Literature data on Me/Ca ratios in endolymph and otolith were used to calculate partitioning coefficient. The latter were compared to partitioning coefficient determined in inorganic precipitation experiments. The literature data used are summarized in Table 2.

The literature on inorganic system provides many measurements of the partitioning coefficient DIn from different experimental designs. We selected the full range of values to get a realistic overall picture of the inorganic system. For the otolith-endolymph system the literature was limited. Only three papers gave us enough data to estimate the partitioning coefficient of the elements into the otolith. In the study of Thomas et al. (2017) they used a marine species, Acanthopagrus butcheri (Sp1), and the number of individuals measured was N=3. Otoliths were diluted and measured with an inductively coupled plasma mass spectrometer (ICP-MS) as the endolymph fluid. They provide the concentration of foreign elements (Me) normalized to the concentration calcium of (Ca) in the otolith and the endolymph ratio, R=[Me][Ca]-1mmolmol-1 with the ± SD and the range (R) = min(R) - max(R), as well the partitioning coefficient (D×100). We estimate the range of the D using a simple formula of range ratio (Eq. 1): 1rangeDe=maxDe-min(De)=max(Rotolith)min(Rendolymph)-min(Rotolith)max(Rendolymph)

In the other two available studies with data meeting the criteria required for these estimates, were in a form of “concentration of foreign elements” in the otolith and in the endolymph (Melancon et al., 2008, 2009). The species that were used in these studies were the freshwater species burbot Lota lota (Sp2), lake trout Salvelinus namaycush (Sp3) and a walleye Sander vitreus (Sp4), the number of the individuals (N) that were used were Nburbot=18 and Ntrout=11 and Nwalley=8, respectively. In these studies, the concentrations of the elements in the otoliths were quantified by laser ablation (LA-ICP-MS) and they performed a series of ablations at the growing otolith edges that were in contact with the endolymph and represent the last 30 to 60 d of growth. They provide the average concentration of the foreign elements av [Me] ± SD (ppm) in the otolith and in the endolymph, which we converted to mmol mol⁻¹. The ratio R=[Me][Ca]-1mmolmol-1 in the otolith and in the endolymph and the av (D) ± SD (D) was estimated using Eqs. (2) and (3) 2av(De)=av(Rotolith)av(Rendolymph)3SDDe=avDe×SDRotolithavRotolith2+SDRendolymphavRendolymph2

Then the ratio and the partitioning coefficient, in the different parts of the ion transport pathway that the elements need to cross to precipitate in the otolith, were estimated. Only one paper provided sufficient data for this purpose (Melancon et al., 2009). The ion transport pathway starts from the ambient water to blood, then from blood to endolymph and the final step is from endolymph to otolith (key figure). The partitioning coefficient that describes the last step of endolymph to otolith was estimated (Eq. 4). Some extra variables were also estimated. The first was the D commonly used in biomineralization studies. This Dw is the partitioning coefficient using as parent solution the ambient water (Eq. 5). The other two Me/Ca were estimated based on the idea that the last step of the precipitation is purely inorganic (Eqs. 7 and 8). The first of those (Eq. 7), is the ratio that the otolith would have, if the last precipitation step was completely inorganic and the parent solution was the endolymph (Rotolith1). The second (Eq. 8) is the theoretical ratio if the parent solution was water (Rotolith2).

4De=RotolithRendolymph5Dw=RotolithRwater6DIn=RcrystalRfluid7Rotolith1=rangeDIn×Rendolymph8Rotolith2=range(DIn)×Rwater

We address the following question. Does the numerical value of the foreign element partitioning coefficient from endolymph into otolith equal that of the partitioning coefficient from an aqueous solution into pure aragonite? As mentioned in the introduction, Fig. 1 illustrates the range of the Sr partitioning coefficient (D) in different calcifying marine organisms, we used as parent solution seawater and the ratios of the elements in each organism from the literature (Broecker and Peng, 1982; Cohen et al., 2006; Langer et al., 2018; Lorens and Bender, 1980; Mitsuguchi et al., 2003).

