# Controls on potassium incorporation in foraminifera and other marine calcifying organisms

Romi Nambiar, Hagar Hauzer, William Gray, Michael Henehan, Laura Cotton, Jonathan Erez, Yair Rosenthal, Willem Renema, Wolfgang Müller, David Evans

► To cite this version:

Romi Nambiar, Hagar Hauzer, William Gray, Michael Henehan, Laura Cotton, et al.. Controls on potassium incorporation in foraminifera and other marine calcifying organisms. Geochimica et Cosmochimica Acta, 2023, 351, pp.125-138. 10.1016/j.gca.2023.04.020. hal-04092650

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# Controls on potassium incorporation in foraminifera and other marine calcifying organisms

Romi Nambiar<sup>a,b,*</sup>, Hagar Hauzer<sup>c,d</sup>, William R. Gray<sup>e</sup>, Michael J. Henehan<sup>f</sup>, Laura Cotton<sup>g</sup>, Jonathan Erez<sup>c</sup>, Yair Rosenthal<sup>h</sup>, Willem Renema<sup>ij</sup>, Wolfgang Müller<sup>a,b</sup>, David Evans<sup>a,b</sup>

<sup>a</sup>Institute of Geosciences, Goethe University, Frankfurt, Altenhöferallee 1, 60438 Frankfurt am Main, Germany

<sup>b</sup>FIERCE, Frankfurt Isotope & Element Research Center, Goethe University, Altenhöferallee 1, 60438 Frankfurt am Main, Germany

<sup>c</sup>The Fredy & Nadine Herrmann Institute of Earth Sciences, the Hebrew University of Jerusalem, Israel

<sup>d</sup>Israel Oceanographic and Limnological Research, National Institute of Oceanography, Haifa, Israel

<sup>e</sup>Laboratoire des Sciences du Climat et de l'Environnement (LSCE/IPSL), Université Paris-Saclay, Gif-sur-Yvette, France

<sup>f</sup>Section 3.3 Earth Surface Geochemistry, Deutsches GeoForschungsZentrum GFZ, 14473, Potsdam, Germany

<sup>g</sup>Natural History Museum of Denmark, University of Copenhagen, Denmark

<sup>h</sup>Department of Marine and Coastal Sciences, Rutgers, State University of New Jersey, New Brunswick, NJ, USA

<sup>i</sup>Naturalis Biodiversity Center, Leiden, Netherlands

<sup>j</sup>University of Amsterdam, Institute for Biodiversity and Ecosystem Dynamics, Amsterdam, NL

## Abstract

Seawater chemistry exerts an important control on the incorporation of trace elements into the shells of marine calcifying organisms. Variability in the major ion chemistry of seawater is also an indicator of past geological processes, and so the influence of seawater chemistry on carbonate trace element incorporation can be harnessed to determine changes in the composition of seawater through time. Here, we investigate whether key oceanographic parameters (temperature, salinity, and the carbonate system) affect the incorporation of potassium (K) into foraminiferal calcite, and explore the utility of K/Ca ratios in foraminifera as an indicator of past variability in the seawater Ca²⁺ concentration. We measured both low-Mg and high-Mg modern foraminifera, including planktonic (Globigerinoides ruber) and shallow-dwelling larger benthic (Operculina ammonoides) species, using laser-ablation sector-field inductively-coupled plasma mass spectrometry (LA-SF-ICPMS). Both species show no resolvable influence of temperature, salinity, pH, or [CO₃²⁻] on K incorporation. In order to determine the effect of the seawater Ca concentration ([Ca²⁺]sw) on K incorporation, we
analysed laboratory-cultured *O. ammonoides*, the close living relative of the abundant Eocene *Nummulites*, grown at four different [Ca²⁺]sw. We find a significant relationship between seawater and shell K/Ca, albeit with a shallower slope compared to most other trace elements which we suggest is driven by a crystal growth rate effect on K incorporation, constrained using culture experiments of *O. ammonoides* grown at different pH. If the K⁺ concentration has remained relatively constant throughout the Phanerozoic Eon, our data may pave the way forward for the use of K/Ca as a direct proxy for past [Ca²⁺]sw variability. Alternatively, coupling K/Ca with the Na/Ca proxy would allow more accurate reconstruction of [Ca²⁺]sw or verification of whether [K⁺]sw or [Na⁺]sw has indeed remained within narrow bounds.

