann et al., 2017). This undermines the brachiopod shell
MgCO<inline-formula><mml:math id="M54" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>–temperature relationships which uses a dataset that consists of thecideid,
rhynchonellide and terebratulide (Brand et al.,
2013, 2019).</p>
      <p id="d1e817">While <inline-formula><mml:math id="M55" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> ratios are mostly used to assess the shell preservation of
fossil specimens (Brand and Veizer, 1980), this ratio also
constitutes a potential marine paleothermometer applicable to brachiopod
shells, as is the case for corals (McCulloch
et al., 1994; Shen et al., 1996; Marshall and McCulloch, 2002; Swart et al.,
2002; Ayling et al., 2006; DeLong et al., 2011). Previous studies already
suggested <inline-formula><mml:math id="M56" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> ratios as marine paleothermometers for brachiopod shells
owing to their correlations with oxygen isotope ratios and seawater
temperature (Lowenstam,
1961; Mii and Grossman, 1994; Pérez-Huerta et al., 2008; Butler et al.,
2015; Ullmann et al., 2017). Similarly, the brachiopod <inline-formula><mml:math id="M57" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> ratio was also
suggested as a potential temperature proxy in the seminal study of
Delaney et al. (1989). Subsequent studies have also
confirmed that <inline-formula><mml:math id="M58" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> may constitute a potentially accurate thermometer in
brachiopods (Dellinger
et al., 2018; Rollion-Bard et al., 2019; Washington et al., 2020) and in
corals (Montagna et
al., 2014; Marchitto et al., 2018). For this latter group, however, the <inline-formula><mml:math id="M59" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Mg</mml:mi></mml:mrow></mml:math></inline-formula>
ratio has been considered to be a much more precise thermometer than <inline-formula><mml:math id="M60" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> (Montagna et al.,
2014; Marchitto et al., 2018) despite some identified caveats such as the
scrambling role of organic matter (Cuny-Guirriec et al., 2019).</p>
      <p id="d1e893">On top of element <inline-formula><mml:math id="M61" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> Ca proxies, clumped isotope (<inline-formula><mml:math id="M62" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) thermometry
has been developed more recently in relation to different carbonate materials
(Ghosh et al., 2006;
Zaarur et al., 2013). This parameter measures the anomaly of
<inline-formula><mml:math id="M63" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">13</mml:mn></mml:msup></mml:math></inline-formula>C–<inline-formula><mml:math id="M64" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:math></inline-formula>O bonds within the carbonate lattice relative to their
stochastic abundance. <inline-formula><mml:math id="M65" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> values are strongly correlated to
crystallization temperature and are independent from <inline-formula><mml:math id="M66" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M67" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">sw</mml:mi></mml:msub></mml:math></inline-formula>.
This proxy has been applied to different marine calcifying organisms to
estimate <inline-formula><mml:math id="M68" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M69" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">sw</mml:mi></mml:msub></mml:math></inline-formula> in the deep past
(Petersen
et al., 2016; Bergmann et al., 2018; Henkes et al., 2018; Wierzbowski et
al., 2018; Price et al., 2020; Vickers et al., 2020, 2021; de Winter et al.,
2021; Meckler et al., 2022). Although promising, brachiopod shell <inline-formula><mml:math id="M70" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> composition was only used in a couple of studies to estimate past
temperatures (Henkes et al., 2013; Came
et al., 2014). Indeed, the few existing modern-brachiopod <inline-formula><mml:math id="M71" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>–temperature data are in good agreement with the canonical <inline-formula><mml:math id="M72" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>–temperature relationship established for other biogenic and
abiogenic calcium carbonate minerals (Henkes et al., 2013; Came et al.,
2014). Recent compilation of <inline-formula><mml:math id="M73" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>–<inline-formula><mml:math id="M74" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> calibration data from
different laboratories using the new carbonate-based standardization
(Bernasconi
et al., 2018, 2021) concluded with a unique <inline-formula><mml:math id="M75" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>–<inline-formula><mml:math id="M76" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> relationship
for synthetic and natural carbonates (Anderson et al., 2021). The
establishment of such a unique calibration equation strengthens the good
agreement observed between natural and synthetic <inline-formula><mml:math id="M77" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>–<inline-formula><mml:math id="M78" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>
relationships and would suggest that this calibration is valid when applied
to brachiopod shells, especially as empirical calibrations are in very good
agreement with theoretical predictions (Jautzy et
al., 2020). However, <inline-formula><mml:math id="M79" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> measurements from brachiopod shells
are absent from this compilation, and other studies suggest that they may be
subjected to significant deviations from <inline-formula><mml:math id="M80" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>–<inline-formula><mml:math id="M81" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> relationships that are
likely related to differences in growth rates
(Bajnai et al., 2018, 2020).</p>
      <p id="d1e1103">Beside, a number of studies suggested that living temperature alone may not
explain the variability of those different parameters within brachiopod
shells. First, biogenic carbonate precipitation rate depends on
environmental and biological factors (temperature and salinity tolerance,
age, reproduction period, ontogeny, etc.), which causes biases in
the paleoenvironment record extracted from the shell
(Peck et al., 1997;
Schöne, 2008). Brachiopod shell calcite is secreted by the outer
epithelial cells of the mantle<?pagebreak page1383?> (Williams,
1968; Simonet Roda et al., 2019a, b, 2022). Calcite elements are in close
relationship with organic matrices which control the mineral growth (Williams,
1968; Gaspard et al., 2008; Gaspard and Nouet, 2016; Simonet Roda et al.,
2019a, b, 2022). Finally, nanoparticles are transported via ion transport
through the cell membrane, highlighting calcite precipitation as an
amorphous calcium carbonate precursor stage (Griesshaber et al.,
2009; Schmahl et al., 2012). The chemistry of the calcifying environment of
brachiopod shell calcite is poorly constrained (Immenhauser et al., 2016)
Testing thermodynamic equilibrium at the mineralization site is therefore,
to date, out of reach. Consequently, the chemistry of brachiopod shells is
usually compared to that of the surrounding water in order to approach the
processes involved in biomineralization from a chemical point of view.
Numerous studies highlighted that brachiopod shell calcite does not
precipitate sensu stricto in isotopic equilibrium with the surrounding water but, at best,
mimics thermodynamic equilibrium (Carpenter
and Lohmann, 1995; Auclair et al., 2003; Parkinson et al., 2005; Yamamoto et
al., 2010a, b; Cusack et al., 2012; Takayanagi et al., 2012, 2013, 2015;
Bajnai et al., 2018, 2020; Romanin et al., 2018; Rollion-Bard et al., 2019).
Brand et al. (2019) characterize their oxygen isotope fractionation equation
as representing a brachiopod based-equilibrium. This term is opposed to
the thermodynamic equilibrium, which is best described by very-slow-growing
calcites (Coplen, 2007;
Daëron et al., 2019), thus ensuring isotopic equilibration of the
dissolved inorganic carbon (DIC) species with water
(Watkins et al., 2013, 2014).
Trace element incorporation into calcite is also affected by kinetic
effects. In synthetic carbonates, the relative abundance of elements such as
Sr, Na and Li rises with higher growth rates (Lorens,
1981; Busenberg and Plummer, 1985; Tesoriero and Pankow, 1996; Gabitov et
al., 2011, 2014). Such kinetic trends were evidenced at an intra-individual
level among brachiopods by the negative correlation of element <inline-formula><mml:math id="M82" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> Ca ratios
with stable isotope values (<inline-formula><mml:math id="M83" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>C, <inline-formula><mml:math id="M84" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O; Ullmann et al., 2017;
Rollion-Bard et al., 2019).</p>
      <p id="d1e1135">In this study, we assess the potential of various geochemical proxies
(<inline-formula><mml:math id="M85" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O, <inline-formula><mml:math id="M86" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M87" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>; <inline-formula><mml:math id="M88" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M89" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M90" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>) as
recorders of seawater temperature by analysing a new set of modern
articulated brachiopod shells collected from various depths and latitudes
during institutional oceanographic cruises and covering a broad range of
water temperatures comprised between <inline-formula><mml:math id="M91" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.9</mml:mn></mml:mrow></mml:math></inline-formula> and 25.5 <inline-formula><mml:math id="M92" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C. We discuss the validity and robustness of our oxygen isotope
fractionation equation established with measured <inline-formula><mml:math id="M93" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M94" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:math></inline-formula> of
calcite and with seawater temperature and <inline-formula><mml:math id="M95" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M96" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:math></inline-formula> estimated from
oceanographic data. The dependence of elemental ratios on seawater
temperature is discussed in light of this new available dataset of
modern brachiopods. Finally, we highlight kinetic effects as non-negligible
sources of isotopic and trace element variability.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Material and methods</title>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Sample collection and environmental parameters</title>
      <p id="d1e1284">The studied material consists of 37 articulated brachiopod shells that were
collected in situ during institutional oceanographic cruises or other scientific
missions (see Supplement for details). The sampling location was
documented with depth and geographic coordinates for most samples.
Temperature and salinity, which were not measured in situ for most samples, were
estimated independently using the NOAA World Ocean Atlas 2018
(Locarnini et al.,
2018; Zweng et al., 2018) or, whenever available, using long-term local
records in the literature (Table 1). For both temperature and salinity, mean
annual values (MAT), as well as higher and lower monthly averages, were
considered. Similarly, <inline-formula><mml:math id="M97" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M98" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">sw</mml:mi></mml:msub></mml:math></inline-formula> values were usually not
measured in situ but were calculated from the salinity data with the appropriate
regional <inline-formula><mml:math id="M99" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M100" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">sw</mml:mi></mml:msub></mml:math></inline-formula>–<inline-formula><mml:math id="M101" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> relationship from
LeGrande and Schmidt (2006). The oceanographic parameters
used in this study are listed in Table 1.</p>

