Data from Globigerinoides ruber (white) used in this study are collated from numerous experiments across a range of temperature, pH and major ion seawater chemistries, cultured at the Interuniversity Institute of Eilat between January 2010 and November 2013. These cultures include both sensu stricto and sensu lato morphotypes . A detailed description of culturing methods is provided elsewhere . Briefly, for all experiments, foraminifera were towed from the Gulf of Aqaba (Eilat) (depth < 20 m, temperature 22–24 ∘C, salinity ∼ 40.4 psu), and cultured in individual 120 mL airtight flasks within temperature-controlled water baths. Illumination was provided by a metal halide lamp (420 W) with an intensity of ∼ 200 µmol photons m-2 s-1 (13 h light : 11 h dark), equivalent to irradiance at 15–20 m depth in the open waters of the northern Gulf of Aqaba . Every 1–2 days, individuals were transferred to a Petri dish, measured using an optical micrometer under a Zeiss inverted light microscope, and fed a juvenile brine shrimp. After gametogenesis, foraminifera were rinsed in deionised water, dried and stored for subsequent analysis.

Here we consider changes in calcification intensity in foraminifera that were originally cultured to investigate two different geochemical proxy systems: boron isotopes and Mg / Ca . The experimental design varies slightly between these two cases, so we discuss any such differences where they arise. In all experiments, culture solution pH was determined using an electrode calibrated against NBS buffers. The same electrode was also used to measure the pH of a range of prepared seawater solutions which were subsequently analysed for dissolved inorganic carbon (DIC) concentrations and total alkalinity (TAlk), allowing us to cross-calibrate our electrode-derived pH values against calculated pH on the total scale using CO2sys.m , the constants of , , and boron concentrations from . Because pH control for boron isotope experiments was paramount, in these experiments each individual flask pH was measured every 2–3 days, and flasks that experienced pH drift had culture seawater solution replaced from a stock solution stored throughout the experiment in airtight bottles without headspace. Uncertainty on pH is therefore calculated as two standard errors on the mean of each culture flask pHs during cultures. For those experiments intended to test Mg incorporation , pH monitoring during culture was less frequent, and this is reflected in a more conservative approximation of pH uncertainty in these cultures. In total, we collate calcification intensity data from 11 separate culture experiments, with temperatures ranging from 22.8 to 27.8 ∘C, seawater Mg / Ca ratios ranging from 2.17 to 6.25 mol mol-1, and pH (total scale) ranging from 7.54 to 8.20. Some estimates of future anthropogenic ocean acidification suggest a pH drop of 0.5 units by 2100 , and so this wide pH range allows us to investigate the possible changes in calcification over the next century.

Dried cultured foraminifera were imaged and major and perpendicular axes measured using Macnification software (Orbicule Inc., v2.0). They were then weighed individually on microbalances at Royal Holloway University of London (Exps. DE3 & DE4), Yale University (Exp. MH2), and the University of Bristol (Exp. MH1). Mean uncertainty assessed by 2 standard deviations of triplicate measurements of individual foraminifera was < ±1 µg. While these foraminifera were not ashed to remove any remnant organic matter prior to weighing, previous comparisons of non-ashed sample weights with mass of CaCO3 determined by inductively coupled plasma mass spectrometry showed no significant difference .

Since it is unfeasible to take direct shell weight measurements from live pre-culture foraminifera without harming the organism, we estimate pre-culture shell mass from test size (major and perpendicular axes measured via ocular micrometer) at the beginning of culture, using a locally defined size–weight relationship for G. ruber, as in previous studies e.g.. Here we expand on our previous size–weight calibration dataset, combining a total of 205 measurements from individuals of G. ruber (mixed morphotypes, ranging in size from 141 to 517 µm) towed from the Gulf of Aqaba (Eilat). The equation of this line (R2=0.61) is shell mass(inµg)=217×(product of axes, in mm2)1.43.