We looked at the partitioning coefficient of six elements (Sr, Ba, Mg, Na, Zn, and Li) in four different species, Sp1–Sp4 (Figs. 2, S1 in the Supplement). For our question, it is helpful to consider several elements, as opposed to just one, because results from a single element might be misleading (Langer et al., 2018). A species comparison will further strengthen the conclusions because the question concerns the endolymph-otolith system in general. The partitioning coefficients De of Na, Mg (mostly), Sr and Ba (in Sp1) fall within the range of inorganic values (Figs. 2, S1). For the remaining elements, Zn and Li, otoliths show a partitioning behaviour different from inorganic aragonite. Taken together these results clearly show that the endolymph-otolith system produces foreign element partitioning coefficients different from the ones determined in synthetic aragonite precipitation. Therefore, we conclude that foreign element partitioning during otolith formation in the endolymph involves processes that do not occur during inorganic aragonite precipitation. An obvious further question is why the partitioning behaviour is both element and species specific. In general, the answer will likely involve specific organic material both in the endolymph and the otolith. In the following we will concretize this somewhat vague hypothesis.

Otolith partitioning coefficients De of Ba and Zn (and Sr in Sp2 and partly Sp3) in freshwater species are lower than those in the inorganic system (Fig. 2). In the case of Sr and Ba incorporation into the organic part of the otolith seems negligible, ruling out a significant influence of otolith organics on partitioning (Izzo et al., 2016). This strongly suggests that endolymph organic material (Borelli et al., 2001; Thomas et al., 2019) forms complexes with divalent cations, fractionating for Sr and Ba. The remaining free ions in solution are incorporated into the growing otolith aragonite, with foreign element partitioning depending on crystal growth rate, in turn depending on various factors such as supersaturation, stoichiometry, and surface topography (Nehrke et al., 2007; Wolthers et al., 2013).

An example of organic material fractionating for Sr and Ba are polysaccharides such as alginates (Yuryev et al., 1979). The situation might be different for Mg which is fractionated against when forming complexes with organics thereby weakening fractionation against Mg into calcite (Mavromatis et al., 2017; Takeuchi et al., 2008). Complexation of foreign elements with inorganic ligands can also affect partitioning into calcium carbonate. In the case of Mg, sulfate complexes lead to an apparently harder fractionation against Mg into calcite (Goetschl et al., 2019; Mucci et al., 1989). Since for Mg, organic and inorganic complexes influence partitioning behaviour differently the overall change in the partitioning coefficient will partly depend on the relative concentrations of these different ligands. Inorganic ligands such as sulfate, phosphate, and carbonate might play a considerable role in modifying partitioning behaviour in calcifying fluids. The modification of the partitioning behaviour will be foreign element specific too. While alkali metal (e.g. Na and Li) complexes are of foreign importance, Zn for example has a high affinity to form inorganic complexes with e.g. sulfate and carbonate (Krȩżel and Maret, 2016; Lewis and Randall, 1921; Olsher et al., 1991; Stanley and Byrne, 1990). However, Li partitioning into calcite is pH dependent (Füger et al., 2019). Since calcifying fluids are likely to feature high pH, Li partitioning into calcitic biominerals, and maybe aragonitic ones too, might display a “high pH signal”.

Why does Ba partitioning in the marine species Sp1 differ so strikingly from the one in the freshwater species (Fig. 2)? Rather than being a species effect, this might be a methodological effect. Otoliths from the freshwater species were analyzed by LA-ICP-MS, where only the edge of the otolith was targeted to achieve a better match with the endolymph analysis (see Material and Methods). Otoliths from the marine species were dissolved whole for solution analysis by ICP-MS. The Ba/Ca of otoliths can vary substantially within single otoliths, often with high values near the otolith core (Hermann et al., 2016). This could explain both the higher De in the marine species and the larger range reaching both below and above the inorganic range (Fig. 2).