<?xmltex \floatpos{p}?><table-wrap id="Ch1.T1" specific-use="star"><?xmltex \currentcnt{1}?><label>Table 1</label><caption><p id="d1e1337">Brachiopod samples with taxonomic identification, sampling location
and environmental parameters. Most environmental parameters are derived from
the World Ocean Atlas 2018 (Locarnini et al.,
2018; Zweng et al., 2018). For a few samples, environmental parameters are
derived from local literature, as listed below. Almost all <inline-formula><mml:math id="M102" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M103" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">sw</mml:mi></mml:msub></mml:math></inline-formula> values are calculated using the regional <inline-formula><mml:math id="M104" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M105" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">sw</mml:mi></mml:msub></mml:math></inline-formula>–salinity relationship published by LeGrande
and Schmidt (2006), unless direct measurements covering seasonal variations
were available in the literature.</p></caption><oasis:table frame="topbot"><?xmltex \begin{scaleboxenv}{.85}[.85]?><oasis:tgroup cols="9">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:colspec colnum="6" colname="col6" align="right"/>
     <oasis:colspec colnum="7" colname="col7" align="right"/>
     <oasis:colspec colnum="8" colname="col8" align="right"/>
     <oasis:colspec colnum="9" colname="col9" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">Specimen</oasis:entry>
         <oasis:entry colname="col2">Taxa</oasis:entry>
         <oasis:entry colname="col3">Living  location</oasis:entry>
         <oasis:entry colname="col4">Depth</oasis:entry>
         <oasis:entry colname="col5">MAT</oasis:entry>
         <oasis:entry colname="col6">Seasonal <inline-formula><mml:math id="M110" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">Salinity</oasis:entry>
         <oasis:entry colname="col8">Seasonal</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M111" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M112" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">sw</mml:mi></mml:msub></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4">(m)</oasis:entry>
         <oasis:entry colname="col5">(<inline-formula><mml:math id="M113" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C)</oasis:entry>
         <oasis:entry colname="col6">variation</oasis:entry>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8">salinity</oasis:entry>
         <oasis:entry colname="col9">(‰ VSMOW)</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">(<inline-formula><mml:math id="M114" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C)</oasis:entry>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
         <oasis:entry colname="col9"/>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row rowsep="1">
         <oasis:entry namest="col1" nameend="col9">New Caledonia </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">FNEO-N4</oasis:entry>
         <oasis:entry colname="col2"><italic>Fallax neocaledonensis</italic></oasis:entry>
         <oasis:entry colname="col3">22<inline-formula><mml:math id="M115" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>54<inline-formula><mml:math id="M116" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> S–167<inline-formula><mml:math id="M117" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>13<inline-formula><mml:math id="M118" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> E</oasis:entry>
         <oasis:entry colname="col4">403–429</oasis:entry>
         <oasis:entry colname="col5">13.4</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M119" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.2</oasis:entry>
         <oasis:entry colname="col7">35.11</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M120" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.05</oasis:entry>
         <oasis:entry colname="col9">0.60</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">FNEO-M2</oasis:entry>
         <oasis:entry colname="col2"><italic>Fallax neocaledonensis</italic></oasis:entry>
         <oasis:entry colname="col3">18<inline-formula><mml:math id="M121" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>46<inline-formula><mml:math id="M122" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> S–163<inline-formula><mml:math id="M123" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>16<inline-formula><mml:math id="M124" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> E</oasis:entry>
         <oasis:entry colname="col4">600</oasis:entry>
         <oasis:entry colname="col5">7.7</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M125" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.6</oasis:entry>
         <oasis:entry colname="col7">34.55</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M126" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.03</oasis:entry>
         <oasis:entry colname="col9">0.45</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">FSAN-3</oasis:entry>
         <oasis:entry colname="col2"><italic>Frenulina sanguinolenta</italic></oasis:entry>
         <oasis:entry colname="col3">20<inline-formula><mml:math id="M127" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>52<inline-formula><mml:math id="M128" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> S–167<inline-formula><mml:math id="M129" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>08<inline-formula><mml:math id="M130" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> E</oasis:entry>
         <oasis:entry colname="col4">5–20</oasis:entry>
         <oasis:entry colname="col5">25.4</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M131" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.8</oasis:entry>
         <oasis:entry colname="col7">35.18</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M132" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.10</oasis:entry>
         <oasis:entry colname="col9">0.62</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SCRO-1</oasis:entry>
         <oasis:entry colname="col2"><italic>Stenosarina crosnieri</italic></oasis:entry>
         <oasis:entry colname="col3">22<inline-formula><mml:math id="M133" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>59<inline-formula><mml:math id="M134" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> S–167<inline-formula><mml:math id="M135" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>19<inline-formula><mml:math id="M136" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> E</oasis:entry>
         <oasis:entry colname="col4">525</oasis:entry>
         <oasis:entry colname="col5">10.0</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M137" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.9</oasis:entry>
         <oasis:entry colname="col7">34.76</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M138" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.01</oasis:entry>
         <oasis:entry colname="col9">0.51</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SCRO-3</oasis:entry>
         <oasis:entry colname="col2"><italic>Stenosarina crosnieri</italic></oasis:entry>
         <oasis:entry colname="col3">22<inline-formula><mml:math id="M139" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>59<inline-formula><mml:math id="M140" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> S–167<inline-formula><mml:math id="M141" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>19<inline-formula><mml:math id="M142" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> E</oasis:entry>
         <oasis:entry colname="col4">525</oasis:entry>
         <oasis:entry colname="col5">10.0</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M143" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.9</oasis:entry>
         <oasis:entry colname="col7">34.76</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M144" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.01</oasis:entry>
         <oasis:entry colname="col9">0.51</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SGLO-S1</oasis:entry>
         <oasis:entry colname="col2"><italic>Stenosarina globosa</italic></oasis:entry>
         <oasis:entry colname="col3">19<inline-formula><mml:math id="M145" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>06<inline-formula><mml:math id="M146" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> S–163<inline-formula><mml:math id="M147" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>30<inline-formula><mml:math id="M148" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> E</oasis:entry>
         <oasis:entry colname="col4">215–225</oasis:entry>
         <oasis:entry colname="col5">19.7</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M149" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.7</oasis:entry>
         <oasis:entry colname="col7">35.61</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M150" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.01</oasis:entry>
         <oasis:entry colname="col9">0.73</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SGLO-M1</oasis:entry>
         <oasis:entry colname="col2"><italic>Stenosarina globosa</italic></oasis:entry>
         <oasis:entry colname="col3">18<inline-formula><mml:math id="M151" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>59<inline-formula><mml:math id="M152" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> S–163<inline-formula><mml:math id="M153" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>24<inline-formula><mml:math id="M154" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> E</oasis:entry>
         <oasis:entry colname="col4">320</oasis:entry>
         <oasis:entry colname="col5">16.4</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M155" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.7</oasis:entry>
         <oasis:entry colname="col7">35.40</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M156" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.02</oasis:entry>
         <oasis:entry colname="col9">0.68</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">SGLO-M2</oasis:entry>
         <oasis:entry colname="col2"><italic>Stenosarina globosa</italic></oasis:entry>
         <oasis:entry colname="col3">18<inline-formula><mml:math id="M157" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>59<inline-formula><mml:math id="M158" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> S–163<inline-formula><mml:math id="M159" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>24<inline-formula><mml:math id="M160" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> E</oasis:entry>
         <oasis:entry colname="col4">320</oasis:entry>
         <oasis:entry colname="col5">16.4</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M161" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.7</oasis:entry>
         <oasis:entry colname="col7">35.40</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M162" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.02</oasis:entry>
         <oasis:entry colname="col9">0.68</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry namest="col1" nameend="col9">Guadeloupe </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TGAL-3</oasis:entry>
         <oasis:entry colname="col2"><italic>Tichosina cubensis</italic></oasis:entry>
         <oasis:entry colname="col3">15<inline-formula><mml:math id="M163" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>53<inline-formula><mml:math id="M164" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> N–61<inline-formula><mml:math id="M165" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>25<inline-formula><mml:math id="M166" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> W</oasis:entry>
         <oasis:entry colname="col4">262–266</oasis:entry>
         <oasis:entry colname="col5">16.6</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M167" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.0</oasis:entry>
         <oasis:entry colname="col7">36.22</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M168" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.04</oasis:entry>
         <oasis:entry colname="col9">0.82</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TGAL-4</oasis:entry>
         <oasis:entry colname="col2"><italic>Tichosina cubensis</italic></oasis:entry>
         <oasis:entry colname="col3">15<inline-formula><mml:math id="M169" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>53<inline-formula><mml:math id="M170" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> N–61<inline-formula><mml:math id="M171" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>25<inline-formula><mml:math id="M172" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> W</oasis:entry>
         <oasis:entry colname="col4">262–266</oasis:entry>
         <oasis:entry colname="col5">16.6</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M173" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.0</oasis:entry>
         <oasis:entry colname="col7">36.22</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M174" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.04</oasis:entry>
         <oasis:entry colname="col9">0.82</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TCUB-2</oasis:entry>
         <oasis:entry colname="col2"><italic>Tichosina cubensis</italic></oasis:entry>
         <oasis:entry colname="col3">16<inline-formula><mml:math id="M175" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>20<inline-formula><mml:math id="M176" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> N–60<inline-formula><mml:math id="M177" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>57<inline-formula><mml:math id="M178" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> W</oasis:entry>
         <oasis:entry colname="col4">250</oasis:entry>
         <oasis:entry colname="col5">17.3</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M179" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.2</oasis:entry>
         <oasis:entry colname="col7">36.38</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M180" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.03</oasis:entry>
         <oasis:entry colname="col9">0.85</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TCUB-3</oasis:entry>
         <oasis:entry colname="col2"><italic>Tichosina cubensis</italic></oasis:entry>
         <oasis:entry colname="col3">16<inline-formula><mml:math id="M181" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>20<inline-formula><mml:math id="M182" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> N–60<inline-formula><mml:math id="M183" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>57<inline-formula><mml:math id="M184" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> W</oasis:entry>
         <oasis:entry colname="col4">250</oasis:entry>
         <oasis:entry colname="col5">17.3</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M185" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.2</oasis:entry>
         <oasis:entry colname="col7">36.38</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M186" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.03</oasis:entry>
         <oasis:entry colname="col9">0.85</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TPLI-2</oasis:entry>
         <oasis:entry colname="col2"><italic>Tichosina cf. plicata</italic></oasis:entry>
         <oasis:entry colname="col3">16<inline-formula><mml:math id="M187" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>21<inline-formula><mml:math id="M188" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> N–60<inline-formula><mml:math id="M189" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>54<inline-formula><mml:math id="M190" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> W</oasis:entry>
         <oasis:entry colname="col4">111–162</oasis:entry>
         <oasis:entry colname="col5">23.6<inline-formula><mml:math id="M191" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 2</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M192" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.0</oasis:entry>
         <oasis:entry colname="col7">36.8 <inline-formula><mml:math id="M193" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.1</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M194" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.15</oasis:entry>
         <oasis:entry colname="col9">0.92</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TPLI-5</oasis:entry>
         <oasis:entry colname="col2"><italic>Tichosina cf. plicata</italic></oasis:entry>
         <oasis:entry colname="col3">16<inline-formula><mml:math id="M195" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>21<inline-formula><mml:math id="M196" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> N–60<inline-formula><mml:math id="M197" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>54<inline-formula><mml:math id="M198" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> W</oasis:entry>
         <oasis:entry colname="col4">111–162</oasis:entry>
         <oasis:entry colname="col5">23.6<inline-formula><mml:math id="M199" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 2</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M200" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.0</oasis:entry>
         <oasis:entry colname="col7">36.8 <inline-formula><mml:math id="M201" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.1</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M202" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.15</oasis:entry>
         <oasis:entry colname="col9">0.92</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TDES-G1</oasis:entry>
         <oasis:entry colname="col2"><italic>Tichosina</italic> sp.</oasis:entry>
         <oasis:entry colname="col3">16<inline-formula><mml:math id="M203" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>21<inline-formula><mml:math id="M204" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> N–60<inline-formula><mml:math id="M205" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>54<inline-formula><mml:math id="M206" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> W</oasis:entry>
         <oasis:entry colname="col4">111–162</oasis:entry>
         <oasis:entry colname="col5">23.6<inline-formula><mml:math id="M207" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 2</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M208" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.0</oasis:entry>
         <oasis:entry colname="col7">36.8 <inline-formula><mml:math id="M209" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.1</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M210" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.15</oasis:entry>
         <oasis:entry colname="col9">0.92</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TDES-G3</oasis:entry>
         <oasis:entry colname="col2"><italic>Tichosina</italic> sp.</oasis:entry>
         <oasis:entry colname="col3">16<inline-formula><mml:math id="M211" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>21<inline-formula><mml:math id="M212" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> N–60<inline-formula><mml:math id="M213" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>54<inline-formula><mml:math id="M214" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> W</oasis:entry>
         <oasis:entry colname="col4">111–162</oasis:entry>
         <oasis:entry colname="col5">23.6<inline-formula><mml:math id="M215" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 2</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M216" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.0</oasis:entry>
         <oasis:entry colname="col7">36.8 <inline-formula><mml:math id="M217" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.1</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M218" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.15</oasis:entry>
         <oasis:entry colname="col9">0.92</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TDES-B2</oasis:entry>
         <oasis:entry colname="col2"><italic>Tichosina cf. cubensis</italic></oasis:entry>
         <oasis:entry colname="col3">16<inline-formula><mml:math id="M219" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>21<inline-formula><mml:math id="M220" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> N–60<inline-formula><mml:math id="M221" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>54<inline-formula><mml:math id="M222" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> W</oasis:entry>
         <oasis:entry colname="col4">111–162</oasis:entry>
         <oasis:entry colname="col5">23.6<inline-formula><mml:math id="M223" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 2</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M224" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.0</oasis:entry>
         <oasis:entry colname="col7">36.8 <inline-formula><mml:math id="M225" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.1</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M226" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.15</oasis:entry>
         <oasis:entry colname="col9">0.92</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TDES-B4</oasis:entry>
         <oasis:entry colname="col2"><italic>Tichosina cf. cubensis</italic></oasis:entry>
         <oasis:entry colname="col3">16<inline-formula><mml:math id="M227" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>21<inline-formula><mml:math id="M228" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> N–60<inline-formula><mml:math id="M229" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>54<inline-formula><mml:math id="M230" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> W</oasis:entry>
         <oasis:entry colname="col4">111–162</oasis:entry>
         <oasis:entry colname="col5">23.6<inline-formula><mml:math id="M231" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 2</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M232" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.0</oasis:entry>
         <oasis:entry colname="col7">36.8 <inline-formula><mml:math id="M233" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.1</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M234" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.15</oasis:entry>
         <oasis:entry colname="col9">0.92</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">TLAT-5</oasis:entry>
         <oasis:entry colname="col2"><italic>Terebratulina latifrons</italic></oasis:entry>
         <oasis:entry colname="col3">16<inline-formula><mml:math id="M235" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>21<inline-formula><mml:math id="M236" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> N–60<inline-formula><mml:math id="M237" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>54<inline-formula><mml:math id="M238" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> W</oasis:entry>
         <oasis:entry colname="col4">111–162</oasis:entry>
         <oasis:entry colname="col5">23.6<inline-formula><mml:math id="M239" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 2</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M240" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.0</oasis:entry>
         <oasis:entry colname="col7">36.8 <inline-formula><mml:math id="M241" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.1</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M242" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.15</oasis:entry>
         <oasis:entry colname="col9">0.92</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry namest="col1" nameend="col9">New Zealand </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">WB5<inline-formula><mml:math id="M243" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2"><italic>Terebratella sanguinea</italic></oasis:entry>
         <oasis:entry colname="col3">45<inline-formula><mml:math id="M244" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>20.86<inline-formula><mml:math id="M245" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> S–167<inline-formula><mml:math id="M246" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>02.86<inline-formula><mml:math id="M247" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> E</oasis:entry>
         <oasis:entry colname="col4">12–20</oasis:entry>
         <oasis:entry colname="col5">13.6</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M248" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">3.3</mml:mn></mml:mrow></mml:math></inline-formula>; <inline-formula><mml:math id="M249" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.7</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">34.70</oasis:entry>
         <oasis:entry colname="col8"/>
         <oasis:entry colname="col9">0.33</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">WB6<inline-formula><mml:math id="M250" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2"><italic>Liothyrella neozelanica</italic></oasis:entry>
         <oasis:entry colname="col3">45<inline-formula><mml:math id="M251" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>19<inline-formula><mml:math id="M252" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula>30<inline-formula><mml:math id="M253" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> S–166<inline-formula><mml:math id="M254" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>59<inline-formula><mml:math id="M255" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula>24<inline-formula><mml:math id="M256" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> E</oasis:entry>
         <oasis:entry colname="col4">20–30</oasis:entry>
         <oasis:entry colname="col5">13.2</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M257" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 2.5</oasis:entry>
         <oasis:entry colname="col7">34.70</oasis:entry>
         <oasis:entry colname="col8"/>
         <oasis:entry colname="col9">0.33</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">WB8</oasis:entry>
         <oasis:entry colname="col2"><italic>Notosaria nigricans</italic></oasis:entry>
         <oasis:entry colname="col3">45<inline-formula><mml:math id="M258" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>21<inline-formula><mml:math id="M259" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula>36<inline-formula><mml:math id="M260" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> S–170<inline-formula><mml:math id="M261" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>50<inline-formula><mml:math id="M262" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula>24<inline-formula><mml:math id="M263" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> E</oasis:entry>
         <oasis:entry colname="col4">20</oasis:entry>
         <oasis:entry colname="col5">10.4</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M264" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 2.0</oasis:entry>
         <oasis:entry colname="col7">34.34</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M265" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.05</oasis:entry>
         <oasis:entry colname="col9">0.16</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">WB9A<inline-formula><mml:math id="M266" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2"><italic>Calloria inconspicua</italic></oasis:entry>
         <oasis:entry colname="col3">43<inline-formula><mml:math id="M267" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>34<inline-formula><mml:math id="M268" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula>27<inline-formula><mml:math id="M269" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> S–172<inline-formula><mml:math id="M270" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>40<inline-formula><mml:math id="M271" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> 07<inline-formula><mml:math id="M272" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> E</oasis:entry>
         <oasis:entry colname="col4">20</oasis:entry>
         <oasis:entry colname="col5">14.0</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M273" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 4</oasis:entry>
         <oasis:entry colname="col7">33.40</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M274" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.90</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M275" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.26</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry namest="col1" nameend="col9">Crozet Islands </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">WB4A</oasis:entry>
         <oasis:entry colname="col2"><italic>Aerothyris kerguelenensis</italic></oasis:entry>
         <oasis:entry colname="col3">45<inline-formula><mml:math id="M276" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>57<inline-formula><mml:math id="M277" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula>36<inline-formula><mml:math id="M278" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> S–50<inline-formula><mml:math id="M279" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>03<inline-formula><mml:math id="M280" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula>24<inline-formula><mml:math id="M281" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> E</oasis:entry>
         <oasis:entry colname="col4">200</oasis:entry>
         <oasis:entry colname="col5">3.9</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M282" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.6</oasis:entry>
         <oasis:entry colname="col7">33.97</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M283" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.02</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M284" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.30</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">WB4B</oasis:entry>
         <oasis:entry colname="col2"><italic>Aerothyris kerguelenensis</italic></oasis:entry>
         <oasis:entry colname="col3">46<inline-formula><mml:math id="M285" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>06<inline-formula><mml:math id="M286" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula>0<inline-formula><mml:math id="M287" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> S–50<inline-formula><mml:math id="M288" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>38<inline-formula><mml:math id="M289" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula>18<inline-formula><mml:math id="M290" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> E</oasis:entry>
         <oasis:entry colname="col4">212–230</oasis:entry>
         <oasis:entry colname="col5">3.7</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M291" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.6</oasis:entry>
         <oasis:entry colname="col7">34.01</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M292" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.03</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M293" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.29</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">AKER-52</oasis:entry>
         <oasis:entry colname="col2"><italic>Aerothyris kerguelenensis</italic></oasis:entry>
         <oasis:entry colname="col3">45<inline-formula><mml:math id="M294" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>48<inline-formula><mml:math id="M295" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula>06<inline-formula><mml:math id="M296" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> S–49<inline-formula><mml:math id="M297" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>45<inline-formula><mml:math id="M298" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula>45<inline-formula><mml:math id="M299" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> E</oasis:entry>
         <oasis:entry colname="col4">355</oasis:entry>
         <oasis:entry colname="col5">3.1</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M300" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.3</oasis:entry>
         <oasis:entry colname="col7">34.16</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M301" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.01</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M302" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.25</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">AKER-66</oasis:entry>
         <oasis:entry colname="col2"><italic>Aerothyris kerguelenensis</italic></oasis:entry>
         <oasis:entry colname="col3">46<inline-formula><mml:math id="M303" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>40<inline-formula><mml:math id="M304" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula>00<inline-formula><mml:math id="M305" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> S–51<inline-formula><mml:math id="M306" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>40<inline-formula><mml:math id="M307" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula>30<inline-formula><mml:math id="M308" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> E</oasis:entry>
         <oasis:entry colname="col4">325</oasis:entry>
         <oasis:entry colname="col5">2.8</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M309" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.6</oasis:entry>
         <oasis:entry colname="col7">34.16</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M310" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.01</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M311" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.25</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">AKER-12</oasis:entry>
         <oasis:entry colname="col2"><italic>Aerothyris kerguelenensis</italic></oasis:entry>
         <oasis:entry colname="col3">46<inline-formula><mml:math id="M312" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>07<inline-formula><mml:math id="M313" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula>24<inline-formula><mml:math id="M314" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> S–50<inline-formula><mml:math id="M315" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>46<inline-formula><mml:math id="M316" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula>18<inline-formula><mml:math id="M317" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> E</oasis:entry>
         <oasis:entry colname="col4">290–305</oasis:entry>
         <oasis:entry colname="col5">3.2</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M318" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.2</oasis:entry>
         <oasis:entry colname="col7">34.11</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M319" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.01</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M320" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.26</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">AKER-73</oasis:entry>
         <oasis:entry colname="col2"><italic>Aerothyris kerguelenensis</italic></oasis:entry>
         <oasis:entry colname="col3">46<inline-formula><mml:math id="M321" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>28<inline-formula><mml:math id="M322" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula>30<inline-formula><mml:math id="M323" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> S–51<inline-formula><mml:math id="M324" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>35<inline-formula><mml:math id="M325" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula>00<inline-formula><mml:math id="M326" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> E</oasis:entry>
         <oasis:entry colname="col4">207–215</oasis:entry>
         <oasis:entry colname="col5">3.3</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M327" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.8</oasis:entry>
         <oasis:entry colname="col7">34.00</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M328" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.02</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M329" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.29</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">AKER-68</oasis:entry>
         <oasis:entry colname="col2"><italic>Aerothyris kerguelenensis</italic></oasis:entry>
         <oasis:entry colname="col3">46<inline-formula><mml:math id="M330" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>32<inline-formula><mml:math id="M331" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula>54<inline-formula><mml:math id="M332" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> S–51<inline-formula><mml:math id="M333" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>47<inline-formula><mml:math id="M334" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula>00<inline-formula><mml:math id="M335" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> E</oasis:entry>
         <oasis:entry colname="col4">200</oasis:entry>
         <oasis:entry colname="col5">3.4</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M336" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.8</oasis:entry>
         <oasis:entry colname="col7">33.99</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M337" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.03</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M338" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.29</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">AKER-79</oasis:entry>
         <oasis:entry colname="col2"><italic>Aerothyris kerguelenensis</italic></oasis:entry>
         <oasis:entry colname="col3">45<inline-formula><mml:math id="M339" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>51<inline-formula><mml:math id="M340" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula>24<inline-formula><mml:math id="M341" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> S–50<inline-formula><mml:math id="M342" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>44<inline-formula><mml:math id="M343" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula>00<inline-formula><mml:math id="M344" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> E</oasis:entry>
         <oasis:entry colname="col4">140</oasis:entry>
         <oasis:entry colname="col5">4.2</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M345" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.6</oasis:entry>
         <oasis:entry colname="col7">33.90</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M346" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.01</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M347" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.31</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">AKER-61</oasis:entry>
         <oasis:entry colname="col2"><italic>Aerothyris kerguelenensis</italic></oasis:entry>
         <oasis:entry colname="col3">46<inline-formula><mml:math id="M348" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>28<inline-formula><mml:math id="M349" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula>00<inline-formula><mml:math id="M350" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> S–51<inline-formula><mml:math id="M351" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>53<inline-formula><mml:math id="M352" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> 12<inline-formula><mml:math id="M353" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> E</oasis:entry>
         <oasis:entry colname="col4">105</oasis:entry>
         <oasis:entry colname="col5">4.1</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M354" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.2</oasis:entry>
         <oasis:entry colname="col7">33.85</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M355" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.01</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M356" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.33</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry namest="col1" nameend="col9">Antarctica </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">WB1A</oasis:entry>
         <oasis:entry colname="col2"><italic>Magellania fragilis</italic></oasis:entry>
         <oasis:entry colname="col3">66<inline-formula><mml:math id="M357" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>38<inline-formula><mml:math id="M358" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> S–143<inline-formula><mml:math id="M359" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>05<inline-formula><mml:math id="M360" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> E</oasis:entry>
         <oasis:entry colname="col4">862–875</oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M361" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.9</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M362" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">0.3</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">34.70</oasis:entry>
         <oasis:entry colname="col8">–</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M363" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.13</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">MFRA-CEA</oasis:entry>
         <oasis:entry colname="col2"><italic>Magellania fragilis</italic></oasis:entry>
         <oasis:entry colname="col3">66<inline-formula><mml:math id="M364" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>38<inline-formula><mml:math id="M365" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> S–143<inline-formula><mml:math id="M366" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>05<inline-formula><mml:math id="M367" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> E</oasis:entry>
         <oasis:entry colname="col4">862–875</oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M368" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.9</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M369" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">0.3</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">34.70</oasis:entry>
         <oasis:entry colname="col8">–</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M370" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.13</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">LUVA-PAL<inline-formula><mml:math id="M371" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2"><italic>Liothyrella uva</italic></oasis:entry>
         <oasis:entry colname="col3">67<inline-formula><mml:math id="M372" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>34<inline-formula><mml:math id="M373" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> S–68<inline-formula><mml:math id="M374" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>08<inline-formula><mml:math id="M375" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula>  W</oasis:entry>
         <oasis:entry colname="col4">10–30</oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M376" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.1</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M377" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.4</oasis:entry>
         <oasis:entry colname="col7">33.30</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M378" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.20</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M379" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.65</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry namest="col1" nameend="col9">Norway </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">MCRA-SKA<inline-formula><mml:math id="M380" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2"><italic>Macandrevia cranium</italic></oasis:entry>
         <oasis:entry colname="col3">63<inline-formula><mml:math id="M381" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>52<inline-formula><mml:math id="M382" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> N–11<inline-formula><mml:math id="M383" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>04<inline-formula><mml:math id="M384" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> E</oasis:entry>
         <oasis:entry colname="col4">40–100</oasis:entry>
         <oasis:entry colname="col5">7</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M385" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1</oasis:entry>
         <oasis:entry colname="col7">33.5</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M386" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.5</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M387" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.56</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry namest="col1" nameend="col9">Offshore Angola </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">MAF-5</oasis:entry>
         <oasis:entry colname="col2"><italic>Macandrevia africana</italic></oasis:entry>
         <oasis:entry colname="col3">12<inline-formula><mml:math id="M388" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>21.4<inline-formula><mml:math id="M389" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> S–11<inline-formula><mml:math id="M390" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>02.7<inline-formula><mml:math id="M391" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> E</oasis:entry>
         <oasis:entry colname="col4">3431</oasis:entry>
         <oasis:entry colname="col5">2.5</oasis:entry>
         <oasis:entry colname="col6">–</oasis:entry>
         <oasis:entry colname="col7">34.90</oasis:entry>
         <oasis:entry colname="col8">–</oasis:entry>
         <oasis:entry colname="col9">0.05</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup><?xmltex \end{scaleboxenv}?></oasis:table><table-wrap-foot><p id="d1e1380"><inline-formula><mml:math id="M106" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula> Goodwin and Cornelisen (2012); <inline-formula><mml:math id="M107" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula> Woods et
al. (2014); <inline-formula><mml:math id="M108" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> Meredith et al. (2013);
<inline-formula><mml:math id="M109" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msup></mml:math></inline-formula> Jacobson (1983).</p></table-wrap-foot><?xmltex \gdef\@currentlabel{1}?></table-wrap>