Existing metrics for calcification (as discussed in Sect. ), cannot be applied directly to laboratory cultures of planktonic species, as many chambers are precipitated prior to collection. Previous studies therefore used mean test weight of cultured foraminifera from a given size range e.g., or made corrections for pre-culture mass and time spent in culture to describe how calcification responded to culture conditions. Here, we have developed a new metric, calcification intensity (CI; Eq. ), that accounts for both the size/mass of foraminifera upon collection, as well as the (often differential) amount of mass added between culture experiments: CI=ΔmassΔarea, where Δmass is the difference in mass between the start and end of the culture (expressed in µg) and Δarea is the difference in product of the major and minor axes (in mm2) between the start and end of the culture. We quantify calcification in cultured foraminifera in this simple way because it allows for more complete consideration of mass grown outside of culture, and relies only on pre- and post-culture dimensions and mass that are routinely measured. We note that for our experiments, pre-culture mass was estimated from a relationship of size to mass (Eq. ) constructed from foraminifera towed from in the Gulf of Aqaba (Eilat) at the same time as our culture experiments. pH measured at the time of sampling these tows was 8.10 ± 0.05 (2 SE), approximately at the middle of our range of experimental pH. Thus while the size–mass calibration presented here is suitable for our investigations, we suggest that future culture studies considering CI should characterise this relationship in the populations from which their cultured individuals were sampled. We note also that since this metric uses cross-sectional area as a measure of size, direct comparison of CI values across different foraminiferal species is not advisable without considering the effect of species-specific chamber morphologies (i.e. flattened vs. spheroidal chambers).

Planktonic foraminifera are single-celled eukaryotes with calcium carbonate tests that show distinct morphological changes throughout ontogeny . Planktonic foraminifera grow by sequentially adding calcium carbonate chambers along a primary coiling axis, and it is thought that they lay down an extra layer of calcite (“secondary calcite”) over existing chambers when a new chamber is formed . Over ontogeny coiling behaviour often changes, as do the relative size, shape, abundance of perforations (i.e. “porosity”) and wall thickness of the calcium carbonate chambers e.g.. Finally, immediately before foraminifera reproduce and die, many species although not G. ruber; precipitate a thick final layer of carbonate known as gametogenic calcite. Other species appear to secondarily thicken their tests following precipitation of their final chamber and some may form a crust e.g., although this has not yet been observed in G. ruber. Studies of calcification in foraminifera must therefore disentangle the effects of environmental factors from these known ontogenetic phenomena. In open-ocean studies (e.g. sediment trap, core top), SNW measurements are commonly taken from within narrow size ranges to minimise the effect of size-dependent variation in calcification as discussed in. However, normalisation for size effectively assumes that there is no ontogenetic variation in calcification or that all individuals come from the same ontogenetic stage, which is unlikely, particularly when comparing results across different studies. In laboratory cultures, there are additional difficulties in assessing CI as it is generally not possible to select a narrow starting size range (given specimen limitation), and the number of chambers added by each individual over the course of culture experiments is highly variable. Therefore, to provide a quantitative framework for exploring the relationship between CI and ontogeny, and to explore how existing calcification metrics may be biased by the use of large or variable size fractions, we developed an ontogenetic model of CI using empirical observations from G. ruber.

To supplement modelling and culturing, and to examine the extent to which the physiological controls observed in culture are preserved in fossil assemblages, we also examined SNW in core-top G. ruber. Core-top sites and locations are given in the Supplement, and span a range of bottom water calcite saturation state (Ωcalcite) from 0.78 to 4.06. Pre-industrial surface ocean carbonate system conditions for each site were estimated using modern alkalinity relationships from, air–sea pCO2 disequilibrium from and local hydrography from following . Deep-ocean carbonate chemistry and calcite saturation state were calculated from DIC and TAlk estimates at depth from . Carbonate system calculations were carried out as in Sect.  above, with pressure corrections from according to each core site's bathymetry.

For size-normalisation of shell weight measurements, we follow the “area density” (ρA) approach of , as used elsewhere . From each core-top sample, individual specimens (n=8–26) of G. ruber sensu stricto and sensu lato were picked from discrete sieve size fractions, imaged (umbilical side up), and weighed, and their cross-sectional or silhouette area determined using Macnification (Orbicule Inc., v2.0). ρA was calculated as mass (in µg) over silhouette area (in mm2). As in and , the mean ρA and silhouette area in each core-top sample was then used in multivariate statistical analysis.