Keywords: Larger Benthic Foraminifera (LBF), culture calibration, K/Ca, Na/Ca, seawater chemistry, LA-SF-ICPMS

Email address: Nambiar@geo.uni-frankfurt.de (R. Nambiar)

<footnote>*Corresponding author.</footnote>
1. Introduction

Trace elements in marine carbonates are widely used for palaeoclimatic reconstruction.

Foraminifera are an important archive for this purpose because of their widespread abundance and good preservation potential. However, shell precipitation from the surrounding seawater is a complex, biologically controlled process (Bentov et al., 2009; De Nooijer et al., 2009). The biogeochemical imprints of this process, termed ‘vital effects’, are not necessarily predictable from a simple chemical thermodynamic perspective (e.g. Erez, 2003), which means that the relationship between shell chemistry and ambient physical or chemical conditions must currently be empirically calibrated (Hauzer et al., 2018; Keul et al., 2013; Lea et al., 1999; Zhou et al., 2021). Using this approach, a wide range of chemical signatures in marine carbonates have been established as palaeo-proxies.

For example, trace element ratios have been extensively applied to reconstruct parameters such as ocean temperature (Mg/Ca and Li/Mg; Rosenthal et al., 1997; Lea et al., 1999; Anand et al., 2003; Marchitto et al., 2018; Gray and Evans, 2019), the carbonate system (B/Ca, Zn/Ca; Marchitto et al., 2000; Yu et al., 2010; Brown et al., 2011; Allen and Hönisch, 2012; Van Dijk et al., 2017), salinity (Ba/Ca; Weldeab et al., 2007), nutrient concentration (Cd/Ca; Boyle, 1981; Rickaby and Elderfield, 1999). On longer (multi-million year) timescales, the application of foraminiferal trace element proxies is complicated by the fact that variability in seawater chemistry also affects the incorporation of trace elements into foraminifer’s shells. For instance, variability in seawater Mg/Ca affects the Mg/Ca of foraminifera and thus complicates its use as palaeotemperature proxy (Evans and Müller, 2012; Hasiuk and Lohmann, 2010; Segev and Erez, 2006). Because ocean chemistry has undergone substantial secular changes throughout the Phanerozoic (Lowenstein et al., 2001; Turchyn and DePaolo, 2019; Wilkinson and Algeo, 1989), this issue constitutes a major source of uncertainty in the
application of element/Ca proxies in deep time. To enable the accurate application of trace element-
based palaeoclimatic proxies beyond the residence time of calcium (~1 Myr; Broecker and Peng,
1982), precise and accurate reconstructions of seawater major ion chemistry are required.

Long-term changes in seawater chemistry are driven by variations in geological factors such
as hydrothermal discharge from the global mid-ocean ridge system, the rate and type of material
being terrestrially weathered, dolomitisation, and reverse weathering (e.g. Lowenstein et al., 2014;
Coogan and Dosso, 2015; Higgins and Schrag, 2015). Moreover, the major ion chemistry of seawater
is in itself a potential tracer of these geochemical processes. Several studies have reconstructed
seawater El/Ca with a temporal resolution similar to that of the residence time of Ca²⁺ in seawater
using different marine carbonates (Coggon et al., 2010; Delaney et al., 1989; Dickson, 2002; Evans et
al., 2018a; Gothmann et al., 2015; Wit et al., 2017). Recently, the Na/Ca ratio of foraminifera calcite
has shown to be much more sensitive to changes in [Ca²⁺]sw than seawater salinity, and given the
long residence time of Na⁺ in seawater (~100 Myr; Broecker, 1982), Na/Ca may be interpreted purely
in terms of [Ca²⁺]sw changes (Hauzer et al., 2018; Le Houedec et al., 2021; Zhou et al., 2021). The
approach of directly reconstructing [Ca²⁺]sw using a trace element ratio containing an element with
an extremely long residence time suggests the possibility that other elements with a long-term near-
constant concentration may offer similar information.