</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Sample preparation</title>
      <p id="d1e5143">Encrusting organisms covering the shells were first mechanically removed
using stainless steel dental tools, and each shell was then placed in diluted
bleach (NaClO 5 %) for 5 to 10 min in an ultrasonic bath to remove
organic matter and other contaminants. As preliminary tests have revealed
that the more delicate shells (e.g. <italic>Macandrevia africana</italic>; Cooper, 1975) broke apart during the
ultrasonic bath, immersion in diluted bleach for a few hours without the
ultrasonic bath was subsequently preferred for a few specimens. In all cases,
the specimens were rinsed with deionized water and oven dried at
50 <inline-formula><mml:math id="M392" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C for a few hours.</p>
      <?pagebreak page1385?><p id="d1e5158">The sampling of brachiopod shell calcite was performed following the
recommendations of Romanin et al. (2018). The umbo, edges and muscle scar area were avoided because they
record major kinetic or metabolic effects (Carpenter
and Lohmann, 1995; Auclair et al., 2003; Parkinson et al., 2005; Yamamoto et
al., 2010b; Ullmann et al., 2017; Romanin et al., 2018), and sampling was
focused on the middle part of the shell. Considering the complex structure
of brachiopod shells (Williams,
1968; Gaspard et al., 2018; Simonet Roda et al., 2022) relative to the
precision of our sampling method (dental tools and engraving bit), we were
unable to prepare pure samples for each layer of the brachiopod shell
(acicular primary layer, fibrous secondary layer and columnar tertiary
layer). In this study, we differentiate the outer layers, i.e. a mix of the
primary acicular layer and some amount of the outer secondary fibrous layer,
which record significant kinetic effects (Carpenter
and Lohmann, 1995; Auclair et al., 2003; Parkinson et al., 2005; Bajnai et
al., 2018; Romanin et al., 2018; Rollion-Bard et al., 2019), from the inner
layers, i.e. the inner secondary fibrous layer and/or the tertiary
columnar layer when present. Outer shell layers were removed manually with
dental tools, and resulting powders were kept to compare their elemental
ratios, <inline-formula><mml:math id="M393" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O and <inline-formula><mml:math id="M394" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>C with those of the inner shell layers
(Carpenter and
Lohmann, 1995; Auclair et al., 2003; Pérez-Huerta et al., 2008). After
removal of the outer layers, the inner layers were sampled using an
engraving bit fitted to a DREMEL Micro™ drill adjusted to the lowest
possible speed. For each sample, the powder was used for all selected
geochemical analyses which correspond to <inline-formula><mml:math id="M395" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O, <inline-formula><mml:math id="M396" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>C, <inline-formula><mml:math id="M397" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and element concentration. As clumped isotope
analyses require large amounts of material (<inline-formula><mml:math id="M398" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> mg is necessary
to operate multiple replicate analyses), a large area (a few
cm<inline-formula><mml:math id="M399" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula>) was sampled in the middle part of the shell, allowing
several mg of calcitic powder to be collected. It is worth noting that
this large sampling area may correspond to several months or years of shell
growth, depending on the species.</p>
      <p id="d1e5236">This sampling protocol was applied to most of our samples, except for the
smallest and most fragile shells that quickly broke apart during sampling.
Consequently, in the case of the small shells of <italic>Terebratulina latifrons</italic>, <italic>Frenulina sanguinolenta</italic> and some specimens of
<italic>Fallax neocaledonensis</italic>, the outer layers were kept, and only the area covering the umbo up to the
muscle scar was avoided for sampling. The weakness and thinness of <italic>M. africana</italic>
precluded a total removal of the outer layers; however, the umbo, muscle
scars and edges were removed from the bulk shell. Fragments of these more
fragile shells were ground to a fine powder in an agate mortar.</p>
</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><title>Carbon and oxygen stable isotopes</title>
      <p id="d1e5259">Stable isotope compositions of the sampled powders were determined using a MultiPrep™ Autosampler coupled to a dual-inlet GV
IsoPrime<sup>®</sup> mass spectrometer. For each sample, an aliquot of
about 400 <inline-formula><mml:math id="M400" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>g of calcium carbonate was reacted with anhydrous
oversaturated phosphoric acid at 90 <inline-formula><mml:math id="M401" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C for 20 min. Oxygen
isotope ratios of calcium carbonate were computed assuming an acid
fractionation factor <inline-formula><mml:math id="M402" display="inline"><mml:mrow><mml:mn mathvariant="normal">1000</mml:mn><mml:mi>ln⁡</mml:mi><mml:mi mathvariant="italic">α</mml:mi></mml:mrow></mml:math></inline-formula>(CO<inline-formula><mml:math id="M403" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>–CaCO<inline-formula><mml:math id="M404" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>) of 8.1 between
carbon dioxide and calcite (Swart et
al., 1991). All sample measurements were duplicated and adjusted to the
international references NIST NBS18 (<inline-formula><mml:math id="M405" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M406" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">VPDB</mml:mi></mml:msub></mml:math></inline-formula> <inline-formula><mml:math id="M407" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M408" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">23.2</mml:mn></mml:mrow></mml:math></inline-formula> ‰; <inline-formula><mml:math id="M409" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>C<inline-formula><mml:math id="M410" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">VPDB</mml:mi></mml:msub></mml:math></inline-formula> <inline-formula><mml:math id="M411" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M412" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5.01</mml:mn></mml:mrow></mml:math></inline-formula> ‰) and NBS19 (<inline-formula><mml:math id="M413" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M414" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">VPDB</mml:mi></mml:msub></mml:math></inline-formula> <inline-formula><mml:math id="M415" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M416" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2.20</mml:mn></mml:mrow></mml:math></inline-formula> ‰; <inline-formula><mml:math id="M417" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>C<inline-formula><mml:math id="M418" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">VPDB</mml:mi></mml:msub></mml:math></inline-formula> <inline-formula><mml:math id="M419" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M420" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula>1.95 ‰) and an internal standard of Carrara Marble
(<inline-formula><mml:math id="M421" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M422" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">VPDB</mml:mi></mml:msub></mml:math></inline-formula> <inline-formula><mml:math id="M423" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M424" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.84</mml:mn></mml:mrow></mml:math></inline-formula> ‰; <inline-formula><mml:math id="M425" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>C<inline-formula><mml:math id="M426" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">VPDB</mml:mi></mml:msub></mml:math></inline-formula> <inline-formula><mml:math id="M427" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M428" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula>2.03 ‰). Since 2019,
reproducibility of the Carrara Marble in-house standard has been <inline-formula><mml:math id="M429" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.096</mml:mn></mml:mrow></mml:math></inline-formula> ‰ for <inline-formula><mml:math id="M430" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O (<inline-formula><mml:math id="M431" display="inline"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi mathvariant="italic">σ</mml:mi></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M432" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1062</mml:mn></mml:mrow></mml:math></inline-formula>)
and <inline-formula><mml:math id="M433" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.066</mml:mn></mml:mrow></mml:math></inline-formula> ‰ for <inline-formula><mml:math id="M434" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>C (<inline-formula><mml:math id="M435" display="inline"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi mathvariant="italic">σ</mml:mi></mml:mrow></mml:math></inline-formula>,
<inline-formula><mml:math id="M436" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1062</mml:mn></mml:mrow></mml:math></inline-formula>). These stable isotope data are completed with <inline-formula><mml:math id="M437" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O
and <inline-formula><mml:math id="M438" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>C data obtained from clumped isotope measurements, for
which the analytical procedures are reported in detail in Sect. 2.5.</p><?xmltex \hack{\newpage}?>
</sec>
<sec id="Ch1.S2.SS4">
  <label>2.4</label><title>Elemental ratios</title>
      <p id="d1e5651">Elemental concentrations were obtained by dissolving 2 to 20 mg of carbonate
powder in 10 mL HNO<inline-formula><mml:math id="M439" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> (2 %). For all samples, pairs of aliquots were
prepared with <inline-formula><mml:math id="M440" display="inline"><mml:mrow><mml:mn mathvariant="normal">10</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M441" display="inline"><mml:mrow><mml:mn mathvariant="normal">100</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math></inline-formula> dilutions, depending on the considered
trace and major elements, along with a fixed amount of Sc and In that were
added to correct concentrations from instrument drift. Solutions were
analysed using an inductively coupled plasma-optical emission spectrometer
(iCAP 7000 ICP-OES) and a quadrupole ICP-mass spectrometer (i-CAP-Q ICP-MS)
for minor and trace elements, respectively. The <inline-formula><mml:math id="M442" display="inline"><mml:mrow><mml:mn mathvariant="normal">100</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math></inline-formula> diluted aliquots were
used to calculate Ca concentration, while the <inline-formula><mml:math id="M443" display="inline"><mml:mrow><mml:mn mathvariant="normal">10</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math></inline-formula> diluted aliquots served for
Mg, Sr, Na and Li concentrations. The calculated element <inline-formula><mml:math id="M444" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> Ca ratios are
reported in mmol <inline-formula><mml:math id="M445" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> mol for <inline-formula><mml:math id="M446" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M447" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M448" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> and in <inline-formula><mml:math id="M449" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>mol <inline-formula><mml:math id="M450" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> mol for
<inline-formula><mml:math id="M451" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>. The reproducibility of measurements was assessed through the analysis
of the carbonate standard CCH1 (Roelandts and Duchesne,
1988).</p>
</sec>
<sec id="Ch1.S2.SS5">
  <label>2.5</label><title>Clumped isotopes</title>
      <p id="d1e5791">Carbonate samples were converted to CO<inline-formula><mml:math id="M452" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> by phosphoric acid reaction at
90 <inline-formula><mml:math id="M453" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C in a common, stirred acid bath for 15 min. The initial
phosphoric acid concentration was 103 % (1.91 g cm<inline-formula><mml:math id="M454" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>), and each batch
of acid was used for 7 d. After cryogenic removal of water, the evolved
CO<inline-formula><mml:math id="M455" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> was helium-flushed at 25 mL min<inline-formula><mml:math id="M456" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> through a purification column
packed with Porapak Q (<inline-formula><mml:math id="M457" display="inline"><mml:mrow><mml:mn mathvariant="normal">50</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">80</mml:mn></mml:mrow></mml:math></inline-formula> mesh, 1 m length, 2.1 mm ID) and held at
<inline-formula><mml:math id="M458" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>20 <inline-formula><mml:math id="M459" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C, then it was quantitatively recollected by cryogenic trapping
and transferred into an IsoPrime 100™ dual-inlet mass spectrometer
equipped with six Faraday collectors (<inline-formula><mml:math id="M460" display="inline"><mml:mrow><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:math></inline-formula> 44–49). Each analysis took about
2.5 h, during which analyte gas and working reference gas were allowed
to flow from matching 10 mL reservoirs into the source through deactivated
fused-silica capillaries (65 cm length, 110 <inline-formula><mml:math id="M461" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>m ID). Every 20 min,
gas pressures were adjusted to achieve <inline-formula><mml:math id="M462" display="inline"><mml:mrow><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M463" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 44 current of 80 nA, with
differences between analyte gas and working gas generally being below 0.1 nA.
Pressure-dependent background current corrections were measured 12 times for
each analysis. All background measurements from a given session were then
used to determine a mass-specific relationship linking background intensity
(<inline-formula><mml:math id="M464" display="inline"><mml:mrow><mml:msub><mml:mi>Z</mml:mi><mml:mi>m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), total <inline-formula><mml:math id="M465" display="inline"><mml:mrow><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M466" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 44 intensity (<inline-formula><mml:math id="M467" display="inline"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mn mathvariant="normal">44</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) and time (<inline-formula><mml:math id="M468" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula>) as follows:
            <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M469" display="block"><mml:mrow><mml:msub><mml:mi>Z</mml:mi><mml:mi>m</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>a</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mn mathvariant="normal">44</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mi>P</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          with <inline-formula><mml:math id="M470" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula> being a polynomial of degree 2 to 4.</p>
      <p id="d1e6002">Background-corrected ion current ratios (<inline-formula><mml:math id="M471" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">45</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> to <inline-formula><mml:math id="M472" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">49</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) were
converted to <inline-formula><mml:math id="M473" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>C, <inline-formula><mml:math id="M474" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O and “raw” <inline-formula><mml:math id="M475" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> values as described by Daëron et al. (2016) using the IUPAC oxygen-17 correction parameters.
The isotopic composition (<inline-formula><mml:math id="M476" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>C, <inline-formula><mml:math id="M477" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O) of our
working reference gas was computed based on the nominal isotopic composition
of carbonate standard ETH-3 (Bernasconi et al.,
2018) and an oxygen-18 acid fractionation factor of 1.00813
(Kim et al., 2007). Raw <inline-formula><mml:math id="M478" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> values<?pagebreak page1386?> were
then converted to the I-CDES (Intercarb-Carbon Dioxide Equilibrium Scale) <inline-formula><mml:math id="M479" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> reference frame by comparison
with four ETH carbonate standards
(ETH
1–4; Bernasconi et al., 2021) using a pooled-regression approach
(Daëron, 2021). Full
analytical errors are derived from the external reproducibility of unknowns
and standards (<inline-formula><mml:math id="M480" display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M481" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 89) and conservatively account for the uncertainties
in raw <inline-formula><mml:math id="M482" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> measurements, as well as those associated with the
conversion to the absolute <inline-formula><mml:math id="M483" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> reference frame.</p>
</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Results</title>
      <p id="d1e6155">All geochemical results obtained from modern brachiopods (<inline-formula><mml:math id="M484" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>C,
<inline-formula><mml:math id="M485" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O, <inline-formula><mml:math id="M486" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M487" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M488" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M489" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M490" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>) are
reported in Table 2. Linear regression models of <inline-formula><mml:math id="M491" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M492" display="inline"><mml:msub><mml:mi/><mml:mtext>c-w</mml:mtext></mml:msub></mml:math></inline-formula>,
<inline-formula><mml:math id="M493" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M494" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M495" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M496" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M497" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>, alongside mean annual temperature
(MAT), are reported in Fig. 1 and Table 3.</p>