Model parameter combinations within the prescribed tolerances of the size–weight ratios seen in non-cultured populations of G. ruber (white, mixed morphotype) are displayed in Fig. a, d, g. Using the validated subsets of each model, we calculated CI as it evolved through the ontogenetic growth of each individual modelled foraminifera (Fig. b, e, h). All models suggest that CI should increase rapidly with test size up to size of ∼ 0.05 mm2 (equating to a major axis of approximately 210 µm). Beyond this size there is considerably more scope for inter-individual (i.e. inter-model run) variability, but most model runs continue to show increasing CI with size throughout the remainder of their ontogeny.

From the perspective of foraminiferal cultures, these models predict a strong dependency of CI on foraminifer size on collection, and also the number of chambers precipitated in culture. For instance, cultures in which foraminifer added three chambers on average are expected to have a higher CI than cultures in which most foraminifera added two chambers. Panels (c), (f) and (i) of Fig.  explore this effect of chamber addition on CI. For each model, frequency distributions of modelled change in CI (ΔCI) after two and three chamber additions are shown, relative to a baseline addition of one chamber and a starting size of 100 µm maximum axis diameter. The median increase of calculated CI with each chamber addition is 17 µg mm-2, and was largely insensitive to the base model – a similar dependency of chamber addition on CI was observed in models 1–3 (Fig. c, f, i). Because the mean number of chambers added per individual varied between culture experiments, we therefore normalise our culture CI data for the mean number of chambers precipitated in culture (detailed in Sect. ).

In addition to discerning ontogenetic trends in CI, these models also help to constrain which morphological parameters exert the most coherent control on CI. For almost any given model parameter, the full range of CI observed in culture can be produced given the right combination of other morphological parameters. For example, CIs of between 120 and 250 µg mm-2 can be produced irrespective of the chamber aspect ratio. In other words, whilst a change in chamber aspect ratio can affect CI, any such change can also be offset by a compensatory change in other model parameters. The only exceptions to this in our model are the variation in the coefficients a and b in Eq. () – the parameters that determine the non-linear growth function of wall thickness. Specifically, very low CIs in adult-sized foraminifera were only observed with a and b at their lowermost and uppermost limit respectively (Fig. ). In contrast to all other parameters, CI change as forced by the shape of the regression between wall thickness and chamber size/number cannot be compensated for by other prescribed ontogenetic parameters.

Consistent with the modelling results and chamber addition. A logarithmic regression of individuals' CI versus their size at the beginning of culture experiments (Fig. a) yields an R2 of 0.37. Once normalised according to the mean number of chambers added during each culture experiment (see Sect.  and Fig. c), the coherence of this relationship with size becomes stronger, with an R2 of 0.59 (Fig. b). We chose logarithmic regression fits because in most of our models for G. ruber CI change through ontogeny approximates to a logarithmic relationship within the range in test size of our cultured specimens (see Fig. b).

To investigate the effect of culture conditions on CI, the residuals from the logarithmic regression fit in Fig. b (given in Table ) are compared to environmental parameters (Fig. ). No significant variation with Mg / Casw was observed (Fig. ), consistent with previous observations that varying seawater [Mg] does not change growth rates in foraminifera . Similarly, no effect of temperature on CI was observed (Fig. b). However, a statistically significant correlation with pH was found (R2=0.47, p=0.01; Fig. c). Other studies often parameterise carbonate system changes in terms of carbonate ion concentration, [CO32-] e.g., or [DIC] / [H+] . We also tested residual CI against these parameters, using carbonate speciation constants adjusted for changing Mg / Casw according to . There was little difference in correlation coefficient in the case of [DIC] / [H+] (R2=0.47 for [DIC] / [H+] and pH), but in the case of [CO32-] correlation was weaker (R2=0.40). We opt to primarily focus on pH in figures and discussions here as a less abstracted parameter, but we cannot rule out [DIC] / [H+] as being the primary driver, as suggested by . Finally, while suggest [DIC] may be the most important carbonate parameter affecting calcification, we see no significant correlation between [DIC] and residual CI (R2=-0.07, p=0.553).