Potassium is a major element in seawater (Ksw), with a present-day concentration of 10.2
mmol kg⁻¹ and a residence time of ~12 million years (Broecker, 1982). The major source of potassium
in the ocean is from riverine input and high-temperature hydrothermal processes, whereas removal
of K⁺ from seawater takes places by formation of authigenic clay formation by reverse weathering
and low temperature hydrothermal processes (Bloch and Bischoff, 1979; Kronberg, 1985;
Michalopoulos and Aller, 1995). The seawater Sr, Li and Os isotope records have been used to argue for a substantial increase in continental weathering through the Cenozoic (particularly the Neogene) (McCauley and DePaolo, 1997; Misra and Froelich, 2012; Raymo and Ruddiman, 1992), although several other processes may impact these systems (e.g. Coogan and Dosso, 2015). Indeed, other processes, such as a decrease in reverse weathering (Dunlea et al., 2017; Higgins and Schrag, 2015; Isson and Planavsky, 2018; Misra and Froelich, 2012), high-temperature hydrothermal processes (Hardie, 1996; Horita et al., 2002), and low-temperature hydrothermal processes (Coogan and Dosso, 2015) have also been proposed to have driven seawater chemistry changes over the same interval.

Despite evidence for past variability in several processes that are important components of the K cycle, the concentration of K<sub>sw</sub> has been suggested to have remained relatively constant throughout the Phanerozoic (9-11 mmol kg<sup>-1</sup>) on the basis of modelling data from fluid inclusions trapped in evaporitic sequences (Horita et al., 2002; Lowenstein et al., 2001). If K<sub>sw</sub> has indeed remained within narrow bounds, the K/Ca ratio of marine carbonates may be an additional direct tool for the reconstruction of past changes in [Ca<sup>2+</sup>]<sub>sw</sub>. Moreover, coupling this system with Na/Ca, within a multi-proxy approach, would allow (e.g.) the constancy of Phanerozoic K<sub>sw</sub> to be verified. To evaluate the potential of K/Ca measurements of marine carbonates for this purpose, we investigated 1) two symbiont-bearing species collected from the modern ocean: the low-Mg calcite planktonic foraminifera *Globigerinoides ruber* (white) and the high-Mg calcite, larger benthic foraminifera *Operculina* sp. from globally distributed sites characterised by a wide range in seawater parameters to determine the impact of environmental parameters on K incorporation, 2) cultured *Operculina ammonoides* grown at different seawater [Ca<sup>2+</sup>] and temperature (Hauzer et al., 2018) to determine whether the proxy functions as hypothesised, and 3) cultured *O. ammonoides* grown at different pH
values beyond the modern range, to understand whether the changing seawater carbonate system might influence foraminifera K/Ca. Finally, we compiled literature data of the K/Ca and Na/Ca of a diverse range of biogenic CaCO₃ to understand the broader controls on K and Na incorporation.

## 2. Materials and methods

### 2.1. Modern foraminifera

Larger benthic foraminifera (LBF) of the genus *Operculina* were hand-sampled from SW Sulawesi, NE Kalimantan, Jakarta Bay, the Gulf of Eilat (*Operculina ammonoides*) and the Great Barrier Reef (*Operculina* sp.) (Tab. 1). These samples have been previously investigated for the purposes of producing a Mg/Ca-temperature field calibration (Evans et al., 2013), with further details of sample collection given in Renema (2006; 2008).

In order to relate shell geochemistry to environmental parameters, mean annual sea surface temperature (SST) and salinity data were taken from the 1° resolution version of the World Ocean Atlas 2018 (Locarnini et al., 2018; Zweng et al., 2019) for all *Operculina* samples except those from the Gulf of Eilat (Eil 19), for which data from the monitoring station of the Interuniversity Institute for Marine Sciences in Eilat (https://www.iui-eilat.ac.il) was used. These samples were earlier measured for Mg/Ca variability along the whorl which coincide with seawater temperature dataset (Evans and Müller, 2013). In contrast to the other sample sites, the Gulf of Eilat is characterised by a large seasonal variability in temperature. Given that the samples analysed here represents the last ~6 months, the November-April mean was used, i.e. the six-month period before the sample collection date. (for detailed information, see Evans et al., 2013). In order to determine the possible influence of the seawater carbonate system on shell geochemistry, the nearest available pH values were taken from Gregor and Gruber (2021). Seawater [CO₃²⁻] was calculated using CO2sys_v3.0 (Pierrot et al., 2021)
using the *in situ* temperature and salinity from the WOA and total alkalinity (TAlk) as the second carbonate system parameter, taken from Gregor and Gruber (2021). The dissociation constants for KHSO₄ from Dickson et al., (1990) and the total boron–salinity relationship by Lee et al., (2010) were used. The values of the carbonate system dissociation constants K₁ and K₂ were those from Lueker et al., (2000). The larger benthic foraminifera investigated in this study span a range in seawater temperature, salinity, pH, and [CO₃²⁻] ranging from 21.9 to 28.5°C, 32.4 to 40.7 on the practical salinity scale, 8.05 to 8.19 pH units and 207.2 to 284.1 µmol kg⁻¹, respectively (Tab. 1).