The situation for Zn is different from the one for Sr and Ba because 40 %–60 % of the Zn reside in otolith organics (McFadden et al., 2016; Miller et al., 2006). Although an effect of endolymph organics cannot be ruled out for Zn, it is equally possible that partitioning into otolith organics is different from partitioning into otolith aragonite. Differential partitioning between the organic and the mineral part of mollusc shells has been reported, supporting this possibility (Schöne et al., 2010). Additionally, organic complexes with Zn can comprise the majority of total Zn, for example in surface seawater down to 500 m (Bruland, 1989). These naturally occurring organic ligands in seawater will be important in calcifiers using seawater as substrate supply for calcification, e.g. foraminifera (Elderfield et al., 1996). The influence of organic material in the calcifying fluid on foreign element partitioning shows that the localization of the foreign element in the mineral part of the biomineral does not justify the conclusion that the partitioning process is inorganic. This reasoning has nevertheless been applied to Mg partitioning into foraminiferal calcite (Branson et al., 2013). The latter authors show that Mg resides in foraminiferal calcite and from this observation conclude that its partitioning behaviour of Mg is inorganic. Since Mg is an important temperature proxy (Elderfield and Ganssen, 2000), this example illustrates the usefulness of the endolymph-otolith system for the development of a process-based understanding of proxy signal formation more generally.

Please note that foraminiferal shells are calcitic while otoliths are aragonitic. This difference in the calcium carbonate polymorph used by different organisms has implications for numerical values of partitioning coefficients (Langer et al., 2018), but has no bearing on the argument made above. We claim that the fact that Mg resides in the mineral phase of a biomineral, as opposed to the organic phase, is not sufficient to support the inference that the partitioning process is a case of inorganic co-precipitation. This claim holds regardless of the calcium carbonate mineral into which Mg is incorporated, and regardless of the Mg/Ca of the respective mineral. Foraminifera, for example, comprise low-Mg (e.g. Ammonia), intermediate-Mg (e.g. Amphistegina), and high-Mg (e.g. Heterostegina) species (Mewes et al., 2014, 2015; Raitzsch et al., 2010). In the example mentioned above (Branson et al., 2013), both a low-Mg species (Orbulina) and an intermediate-Mg species (Amphistegina) are discussed. The author's argument, as well as our findings, apply equally to both species; and would do so for any other species.

To sum up, foreign elements might reside either in the mineral (e.g. aragonite in otoliths) or the organic part of the biomineral. Partitioning of foreign elements into the organic part is most likely different from partitioning into the mineral part. Hence partitioning is not homogeneous across a biomineral. The calcifying fluid often contains organic and, potentially, inorganic ligands that form complexes with foreign elements thereby influencing partitioning into the biomineral.

The partitioning behaviour of Mg and Na seems to suggest that these elements are coprecipitated into aragonite in a manner akin to synthetic aragonite formation (Fig. 2). If this was indeed so this would nevertheless not contradict our conclusion (see above), namely foreign element partitioning into otoliths involves processes other than aragonite precipitation from an aqueous solution of inorganic ions. The latter conclusion rests on the behaviour of the other elements as discussed above and is not invalidated by a putatively different behaviour of Mg and Na. However, the behaviour of Mg and Na might as well merely appear inorganic numerically (in terms of De) but the processes underlying De might involve organic material, i.e. the overall process of partitioning might be very different from inorganic precipitation. This phenomenon has been described for different calcifiers and is known by the term “invisible vital effect” (Nehrke and Langer, 2023, and references therein).

The likelihood of an invisible vital effect in De is nevertheless much smaller than in the D calculated traditionally, i.e. using the external water Me/Ca (seawater or freshwater) as denominator. We added the traditional partitioning coefficient (Dw) to our dataset (Fig. 2). For Mg and Zn, Dw falls within the range of inorganic values, but from this we cannot conclude that Mg and Zn partitioning proceeds via inorganic precipitation from external water. We know that for ions to enter the endolymph they need to be transported via the blood (Hüssy et al., 2021; McCormick and McKinlay, 2000; Sturrock et al., 2015) so that there are at least two partitioning steps operative before the endolymph-otolith step. We look at these partitioning steps in the following section.