<?xmltex \floatpos{p}?><table-wrap id="Ch1.T2" specific-use="star"><?xmltex \currentcnt{2}?><label>Table 2</label><caption><p id="d1e6323">Geochemical data of modern-brachiopod samples. Stable isotope
values and element <inline-formula><mml:math id="M498" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> Ca ratios.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="8">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:colspec colnum="6" colname="col6" align="right"/>
     <oasis:colspec colnum="7" colname="col7" align="right"/>
     <oasis:colspec colnum="8" colname="col8" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">Specimen</oasis:entry>
         <oasis:entry colname="col2">Shell</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M499" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>C</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M500" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M501" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M502" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M503" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7"><inline-formula><mml:math id="M504" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M505" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">layer</oasis:entry>
         <oasis:entry colname="col3">(‰ VPDB)</oasis:entry>
         <oasis:entry colname="col4">(‰ VPDB)</oasis:entry>
         <oasis:entry colname="col5">(‰ I-CDES)</oasis:entry>
         <oasis:entry colname="col6">(mmol <inline-formula><mml:math id="M506" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> mol)</oasis:entry>
         <oasis:entry colname="col7">(mmol <inline-formula><mml:math id="M507" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> mol)</oasis:entry>
         <oasis:entry colname="col8">(<inline-formula><mml:math id="M508" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>mol <inline-formula><mml:math id="M509" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> mol)</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row rowsep="1">
         <oasis:entry namest="col1" nameend="col8">New Caledonia </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">FNEO-N4</oasis:entry>
         <oasis:entry colname="col2">Bulk</oasis:entry>
         <oasis:entry colname="col3">1.9</oasis:entry>
         <oasis:entry colname="col4">1.3</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">FNEO-N4</oasis:entry>
         <oasis:entry colname="col2">Bulk</oasis:entry>
         <oasis:entry colname="col3">1.9</oasis:entry>
         <oasis:entry colname="col4">1.3</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">13.35</oasis:entry>
         <oasis:entry colname="col7">1.06</oasis:entry>
         <oasis:entry colname="col8">30.21</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">FNEO-M2</oasis:entry>
         <oasis:entry colname="col2">Bulk<inline-formula><mml:math id="M510" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">1.9</oasis:entry>
         <oasis:entry colname="col4">2.1</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">FNEO-M2</oasis:entry>
         <oasis:entry colname="col2">Bulk<inline-formula><mml:math id="M511" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">2.0</oasis:entry>
         <oasis:entry colname="col4">2.1</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">24.90</oasis:entry>
         <oasis:entry colname="col7">1.36</oasis:entry>
         <oasis:entry colname="col8">33.47</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">FSAN-3</oasis:entry>
         <oasis:entry colname="col2">Bulk<inline-formula><mml:math id="M512" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">1.5</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M513" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.2</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">FSAN-3</oasis:entry>
         <oasis:entry colname="col2">Bulk<inline-formula><mml:math id="M514" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">1.4</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M515" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.2</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">14.65</oasis:entry>
         <oasis:entry colname="col7">1.08</oasis:entry>
         <oasis:entry colname="col8">22.45</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SCRO-1</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">2.7</oasis:entry>
         <oasis:entry colname="col4">2.0</oasis:entry>
         <oasis:entry colname="col5">0.6387</oasis:entry>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SCRO-3</oasis:entry>
         <oasis:entry colname="col2">Outer</oasis:entry>
         <oasis:entry colname="col3">2.3</oasis:entry>
         <oasis:entry colname="col4">2.0</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">13.21</oasis:entry>
         <oasis:entry colname="col7">1.07</oasis:entry>
         <oasis:entry colname="col8">28.90</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SCRO-3</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">3.2</oasis:entry>
         <oasis:entry colname="col4">2.1</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">3.76</oasis:entry>
         <oasis:entry colname="col7">0.45</oasis:entry>
         <oasis:entry colname="col8">4.09</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SGLO-S1</oasis:entry>
         <oasis:entry colname="col2">Outer</oasis:entry>
         <oasis:entry colname="col3">2.0</oasis:entry>
         <oasis:entry colname="col4">0.2</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">11.15</oasis:entry>
         <oasis:entry colname="col7">1.02</oasis:entry>
         <oasis:entry colname="col8">25.53</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SGLO-S1</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">3.1</oasis:entry>
         <oasis:entry colname="col4">0.4</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">6.68</oasis:entry>
         <oasis:entry colname="col7">0.60</oasis:entry>
         <oasis:entry colname="col8">5.21</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SGLO-M1</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">2.9</oasis:entry>
         <oasis:entry colname="col4">1.1</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">6.70</oasis:entry>
         <oasis:entry colname="col7">0.55</oasis:entry>
         <oasis:entry colname="col8">6.01</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SGLO-M1</oasis:entry>
         <oasis:entry colname="col2">Outer</oasis:entry>
         <oasis:entry colname="col3">2.0</oasis:entry>
         <oasis:entry colname="col4">0.9</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">10.72</oasis:entry>
         <oasis:entry colname="col7">0.94</oasis:entry>
         <oasis:entry colname="col8">26.91</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SGLO-M1</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">3.0</oasis:entry>
         <oasis:entry colname="col4">1.1</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SGLO-M2</oasis:entry>
         <oasis:entry colname="col2">Outer</oasis:entry>
         <oasis:entry colname="col3">1.9</oasis:entry>
         <oasis:entry colname="col4">0.9</oasis:entry>
         <oasis:entry colname="col5">0.6388</oasis:entry>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">SGLO-M2</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">2.8</oasis:entry>
         <oasis:entry colname="col4">0.9</oasis:entry>
         <oasis:entry colname="col5">0.6210</oasis:entry>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry namest="col1" nameend="col8">Guadeloupe </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TGAL-3</oasis:entry>
         <oasis:entry colname="col2">Bulk</oasis:entry>
         <oasis:entry colname="col3">2.0</oasis:entry>
         <oasis:entry colname="col4">1.2</oasis:entry>
         <oasis:entry colname="col5">0.6312</oasis:entry>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TGAL-4</oasis:entry>
         <oasis:entry colname="col2">Outer</oasis:entry>
         <oasis:entry colname="col3">1.5</oasis:entry>
         <oasis:entry colname="col4">1.1</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">15.56</oasis:entry>
         <oasis:entry colname="col7">1.12</oasis:entry>
         <oasis:entry colname="col8">30.04</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TGAL-4</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">2.7</oasis:entry>
         <oasis:entry colname="col4">1.3</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">6.87</oasis:entry>
         <oasis:entry colname="col7">0.53</oasis:entry>
         <oasis:entry colname="col8">3.89</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TGAL-4</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">2.8</oasis:entry>
         <oasis:entry colname="col4">1.4</oasis:entry>
         <oasis:entry colname="col5">0.6113</oasis:entry>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TCUB-2</oasis:entry>
         <oasis:entry colname="col2">Bulk</oasis:entry>
         <oasis:entry colname="col3">1.8</oasis:entry>
         <oasis:entry colname="col4">1.1</oasis:entry>
         <oasis:entry colname="col5">0.6248</oasis:entry>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TCUB-3</oasis:entry>
         <oasis:entry colname="col2">Outer</oasis:entry>
         <oasis:entry colname="col3">1.5</oasis:entry>
         <oasis:entry colname="col4">1.0</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">8.25</oasis:entry>
         <oasis:entry colname="col7">0.85</oasis:entry>
         <oasis:entry colname="col8">18.77</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TCUB-3</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">2.3</oasis:entry>
         <oasis:entry colname="col4">1.2</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">4.87</oasis:entry>
         <oasis:entry colname="col7">0.50</oasis:entry>
         <oasis:entry colname="col8">3.86</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TCUB-3</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">2.3</oasis:entry>
         <oasis:entry colname="col4">1.3</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TPLI-2</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">2.8</oasis:entry>
         <oasis:entry colname="col4">0.1</oasis:entry>
         <oasis:entry colname="col5">0.5974</oasis:entry>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TPLI-5</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">3.0</oasis:entry>
         <oasis:entry colname="col4">0.5</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">9.82</oasis:entry>
         <oasis:entry colname="col7">0.63</oasis:entry>
         <oasis:entry colname="col8">5.29</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TDES-G1</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">2.7</oasis:entry>
         <oasis:entry colname="col4">0.2</oasis:entry>
         <oasis:entry colname="col5">0.6049</oasis:entry>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TDES-G3</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">2.8</oasis:entry>
         <oasis:entry colname="col4">0.3</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TDES-G3</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">2.6</oasis:entry>
         <oasis:entry colname="col4">0.2</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">3.82</oasis:entry>
         <oasis:entry colname="col7">0.56</oasis:entry>
         <oasis:entry colname="col8">3.28</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TDES-B2</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">2.6</oasis:entry>
         <oasis:entry colname="col4">0.3</oasis:entry>
         <oasis:entry colname="col5">0.6086</oasis:entry>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TDES-B4</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">2.6</oasis:entry>
         <oasis:entry colname="col4">0.4</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TDES-B4</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">2.7</oasis:entry>
         <oasis:entry colname="col4">0.5</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">6.96</oasis:entry>
         <oasis:entry colname="col7">0.58</oasis:entry>
         <oasis:entry colname="col8">4.64</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TLAT-5</oasis:entry>
         <oasis:entry colname="col2">Bulk<inline-formula><mml:math id="M516" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">1.1</oasis:entry>
         <oasis:entry colname="col4">0.2</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">TLAT-5</oasis:entry>
         <oasis:entry colname="col2">Bulk<inline-formula><mml:math id="M517" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">1.0</oasis:entry>
         <oasis:entry colname="col4">0.2</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">25.30</oasis:entry>
         <oasis:entry colname="col7">1.22</oasis:entry>
         <oasis:entry colname="col8">28.60</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry namest="col1" nameend="col8">New Zealand </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">WB5</oasis:entry>
         <oasis:entry colname="col2">Outer</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M518" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M519" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.6</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">6.69</oasis:entry>
         <oasis:entry colname="col7">1.46</oasis:entry>
         <oasis:entry colname="col8">40.84</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">WB5</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">0.5</oasis:entry>
         <oasis:entry colname="col4">0.5</oasis:entry>
         <oasis:entry colname="col5">0.6639</oasis:entry>
         <oasis:entry colname="col6">4.28</oasis:entry>
         <oasis:entry colname="col7">1.13</oasis:entry>
         <oasis:entry colname="col8">38.39</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">WB6</oasis:entry>
         <oasis:entry colname="col2">Outer</oasis:entry>
         <oasis:entry colname="col3">1.9</oasis:entry>
         <oasis:entry colname="col4">1.1</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">12.50</oasis:entry>
         <oasis:entry colname="col7">1.43</oasis:entry>
         <oasis:entry colname="col8">35.07</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">WB6</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">2.9</oasis:entry>
         <oasis:entry colname="col4">1.6</oasis:entry>
         <oasis:entry colname="col5">0.6295</oasis:entry>
         <oasis:entry colname="col6">11.14</oasis:entry>
         <oasis:entry colname="col7">0.82</oasis:entry>
         <oasis:entry colname="col8">15.92</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">WB8</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">2.1</oasis:entry>
         <oasis:entry colname="col4">1.3</oasis:entry>
         <oasis:entry colname="col5">0.6500</oasis:entry>
         <oasis:entry colname="col6">11.48</oasis:entry>
         <oasis:entry colname="col7">1.24</oasis:entry>
         <oasis:entry colname="col8">46.68</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">WB9A</oasis:entry>
         <oasis:entry colname="col2">Outer</oasis:entry>
         <oasis:entry colname="col3">0.4</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M520" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.5</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">WB9A</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">2.4</oasis:entry>
         <oasis:entry colname="col4">0.9</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">5.73</oasis:entry>
         <oasis:entry colname="col7">1.04</oasis:entry>
         <oasis:entry colname="col8">34.38</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table><?xmltex \gdef\@currentlabel{2}?></table-wrap>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T3" specific-use="star"><?xmltex \currentcnt{2}?><label>Table 2</label><caption><p id="d1e7693">Continued.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="8">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:colspec colnum="6" colname="col6" align="right"/>
     <oasis:colspec colnum="7" colname="col7" align="right"/>
     <oasis:colspec colnum="8" colname="col8" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">Specimen</oasis:entry>
         <oasis:entry colname="col2">Shell</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M522" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>C</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M523" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M524" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M525" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M526" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7"><inline-formula><mml:math id="M527" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M528" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">layer</oasis:entry>
         <oasis:entry colname="col3">(‰ VPDB)</oasis:entry>
         <oasis:entry colname="col4">(‰ VPDB)</oasis:entry>
         <oasis:entry colname="col5">(‰ I-CDES)</oasis:entry>
         <oasis:entry colname="col6">(mmol <inline-formula><mml:math id="M529" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> mol)</oasis:entry>
         <oasis:entry colname="col7">(mmol <inline-formula><mml:math id="M530" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> mol)</oasis:entry>
         <oasis:entry colname="col8">(<inline-formula><mml:math id="M531" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>mol <inline-formula><mml:math id="M532" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> mol)</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row rowsep="1">
         <oasis:entry namest="col1" nameend="col8">Crozet Islands </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">WB4A</oasis:entry>
         <oasis:entry colname="col2">Outer</oasis:entry>
         <oasis:entry colname="col3">1.1</oasis:entry>
         <oasis:entry colname="col4">2.0</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">5.59</oasis:entry>
         <oasis:entry colname="col7">1.18</oasis:entry>
         <oasis:entry colname="col8">49.33</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">WB4A</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">2.5</oasis:entry>
         <oasis:entry colname="col4">3.0</oasis:entry>
         <oasis:entry colname="col5">0.6664</oasis:entry>
         <oasis:entry colname="col6">5.13</oasis:entry>
         <oasis:entry colname="col7">1.00</oasis:entry>
         <oasis:entry colname="col8">41.10</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">WB4B</oasis:entry>
         <oasis:entry colname="col2">Outer</oasis:entry>
         <oasis:entry colname="col3">1.1</oasis:entry>
         <oasis:entry colname="col4">2.2</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">5.57</oasis:entry>
         <oasis:entry colname="col7">1.20</oasis:entry>
         <oasis:entry colname="col8">51.41</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">WB4B</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">1.9</oasis:entry>
         <oasis:entry colname="col4">2.8</oasis:entry>
         <oasis:entry colname="col5">0.6752</oasis:entry>
         <oasis:entry colname="col6">5.08</oasis:entry>
         <oasis:entry colname="col7">1.01</oasis:entry>
         <oasis:entry colname="col8">40.80</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">AKER-52</oasis:entry>
         <oasis:entry colname="col2">Outer</oasis:entry>
         <oasis:entry colname="col3">1.4</oasis:entry>
         <oasis:entry colname="col4">2.8</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">8.46</oasis:entry>
         <oasis:entry colname="col7">1.18</oasis:entry>
         <oasis:entry colname="col8">48.79</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">AKER-52</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">2.0</oasis:entry>
         <oasis:entry colname="col4">3.4</oasis:entry>
         <oasis:entry colname="col5">0.6670</oasis:entry>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">AKER-52</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">2.0</oasis:entry>
         <oasis:entry colname="col4">3.2</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">7.47</oasis:entry>
         <oasis:entry colname="col7">0.94</oasis:entry>
         <oasis:entry colname="col8">44.70</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">AKER-66</oasis:entry>
         <oasis:entry colname="col2">Outer</oasis:entry>
         <oasis:entry colname="col3">2.3</oasis:entry>
         <oasis:entry colname="col4">3.2</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">9.94</oasis:entry>
         <oasis:entry colname="col7">1.37</oasis:entry>
         <oasis:entry colname="col8">48.01</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">AKER-66</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">2.5</oasis:entry>
         <oasis:entry colname="col4">2.7</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">3.57</oasis:entry>
         <oasis:entry colname="col7">0.60</oasis:entry>
         <oasis:entry colname="col8">16.27</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">AKER-12</oasis:entry>
         <oasis:entry colname="col2">Outer</oasis:entry>
         <oasis:entry colname="col3">0.9</oasis:entry>
         <oasis:entry colname="col4">2.6</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">7.46</oasis:entry>
         <oasis:entry colname="col7">1.25</oasis:entry>
         <oasis:entry colname="col8">51.65</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">AKER-12</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">1.9</oasis:entry>
         <oasis:entry colname="col4">2.5</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">3.92</oasis:entry>
         <oasis:entry colname="col7">0.89</oasis:entry>
         <oasis:entry colname="col8">38.68</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">AKER-73</oasis:entry>
         <oasis:entry colname="col2">Outer</oasis:entry>
         <oasis:entry colname="col3">0.6</oasis:entry>
         <oasis:entry colname="col4">2.0</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">9.75</oasis:entry>
         <oasis:entry colname="col7">1.26</oasis:entry>
         <oasis:entry colname="col8">46.63</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">AKER-73</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">2.0</oasis:entry>
         <oasis:entry colname="col4">2.4</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">6.80</oasis:entry>
         <oasis:entry colname="col7">1.08</oasis:entry>
         <oasis:entry colname="col8">46.41</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">AKER-68</oasis:entry>
         <oasis:entry colname="col2">Outer</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M533" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.1</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">1.3</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">5.53</oasis:entry>
         <oasis:entry colname="col7">1.37</oasis:entry>
         <oasis:entry colname="col8">51.73</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">AKER-68</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">1.6</oasis:entry>
         <oasis:entry colname="col4">2.6</oasis:entry>
         <oasis:entry colname="col5">0.6811</oasis:entry>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">AKER-68</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">1.2</oasis:entry>
         <oasis:entry colname="col4">2.0</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">4.92</oasis:entry>
         <oasis:entry colname="col7">1.06</oasis:entry>
         <oasis:entry colname="col8">46.71</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">AKER-79</oasis:entry>
         <oasis:entry colname="col2">Outer</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M534" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.1</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">1.2</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">6.57</oasis:entry>
         <oasis:entry colname="col7">1.33</oasis:entry>
         <oasis:entry colname="col8">49.67</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">AKER-79</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">0.5</oasis:entry>
         <oasis:entry colname="col4">1.3</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">AKER-61</oasis:entry>
         <oasis:entry colname="col2">Outer</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M535" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2.2</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">0.3</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">6.09</oasis:entry>
         <oasis:entry colname="col7">1.55</oasis:entry>
         <oasis:entry colname="col8">58.47</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">AKER-61</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">1.5</oasis:entry>
         <oasis:entry colname="col4">2.1</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">4.94</oasis:entry>
         <oasis:entry colname="col7">1.06</oasis:entry>
         <oasis:entry colname="col8">48.80</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">AKER-61</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">1.4</oasis:entry>
         <oasis:entry colname="col4">2.3</oasis:entry>
         <oasis:entry colname="col5">0.6869</oasis:entry>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry namest="col1" nameend="col8">Antarctica </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">MFRA-CEA</oasis:entry>
         <oasis:entry colname="col2">Outer</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M536" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.5</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">2.7</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">5.39</oasis:entry>
         <oasis:entry colname="col7">1.37</oasis:entry>
         <oasis:entry colname="col8">56.75</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">MFRA-CEA</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">1.0</oasis:entry>
         <oasis:entry colname="col4">3.7</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">6.84</oasis:entry>
         <oasis:entry colname="col7">1.13</oasis:entry>
         <oasis:entry colname="col8">55.35</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">MFRA-CEA</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">1.0</oasis:entry>
         <oasis:entry colname="col4">4.0</oasis:entry>
         <oasis:entry colname="col5">0.6921</oasis:entry>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">WB1A</oasis:entry>
         <oasis:entry colname="col2">Bulk</oasis:entry>
         <oasis:entry colname="col3">0.8</oasis:entry>
         <oasis:entry colname="col4">3.6</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">5.70</oasis:entry>
         <oasis:entry colname="col7">1.21</oasis:entry>
         <oasis:entry colname="col8">36.69</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">LUVA-PAL</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">0.5</oasis:entry>
         <oasis:entry colname="col4">2.9</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">13.47</oasis:entry>
         <oasis:entry colname="col7">1.56</oasis:entry>
         <oasis:entry colname="col8">54.82</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">LUVA-PAL</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">0.6</oasis:entry>
         <oasis:entry colname="col4">3.3</oasis:entry>
         <oasis:entry colname="col5">0.6941</oasis:entry>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">LUVA-PAL</oasis:entry>
         <oasis:entry colname="col2">Outer</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M537" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.7</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">1.9</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">20.17</oasis:entry>
         <oasis:entry colname="col7">2.05</oasis:entry>
         <oasis:entry colname="col8">56.02</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry namest="col1" nameend="col8">Norway </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">MCRA-SKA</oasis:entry>
         <oasis:entry colname="col2">Outer</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M538" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.3</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">0.5</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">MCRA-SKA</oasis:entry>
         <oasis:entry colname="col2">Inner</oasis:entry>
         <oasis:entry colname="col3">0.2</oasis:entry>
         <oasis:entry colname="col4">1.3</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">7.28</oasis:entry>
         <oasis:entry colname="col7">1.24</oasis:entry>
         <oasis:entry colname="col8">53.14</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry namest="col1" nameend="col8">Offshore Angola </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">MAF-5</oasis:entry>
         <oasis:entry colname="col2">Bulk</oasis:entry>
         <oasis:entry colname="col3">1.7</oasis:entry>
         <oasis:entry colname="col4">3.6</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">MAF-5</oasis:entry>
         <oasis:entry colname="col2">Bulk</oasis:entry>
         <oasis:entry colname="col3">1.6</oasis:entry>
         <oasis:entry colname="col4">3.5</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">12.54</oasis:entry>
         <oasis:entry colname="col7">1.01</oasis:entry>
         <oasis:entry colname="col8">54.74</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table><table-wrap-foot><p id="d1e7696"><inline-formula><mml:math id="M521" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula> Samples with the anterior part of the shell.</p></table-wrap-foot><?xmltex \gdef\@currentlabel{2}?></table-wrap>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T4" specific-use="star"><?xmltex \currentcnt{3}?><label>Table 3</label><caption><p id="d1e8815">Linear regression model parameters for the geochemical
parameter–temperature relationship tested and displayed in Fig. 1.</p></caption><oasis:table frame="topbot"><?xmltex \begin{scaleboxenv}{.92}[.92]?><oasis:tgroup cols="10">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:colspec colnum="6" colname="col6" align="right"/>
     <oasis:colspec colnum="7" colname="col7" align="right"/>
     <oasis:colspec colnum="8" colname="col8" align="right"/>
     <oasis:colspec colnum="9" colname="col9" align="right"/>
     <oasis:colspec colnum="10" colname="col10" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">Regression</oasis:entry>
         <oasis:entry colname="col2">Sample and/or</oasis:entry>
         <oasis:entry colname="col3">No. of</oasis:entry>
         <oasis:entry colname="col4">Slope</oasis:entry>
         <oasis:entry colname="col5">Intercept</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M539" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">slope</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7"><inline-formula><mml:math id="M540" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">intercept</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M541" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">residual</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M542" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula> slope</oasis:entry>
         <oasis:entry colname="col10"><inline-formula><mml:math id="M543" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">model</oasis:entry>
         <oasis:entry colname="col2">subsample</oasis:entry>
         <oasis:entry colname="col3">points</oasis:entry>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8"/>
         <oasis:entry colname="col9"/>
         <oasis:entry colname="col10"/>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">MAT (<inline-formula><mml:math id="M544" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C)</oasis:entry>
         <oasis:entry colname="col2">All data</oasis:entry>
         <oasis:entry colname="col3">74</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M545" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5.1</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">18.7</oasis:entry>
         <oasis:entry colname="col6">0.2</oasis:entry>
         <oasis:entry colname="col7">0.5</oasis:entry>
         <oasis:entry colname="col8">3.0</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M546" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.001</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col10">0.87</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">vs.</oasis:entry>
         <oasis:entry colname="col2">Outer layers</oasis:entry>
         <oasis:entry colname="col3">21</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M547" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4.4</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">15.2</oasis:entry>
         <oasis:entry colname="col6">0.6</oasis:entry>
         <oasis:entry colname="col7">1.3</oasis:entry>
         <oasis:entry colname="col8">3.7</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M548" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.001</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col10">0.71</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M549" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O (‰)</oasis:entry>
         <oasis:entry colname="col2">Inner layers</oasis:entry>
         <oasis:entry colname="col3">40</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M550" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5.4</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">20.2</oasis:entry>
         <oasis:entry colname="col6">0.2</oasis:entry>
         <oasis:entry colname="col7">0.5</oasis:entry>
         <oasis:entry colname="col8">2.1</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M551" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.001</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col10">0.94</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">Bulk sample</oasis:entry>
         <oasis:entry colname="col3">13</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M552" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4.9</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">19.3</oasis:entry>
         <oasis:entry colname="col6">0.2</oasis:entry>
         <oasis:entry colname="col7">0.5</oasis:entry>
         <oasis:entry colname="col8">1.6</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M553" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.001</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col10">0.97</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">Bulk <inline-formula><mml:math id="M554" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> inner layers</oasis:entry>
         <oasis:entry colname="col3">53</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M555" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5.2</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">19.9</oasis:entry>
         <oasis:entry colname="col6">0.2</oasis:entry>
         <oasis:entry colname="col7">0.4</oasis:entry>
         <oasis:entry colname="col8">2.0</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M556" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.001</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col10">0.95</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M557" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (‰ I-CDES) vs.</oasis:entry>
         <oasis:entry colname="col2">All data</oasis:entry>
         <oasis:entry colname="col3">20</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M558" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0036</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">0.688</oasis:entry>
         <oasis:entry colname="col6">0.0003</oasis:entry>
         <oasis:entry colname="col7">0.005</oasis:entry>
         <oasis:entry colname="col8">0.011</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M559" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.001</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col10">0.86</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">MAT (<inline-formula><mml:math id="M560" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C)</oasis:entry>
         <oasis:entry colname="col2">Inner layers</oasis:entry>
         <oasis:entry colname="col3">17</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M561" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0036</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">0.688</oasis:entry>
         <oasis:entry colname="col6">0.0004</oasis:entry>
         <oasis:entry colname="col7">0.005</oasis:entry>
         <oasis:entry colname="col8">0.013</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M562" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.001</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col10">0.86</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M563" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> (mmol <inline-formula><mml:math id="M564" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> mol)</oasis:entry>
         <oasis:entry colname="col2">All data</oasis:entry>
         <oasis:entry colname="col3">47</oasis:entry>
         <oasis:entry colname="col4">0.13</oasis:entry>
         <oasis:entry colname="col5">7.7</oasis:entry>
         <oasis:entry colname="col6">0.09</oasis:entry>
         <oasis:entry colname="col7">1.1</oasis:entry>
         <oasis:entry colname="col8">5.0</oasis:entry>
         <oasis:entry colname="col9">0.16</oasis:entry>
         <oasis:entry colname="col10">0.04</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">vs.</oasis:entry>
         <oasis:entry colname="col2">Outer layers</oasis:entry>
         <oasis:entry colname="col3">18</oasis:entry>
         <oasis:entry colname="col4">0.14</oasis:entry>
         <oasis:entry colname="col5">8.3</oasis:entry>
         <oasis:entry colname="col6">0.14</oasis:entry>
         <oasis:entry colname="col7">1.5</oasis:entry>
         <oasis:entry colname="col8">4.0</oasis:entry>
         <oasis:entry colname="col9">0.36</oasis:entry>
         <oasis:entry colname="col10">0.05</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">MAT (<inline-formula><mml:math id="M565" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C)</oasis:entry>
         <oasis:entry colname="col2">Inner layers</oasis:entry>
         <oasis:entry colname="col3">23</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M566" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0025</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">6.6</oasis:entry>
         <oasis:entry colname="col6">0.07</oasis:entry>
         <oasis:entry colname="col7">0.9</oasis:entry>
         <oasis:entry colname="col8">2.7</oasis:entry>
         <oasis:entry colname="col9">0.94</oasis:entry>
         <oasis:entry colname="col10"><inline-formula><mml:math id="M567" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.01</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M568" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> (mmol <inline-formula><mml:math id="M569" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> mol)</oasis:entry>
         <oasis:entry colname="col2">All data</oasis:entry>
         <oasis:entry colname="col3">47</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M570" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.021</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">1.27</oasis:entry>
         <oasis:entry colname="col6">0.005</oasis:entry>
         <oasis:entry colname="col7">0.06</oasis:entry>
         <oasis:entry colname="col8">0.3</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M571" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.001</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col10">0.28</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">vs.</oasis:entry>
         <oasis:entry colname="col2">Outer layers</oasis:entry>
         <oasis:entry colname="col3">18</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M572" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.022</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">1.45</oasis:entry>
         <oasis:entry colname="col6">0.007</oasis:entry>
         <oasis:entry colname="col7">0.08</oasis:entry>
         <oasis:entry colname="col8">0.2</oasis:entry>
         <oasis:entry colname="col9">0.008</oasis:entry>
         <oasis:entry colname="col10">0.36</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">MAT (<inline-formula><mml:math id="M573" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C)</oasis:entry>
         <oasis:entry colname="col2">Inner layers</oasis:entry>
         <oasis:entry colname="col3">23</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M574" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.024</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">1.13</oasis:entry>
         <oasis:entry colname="col6">0.006</oasis:entry>
         <oasis:entry colname="col7">0.08</oasis:entry>
         <oasis:entry colname="col8">0.2</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M575" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.001</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col10">0.44</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M576" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M577" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>mol <inline-formula><mml:math id="M578" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> mol)</oasis:entry>
         <oasis:entry colname="col2">All data</oasis:entry>
         <oasis:entry colname="col3">47</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M579" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.7</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">51.1</oasis:entry>
         <oasis:entry colname="col6">0.2</oasis:entry>
         <oasis:entry colname="col7">2.5</oasis:entry>
         <oasis:entry colname="col8">11</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M580" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.001</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col10">0.61</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">vs.</oasis:entry>
         <oasis:entry colname="col2">Outer layers</oasis:entry>
         <oasis:entry colname="col3">18</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M581" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.7</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">55.6</oasis:entry>
         <oasis:entry colname="col6">0.2</oasis:entry>
         <oasis:entry colname="col7">1.7</oasis:entry>
         <oasis:entry colname="col8">5</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M582" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.001</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col10">0.86</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">MAT (<inline-formula><mml:math id="M583" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C)</oasis:entry>
         <oasis:entry colname="col2">Inner layers</oasis:entry>
         <oasis:entry colname="col3">23</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M584" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2.1</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">49.5</oasis:entry>
         <oasis:entry colname="col6">0.3</oasis:entry>
         <oasis:entry colname="col7">4.1</oasis:entry>
         <oasis:entry colname="col8">12</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M585" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.001</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col10">0.67</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M586" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> (mmol <inline-formula><mml:math id="M587" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> mol)</oasis:entry>
         <oasis:entry colname="col2">All data</oasis:entry>
         <oasis:entry colname="col3">47</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M588" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.32</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">12.7</oasis:entry>
         <oasis:entry colname="col6">0.06</oasis:entry>
         <oasis:entry colname="col7">0.7</oasis:entry>
         <oasis:entry colname="col8">3</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M589" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.001</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col10">0.38</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">vs.</oasis:entry>
         <oasis:entry colname="col2">Outer layers</oasis:entry>
         <oasis:entry colname="col3">18</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M590" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.31</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">14.4</oasis:entry>
         <oasis:entry colname="col6">0.06</oasis:entry>
         <oasis:entry colname="col7">0.6</oasis:entry>
         <oasis:entry colname="col8">2</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M591" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.001</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col10">0.60</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">MAT (<inline-formula><mml:math id="M592" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C)</oasis:entry>
         <oasis:entry colname="col2">Inner layers</oasis:entry>
         <oasis:entry colname="col3">23</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M593" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.38</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">11.2</oasis:entry>
         <oasis:entry colname="col6">0.08</oasis:entry>
         <oasis:entry colname="col7">1.0</oasis:entry>
         <oasis:entry colname="col8">3</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M594" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.001</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col10">0.53</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup><?xmltex \end{scaleboxenv}?></oasis:table><?xmltex \gdef\@currentlabel{3}?></table-wrap>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1" specific-use="star"><?xmltex \currentcnt{1}?><?xmltex \def\figurename{Figure}?><label>Figure 1</label><caption><p id="d1e10028">Geochemical data and linear regression model for each geochemical
parameter tested for its relationship with brachiopod living temperature.
Parameters associated with each regression model are listed in Table 3.</p></caption>
        <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://bg.copernicus.org/articles/20/1381/2023/bg-20-1381-2023-f01.png"/>