*Globigerinoides ruber* (white) were sampled from sediment traps in the Arabian Sea (AS02-M5) and Bay of Bengal (NBT-09, CBBT-06, and SBBT-09). These samples have been previously investigated for the purposes of refining the Mg/Ca-temperature calibration by Gray et al. (2018). Foraminifera were picked from the 200 to 400 µm size fraction. Temperature and salinity used in this study are the same as those reported in Gray et al. (2018) (Tab. 1). In addition, we analysed *G. ruber* (white) from a globally-spaced set of core-top samples which have been previously investigated to better understand B/Ca as a potential carbonate system proxy (Henehan et al., 2015). These foraminifera were picked from the 300-350 µm size fraction except for sample MC420, which was picked from the 355-400 µm fraction. Temperature and salinity used to relate shell geochemistry are those reported in Henehan et al. (2015) (Tab. 1). *In situ* carbonate chemistry data have been previously reported from both the sediment trap and core to sample sets utilized here, but were calculated in different ways. To ensure consistency in data treatment, the carbonate system parameters were therefore recalculated here. The [CO₃²⁻] values was calculated using CO2sys_v3.0 (Pierrot et al., 2021) taking the nearest available pH and TAlk values from Gregor and Gruber (2021). The constants of Lueker et al., (2000), Lee et al., (2010), and Dickson et al., (1990) were used. The sample location
111 details of all *G. ruber* measured in this study are given in Tab. 1. Together, the planktonic foraminifera
112 investigated in this study from both sediment traps and core tops span a range in seawater
113 temperature, salinity, pH, and [CO₃²⁻] ranging from 22.0 to 28.7°C, 32.7 to 36.4 on the practical salinity
114 scale, 8.05 to 8.12 pH units (total scale) and 204.1 to 238.8 µmol kg⁻¹, respectively (Tab. 1).

115 **Tab. 1.** Sample site details of the modern foraminifera analysed here.

i) Larger Benthic foraminifera; all species are *Operculina ammonoides* except SS 07G14 (*Operculina* sp.)

<table><thead><tr><th>Sample ID</th><th>latitude</th><th>longitude</th><th>Water depth (m)</th><th>T (°C)</th><th>1 SD</th><th>S</th><th>1 SD</th><th>pH (total scale)</th><th>1 SD</th><th>[CO<sub>3</sub><sup>2-</sup>]* (µM)</th><th>1 SD</th><th>n</th></tr></thead><tbody><tr><td>Pd 2805<sup>a</sup></td><td>-5.03</td><td>119.33</td><td>20</td><td>28.0</td><td>1.1</td><td>33.4</td><td>0.9</td><td>8.06</td><td>0.02</td><td>209.0</td><td>11.2</td><td>4</td></tr><tr><td>KKE30<sup>b</sup></td><td>-5.11</td><td>119.29</td><td>30</td><td>27.7</td><td>1.1</td><td>33.5</td><td>0.9</td><td>8.06</td><td>0.02</td><td>208.2</td><td>11.3</td><td>5</td></tr><tr><td>SER 33<sup>c</sup></td><td>-5.86</td><td>106.7</td><td>14-24</td><td>28.5</td><td>0.8</td><td>32.4</td><td>0.8</td><td>8.07</td><td>0.02</td><td>212.1</td><td>10.3</td><td>4</td></tr><tr><td>SS 07G14<sup>b</sup></td><td>-19.73</td><td>150.22</td><td>74</td><td>24.9</td><td>1.0</td><td>35.3</td><td>0.2</td><td>8.09</td><td>0.03</td><td>219.9</td><td>14.4</td><td>7</td></tr><tr><td>Eil 19<sup>b</sup></td><td>29.54</td><td>34.97</td><td>10-15</td><td>21.9</td><td>0.8</td><td>40.7</td><td>0.1</td><td>8.19</td><td>0.02</td><td>284.1</td><td>14.2</td><td>7</td></tr><tr><td>BBx 49A<sup>b</sup></td><td>1.39</td><td>118.82</td><td>48</td><td>27.8</td><td>0.9</td><td>34.2</td><td>0.2</td><td>8.05</td><td>0.02</td><td>207.2</td><td>10.0</td><td>8</td></tr><tr><td>Pd 2801<sup>a</sup></td><td>-5.03</td><td>119.33</td><td>20</td><td>28.0</td><td>1.1</td><td>33.4</td><td>0.9</td><td>8.06</td><td>0.02</td><td>209.0</td><td>11.2</td><td>4</td></tr></tbody></table>