Core-top results are given in Table S2. Multiple linear regression analysis demonstrates that deep-ocean carbonate system conditions at the core-top site, test size, and morphospecies identity were all statistically significant controls on ρA within the set of core-top samples measured here. Together, these three factors could explain 86 % of the variance in ρA seen in our core-top assemblages (for regression statistics, see Table S3). We used the relaimpo R package to determine relative importance of these factors, and found bottom water pH at the site of deposition to be the strongest determinant of ρA (as shown in Fig.  a and b, and Table S3). Shell size (as parameterised by shell silhouette area; Fig. c), and species type within the broader G. ruber plexus (Fig. b, c) were found to be secondary, but nevertheless significant factors. Where both G. ruber sensu stricto and sensu lato (encompassing both G. elongatus and G. pyramidalis; ) were measured at the same site, G. ruber sensu stricto displayed significantly lower values of ρA (paired t-test; p=0.01). Despite the observations from our culture experiments, estimated surface-ocean pH was not found to be a significant control on ρA in the core-top samples, and would be excluded from the model by stepwise parameter reduction according to its Akaike information criterion (AIC). We include it here for illustrative purposes only given the focus of our study (Fig. ), since it has little effect on the overall model fit (R2=0.86 in both cases), or the relative importance of other factors in the regression. We note also that we tested other deep and surface water carbonate system parameters in lieu of pH (Ω, Δ[CO32-], etc.), but in all cases pH produced stronger model fits.

While some progress has been made in explaining differential responses of groups of marine calcifiers to acidification e.g., highly divergent responses within the major groups of calcifiers continue to pose a challenge to our understanding. For example, coccolithophores were more heavily calcified during geological epochs characterised by higher CO2, and lower pH e.g., even if this result has not always been reproduced in culture . Additionally, despite observations of decreasing pH and [CO32-] negatively impacting calcification in most planktonic and reef-dwelling foraminifera e.g. in agreement with results from our cultures (Fig. ), benthic foraminifera became more heavily calcified or exhibited little response over the Palaeocene–Eocene Thermal Maximum (PETM) and ETM2 . Examining this finding in the context of our model allows us to investigate the morphological responses to pH change that could produce these patterns, and so begin to form a unifying hypothesis to explain these various apparently contradictory observations. To do this, we must first consider how foraminiferal morphology itself might affect calcification.

Our model predicts that calcification intensity – a metric for how heavily calcified cultured foraminifera are – is dependent on foraminifera size on collection as well as the number of chambers precipitated in culture, as we observe (Figs. , ). But beyond this, varying permutations of model parameters (as laid out in Appendix ) reveals that CI is most strongly dependent on covariation of the coefficients that describe the increase in wall thickness with ontogeny (a and b in Eq. ). It appears that the overall shape of this regression, rather than either of its constituent coefficients alone, is most important in controlling CI. Furthermore, the size–wall thickness coefficients drive CI in models 1 and 3, but varying maximum wall thickness in isolation has no systematic effect (model 2). These observations lead us to hypothesise that it is not simply that large adult foraminifera lay down less calcite in their walls in response to acidification, but rather that the slope of the regression between wall thickness and chamber diameter is shallower. This mechanism, if correct, would produce two physiological responses: (1) lower pH will result in a thinning of shell walls when the foraminifer is larger, and (2) smaller foraminifera will exhibit ambiguous, or even positive, responses to acidification. These hypothesised responses are represented in Fig. .

Although it is perhaps counter-intuitive to envisage such contrasting calcification responses to acidification with size, such a hypothesis may have a mechanistic foundation in the physiology of biomineralisation, when one considers two important observations of calcite precipitation in foraminifera. Firstly, based on test oxygen isotope ratios, it seems that foraminifera precipitate calcite from a species-specific combination of HCO3- and CO32- . Secondly, small foraminifera may not have large internal calcium and/or carbon pools , whereas large foraminifera do . This is because smaller foraminifera build chambers that require far less material volumetrically, and so they can potentially source the ions required for calcification on the same timescales as chamber precipitation. In this way, lower pH could have less of an effect on their wall thickness, or even favour more heavily calcified chambers, if associated with a rise in [DIC]. Increased availability of carbon for calcification could promote calcification, decreasing the volume of seawater needing to be cycled to produce a given amount of calcite for chamber formation. Once planktonic and benthic foraminifera reach a certain size, however, the large amounts of CaCO3 required to build a new chamber may necessitate prior storage of carbon internally as shown by. Importantly, the efficiency of this internal storage mechanism is thought to be related to the ability of the organisms to raise the pH of vacuolised seawater . Therefore, lower seawater pH acts against the efficiency of this carbon concentrating mechanism, meaning that chamber formation is more difficult. Alternatively, it has been suggested that foraminifera acquire the carbon needed for calcification through proton pumping into their microenvironment in order to promote diffusion of CO2(aq) into the cytoplasm . This model is also consistent with our findings, as larger foraminifera generally have a lower surface area / volume ratio, and therefore the efficiency of this mechanism may be reduced in larger individuals. Our data does not allow us to differentiate between these biomineralisation models (which may not be mutually exclusive) but provides a framework within either to understand the response of calcification to the carbonate system.