In the freshwater species Sp2 (Fig. 3) and Sp3 (Fig. S2) were the only dataset that allows us to trace the pathway of foreign elements from external water into the otolith. In Fig. 3 we use Me/Ca (R) in different reservoirs along the ion transport pathway as given in the literature, and we additionally calculate two further values: (1) the Rotolith2 that results from multiplying Rw by DIn; (2) the Rotolith1 that results from multiplying Re by DIn. The DIn that are used are selected to minimize the offset between otolith (measured) and otolith (calculated). The aim of the figures is to illustrate the resulting (R) of different partitioning steps as they actually occur (coloured reservoirs), as opposed to the ones that would theoretically occur if DIn were applied.

Several things can be gleaned from this figure. The first concerns the match/mismatch of otolith and otolith1. A match indicates that partitioning from endolymph to otolith could be inorganic. This is the case for Sr, Mg, and Na. Note that the same conclusion can be drawn from Fig. 2 with the exception of DSr which does not fall within the inorganic range but is close to it. The reason for this discrepancy is that in Fig. 2a mean and standard deviation is given whereas in Fig. 3 the minimum value of DIn is used. The latter choice represents a conservative approach aiming at a match between otolith and otolith1. The case of Sr is therefore borderline, but its behaviour could still be considered inorganic. In stark contrast, the behaviour of Ba and Zn is clearly not inorganic.

The traditional way of calculating partitioning coefficients is from the ambient water to the biomineral because the composition of the calcifying fluid is unknown (e.g. Langer et al., 2006). This poses the central problem of the vital effect. The main question we are asking here is: can the problem of the vital effect be solved by knowledge of the composition of the calcifying fluid. The answer is yes for Sr and Na, and no for Ba, Zn, and Mg. Note that Dw of Zn and Mg show an invisible vital effect, so that using the correct parent solution can confer no numerical advantage. There is nevertheless knowledge to be gained. Knowing the values of otolith2 (Zn and Mg) merely tells us that there will be partitioning steps along the way from water into otolith, but the localization of partitioning along this pathway remains the classic “black box” (Nehrke and Langer, 2023). Here we can take a look into the black box in unprecedented detail. The step from water into blood fractionates weakly for Mg but strongly for Zn, while the following step into the endolymph fractionates weakly against both Mg and Zn. The last step from endolymph to otolith fractionates strongly against both Zn and Mg. While this step could be inorganic for Mg, it is more complex for Zn, i.e. the interaction of Zn with organics (as discussed above) contributes to this partitioning step. Biological partitioning steps are hard to predict in general, and in particular if the foreign element and Ca are transported by separate transport systems.

While Ca, Na, Mg, and Zn are essential elements, i.e. needed in physiological processes, there is no known physiological role for Sr and Ba, which are therefore considered non-essential (Lall and Kaushik, 2021; Marshall, 2002; Pors Nielsen, 2004; Salisbury and Ross, 1992). When considering foreign element partitioning into biominerals the distinction between essential and non-essential elements is of great importance because essential elements have their own transport systems while non-essential elements are thought to pass through the transport systems of essential elements (Langer et al., 2006, 2009). This means that partitioning from one reservoir into another (e.g. from water into blood) can be conceptualized easier for non-essential elements, because only the partitioning of individual transport systems has to be known. If one transport system transports the foreign element and another transports Ca the situation is more complicated because the two systems can be regulated independently. In the case of the non-essential elements Sr and Ba it is usually expected that they partition similarly if not with identical partitioning coefficient (Allen and Sanders, 1994; Langer et al., 2006, 2009; Nachshen and Blaustein, 1982). It is therefore surprising that the step from water to blood fractionates for Ba but against Sr, whereas the step from blood to endolymph does not fractionate at all (or only minimally) for both elements (Fig. 3). The partitioning from endolymph to otolith is against both Sr and Ba, i.e. according to expectation. The fact that Ba fractionation is harder than Sr fractionation could be explained by differential Sr and Ba partitioning of cellular transporters as well as organic polymers (e.g. Nachshen and Blaustein, 1982; Yuryev et al., 1979).