ii) Planktonic foraminifera (*Globigerinoides ruber*)

<table><thead><tr><th>Sample ID</th><th>latitude</th><th>longitude</th><th>Water depth (m)</th><th>T (°C)</th><th>1 SD</th><th>S</th><th>1 SD</th><th>pH (total scale)</th><th>1 SD</th><th>[CO<sub>3</sub><sup>2-</sup>]* (µM)</th><th>1 SD</th><th>n</th></tr></thead><tbody><tr><td>NBBT-09 No.5<sup>d</sup></td><td>17.38</td><td>89.70</td><td>1450</td><td>27.1</td><td>1.0</td><td>32.7</td><td>0.7</td><td>8.07</td><td>0.02</td><td>204.1</td><td>11.3</td><td>5</td></tr><tr><td>CBBT-06 No.9<sup>d</sup></td><td>11.03</td><td>84.43</td><td>899</td><td>28.6</td><td>0.5</td><td>33.8</td><td>0.3</td><td>8.07</td><td>0.02</td><td>217.2</td><td>9.5</td><td>9</td></tr><tr><td>SBBT-09 No.4<sup>d</sup></td><td>5.40</td><td>86.77</td><td>886</td><td>28.2</td><td>0.4</td><td>34.3</td><td>0.3</td><td>8.06</td><td>0.01</td><td>219.4</td><td>8.9</td><td>10</td></tr><tr><td>SBBT-09 No.2<sup>d</sup></td><td>5.40</td><td>86.77</td><td>886</td><td>28.2</td><td>0.3</td><td>34.3</td><td>0.2</td><td>8.06</td><td>0.01</td><td>219.1</td><td>8.8</td><td>10</td></tr><tr><td>AS02-M5 No.4<sup>d</sup></td><td>10.00</td><td>65.01</td><td>2363</td><td>27.2</td><td>0.6</td><td>36.1</td><td>0.4</td><td>8.06</td><td>0.01</td><td>229.6</td><td>10.1</td><td>9</td></tr><tr><td>AS02-M5 No.12<sup>d</sup></td><td>10.00</td><td>65.01</td><td>2363</td><td>28.7</td><td>0.4</td><td>36.0</td><td>0.2</td><td>8.06</td><td>0.01</td><td>238.8</td><td>10.1</td><td>10</td></tr><tr><td>MC423<sup>e</sup></td><td>17.75</td><td>-65.59</td><td>1813</td><td>27.5</td><td>1.0</td><td>35.6</td><td>0.4</td><td>8.07</td><td>0.02</td><td>231.2</td><td>12.5</td><td>10</td></tr><tr><td>MC420<sup>e</sup></td><td>17.04</td><td>-66.00</td><td>4705</td><td>27.6</td><td>0.5</td><td>35.5</td><td>0.2</td><td>8.07</td><td>0.02</td><td>229.4</td><td>11.4</td><td>10</td></tr><tr><td>MC497<sup>e</sup></td><td>23.53</td><td>63.31</td><td>1000</td><td>26.9</td><td>1.8</td><td>36.4</td><td>0.1</td><td>8.05</td><td>0.02</td><td>227.4</td><td>14.8</td><td>10</td></tr><tr><td>G4<sup>e</sup></td><td>-28.42</td><td>167.25</td><td>831</td><td>22.0</td><td>2.0</td><td>35.8</td><td>0.1</td><td>8.12</td><td>0.02</td><td>218.3</td><td>15.4</td><td>10</td></tr></tbody></table>

a: Renema, 2002; b: Evans et al., 2013; c: Renema, 2008; d: Gray et al., 2018; e: Henehan et al., 2015; *derived using CO2Sys_v3.0 (see text for detail); n= no. of sample analysed; T= temperature; S=salinity
117