Besides our observed response of planktonic foraminiferal wall thickness to changes in seawater carbonate chemistry (Fig. ), there is other empirical evidence to support our size-dependent model (see Fig. ). Field studies indicate that large shallow-water species of planktonic foraminifera respond to decreased pH by producing thinner walls . Among benthic foraminifera, culture experiments in Elphidium also revealed reduced calcification at low pH . While there are as yet few data from smaller species of planktonic foraminifera and early ontogenetic stage individuals of larger planktonic foraminiferal species, there are some lines of evidence from small benthic foraminifera that could support the inverse calcification response that we propose. found that small benthic foraminifera became more heavily calcified during the PETM, when ocean pH was lower . By contrast, during the high pH “carbonate overshoot” in the aftermath of the event , these foraminifera displayed thinner walls . Diverse small benthic foraminifera assemblages have also been found living in highly undersaturated oligohaline conditions . Indeed, while biomineralisation pathways clearly differ, recent work favours a similarly positive response of calcification to increased aqueous pCO2 with lower pH in the much smaller coccolithophores .

Size-dependent calcification could yet provide a common mechanism to unify the often variable responses observed in foraminifera to date. However, we note that there may be different ecophysiological factors driving calcification in benthic and planktonic foraminifera, and that it remains untested as to what extent calcification mechanisms in juvenile individuals of large foraminiferal species may be comparable to adult individuals of smaller species. We suggest therefore that this hypothesis requires further investigation. At present, there are insufficient measurements of changes in calcification and morphology through ontogeny to robustly test this model, or indeed to re-interpret existing SNW data with confidence. Comparative CT scans of foraminifera, including examination of individuals grown under different pH conditions, could provide such a test by constraining ontogenetic variation in calcite as in, while further multi-species culture experiments would no doubt be beneficial.

Published investigations using SNW as an environmental proxy commonly assume that the SNW metrics themselves are independent of size or ontogeny. Our modelling approach shows that there is in fact a strong effect of test size on SNW. Modelled area density ρA, a commonly used SNW metric is shown in Fig. a as a function of test diameter. Virtually all model runs predict a positive relationship between ρA and test size, although the exact nature of this relationship varies with model parameterisation. This suggests that at least some of the variability between and within published studies could derive from the widely divergent shell sizes and sieve size ranges used (Fig. b). Our models similarly reveal a strong size dependency in volume-normalised approaches, such as that used by across the PETM. All model runs predict that the foraminiferal calcite volume / total volume ratio exhibits a strong dependence on test size (Fig. S2 in the Supplement).

It has been suggested, given that some size–mass (or volume–mass) relationships in planktonic foraminifera appear approximately linear , that the use of area- and volume-normalised weight to estimate SNW is not complicated by spatial or temporal variations in mean body size. In fact, a linear relationship between mass and area or between mass and volume directly implies that area density is size-dependent, given mass=k×mm3, where k is a constant equal to the slope. If volume is approximated from area by raising to the power of 3/2 , then ρA=mass(axis1axis2)≈k×(axis1axis2)3/2(axis1axis2)≈k×(axis1axis2)1/2, which predicts a linear dependence of ρA on body size (given aspect ratio in Table ), such that ρA≈k×axis121.16≈axis1×k1.16. For G. ruber, the slope of this relationship between size and ρA approximates to 2.6×10-3. This means that a 100 µm increase in test major axis would lead to an ρA increase of ∼ 38 µg mm-2 due to the change in body size alone, demonstrating consistency between these simple calculations and our model (Fig. 6a). This response is of the same magnitude as the area density response to carbonate system changes reported in other studies e.g.. Higher overall ρA observed by for T. sacculifer in larger size fractions may constitute further evidence of a positive size effect on ρA. Similarly, we also find that cross-sectional area is a significant predictor of ρA in our core-top foraminifera (Fig. ).