      </fig>

<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Carbon and oxygen stable isotopes</title>
      <p id="d1e10044">The whole dataset of <inline-formula><mml:math id="M595" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>C and <inline-formula><mml:math id="M596" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O values (<inline-formula><mml:math id="M597" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">73</mml:mn></mml:mrow></mml:math></inline-formula>) from
modern-brachiopod shells ranges from <inline-formula><mml:math id="M598" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>2.2 ‰ to
3.2 ‰ and from <inline-formula><mml:math id="M599" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>1.2 ‰ to
4.0 ‰, respectively. There is a robust negative
linear correlation (<inline-formula><mml:math id="M600" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0.73</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M601" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> slope <inline-formula><mml:math id="M602" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 0.001) between <inline-formula><mml:math id="M603" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M604" display="inline"><mml:msub><mml:mi/><mml:mtext>c-w</mml:mtext></mml:msub></mml:math></inline-formula> (<inline-formula><mml:math id="M605" display="inline"><mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M606" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:math></inline-formula> <inline-formula><mml:math id="M607" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M608" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M609" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:math></inline-formula>) and MAT (Fig. 1; Table 3). The correlation
observed in bulk shell samples is indistinguishable from that in inner-layer
samples (Fig. 1a). On the contrary, the correlation obtained from outer-layer samples shows a significant offset in relation to both inner-layer and bulk-layer samples. This is in line with the differences between the outer and
inner layers observed within the same specimen, which are in most cases
above analytical uncertainties and range from <inline-formula><mml:math id="M610" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>3.7 ‰ to
<inline-formula><mml:math id="M611" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.2 ‰ (mean <inline-formula><mml:math id="M612" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M613" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>1.4 <inline-formula><mml:math id="M614" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.4 ‰; 2<inline-formula><mml:math id="M615" display="inline"><mml:mi mathvariant="italic">σ</mml:mi></mml:math></inline-formula>; <inline-formula><mml:math id="M616" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">17</mml:mn></mml:mrow></mml:math></inline-formula>) and <inline-formula><mml:math id="M617" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.8 ‰ to 0.5 ‰ (mean <inline-formula><mml:math id="M618" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M619" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.4</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.3</mml:mn></mml:mrow></mml:math></inline-formula> ‰; 2<inline-formula><mml:math id="M620" display="inline"><mml:mi mathvariant="italic">σ</mml:mi></mml:math></inline-formula>; <inline-formula><mml:math id="M621" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">17</mml:mn></mml:mrow></mml:math></inline-formula>) for <inline-formula><mml:math id="M622" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>C and <inline-formula><mml:math id="M623" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O, respectively. Our new set of data from
inner- and bulk-layers samples provides the following oxygen isotope
fractionation equation:
            <disp-formula id="Ch1.E3" content-type="numbered"><label>3</label><mml:math id="M624" display="block"><mml:mrow><mml:mi>T</mml:mi><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5.0</mml:mn><mml:mo>(</mml:mo><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.2</mml:mn><mml:mo>)</mml:mo><mml:mo>(</mml:mo><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mi mathvariant="normal">c</mml:mi></mml:msub><mml:mspace width="0.33em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mi mathvariant="normal">sw</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mn mathvariant="normal">19.4</mml:mn><mml:mo>(</mml:mo><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.4</mml:mn><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          with <inline-formula><mml:math id="M625" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> being the temperature in <inline-formula><mml:math id="M626" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C and <inline-formula><mml:math id="M627" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M628" display="inline"><mml:msub><mml:mi/><mml:mtext>c-w</mml:mtext></mml:msub></mml:math></inline-formula> (<inline-formula><mml:math id="M629" display="inline"><mml:mo lspace="0mm">=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M630" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M631" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">c</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) being the oxygen isotope
fractionation between brachiopod calcite and seawater, excluding data from
the outer-shell layers. As opposed to the ordinary least-squares regression
used in Fig. 1 and Table 3, this equation is established using a York
regression (York et al., 2004) using seasonal variation for
temperature uncertainties and propagated uncertainties from <inline-formula><mml:math id="M632" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M633" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:math></inline-formula> measurements and <inline-formula><mml:math id="M634" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M635" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:math></inline-formula> estimates for
<inline-formula><mml:math id="M636" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M637" display="inline"><mml:msub><mml:mi/><mml:mtext>c-w</mml:mtext></mml:msub></mml:math></inline-formula> uncertainties.</p>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><?xmltex \opttitle{Trace element\,$/$\,Ca ratios}?><title>Trace element <inline-formula><mml:math id="M638" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> Ca ratios</title>
      <p id="d1e10537">The <inline-formula><mml:math id="M639" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M640" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M641" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M642" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> ratios of modern-brachiopod shells range
from 3.57 to 25.30 mmol <inline-formula><mml:math id="M643" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> mol, 0.45 to 2.05 mmol <inline-formula><mml:math id="M644" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> mol, 3.28 to 58.47 <inline-formula><mml:math id="M645" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>mol <inline-formula><mml:math id="M646" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> mol and 1.86 to 18.28 mmol <inline-formula><mml:math id="M647" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> mol, respectively (<inline-formula><mml:math id="M648" display="inline"><mml:mrow><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">47</mml:mn></mml:mrow></mml:math></inline-formula>). <inline-formula><mml:math id="M649" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> ratios show
significant but weak negative correlations (<inline-formula><mml:math id="M650" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.28</mml:mn><mml:mo>&lt;</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.44</mml:mn></mml:mrow></mml:math></inline-formula>; <inline-formula><mml:math id="M651" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> slope <inline-formula><mml:math id="M652" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 0.01) with temperature. <inline-formula><mml:math id="M653" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> ratios show
significant and good negative correlations (<inline-formula><mml:math id="M654" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.61</mml:mn><mml:mo>&lt;</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.86</mml:mn></mml:mrow></mml:math></inline-formula>; <inline-formula><mml:math id="M655" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> slope <inline-formula><mml:math id="M656" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 0.001) with temperature, with the strongest
correlation (<inline-formula><mml:math id="M657" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M658" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.86) being reached in outer-layer
samples. <inline-formula><mml:math id="M659" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> ratios show significant negative correlations (<inline-formula><mml:math id="M660" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.38</mml:mn><mml:mo>&lt;</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.60</mml:mn></mml:mrow></mml:math></inline-formula>; <inline-formula><mml:math id="M661" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> slope <inline-formula><mml:math id="M662" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 0.001) with temperature.
The concentrations of these three elements (Sr, Li and Na) in brachiopod shells
are strongly positively correlated with each other (<inline-formula><mml:math id="M663" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.66</mml:mn><mml:mo>&lt;</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.93</mml:mn></mml:mrow></mml:math></inline-formula> for the whole dataset), especially when
considering only inner-layers sample (<inline-formula><mml:math id="M664" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.84</mml:mn><mml:mo>&lt;</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.96</mml:mn></mml:mrow></mml:math></inline-formula>). No significant correlation (<inline-formula><mml:math id="M665" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> slope <inline-formula><mml:math id="M666" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 0.2) of
<inline-formula><mml:math id="M667" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> with temperature is observed in the dataset (Fig. 1; Table 3).
Measured element <inline-formula><mml:math id="M668" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> Ca ratios are systematically higher in the outer layers
than in the inner layers of brachiopod shells (Student's <inline-formula><mml:math id="M669" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula> test: <inline-formula><mml:math id="M670" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M671" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 0.01; Fig. 1c–e).</p>
</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>Clumped isotopes</title>
      <p id="d1e10894"><inline-formula><mml:math id="M672" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> values obtained from the selected brachiopod shells range from
<inline-formula><mml:math id="M673" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.59</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.01</mml:mn></mml:mrow></mml:math></inline-formula> ‰ to <inline-formula><mml:math id="M674" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.69</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.01</mml:mn></mml:mrow></mml:math></inline-formula> ‰ I-CDES and are
strongly correlated with ambient temperature (Table 3; Fig. 1b).
Temperatures inferred from clumped isotope data were calculated using the
INTERCARB calibration determined by Anderson et al. (2021), who
reprocessed the data coming from various laboratories using the same
carbonate standards for data correction. Clumped isotope temperatures are
significantly lower than estimated MAT, with a mean deviation from
environmental temperatures of <inline-formula><mml:math id="M675" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2.4</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1.3</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M676" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C (95 % CI (confidence interval);
<inline-formula><mml:math id="M677" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">19</mml:mn></mml:mrow></mml:math></inline-formula>).</p>
</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Interpretation and discussion</title>
<sec id="Ch1.S4.SS1">
  <label>4.1</label><title>Brachiopod shell paleothermometers</title>
<sec id="Ch1.S4.SS1.SSS1">
  <label>4.1.1</label><?xmltex \opttitle{Validity and robustness of our {$\protect\chem{{}^{{18}}O/^{{16}}O}$}-based fractionation equation}?><title>Validity and robustness of our <inline-formula><mml:math id="M678" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi/><mml:mn mathvariant="normal">18</mml:mn></mml:msup><mml:mi mathvariant="normal">O</mml:mi><mml:msup><mml:mo>/</mml:mo><mml:mn mathvariant="normal">16</mml:mn></mml:msup><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula>-based fractionation equation</title>
      <p id="d1e11009">The oxygen isotope fractionation equation derived from our data deviates
substantially from that determined by Brand et al. (2019), which is also derived from articulated brachiopod shells (Fig. 2). The two equations follow
similar trends and are only offset by <inline-formula><mml:math id="M679" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.6 ‰ at tropical temperatures (20–30 <inline-formula><mml:math id="M680" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C; Fig. 2a), with the equation from Brand et al. (2019) predicting a lower
fractionation factor. At temperate and polar temperatures (20 to
0 <inline-formula><mml:math id="M681" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C), our new equation highlights a higher sensitivity of oxygen
fractionation to temperature than that of Brand et al. (2019; Fig. 2).
The two equations overlap at around 10 <inline-formula><mml:math id="M682" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C and deviate
substantially around <inline-formula><mml:math id="M683" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0 <inline-formula><mml:math id="M684" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C, with a <inline-formula><mml:math id="M685" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M686" display="inline"><mml:msub><mml:mi/><mml:mtext>c-w</mml:mtext></mml:msub></mml:math></inline-formula> difference of up to <inline-formula><mml:math id="M687" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 1 ‰
between the equation of Brand et al. (2019) and our equation (Fig. 2a), a
pattern also observed in the geochemical datasets (Fig. 2b). Examining the
geochemical dataset revealed that the large offset between the two equations
at low temperatures partly results from the use of a second-order
regression model by Brand et al. (2019), as the regression curve overlaps
with the highest <inline-formula><mml:math id="M688" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M689" display="inline"><mml:msub><mml:mi/><mml:mtext>c-w</mml:mtext></mml:msub></mml:math></inline-formula> data points at temperatures of
<inline-formula><mml:math id="M690" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 1 <inline-formula><mml:math id="M691" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C. We preferred to use a linear regression that was more
appropriate to data in the low-temperature (<inline-formula><mml:math id="M692" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M693" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C)
linear domain of the hyperbolic curve (<inline-formula><mml:math id="M694" display="inline"><mml:mrow><mml:mi mathvariant="italic">α</mml:mi><mml:mo>=</mml:mo><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:msup><mml:mi>T</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>) predicted by equilibrium thermodynamics. Still, the main discrepancies
between the equation proposed herein and that of Brand et al. (2019) are
mainly driven by a difference in the geochemical dataset. The case of the
polar brachiopods <italic>Liothyrella uva</italic> from the island of Rothera (Antarctica) highlights the likely
reasons for this discrepancy at low temperatures. Indeed, <inline-formula><mml:math id="M695" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O
values reported in both studies are the same (Brand et al., 2019),
indicating that the discrepancy lies in the environmental parameters used to
derive the equation. Brand et al. (2019) used published environmental
parameters measured locally in late February for this site, while we
approached this estimation using regional annual averages. This difference
in integration time of the environmental parameters is important<?pagebreak page1389?> because
the month of February records the annual maximum and minimum in seawater
temperature and <inline-formula><mml:math id="M696" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M697" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">sw</mml:mi></mml:msub></mml:math></inline-formula> values, respectively
(Meredith et al., 2013). This particular
brachiopod species has a higher growth rate during the Austral winter than
during the Austral summer (Peck et
al., 1997), further increasing the likely seasonal bias. These discrepancies
are individually relatively small (<inline-formula><mml:math id="M698" display="inline"><mml:mo lspace="0mm">±</mml:mo></mml:math></inline-formula> 1–2 <inline-formula><mml:math id="M699" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C; <inline-formula><mml:math id="M700" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.5</mml:mn></mml:mrow></mml:math></inline-formula> ‰ VSMOW), but put together, they easily explain the
1 ‰ offset between both equations in the low-temperature
range.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2" specific-use="star"><?xmltex \currentcnt{2}?><?xmltex \def\figurename{Figure}?><label>Figure 2</label><caption><p id="d1e11234">Plot comparison of <bold>(a)</bold> regression lines for different
temperature–oxygen isotope fractionations for brachiopod calcite (this study;
Brand et al., 2019), laboratory-precipitated calcite (Kim and O'Neil, 1997)
and slow-growing cave calcite (Daëron et al., 2019); and <bold>(b)</bold> corresponding
datasets for brachiopod calcite (modified after Brand et al., 2019).
Uncertainty envelope of 95 % CI of the York least-squares regression
(York et al., 2004).</p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://bg.copernicus.org/articles/20/1381/2023/bg-20-1381-2023-f02.png"/>