## 2.2. Cultured foraminifera

118

We investigated two sets of laboratory culture experiments in which *Operculina ammonoides* were grown at: 1) varying seawater $Ca^{2+}$ concentration, repeated for three sets of temperature, and 2) varying seawater pH at constant DIC. Details of the culture procedure are given in Evans et al., (2015), Hauzer et al., (2018) and Hauzer, (2022). Briefly, live *O. ammonoides* from the 475-690 µm size fraction were collected from the North Beach, Eilat, Israel, at a depth of ~20-25 m. Prior to the experiment, foraminifera were placed in seawater labelled with the fluorescent marker calcein (50 µM) for 4-5 days and those that showed at least one fluorescent chamber were then transferred to seawater with the desired experimental conditions. The culture seawater medium was additionally spiked with 0.15 µM $BaCl_2$ solution (74 nM $^{135}$Ba) in order to unambiguously identify newly precipitated calcite (Evans et al., 2016). Foraminifera grown under the culture conditions typically had between 3-13 non-fluorescent chambers grown after the calcein mark (Hauzer et al., 2018). These specimens were selected for further analysis; only data from chambers characterised by $^{135}$Ba/$^{138}$Ba higher than the natural abundance were considered in our data analysis.

119

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The culture experiment with varying [$Ca^{2+}]_{sw}$ used in this study is the same as that described in Hauzer *et al.* (2018) and Hauzer (2022), and was originally performed to determine the sensitivity of Na, Mg, Sr and Li incorporation into *O. ammonoides* to changing [$Ca^{2+}]_{sw}$, with the principal aim of establishing Na/Ca as a proxy for past changes in [$Ca^{2+}]_{sw}$. Comprehensive details of the experiment are given in Hauzer et al., (2018). The seawater calcium concentration was modified by adding $CaCl_2$, resulting in [$Ca^{2+}]_{sw}$ of 10.7, 12.7, 15.3, and 18.0 mmol kg$^{-1}$. Given that calcification in the culture jars results in lower TAlk and DIC, the seawater carbonate chemistry was monitored and

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137
replaced regularly in order to maintain quasi-constant conditions. This experiment was conducted at three different temperatures: 22°C, 25°C, and 28°C.

The culture experiment at varying pH with constant DIC was conducted by modifying the TA lk of natural Gulf of Eilat seawater to the desired values by addition of HCl and NaOH (Hauzer, 2022, also see Evans et al., 2018 for further experimental details). As in the case of the [Ca²⁺]ₛ w experiment, the seawater was changed at regular intervals in order to, as far as possible, maintain constant conditions. pH and TA lk were monitored throughout the experimental period in both the culture jars as well as the seawater reservoirs, enabling us to report our trace element data against average measured values throughout the course of the experiments. Seawater pH, adjusted via changing the seawater TA lk at constant DIC, was experimentally varied between 7.5 to 8.3 (NBS scale). The saturation state (Ω_c), calculated using CO2sys using TA lk and pH measured during experimental period showed variability between 1.3 to 8.5 (Tab. S6).

At the end of both experiments, the foraminifera were cleaned with deionised water, treated with 1.5% NaOCl overnight to remove any organic material present, and then washed thoroughly several times with deionised water.