We thus provide theoretical, model, and empirical evidence for a strong test size control on size-normalised weight metrics. This size dependence applies equally to other SNW metrics, as well as the specific metrics directly discussed here. That said, size dependence of SNW metrics may be variably manifest, and variably problematic, in real-world datasets. One implication of this finding is that datasets from different studies using different foraminiferal size fractions are not directly comparable. Given the range of size fractions used in SNW studies (Fig. b), size and ontogenetic stage may explain some of the discrepancies between findings, particularly for those studies using a wide sieve size fraction (e.g. several hundred µm). The magnitude of increase in SNW (here quantified as ρA, Fig. a) with size is likely strongest at smaller body sizes (< ∼ 350 µm) – encompassing size fractions commonly used in both modern calibration and down-core studies (Fig. b). With these findings in mind, here we make recommendations of best practice for future studies. Firstly, in death assemblages, where post-gametogenic foraminifera will likely have added a similar number of chambers within a full life cycle, the influence of ontogeny and body size on SNW can be minimised by using the narrowest possible size fraction of only post-gametogenic individuals, and reporting mean test size. This may of course be challenging over transient climatic events associated with a shift in body size, such as the PETM – in that case, models of calcification with size and ontogeny are needed. Living assemblages may present other difficulties, as individuals of the same size may have more or fewer chambers, and hence differing amounts of secondary calcification. For pre-gametogenic individuals, then, some estimate of chamber number and overall test size is needed. These additional measurements are necessary because the SNW metrics are inherently dependent on foraminifer size, and because changes in the carbonate system may have a differential effect through ontogeny as previously suggested by.

Besides the influence of size on SNW, our study highlights other fundamental caveats about the applicability of SNW as a surface-water proxy. Although our culture data support a primary carbonate system control on calcification, in agreement with other studies e.g., our core-top samples demonstrate that this may be overwhelmed by dissolution processes at the site of deposition (see Fig. ). Indeed, while size and morphospecies are preserved as significant controls on SNW (quantified in this case as ρA; Fig. ), any primary signal of surface carbonate chemistry (for a range in pH of 8.09–8.21) in our core-top sample set has been entirely lost to dissolution. We therefore urge caution before attributing open-ocean SNW patterns exclusively to either primary or secondary processes. In sites where carbonate saturation at the site of deposition is high, it is probably reasonable to attribute SNW changes to surface conditions as inetc.. At depths approaching the lysocline, our data support the earlier uses of SNW as a proxy for the deep sea carbonate system e.g.. In between these end-member scenarios, it may be difficult to untangle competing effects , and so combining shallow-water and deep-water cores is advisable, following .

Previous investigations into the controls on foraminiferal shell weight have often struggled to determine conclusively which environmental controls, if any, impact foraminiferal calcification, as temperature and [CO32-] are often correlated in hydrographic datasets . In our cultures where both temperature and carbonate system parameters were varied, we show that the carbonate system is the most likely driver of CI in G. ruber (Fig. ). Given the significance of planktonic foraminiferal tests to the global pelagic CaCO3 budget , this finding could therefore have important implications for global carbonate alkalinity fluxes, and projections of the response of biogeochemical cycling to anthropogenic ocean acidification. Within the pelagic realm, foraminiferal calcification reduces TAlk and DIC in a 2 : 1 ratio, releasing CO2 and thereby lowering surface ocean pH e.g.. Therefore, it is possible that reduced alkalinity uptake in surface waters may constitute a weak negative feedback on surface ocean acidification. Scaling this in terms of fluxes, considering changes in other calcifying groups like coccolithophorids, and accounting for body size and population size, is beyond the scope of this study. We also note that if the response to acidification is size-related, there may be some role for other environmental parameters that influence body size in foraminifera e.g. temperature, light; in determining their response to anthropogenic ocean acidification. We suggest that modelling of the pelagic ecosystem should include the physiological costs to calcification in each group of marine calcifiers. Such considerations may be critical in addressing current shortfalls in prediction of future biogeochemical changes .