          </fig>

      <p id="d1e11249">We use a published independent dataset of modern-brachiopod <inline-formula><mml:math id="M701" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O values (Bajnai et al., 2018) to test our equation
against other published equations in their ability to predict environmental
temperatures when <inline-formula><mml:math id="M702" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M703" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">sw</mml:mi></mml:msub></mml:math></inline-formula> is known (Fig. 3). This dataset
has a MAT range of 0 to 29 <inline-formula><mml:math id="M704" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C and uses two sets of <inline-formula><mml:math id="M705" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M706" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">sw</mml:mi></mml:msub></mml:math></inline-formula> for most data, one derived from direct measurements and one
derived from <inline-formula><mml:math id="M707" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M708" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">sw</mml:mi></mml:msub></mml:math></inline-formula>–salinity relationships
(LeGrande and Schmidt, 2006). Plus, <inline-formula><mml:math id="M709" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> values are
available for all samples, allowing us to apply the equation of Brand et al. (2013) to the dataset. Isotopic temperatures were calculated and then normalized
as the temperature deviation from environmental temperature (<inline-formula><mml:math id="M710" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:math></inline-formula> in
<inline-formula><mml:math id="M711" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C) with full propagation of uncertainties. Of all the equations
tested, the equations derived from measurements of modern brachiopods (Brand
et al., 2013, 2019; this study) yield the most accurate temperature
predictions. Mean <inline-formula><mml:math id="M712" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:math></inline-formula> are statistically indistinguishable from 0,
using salinity-based <inline-formula><mml:math id="M713" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M714" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">sw</mml:mi></mml:msub></mml:math></inline-formula> estimate results for all four
equations. Interestingly, the accuracy of isotopic temperature estimates is
poorer when measured <inline-formula><mml:math id="M715" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M716" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">sw</mml:mi></mml:msub></mml:math></inline-formula> values are used. The equations
of Brand et al. (2013, 2019) now significantly underestimate growing
temperatures (Fig. 3; <inline-formula><mml:math id="M717" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="normal">mean</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>=</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mn mathvariant="normal">0</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:msub><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.01</mml:mn></mml:mrow></mml:math></inline-formula>),
while our equation yields mean <inline-formula><mml:math id="M718" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:math></inline-formula> values that are statistically
indistinguishable from 0 (<inline-formula><mml:math id="M719" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="normal">mean</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>=</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mn mathvariant="normal">0</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.11</mml:mn></mml:mrow></mml:math></inline-formula>). The
equation of Kim and O'Neil (1997), derived from synthetic
carbonates, and that of Epstein et al. (1953),
derived from molluscs, both underestimate the growing
temperature of brachiopod shells (Fig. 3; <inline-formula><mml:math id="M720" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="normal">mean</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>=</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mn mathvariant="normal">0</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:msub><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.001</mml:mn></mml:mrow></mml:math></inline-formula>) in
both <inline-formula><mml:math id="M721" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M722" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">sw</mml:mi></mml:msub></mml:math></inline-formula> hypotheses. On the other end of the spectrum,
the equation of Daëron et al. (2019), derived from slow-growing calcite,
overestimates the growing temperature of brachiopod shells (Fig. 3, <inline-formula><mml:math id="M723" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="normal">mean</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>=</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mn mathvariant="normal">0</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:msub><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.001</mml:mn></mml:mrow></mml:math></inline-formula>) in both <inline-formula><mml:math id="M724" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M725" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">sw</mml:mi></mml:msub></mml:math></inline-formula>
hypotheses. Although it lessens the accuracy of <inline-formula><mml:math id="M726" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O
temperatures in this dataset, the use of locally measured <inline-formula><mml:math id="M727" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M728" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">sw</mml:mi></mml:msub></mml:math></inline-formula> values over the salinity-based estimates improved their
precision (<inline-formula><mml:math id="M729" display="inline"><mml:mrow><mml:mn mathvariant="normal">4.0</mml:mn><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">5.3</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M730" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C, <inline-formula><mml:math id="M731" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">13</mml:mn></mml:mrow></mml:math></inline-formula>
rather than <inline-formula><mml:math id="M732" display="inline"><mml:mrow><mml:mn mathvariant="normal">5.4</mml:mn><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">6.4</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M733" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C, <inline-formula><mml:math id="M734" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">18</mml:mn></mml:mrow></mml:math></inline-formula>).</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F3"><?xmltex \currentcnt{3}?><?xmltex \def\figurename{Figure}?><label>Figure 3</label><caption><p id="d1e11704">Offsets between the <inline-formula><mml:math id="M735" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O temperatures and MAT from
the modern-brachiopod dataset of Bajnai et al. (2018) using different
fractionation equations. Circles: temperature offset for each sample;
vertical transparent bars: temperature offset 95 % confidence interval for
each sample; horizontal bar: temperature offset arithmetic mean and
associated 95 % confidence interval of the mean. <bold>(a)</bold> Temperature offset for
isotopic temperatures calculated with <inline-formula><mml:math id="M736" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M737" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">sw</mml:mi></mml:msub></mml:math></inline-formula> values
calculated from the LeGrande and Schmidt (2006) database; <inline-formula><mml:math id="M738" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">18</mml:mn></mml:mrow></mml:math></inline-formula>. <bold>(b)</bold> Temperature offset for isotopic temperatures calculated with locally
measured <inline-formula><mml:math id="M739" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M740" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">sw</mml:mi></mml:msub></mml:math></inline-formula> values; <inline-formula><mml:math id="M741" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">13</mml:mn></mml:mrow></mml:math></inline-formula>. OLS refers to ordinary least-squares regression; YLS refers to York least-squares regression (York
et al., 2004).</p></caption>
            <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://bg.copernicus.org/articles/20/1381/2023/bg-20-1381-2023-f03.png"/>

          </fig>

      <p id="d1e11795">Independent from the fractionation equation or the <inline-formula><mml:math id="M742" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M743" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">sw</mml:mi></mml:msub></mml:math></inline-formula>
value used, temperature estimates are associated with large scatter of more
than 4 <inline-formula><mml:math id="M744" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C (<inline-formula><mml:math id="M745" display="inline"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi mathvariant="italic">σ</mml:mi></mml:mrow></mml:math></inline-formula>) around mean <inline-formula><mml:math id="M746" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:math></inline-formula>. We suggest that
this scatter is related primarily to the variability of brachiopod shell
<inline-formula><mml:math id="M747" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O values observed within a population (Fig. 2; Brand et
al., 2019) due to isotopic fractionation mechanisms other than temperature-dependent fractionation, namely kinetic effects, metabolic effects and pH
effects. Using the MgCO<inline-formula><mml:math id="M748" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>-corrected equation of Brand et al. (2013)
instead of that of Brand et al. (2019), both derived from very similar datasets, has
the only effect of slightly improving the precision of the estimates,
decreasing the scatter by <inline-formula><mml:math id="M749" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.6 <inline-formula><mml:math id="M750" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C around the mean
deviation from environmental temperatures. This effect is about 1 order of
magnitude below the remaining dispersal of data.</p>
      <?pagebreak page1390?><p id="d1e11884">For the different equations
derived from modern-brachiopod data, we push further the comparison of the deviation between isotopic temperature calculated with the different equations and environmental temperatures and look at the distribution of these offsets (<inline-formula><mml:math id="M751" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:math></inline-formula>) against seawater temperature (Fig. 4).
This highlights a significant correlation between <inline-formula><mml:math id="M752" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:math></inline-formula> and seawater temperature when applying both the equations of Brand et al. (2013, 2019) to the comparative dataset of Bajnai et al. (2018; <inline-formula><mml:math id="M753" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">uncorrelated</mml:mi></mml:msub><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.001</mml:mn></mml:mrow></mml:math></inline-formula>; Fig. 4). On contrary, there is no
significant correlation between <inline-formula><mml:math id="M754" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:math></inline-formula> and seawater temperature when
applying both our new equations to the comparative dataset of Bajnai et al. (2018; <inline-formula><mml:math id="M755" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">uncorrelated</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0.3</mml:mn></mml:mrow></mml:math></inline-formula>). This comparison highlights that
the application of the equations of Brand et al. (2013, 2019) does not
completely account for temperature as an explicative variable for brachiopod
<inline-formula><mml:math id="M756" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M757" display="inline"><mml:msub><mml:mi/><mml:mtext>c-w</mml:mtext></mml:msub></mml:math></inline-formula> in the dataset of Bajnai et al. (2018).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4" specific-use="star"><?xmltex \currentcnt{4}?><?xmltex \def\figurename{Figure}?><label>Figure 4</label><caption><p id="d1e11970">Distribution of isotopic temperature deviation from living
temperature against living temperature using the equations of <bold>(a)</bold> this
study, <bold>(b)</bold> Brand et al. (2013) and <bold>(c)</bold> Brand et al. (2019) in relation to the dataset of
Bajnai et al. (2018).</p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://bg.copernicus.org/articles/20/1381/2023/bg-20-1381-2023-f04.png"/>

          </fig>

      <?pagebreak page1391?><p id="d1e11988">In the following, we further assess the impact of trace element
incorporation in brachiopod calcite on the fractionation factor between
calcite and water using our new data. Brachiopod calcite can be viewed as a
three-component molar mixture of CaCO<inline-formula><mml:math id="M758" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>, MgCO<inline-formula><mml:math id="M759" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> and SrCO<inline-formula><mml:math id="M760" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>, and
the fractionation factor of this mixture (<inline-formula><mml:math id="M761" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mtext>brach.calcite–water</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>)
of divalent metal carbonates is equivalent to the sum of the mineral–water
fractionation factors weighted from the mineral molar fractions. This bulk
isotopic fractionation factor is thus expressed as follows:
              <disp-formula id="Ch1.E4" content-type="numbered"><label>4</label><mml:math id="M762" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mtext>(brach.calcite–water)</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mi>n</mml:mi></mml:munderover><mml:msub><mml:mi>X</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mtext>(mineral–water)</mml:mtext></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            with the <inline-formula><mml:math id="M763" display="inline"><mml:mi>n</mml:mi></mml:math></inline-formula> (<inline-formula><mml:math id="M764" display="inline"><mml:mrow><mml:mo>=</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:math></inline-formula>) minerals noted as <inline-formula><mml:math id="M765" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M766" display="inline"><mml:mi>X</mml:mi></mml:math></inline-formula> being the molar fraction of each mineral
constituting the brachiopod calcite mixture. As, to our knowledge,
a MgCO<inline-formula><mml:math id="M767" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>–water oxygen isotope fractionation equation has not yet been
established from synthetic carbonates, we used the theoretical fractionation
factors (<inline-formula><mml:math id="M768" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>-</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) of Chacko and Deines (2008) to compare the mixture and pure calcite fractionation factors.
<inline-formula><mml:math id="M769" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mtext>(brach.calcite–water)</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> values, calculated for brachiopod inner calcite
layers with the same range of CaCO<inline-formula><mml:math id="M770" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>, MgCO<inline-formula><mml:math id="M771" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> and SrCO<inline-formula><mml:math id="M772" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> contents as that
recorded by our elemental data, do not exceed 0.18 ‰
compared to the calcite end member at environmental temperatures (mean <inline-formula><mml:math id="M773" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.08 ‰; <inline-formula><mml:math id="M774" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">24</mml:mn></mml:mrow></mml:math></inline-formula>). This difference is mainly explained by
Mg<inline-formula><mml:math id="M775" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> incorporation, as (1) MgCO<inline-formula><mml:math id="M776" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> is more abundant than SrCO<inline-formula><mml:math id="M777" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> in
brachiopod calcite; and (2) <inline-formula><mml:math id="M778" display="inline"><mml:mrow><mml:mn mathvariant="normal">1000</mml:mn><mml:mi>ln⁡</mml:mi><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">MgCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow><mml:mtext>–water</mml:mtext><mml:mo>)</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is higher than
<inline-formula><mml:math id="M779" display="inline"><mml:mrow><mml:mn mathvariant="normal">1000</mml:mn><mml:mi>ln⁡</mml:mi><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow><mml:mtext>–water</mml:mtext><mml:mo>)</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> by about 13 ‰ in this
temperature range, whereas <inline-formula><mml:math id="M780" display="inline"><mml:mrow><mml:mn mathvariant="normal">1000</mml:mn><mml:mi>ln⁡</mml:mi><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SrCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow><mml:mtext>–water</mml:mtext><mml:mo>)</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is lower than
<inline-formula><mml:math id="M781" display="inline"><mml:mrow><mml:mn mathvariant="normal">1000</mml:mn><mml:mi>ln⁡</mml:mi><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow><mml:mtext>–water</mml:mtext><mml:mo>)</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> by only <inline-formula><mml:math id="M782" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 1 ‰
(Chacko and Deines,
2008). This basic calculation illustrates that Mg<inline-formula><mml:math id="M783" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> incorporation into
brachiopod shells with low Mg calcite can affect calcite <inline-formula><mml:math id="M784" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O by no more
than 0.2 ‰, which is about twice the range of analytical
uncertainties at <inline-formula><mml:math id="M785" display="inline"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi mathvariant="italic">σ</mml:mi></mml:mrow></mml:math></inline-formula>. As a consequence, the incorporation of
Mg<inline-formula><mml:math id="M786" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> has a weak effect on the <inline-formula><mml:math id="M787" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O of brachiopod calcite.
The MgCO<inline-formula><mml:math id="M788" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> correction proposed by Brand et
al. (2013) is not really needed for paleoclimatic and paleoceanographic
studies, which most likely justifies why it was later abandoned (Brand et al., 2019).</p>
</sec>
<sec id="Ch1.S4.SS1.SSS2">
  <label>4.1.2</label><title>Brachiopod shell clumped isotopes: an alternative paleothermometer?</title>
      <p id="d1e12404">Although there is a strong correlation between our new <inline-formula><mml:math id="M789" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>
values from brachiopod shells and growing temperatures, <inline-formula><mml:math id="M790" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>
values at a given temperature are generally higher than what is expected
from the state-of-the-art equation of Anderson et al. (2021; Fig. 5).
This observation is in line with the results of Bajnai et al. (2018) gathered in the CDES reference frame. To discuss modern-brachiopod
<inline-formula><mml:math id="M791" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> values in relation to a larger dataset, the data from
Bajnai et al. (2018) were adjusted to the CDES 90 reference
frame for better comparison with our dataset in the I-CDES reference frame (Bernasconi
et al., 2021). We acknowledge that the different standardization protocols
used for the two datasets could hamper the<?pagebreak page1392?> strength of this comparison.
However, this comparison is supported by the good agreement between sample
143 from Bajnai et al. (2018; <inline-formula><mml:math id="M792" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.670</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.008</mml:mn></mml:mrow></mml:math></inline-formula> ‰ CDES 90) and its replicate sample Mv143b
(<inline-formula><mml:math id="M793" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.664</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.006</mml:mn></mml:mrow></mml:math></inline-formula> ‰ I-CDES; Bajnai et al., 2020; Fiebig et
al., 2021). The <inline-formula><mml:math id="M794" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>–temperature relationship derived from this
combined brachiopod dataset yields the following equation:
              <disp-formula id="Ch1.E5" content-type="numbered"><label>5</label><mml:math id="M795" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mrow><mml:mn mathvariant="normal">47</mml:mn><mml:mo>(</mml:mo><mml:msup><mml:mtext>I-CDES90</mml:mtext><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mn mathvariant="normal">0.042</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.002</mml:mn><mml:mo>×</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mn mathvariant="normal">6</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:msup><mml:mi>T</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mn mathvariant="normal">0.124</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.016</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            with <inline-formula><mml:math id="M796" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mrow><mml:mn mathvariant="normal">47</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>(</mml:mo><mml:msup><mml:mtext>I-CDES90</mml:mtext><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> in ‰ and <inline-formula><mml:math id="M797" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> being the temperature in K. This equation, while still nearly within the error
of the equation of Anderson et al. (2021; Fig. 5b), highlights
systematically higher brachiopod <inline-formula><mml:math id="M798" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> values relative to what is
expected from the canonical clumped isotope equation.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5" specific-use="star"><?xmltex \currentcnt{5}?><?xmltex \def\figurename{Figure}?><label>Figure 5</label><caption><p id="d1e12593">Comparison of <inline-formula><mml:math id="M799" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> values from modern brachiopods with the
state-of-the-art <inline-formula><mml:math id="M800" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> calibration of Anderson et al. (2021).
Envelope and error bars are at <inline-formula><mml:math id="M801" display="inline"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi mathvariant="italic">σ</mml:mi></mml:mrow></mml:math></inline-formula>. <bold>(a)</bold> Comparison of York least-squares
regressions (York et al., 2004) derived from two modern-brachiopod datasets (Bajnai et al., 2018; this study) with the equation of
Anderson et al. (2021). <bold>(b)</bold> Comparison of York least-squares regression
derived from the combined modern-brachiopod dataset with the equation of
Anderson et al. (2021). <bold>(c)</bold> Comparison of modern-brachiopod <inline-formula><mml:math id="M802" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> temperatures calculated using the equation of Anderson et al. (2021) with seawater temperatures.</p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://bg.copernicus.org/articles/20/1381/2023/bg-20-1381-2023-f05.png"/>