## 2.3. LA-SF-ICPMS analysis

Prior to analysis, all foraminifera were treated once again with 10% sodium hypochlorite (NaOCl) to oxidise any possible remnant organic material. The samples were then rinsed 3-4 times by ultrasonication in 18.2 MΩcm deionised water, followed by a final ultra-sonication cleaning step in methanol. The sample mounting procedure of the foraminifera in the laser ablation cell differed depending on the species being analysed. Each larger benthic foraminifera was mounted by placing it into pressure-sensitive adhesive. Cultured specimens were placed vertically to target the marginal
cord and the newly formed chambers were ablated starting from the final chamber and working backwards (3-5 chambers total). Most (modern) field-collected LBF specimens were placed horizontally in order to measure the knobs (pustules) (see Fig. 2), while some were analysed on both the knob regions and the marginal cord, in order to compare the data derived from the two areas.
In general, the knobs were targeted where possible (i.e. in modern samples) because the calcite in this region is non-porous, unlike the marginal chord, thus minimizing the risk of contamination from sedimentary particles (see Sec. 3.2 for further details). Planktonic foraminifera were placed directly onto double-sided carbon tape with the umbilical side down, allowing the final three chambers to be ablated.

Trace element measurements were performed using a sector-field ICP-MS (Thermo Element XR) combined with a RESOLution 193 nm ArF laser ablation system equipped with a Laurin Technic S-155 two-volume laser-ablation cell (see Müller et al., 2009) at the Frankfurt Isotope and Element Research Center (FIERCE), Goethe University Frankfurt. Ablation was carried in an atmosphere of He and Ar with an additional diatomic gas, N₂, added downstream of the ablation cell. The instrument was tuned for maximum sensitivity while maintaining Th/U between 0.9-1.0 and ThO⁺/Th⁺<1%. The detailed operating parameters of the LA and ICP-MS setup as applied specifically to this study are described in Tab. S1. Monitored masses (m/z) were ²³Na, ²⁴Mg, ²⁵Mg, ²⁷Al, ³⁹K, ⁴³Ca, and ⁵⁵Mn, with Al/Ca and Mn/Ca used to check that sample cleaning removed all remnant sedimentary particles and that there were no diagenetic overgrowths. Standardisation of the data followed established protocols (Heinrich et al., 2003), using ⁴³Ca as the internal standard and the NIST SRM610 glasses as the external standard, analysed in an identical manner to the samples. Data reduction was performed using an in-house Matlab script (Evans and Müller, 2018) which automatically identifies sample and
gas blank data, subtracts the latter from the former, and calibrates trace element ratios using a
depth-dependent measured/reported element/$^{43}$Ca ratio derived from repeat analysis of the NIST
SRM61x glasses.

Planktonic foraminifera were analysed in high mass resolution mode (Δm/m = 10,000)
whereas the larger benthic foraminifera were analysed in medium mass resolution (Δm/m = 4000).
Although high-resolution is required for complete resolution of ArH⁺ on K⁺ and was initially used to
assess whether sufficient data quality could only be achieved when these are fully separated, we
observed that medium-resolution is sufficiently capable of minimizing the effect of the ArH⁺
interference (Fig. S1), such that we chose medium-resolution for most of the measurements that we
report here as the best trade-off between separation of ³⁸ArH⁺ and ³⁹K⁺ and sensitivity. All samples
were calibrated using sample-standard bracketing by analysing NIST SRM610 under identical
conditions to the samples every ~20-30 minutes (i.e., blocks of ~10 analyses). The reported NIST
SRM610 values of Jochum et al., (2011) were used with the exception of Mg, for which we use that of
Pearce et al., (1997) following the recommendation of Evans and Müller, (2018). The MPI-DING
komatiite glass GOR-128G (Jochum et al., 2006) and the nanopellet form (Garbe-Schönberg and
Müller, 2014; Jochum et al., 2019) of the carbonate standard JCp-1 (Okai et al., 2002) were measured
at random intervals within the sequence using the same analytical conditions in order to assess the
accuracy and precision of our sample data.

The accuracy of Mg/Ca, Sr/Ca, Al/Ca, and Mn/Ca in GOR-128G were within ±5%, whereas
accuracy for Na/Ca and K/Ca was around 10.9% and 10.3% respectively. The higher offset from the
true value in GOR-128G in the case of the alkali elements has previously been shown to be a result
of a difference in the down-hole fractionation factor for the alkali metals in the GOR glass standards
with respect to NIST SRM610 (Evans and Müller, 2018). This is demonstrated by the fact that our long-term Na/Ca accuracy is <5% in JCp-1, which was also the case for Al/Ca, Sr/Ca and Mg/Ca, whereas our Na/Ca and K/Ca data in GOR-128G are inaccurate to a similar degree. Assessing the accuracy of K/Ca measurements by LA-ICPMS is challenging because few CaCO₃ secondary standard materials exist. We measure a long-term average value of JCp-1 that is offset by 8.6% from that given by Okai et al., (2002), determined by Atomic Absorption Spectroscopy, but we do not apply an accuracy correction to our data because this reported value is based on a measurement from one laboratory.