          </fig>

      <p id="d1e12655">A similar underestimation of <inline-formula><mml:math id="M803" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> temperatures using the
equation of Anderson et al. (2021) was recently reported on culture-grown
bivalves (de Winter et al., 2022). The
authors argued that the <inline-formula><mml:math id="M804" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>–<inline-formula><mml:math id="M805" display="inline"><mml:mrow><mml:msup><mml:mi>T</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> relationship is
non-linear, implying that equations including warm (<inline-formula><mml:math id="M806" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">100</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M807" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C) data points, such as that of Anderson et al. (2021),
systematically underestimate temperatures in the 30 to <inline-formula><mml:math id="M808" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M809" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C
range (de Winter et al., 2022). To
test whether the equation of Anderson et al. (2021) is responsible for the
cold bias reported here, we compare our data with three other equations
established in the marine temperature range within the I-CDES reference
frame (Meinicke
et al., 2021; Huyghe et al., 2022; Peral et al., 2022). While applying the
equation of Meinicke et al. (2021) slightly reduced the mean <inline-formula><mml:math id="M810" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>–temperature offset relative to brachiopod living temperature
(<inline-formula><mml:math id="M811" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2.4</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1.2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M812" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C; 2 SE, <inline-formula><mml:math id="M813" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">37</mml:mn></mml:mrow></mml:math></inline-formula>) compared to the equation of Anderson
et al. (2021) (<inline-formula><mml:math id="M814" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3.9</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1.2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M815" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C; 2 SE, <inline-formula><mml:math id="M816" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">37</mml:mn></mml:mrow></mml:math></inline-formula>), applying of
the equation of Peral et al. (2022; <inline-formula><mml:math id="M817" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3.8</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1.2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M818" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C; 2 SE,
<inline-formula><mml:math id="M819" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">37</mml:mn></mml:mrow></mml:math></inline-formula>) or of Huyghe et al. (2022; <inline-formula><mml:math id="M820" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3.0</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1.2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M821" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C; 2 SE,
<inline-formula><mml:math id="M822" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">37</mml:mn></mml:mrow></mml:math></inline-formula>) gave similar offsets (see File S3 in the Supplement for a detailed comparison).
This comparison shows that equations derived from samples precipitated
exclusively in the marine temperature range give very similar offsets and
does not support the hypothesis that the offset is due to very warm data
points (<inline-formula><mml:math id="M823" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">30</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M824" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C) influencing the slope of the linear
regression of Anderson et al. (2021). We also argue that the difference
between the equations of Peral et al. (2018, 2022) and Meinicke et al. (2020, 2021), both based on foraminiferal calcite, can be explained by
different ways of estimating calcification temperature rather than by different
observations, as discussed by Meinicke et al. (2020). At least a fourth of
brachiopod calcite samples show statistically significant deviation from
previously published equations (9 to 14 of the 37 samples considered here,
depending on the equation). We conclude that the <inline-formula><mml:math id="M825" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> offsets
observed in brachiopod calcite reflect primary deviations from previous
observations that should be addressed to prevent temperature biases when
using <inline-formula><mml:math id="M826" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> values of fossil brachiopods as paleotemperature
proxies.</p>
      <?pagebreak page1393?><p id="d1e12930">Our new data suggest that, at a given temperature, brachiopod shell <inline-formula><mml:math id="M827" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> values are higher than what has been observed among foraminifera
(Breitenbach
et al., 2018; Peral et al., 2018, 2022; Daëron et al., 2016; Meinicke et
al., 2020, 2021), laboratory-precipitated calcites (Jautzy
et al., 2020; Anderson et al., 2021; Fiebig et al., 2021), slow-growing cave
calcites (Daëron
et al., 2019; Anderson et al., 2021; Fiebig et al., 2021) and bivalve
calcite (Huyghe et al., 2022). This
observation is more relevant in the Bajnai et al. (2018) dataset, with a mean
<inline-formula><mml:math id="M828" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> temperature deviation from seawater temperatures of <inline-formula><mml:math id="M829" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5.6</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1.6</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M830" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C (2 SE, <inline-formula><mml:math id="M831" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">18</mml:mn></mml:mrow></mml:math></inline-formula>), than in our new dataset, with a mean
<inline-formula><mml:math id="M832" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> temperature deviation from seawater temperatures of <inline-formula><mml:math id="M833" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2.4</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1.3</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M834" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C (2 SE, <inline-formula><mml:math id="M835" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">19</mml:mn></mml:mrow></mml:math></inline-formula>; Fig. 5a). However, we argue that
the difference between the two datasets of modern-brachiopod <inline-formula><mml:math id="M836" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> may largely result from distinct taxonomic assemblages and/or
sampled locations in both datasets. Indeed, our new <inline-formula><mml:math id="M837" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> data
from New Zealand brachiopods agree very well with previous data from the
same brachiopod species and similar locations (Bajnai et al.,
2018; see File S3 in the Supplement). The Bajnai et al. (2018) dataset is dominated by
brachiopods from the suborder Terebratellidina (<inline-formula><mml:math id="M838" display="inline"><mml:mrow><mml:mn mathvariant="normal">12</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">18</mml:mn></mml:mrow></mml:math></inline-formula>), a group for which
the combined dataset shows the most deviation from the Anderson et al. (2021) equation at low (<inline-formula><mml:math id="M839" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> to 5 <inline-formula><mml:math id="M840" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C) temperatures but most importantly in the
middle (8–15 <inline-formula><mml:math id="M841" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C) temperature range (Fig. 5c). This group is
associated with a mean <inline-formula><mml:math id="M842" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> temperature deviation from seawater
temperatures of <inline-formula><mml:math id="M843" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5.6</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1.7</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M844" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C (2 SE, <inline-formula><mml:math id="M845" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">19</mml:mn></mml:mrow></mml:math></inline-formula>) when applying
the Anderson et al. (2021) equation, while the other most represented group
in the combined dataset, the suborder Terebratulidina, better fits the
canonical equation (Fig. 5c) with a mean <inline-formula><mml:math id="M846" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> temperature
deviation from seawater temperatures of <inline-formula><mml:math id="M847" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.8</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1.4</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M848" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C (2 SE,
<inline-formula><mml:math id="M849" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">13</mml:mn></mml:mrow></mml:math></inline-formula>). This apparent taxonomic difference among brachiopod groups suggests
that the deviation observed for brachiopod shell <inline-formula><mml:math id="M850" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> values
relative to other calcifying organisms relates to processes other than
ambient temperatures, controlling bound ordering within the calcite crystal
of brachiopod shells (Bajnai et al., 2018). Such processes
still need to be confidently identified (Sect. 4.2) but likely lie in
the different ways the shell is secreted under different growth rate dynamics
and/or different crystal arrangements. Available brachiopod <inline-formula><mml:math id="M851" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>
values suggest that, while the equation of Anderson et al. (2021) could be
confidently applied to brachiopods of the suborder Terebratulidina (Fig. 5), this would not be the case for species of the suborder Terebratellidina.
For the other brachiopod groups, data are still too scarce to propose an
enlightened conclusion.</p>
</sec>
<sec id="Ch1.S4.SS1.SSS3">
  <label>4.1.3</label><?xmltex \opttitle{{$\protect\chem{Mg/Ca}$} thermometer for brachiopod shells}?><title><inline-formula><mml:math id="M852" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> thermometer for brachiopod shells</title>
      <p id="d1e13236">Our <inline-formula><mml:math id="M853" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> data obtained from the inner layers of brachiopod shells do not
show any significant correlation with growth temperature (<inline-formula><mml:math id="M854" display="inline"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.94</mml:mn></mml:mrow></mml:math></inline-formula>; Fig. 1c; Table 3), at odds with the strong correlation between the <inline-formula><mml:math id="M855" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> molar
ratio of the brachiopod shell secondary layer and the growth temperature found
by Brand et al. (2013, 2019). However, these<?pagebreak page1394?> authors acknowledged that some species do not
follow the trend they illustrated as the GBMgL and suggested that such
deviations resulted from either lower growth rates (Brand et al., 2013) or higher growth rates (Brand et al., 2019) of the
considered species relative to other brachiopods. This issue alone
illustrates how, from the largest dataset of modern brachiopods available so
far (i.e. Brand's database), one cannot firmly determine whether or not
<inline-formula><mml:math id="M856" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> correlates with seawater temperatures. We emphasize that our dataset
lacks brachiopod shell samples from equatorial surface marine waters
(27 <inline-formula><mml:math id="M857" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C <inline-formula><mml:math id="M858" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M859" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M860" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 32 <inline-formula><mml:math id="M861" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C), which record the
highest MgCO<inline-formula><mml:math id="M862" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> molar content in Brand's database (Brand et al.,
2013, 2019). Interestingly, the highest MgCO<inline-formula><mml:math id="M863" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> contents reported by
these authors were measured on brachiopods belonging to the order
Thecideida. This taxonomic singularity is of prime importance because (1) Thecideide brachiopod shells are essentially made of a shell fabric unique
to its group (Simonet Roda et al., 2022), and
secondary shell fabric (fibrous layers, which form the majority of
Rhynchonellida and Terebratulida shells) is restricted to small areas of the
shell, such as the teeth and the inner sockets (Williams,
1968, 1973; Baker, 2006); (2) Thecideide shell is formed from high-Mg calcite
(Ullmann et al., 2017). The exclusion of Thecideida
data from the database published by Brand et al. (2013) produces a
substantially weaker (<inline-formula><mml:math id="M864" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M865" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.23) yet significant (<inline-formula><mml:math id="M866" display="inline"><mml:mrow><mml:mi>p</mml:mi><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.01</mml:mn></mml:mrow></mml:math></inline-formula>) correlation between shell <inline-formula><mml:math id="M867" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> and temperature. In
addition, magnesium has also been shown to be more concentrated in major
growth bands (Gaspard
et al., 2018; Müller et al., 2022) than in other parts of the secondary
shell layer in articulated brachiopods, which could explain the high <inline-formula><mml:math id="M868" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>
values observed from slow-growth and long-lifespan brachiopods
(Brand et al., 2019), especially
when considering samples obtained from a large sampling area covering
multiple growth lines. Given our new data and all these considerations, the
brachiopod <inline-formula><mml:math id="M869" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> should be regarded as an unreliable proxy for annual or
seasonal temperature reconstructions, at least in the <inline-formula><mml:math id="M870" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> to 25 <inline-formula><mml:math id="M871" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C
range (Fig. 1; Brand et al.,
2013, 2019).</p>
      <p id="d1e13432">An alternative or complementary way to explain the scattering of
temperature–<inline-formula><mml:math id="M872" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> paired data may arise in the variability of marine <inline-formula><mml:math id="M873" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>.
All the elements considered in this study (Mg, Sr, Li and Na) have much
larger residence times (10, 3.5, 1.8 and 44 Myr, respectively) than water
molecules in the oceans, meaning that, at first order, they are uniformly
distributed in the main bodies of the oceans
(Lécuyer, 2016). A recent study, however,
has shown that sizable variations in element <inline-formula><mml:math id="M874" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> Ca may occur in the vicinity of
continental margins under the influence of oceanic currents at the
interface with groundwaters or the atmosphere or within water masses
isolated from the global thermohaline circulation (e.g. Black Sea,
Mediterranean Sea, Red Sea; Lebrato et al., 2020).
For example, despite the large residence time of Sr, non-homogeneous marine
strontium isotopic ratios (<inline-formula><mml:math id="M875" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi/><mml:mn mathvariant="normal">87</mml:mn></mml:msup><mml:mi mathvariant="normal">Sr</mml:mi><mml:msup><mml:mo>/</mml:mo><mml:mn mathvariant="normal">86</mml:mn></mml:msup><mml:mi mathvariant="normal">Sr</mml:mi></mml:mrow></mml:math></inline-formula>) have been measured in
coastal environments (southern Okinawa Trough, South China Sea and Kaoping
Canyon) as the result of seawater mixing with groundwaters
(Huang et al., 2011;
El Meknassi et al., 2020). Given the poor constraint on local coastal water
chemistry in the deep time, brachiopod samples from offshore environments
should be preferred for trace-element-based paleotemperature
reconstructions, as was suggested for marine biogenic apatite by
Balter and
Lécuyer (2010).</p>
</sec>
<sec id="Ch1.S4.SS1.SSS4">
  <label>4.1.4</label><?xmltex \opttitle{Potential of other trace element\,$/$\,Ca proxy}?><title>Potential of other trace element <inline-formula><mml:math id="M876" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> Ca proxy</title>
      <p id="d1e13501">Our new brachiopod <inline-formula><mml:math id="M877" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> data show a significant but weak negative
correlation with ambient temperature (<inline-formula><mml:math id="M878" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">slope</mml:mi></mml:msub><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.001</mml:mn></mml:mrow></mml:math></inline-formula>;
<inline-formula><mml:math id="M879" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.40</mml:mn></mml:mrow></mml:math></inline-formula>). This correlation is supported by a weak
positive correlation between <inline-formula><mml:math id="M880" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M881" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M882" display="inline"><mml:msub><mml:mi/><mml:mtext>c-w</mml:mtext></mml:msub></mml:math></inline-formula> of the
inner layers (<inline-formula><mml:math id="M883" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">slope</mml:mi></mml:msub><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.01</mml:mn></mml:mrow></mml:math></inline-formula>; <inline-formula><mml:math id="M884" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.31</mml:mn></mml:mrow></mml:math></inline-formula>), as we
also expect <inline-formula><mml:math id="M885" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O to decrease with increasing temperatures (i.e.
Sect. 4.1). This contradicts the pioneering findings of
Lowenstam (1961), which suggested a negative
correlation between brachiopod shell <inline-formula><mml:math id="M886" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M887" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M888" display="inline"><mml:msub><mml:mi/><mml:mtext>c-w</mml:mtext></mml:msub></mml:math></inline-formula>.
The brachiopod database of Brand et al. (2013) shows no significant
correlation between <inline-formula><mml:math id="M889" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> and temperatures (<inline-formula><mml:math id="M890" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">slope</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.20</mml:mn></mml:mrow></mml:math></inline-formula>). Given
the diverging conclusions from one dataset to another, <inline-formula><mml:math id="M891" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> values of
brachiopod shells do not appear to be controlled by growing temperatures at
the first order.</p>
      <p id="d1e13692"><inline-formula><mml:math id="M892" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> in brachiopod shells is significantly correlated to temperature
(Fig. 1e; Table 3), a covariation initially reported by
Delaney et al. (1989) and confirmed by more recent studies
(Dellinger
et al., 2018; Rollion-Bard et al., 2019; Washington et al., 2020). Most of
the data presented here follow the <inline-formula><mml:math id="M893" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>–temperature trend derived from
literature data (Washington et
al., 2020), with several samples (<inline-formula><mml:math id="M894" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">9</mml:mn></mml:mrow></mml:math></inline-formula>), exclusively collected from the
inner layer, showing significantly lower <inline-formula><mml:math id="M895" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>. Those low <inline-formula><mml:math id="M896" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> values lie
below the <inline-formula><mml:math id="M897" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>–temperature relationship derived from inorganic calcite (Marriott et al., 2004). Similarly, low <inline-formula><mml:math id="M898" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> values from brachiopod shells were reported by previous studies (Delaney et al., 1989;
Washington et al., 2020). Interestingly, most of those low <inline-formula><mml:math id="M899" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> values
belong to samples from the genus <italic>Tichosina</italic> (Delaney et al., 1989;
Washington et al., 2020, Table 2), so one could consider some peculiar
species-dependent trace element partitioning driven by metabolic or kinetic
processes. Caution is warranted, however, because very low <inline-formula><mml:math id="M900" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> values are
also apparent in the other tropical genus studied here, <italic>Stenosarina</italic> Cooper 1977, as well
as in one specimen of <italic>Aerothyris kerguelenensis</italic> among the nine specimens studied there.</p>
      <?pagebreak page1395?><p id="d1e13812">Other environmental parameters or biological processes may control the
element <inline-formula><mml:math id="M901" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> Ca incorporation into calcite. <inline-formula><mml:math id="M902" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M903" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M904" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> show
significant negative correlations with the local salinity (<inline-formula><mml:math id="M905" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.37</mml:mn><mml:mo>&lt;</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.76</mml:mn></mml:mrow></mml:math></inline-formula>; <inline-formula><mml:math id="M906" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> slope <inline-formula><mml:math id="M907" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 0.01), with similar
scattering as that for the temperature relationships. <inline-formula><mml:math id="M908" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> ratios, again, show no
significant correlation with this parameter (<inline-formula><mml:math id="M909" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> slope <inline-formula><mml:math id="M910" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.7). A wider look at
the geochemical dataset highlights very strong correlations of <inline-formula><mml:math id="M911" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M912" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>,
and <inline-formula><mml:math id="M913" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> ratios in brachiopod shells with one another (<inline-formula><mml:math id="M914" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.68</mml:mn><mml:mo>&lt;</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.92</mml:mn></mml:mrow></mml:math></inline-formula>; <inline-formula><mml:math id="M915" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> slope <inline-formula><mml:math id="M916" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 0.01) over the whole
dataset and particularly from inner-layer samples (<inline-formula><mml:math id="M917" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.87</mml:mn><mml:mo>&lt;</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.97</mml:mn></mml:mrow></mml:math></inline-formula>; <inline-formula><mml:math id="M918" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> slope <inline-formula><mml:math id="M919" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 0.01). Correlation in
our dataset is strongest between <inline-formula><mml:math id="M920" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M921" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> and weakest between <inline-formula><mml:math id="M922" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>
and <inline-formula><mml:math id="M923" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>. Similar correlation trends also appear at the intra-specimen
level (Romanin et
al., 2018; Rollion-Bard et al., 2019). Such strong correlations, at both
intra-individual and inter-specific scales, may suggest that the first-order
variability of those different element concentrations within brachiopod
shells may be explained by similar processes, either environmental or
biological. Ullmann et al. (2017) reported a distinct geochemical signature
between brachiopods species, especially within the <inline-formula><mml:math id="M924" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>–<inline-formula><mml:math id="M925" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> space. Our
inner-shell-layer dataset presents a similar distribution within the low-<inline-formula><mml:math id="M926" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> range (<inline-formula><mml:math id="M927" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> mmol <inline-formula><mml:math id="M928" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> mol), where <inline-formula><mml:math id="M929" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> ratios of Terebratulidina
shells are distinctly lower than those of Terebratellidina shells. Owing to
the strong correlation between <inline-formula><mml:math id="M930" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M931" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M932" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>, our dataset
differentiates between Terebratulidina shells with low element <inline-formula><mml:math id="M933" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> Ca ratios (<inline-formula><mml:math id="M934" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.4</mml:mn><mml:mo>&lt;</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.7</mml:mn></mml:mrow></mml:math></inline-formula> mmol <inline-formula><mml:math id="M935" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> mol; <inline-formula><mml:math id="M936" display="inline"><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mo>&lt;</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M937" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>mol <inline-formula><mml:math id="M938" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> mol; <inline-formula><mml:math id="M939" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>&lt;</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:math></inline-formula> mmol <inline-formula><mml:math id="M940" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> mol) and Terebratellidina
shells with high element <inline-formula><mml:math id="M941" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> Ca ratios (<inline-formula><mml:math id="M942" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.9</mml:mn><mml:mo>&lt;</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">1.2</mml:mn></mml:mrow></mml:math></inline-formula> mmol <inline-formula><mml:math id="M943" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> mol;
<inline-formula><mml:math id="M944" display="inline"><mml:mrow><mml:mn mathvariant="normal">35</mml:mn><mml:mo>&lt;</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">60</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M945" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>mol <inline-formula><mml:math id="M946" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> mol; <inline-formula><mml:math id="M947" display="inline"><mml:mrow><mml:mn mathvariant="normal">8</mml:mn><mml:mo>&lt;</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">12</mml:mn></mml:mrow></mml:math></inline-formula> mmol <inline-formula><mml:math id="M948" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> mol), with the exception of the Antarctic brachiopod <italic>Liothyrella uva</italic> (Broderip,
1833; Terebratulidina) which shows the highest <inline-formula><mml:math id="M949" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M950" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M951" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> values
(Fig. 6a–b). With this exception and that reported by
Ullmann et al. (2017), a taxonomic relationship is
not satisfactory, especially considering the significant yet noisy
relationship between element <inline-formula><mml:math id="M952" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> Ca and environmental parameters such as
temperature and salinity within our new dataset. Indeed, we also observe a
strong relationship between brachiopod shell element <inline-formula><mml:math id="M953" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> Ca values and
geographical location (Fig. 6c–d). Tropical shells (Guadeloupe and New
Caledonia – only Terebratulidina) have low element <inline-formula><mml:math id="M954" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> Ca values, the middle
latitudes (New Zealand and Crozet Islands – dominated by Terebratellidina)
have intermediate to high element <inline-formula><mml:math id="M955" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> Ca values, and polar brachiopods
(Antarctica and Norway – mixed assemblage) have high element <inline-formula><mml:math id="M956" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> Ca values.
Despite this first-order distribution, it appears that, within the same
environment, species difference appears to dominate, as is the case in
Doubtful Sound (New Zealand), where <italic>Terebratella sanguinea</italic> (Leach, 1814; Terebratellidina) shells
have higher element <inline-formula><mml:math id="M957" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> Ca values than <italic>Liothyrella neozelanica</italic> (Thomson, 1918; Terebratulidina) shells.</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F6" specific-use="star"><?xmltex \currentcnt{6}?><?xmltex \def\figurename{Figure}?><label>Figure 6</label><caption><p id="d1e14466">Distribution of trace element content of the inner shell layers
among the different brachiopod taxonomic groups (same symbols as in Fig. 5c). The data show a strong correlation between <inline-formula><mml:math id="M958" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M959" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> <bold>(a)</bold> and
<inline-formula><mml:math id="M960" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M961" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> <bold>(b)</bold>, as well as strong latitudinal partitioning of <inline-formula><mml:math id="M962" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> <bold>(c)</bold>
and <inline-formula><mml:math id="M963" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> <bold>(d)</bold> values.</p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://bg.copernicus.org/articles/20/1381/2023/bg-20-1381-2023-f06.png"/>

          </fig>

      <p id="d1e14560">Our new data suggest that temperature is not the prime parameter that can
describe trace element incorporation into articulated brachiopod shell
calcite from a dataset of widely distributed and taxonomically diverse
brachiopods. This conclusion does not exclude the possibility of any
temperature control on trace element incorporation in brachiopod shell
calcite, which may be relevant at the species level, as proposed by
Butler et al. (2015) and observed in other calcifying organisms such as bivalves (Freitas et al., 2006) and
foraminifera (Anand et al., 2003). However, the influence of other
controls on trace element incorporation in brachiopod shell calcite (growth
rate, environment fluid chemistry, etc.; Jurikova et al., 2020)
is strong enough to blur the likely temperature control so that the trace
element <inline-formula><mml:math id="M964" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> Ca ratios studied here are not suited to being used as
paleothermometers.</p>
</sec>
</sec>
<sec id="Ch1.S4.SS2">
  <label>4.2</label><title>Precipitation of brachiopod shell calcite out of equilibrium with
seawater</title>
      <p id="d1e14579">Our new data confirm that brachiopod shell calcite does not precipitate in
isotopic equilibrium with seawater, as highlighted by the significant
deviation from thermodynamic isotopic equilibrium relationships constrained
from very-slow-growing calcite (Daëron
et al., 2019; Anderson et al., 2021, Figs. 2–5). It is worth noting that
most brachiopod shell <inline-formula><mml:math id="M965" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O data (Brand et al., 2019; this
study) plot in between thermodynamic equilibrium isotopic fractionation
(Daëron et al., 2019) and the equation of Kim and
O'Neil (1997; Fig. 2). The deviation of brachiopod shell calcite <inline-formula><mml:math id="M966" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O from thermodynamic equilibrium (<inline-formula><mml:math id="M967" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M968" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">eq</mml:mi></mml:msub></mml:math></inline-formula> <inline-formula><mml:math id="M969" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M970" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M971" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mrow><mml:mi mathvariant="normal">brach</mml:mi><mml:mo>.</mml:mo><mml:mi mathvariant="normal">calcite</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M972" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">equilibrium</mml:mi></mml:msub></mml:math></inline-formula>)
is obvious when we compare our dataset to the equation of Daëron et al. (2019) in the clumped isotope–oxygen isotope fractionation space (Fig. 7a),
with most of our dataset showing higher <inline-formula><mml:math id="M973" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and lower <inline-formula><mml:math id="M974" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O than predicted (Fig. 7b), a feature previously highlighted by
Bajnai et al. (2018). As a result, brachiopod calcite shows
apparent <inline-formula><mml:math id="M975" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M976" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O temperatures that are, respectively,
lower and higher than those predicted by the thermodynamic equilibrium. This
deviation from equilibrium values has a <inline-formula><mml:math id="M977" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>–<inline-formula><mml:math id="M978" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M979" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">eq</mml:mi></mml:msub></mml:math></inline-formula> slope of <inline-formula><mml:math id="M980" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.019</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.005</mml:mn></mml:mrow></mml:math></inline-formula> in our new brachiopod dataset,
indistinguishable from the slope of <inline-formula><mml:math id="M981" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.017</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.003</mml:mn></mml:mrow></mml:math></inline-formula> reported by Bajnai et
al. (2018) using <inline-formula><mml:math id="M982" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M983" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">sw</mml:mi></mml:msub></mml:math></inline-formula> values from the <inline-formula><mml:math id="M984" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M985" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">sw</mml:mi></mml:msub></mml:math></inline-formula> database (LeGrande and Schmidt, 2006).</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F7" specific-use="star"><?xmltex \currentcnt{7}?><?xmltex \def\figurename{Figure}?><label>Figure 7</label><caption><p id="d1e14817">Non-equilibrium fractionation and kinetic effects in brachiopod
shell calcite as evidenced by clumped isotopes and oxygen isotopes. <bold>(a)</bold> Plot
of brachiopod inner shell layers in the <inline-formula><mml:math id="M986" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>–<inline-formula><mml:math id="M987" display="inline"><mml:mrow><mml:mn mathvariant="normal">1000</mml:mn><mml:mi>ln⁡</mml:mi><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>(calcite–water)</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> space compared with the equilibrium line (blue line)
defined by very-slow-growing abiogenic calcite (Daëron et al., 2019;
Anderson et al., 2021). The red highlight shows the results from <italic>A. kerguelenensis</italic> (Crozet Islands) and
their expected geochemical values on the equilibrium line. Note the negative
correlation between <inline-formula><mml:math id="M988" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M989" display="inline"><mml:mrow><mml:mn mathvariant="normal">1000</mml:mn><mml:mi>ln⁡</mml:mi><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>(calcite–water)</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> evidenced in this subset. <bold>(b)</bold> <inline-formula><mml:math id="M990" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M991" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:math></inline-formula>
and <inline-formula><mml:math id="M992" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> offset from their expected equilibrium values
calculated from environmental parameters using the equations of Daëron
et al. (2019) and Anderson et al. (2021), respectively. The trends followed
by these offsets within our new dataset are similar to those reported from
other brachiopod samples by Bajnai et al. (2018).</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://bg.copernicus.org/articles/20/1381/2023/bg-20-1381-2023-f07.png"/>

        </fig>

      <p id="d1e14919">Brachiopod shell <inline-formula><mml:math id="M993" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O data (Brand
et al., 2003, 2013, 2019; this study) also show a large geochemical
variability among brachiopods sampled from similar marine environments (<inline-formula><mml:math id="M994" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>,
<inline-formula><mml:math id="M995" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula>), with a <inline-formula><mml:math id="M996" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O range often higher than 1 ‰
(Fig. 3; Brand et al., 2019). Isotopic fractionation equations (Brand et
al., 2013, 2019; this study) usually rely on <inline-formula><mml:math id="M997" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M998" display="inline"><mml:msub><mml:mi/><mml:mtext>c-w</mml:mtext></mml:msub></mml:math></inline-formula>
values plotted against mean annual temperatures. Thus, it would be tempting
to attribute such scattering of data to seasonal variations in both
temperature and <inline-formula><mml:math id="M999" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M1000" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">sw</mml:mi></mml:msub></mml:math></inline-formula>, but this would only apply to
specimens that lived above or in the upper part of the thermocline. Such
isotopic scattering is indeed expected if we consider datasets based on
multiple sampling along the growth axis of an individual (Yamamoto et al.,
2011; Takayanagi et al., 2015), such as in the case of Brand et al. (2013,
2019). However, seasonal scattering in data resulting from intra-individual
geochemical variability is unlikely for our measurements, which are performed on a
large sampling area that should correspond to multiple months or years of
growth.</p>
      <?pagebreak page1397?><p id="d1e15000"><?xmltex \hack{\newpage}?>For example, we note a large isotopic variability in both <inline-formula><mml:math id="M1001" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O
and <inline-formula><mml:math id="M1002" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> among the nine specimens of <italic>Aerothyris kerguelenensis</italic> from the Crozet Islands even
though the specimens were recovered from depths in the 105 to 355 m range
with a narrow range of temperature (3–5 <inline-formula><mml:math id="M1003" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C) and salinity
(33.8–34.2). These nine samples, all collected from the shell inner layers of
different individuals, record a <inline-formula><mml:math id="M1004" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O variability of
2 ‰, which is equivalent to a temperature range of 8 to
10 <inline-formula><mml:math id="M1005" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C if interpreted as such, and a <inline-formula><mml:math id="M1006" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> variability
of 0.02 ‰, which is equivalent to a temperature range of about
5 <inline-formula><mml:math id="M1007" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C. This subsample shows a significant <inline-formula><mml:math id="M1008" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>–<inline-formula><mml:math id="M1009" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M1010" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">eq</mml:mi></mml:msub></mml:math></inline-formula> slope of <inline-formula><mml:math id="M1011" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.027</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.007</mml:mn></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M1012" display="inline"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi mathvariant="italic">σ</mml:mi></mml:mrow></mml:math></inline-formula>;
<inline-formula><mml:math id="M1013" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">slope</mml:mi></mml:msub><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.01</mml:mn></mml:mrow></mml:math></inline-formula>; <inline-formula><mml:math id="M1014" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.95</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M1015" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:math></inline-formula>), as well as a
strong positive correlation between <inline-formula><mml:math id="M1016" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M1017" display="inline"><mml:msub><mml:mi/><mml:mtext>c-w</mml:mtext></mml:msub></mml:math></inline-formula> and <inline-formula><mml:math id="M1018" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>C (<inline-formula><mml:math id="M1019" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">slope</mml:mi></mml:msub><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.01</mml:mn></mml:mrow></mml:math></inline-formula>; <inline-formula><mml:math id="M1020" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.69</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M1021" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">9</mml:mn></mml:mrow></mml:math></inline-formula>).
These covariations most likely result from kinetic effects as defined by
McConnaughey (1989), here recorded at the intra-specific level.</p>
      <p id="d1e15249">Our new data replicate the observations made by Bajnai et al. (2018) concerning kinetic fractionation in brachiopod shells. In
consequence, we follow their conclusions and consider it to be the case that different growth
rates of the specimens are responsible for the second-order isotopic
variability and the deviation from the stable isotope and clumped isotope
equilibrium observed in brachiopod datasets, both at an inter-specific and
intra-specific level.</p>
      <p id="d1e15252">Neither minor nor trace elements are incorporated into brachiopod shell
calcite in equilibrium with seawater relative to abiogenic calcite
(Rollion-Bard et al.,
2019; Simonet Roda et al., 2022). Kinetic effects are known to influence
trace element incorporation into calcite (Lorens,
1981; Busenberg and Plummer, 1985; Tesoriero and Pankow, 1996; Gabitov et
al., 2011, 2014) and may be a process, among others
(Jurikova et al., 2020), that explains trace element
incorporation into brachiopod shell calcite. Owing to the very limited
knowledge of brachiopod shell growth rates (for only 5 out of 17 species in our
dataset), we are unable to directly test this hypothesis. However, if
kinetic effects have such an influence on element incorporation into brachiopod
shell calcite, we should observe strong negative correlations of <inline-formula><mml:math id="M1022" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M1023" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M1024" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> ratios with <inline-formula><mml:math id="M1025" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M1026" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">eq</mml:mi></mml:msub></mml:math></inline-formula>. We observe such significant
correlations in the new dataset in both the inner- and outer-layer subsets
(<inline-formula><mml:math id="M1027" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.40</mml:mn><mml:mo>&lt;</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.55</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M1028" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> slope <inline-formula><mml:math id="M1029" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 0.01),
with a significant slope change between the two subsets. The variation in
element <inline-formula><mml:math id="M1030" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> Ca related to a similar variation in <inline-formula><mml:math id="M1031" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M1032" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">eq</mml:mi></mml:msub></mml:math></inline-formula>, as
suggested by linear regression models, is about twice as high in the inner-layer subset than in the outer-layer subset. This difference may be
explained by the different pathways brachiopods use to form their different
shell layers (acicular, fibrous and prismatic/columnar;
Simonet Roda et al., 2022). However, while looking
at <italic>Aerothyris kerguelenensis</italic>, which showed the most important kinetic effects according to stable
isotope data, there is no significant correlation of element <inline-formula><mml:math id="M1033" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> Ca ratios with
<inline-formula><mml:math id="M1034" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M1035" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">eq</mml:mi></mml:msub></mml:math></inline-formula>. Element <inline-formula><mml:math id="M1036" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> Ca ratios appear to be independent from
isotope kinetic effects at the species level despite strong correlations of
element <inline-formula><mml:math id="M1037" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> Ca ratios and <inline-formula><mml:math id="M1038" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M1039" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">eq</mml:mi></mml:msub></mml:math></inline-formula> in the multi-specific
dataset.</p>
      <p id="d1e15438">In line with the significant correlation between <inline-formula><mml:math id="M1040" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M1041" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">eq</mml:mi></mml:msub></mml:math></inline-formula> and element <inline-formula><mml:math id="M1042" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> Ca values in brachiopod shell inner layers, the environmental
and taxonomic distributions of isotopic offsets (<inline-formula><mml:math id="M1043" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M1044" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">eq</mml:mi></mml:msub></mml:math></inline-formula>,
<inline-formula><mml:math id="M1045" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> offset) in our dataset are similar to the distribution of
element <inline-formula><mml:math id="M1046" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> Ca values. We observe more deviation from the equilibrium in high-latitude environments than in tropical environments, and we generally observe
more deviation from isotopic equilibrium in Terebratellidina than
in Terebratulidina in the whole dataset, although the difference is not as
striking as that documented for trace elements. As the geographical
distribution of the two suborders in the new dataset is highly biased, this
trend cannot be confidently interpreted as arising from different shell
formation processes in the different groups. However, several examples of
Terebratellidine and Terebratulidine living in the same environment show a
similar pattern. In Doubtful Sound (New Zealand), <italic>Terebratella</italic> <italic>sanguinea</italic> (Terebratellidina)
deviates more from equilibrium isotopic composition than <italic>Liothyrella neozelanica</italic> (Terebratulidina; this study; Bajnai et al., 2018). In Friday Harbor (Washington, USA),
<italic>Terebratalia transversa</italic> (Sowerby, 1846; Terebratellidina) records lower and more variable <inline-formula><mml:math id="M1047" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M1048" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">c</mml:mi></mml:msub></mml:math></inline-formula> than <italic>Terabratulina</italic> sp. (Terebratulidina; Ullmann et
al., 2017). These authors also reported high isotopic variability associated
with the strong correlation of <inline-formula><mml:math id="M1049" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O with <inline-formula><mml:math id="M1050" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>C among
Terebratellidine but not among Terebratulidine.</p>
      <p id="d1e15565">From the relationship between the different parameters studied here, we
suggest that kinetic effects in brachiopod shells may be a major source of
deviation from calcite precipitation in equilibrium with seawater. Kinetic
effects can be, on first approximation, controlled by shell growth rates
(McConnaughey, 1989; Bajnai et al., 2018). Therefore, both
biological and environmental parameters should control the extent of the
kinetic effects. At first order, one can expect species growing larger
shells to record more important kinetic effects. Moreover, shell growth
rates in calcifying organisms increase when environmental conditions are
close to optimal living range and decrease when the conditions strongly
derive from that optimum, a pattern that is dependent on taxon-related
preferences (Schöne, 2008). However, the poor knowledge of
brachiopod shell growth rate, relative to other marine calcifying organisms,
prevents an in-depth appreciation of its exact role. Kinetic effects are
still insufficient to describe all of the deviation from equilibrium observed
here, but our dataset does not allow for a discussion of other potential factors
(Jurikova et al., 2020).</p>
</sec>
</sec>
<sec id="Ch1.S5" sec-type="conclusions">
  <label>5</label><title>Conclusions</title>
      <p id="d1e15578">Our multi-proxy (<inline-formula><mml:math id="M1051" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O, <inline-formula><mml:math id="M1052" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>C, <inline-formula><mml:math id="M1053" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>,
<inline-formula><mml:math id="M1054" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M1055" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M1056" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M1057" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>) geochemical analyses of 37 modern brachiopods
from different locations, spanning living temperatures from <inline-formula><mml:math id="M1058" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.9</mml:mn></mml:mrow></mml:math></inline-formula> to 25.5 <inline-formula><mml:math id="M1059" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C, allowed us to investigate the temperature
relationship of several geochemical markers and to evaluate or re-evaluate
their potential as paleothermometers for brachiopod shell archives. <inline-formula><mml:math id="M1060" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O and <inline-formula><mml:math id="M1061" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> are the most reliable paleothermometers,
although we propose a revised <inline-formula><mml:math id="M1062" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<?pagebreak page1398?> paleotemperature equation
for brachiopod shell calcite, and <inline-formula><mml:math id="M1063" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> values highlight a
significant deviation from the canonical temperature relationship. The
element <inline-formula><mml:math id="M1064" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> Ca ratios investigated here should not be used to infer
environmental temperatures from brachiopod calcite owing to either the
absence (<inline-formula><mml:math id="M1065" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>) or a poor yet significant (<inline-formula><mml:math id="M1066" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M1067" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Li</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M1068" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula>) correlation
with living temperature. Our new dataset confirms previous evidence for the interpretation of non-equilibrium isotopic fractionation interpreted as significant kinetic
effects recorded in the brachiopod shell inner layers. In general, the
precipitation of brachiopod shells that takes place out of isotopic equilibrium
leads to (1) an underestimation of living temperature from <inline-formula><mml:math id="M1069" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:mn mathvariant="normal">47</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>
and (2) an overestimation of living temperature from oxygen isotopes, which,
once the proxies are combined, could lead to (3) an underestimation of living-water <inline-formula><mml:math id="M1070" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M1071" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">sw</mml:mi></mml:msub></mml:math></inline-formula> relative to what would be expected from
equilibrium precipitation. Kinetic effects and, by extension, shell growth
rates could explain the second order of isotopic variability in brachiopod
shells and can be a larger source of isotopic variability than environmental
parameters (temperature, <inline-formula><mml:math id="M1072" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>O<inline-formula><mml:math id="M1073" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">sw</mml:mi></mml:msub></mml:math></inline-formula>) at the local scale. Thus,
we advise that this variability be considered as a significant source of
uncertainties when applying paleotemperature proxies. Although we reject
their use as a paleothermometer, we do not exclude any temperature control
on trace element (Mg, Sr, Li and Na) incorporation into brachiopod shell
calcite. Rather, our findings indicate that other processes, such as kinetic
effects (growth rate) or shell microstructure and their associated
mineralization pathways, have a significant control over trace element
incorporation into brachiopod shell calcite, resulting in the high
scrambling observed in the element <inline-formula><mml:math id="M1074" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> Ca–temperature relationship.</p>
</sec>

      
      </body>
    <back><notes notes-type="codeavailability"><title>Code availability</title>

      <p id="d1e15846">No code has been developed for the purpose of this study. Statistical analysis was done using RStudio build 492. The R package IsoplotR version 4.4 (<uri>https://github.com/pvermees/IsoplotR</uri>, Vermeesch, 2022) was used for its York regression function. Clumped isotope data were processed using the D47crunch Python package (<uri>https://doi.org/10.5281/zenodo.6300900</uri>, Daëron, 2022).</p>
  </notes><notes notes-type="dataavailability"><title>Data availability</title>

      <p id="d1e15858">The new dataset generated for this study is provided in the Supplement.
The WOA 2018 dataset used in this study is available on the website of the National Centers for Environmental Information: National Oceanic and Atmospheric Administration (<uri>https://www.ncei.noaa.gov/access/world-ocean-atlas-2018/</uri>, last access: 31 March 2023).
A version of the dataset to be viewed with Ocean Data View (ODV) is available at <uri>https://odv.awi.de/data/ocean/world-ocean-atlas-2018/</uri> (Ocean Data View, 2023).
The dataset of Bajnai et al. (2018) used in this study is available from the Supplement of the original publication (<ext-link xlink:href="https://doi.org/10.1038/s41598-017-17353-7" ext-link-type="DOI">10.1038/s41598-017-17353-7</ext-link>).</p>
  </notes><app-group>
        <supplementary-material position="anchor"><p id="d1e15870">The supplement related to this article is available online at: <inline-supplementary-material xlink:href="https://doi.org/10.5194/bg-20-1381-2023-supplement" xlink:title="zip">https://doi.org/10.5194/bg-20-1381-2023-supplement</inline-supplementary-material>.</p></supplementary-material>
        </app-group><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e15879">TL and CL designed the study in close collaboration with GS and DG. DG
obtained the samples from various contributors. TL performed shell sampling
in the lab. AVL and TL performed the stable isotope analysis and data
treatment. TL and FAG performed the elemental analysis and data treatment.
TL and MD performed the clumped isotope analysis and data treatment. TL
performed the statistical analysis of the data and wrote the paper with
input from all the authors.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e15885">The contact author has declared that none of the authors has any competing interests.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d1e15891">Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e15897">The authors gratefully thank the leaders and teams of the oceanographic vessels of the
following expeditions: the Walda cruise in the southeast Atlantic Ocean (Michel Segonzac, IFREMER, Brest); sampling from Norway coasts (courtesy of the
Trondheim Biological Station); MD 30 BIOMASS around the Crozet Islands
(Patrick Arnaud, Marseille, France; and Nadia Ameziane, MNHN, who provided the
material); Musorstom 4, SMIB 3 and 6, and Norfolk 1 around Loyauté and Lifou islands in New Caledonia (Bernard Laurin, Université de Bourgogne, Dijon; and
Bertrand Richer de Forges); Karubenthos 2 around the French Caribbean island of Guadeloupe
(Philippe Bouchet with Pierre Lozouet, Laure Corbari and Philippe Maestrati, with
the help of Jerôme Mainguy, MNHN, Paris, France) with a supplementary sampling
(Dominique Lamy, Université des Antilles et de la Guyane); additional material from
New Zealand (Daphne Lee, Marine Biology Lab, University of Otago; David I. MacKinnon, University of Canterbury, Christchurch, New Zealand; and Anthony E. Aldridge; CEAMARC off the French
Antarctic area (Nadia Ameziane and Marc Eléaume, MNHN, Paris,
France); and sampling from Palmer Peninsula, Antarctic (courtesy of Thomas Desvignes, USA).</p><p id="d1e15899">We thank Adrian Immenhauser and two anonymous reviewers for their
constructive comments that helped improve the quality of this paper.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e15904">This research has been supported by the Agence Nationale de la Recherche (grant no. ANR-18-CE31-0020).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e15910">This paper was edited by Tina Treude and reviewed by Adrian Immenhauser and two anonymous referees.</p>
  </notes><ref-list>
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