Nonetheless, it is possible that an accuracy correction on our data of the order of ~9% may be warranted in future if the value of Okai et al., (2002) is reproduced in other laboratories and/or in other test portions of the JCp-1 powder. Precision estimated from repeat measurement of these two secondary standards across the full analytical period represented here (~2 years) was <6% for all element/Ca ratios in GOR-128G (2σ). The precision for K/Ca, Mg/Ca and Sr/Ca in our JCp-1 nanopellet was less than 7% (2σ), whereas Na/Ca and Al/Ca precision was ~10% (2σ), which we attribute to the lower concentration and possible presence of minor inhomogeneities in this standard material.

Precise details of data quality are given in Tab. S2.
219

**3. Results**

220

**3.1. Influence of seawater parameters on K incorporation in *Globigerinoides ruber* (white)**

<figure><img src="image_2.png" /></figure>

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**Fig. 1.** K/Ca values of modern *G. ruber* plotted against a) temperature, b) salinity, c) [CO₃²⁻] and d) pH. Sediment trap-collected foraminifera are depicted with circles and core top foraminifera with triangles. All error bars are 1SD. The solid line represents the 95% confidence interval on the linear regressions. Sample site details are given in Tab. 1.

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The Al/Ca and Mn/Ca of all the planktonic foraminifera were lower than 0.15 mmol mol⁻¹ (Tab. S3), demonstrating that contamination from remnant detrital material, if present, was effectively removed by our cleaning procedure. The mean value of K/Ca in *G. ruber* from sediment-trap samples (0.22±0.05 mmol mol⁻¹) and core-top (0.24±0.03 mmol mol⁻¹) samples are statistically indistinguishable based on a Student's t-test at the 95% confidence interval, such that we combine both datasets together. The similarity in the mean value of *G. ruber* K/Ca measured in core-top samples and sediment trap samples suggests minimal to no effect of early-stage diagenesis. The K/Ca in modern *G. ruber* ranges from 0.13 to 0.29 mmol mol⁻¹ (Fig. 1; Tab. S3). We find no significant
relationship between K/Ca and temperature (R² = 0.03; *p* = 0.80), salinity (R² = 0.24; *p* = 0.15), [CO₃²⁻] (R² = 0.19; *p* = 0.20), or pH (R² = 0.00; *p* = 0.99). Multiple linear regression analysis of K/Ca against all possible combinations of pH, temperature, [CO₃²⁻], and salinity also yielded no statistically significant relationship, demonstrating no resolvable influence of seawater composition on K incorporation into the shells of this species. However, considering only sediment trap samples, a significant relationship of K/Ca with temperature is observed (m = 0.068, R² = 0.66; *p* = 0.049).

## 3.2. Influence of seawater parameters on K incorporation in *Operculina ammonoides* collected from the modern ocean

<figure><img src="image_3.png" /><figcaption>**Fig. 2.** Possible intra-shell element heterogeneity of *Operculina ammonoides* investigated using samples from the Gulf of Eilat (Eil 19). a,b) Representative specimens of *Operculina ammonoides* showing the regions of the shell investigated here (knob areas and marginal cord). c-f) Box plots of the measurements performed on knobs (n=18) and marginal cord (n=13). Each open circle represents an individual ablated spot. Filled squares shows the average value. Error bars on the average values are 2SE.</figcaption></figure>

The larger benthic foraminifera *O. ammonoides* forms a complex shell structure with several distinct structural components (Carpenter, 1862; Hohenegger, 2011), consisting of septa, chamber
walls, knob structures, and the marginal cord (see Fig. 2). To first understand whether measured trace element ratios in *O. ammonoides* are sensitive to the choice of which part of the shell is being analysed, i.e. to investigate possible heterogeneity in shell geochemistry, and given that elemental banding in the chamber wall of benthic foraminifera (including K/Ca) has been reported (Geerken et al., 2019), we analysed both the marginal cord (porous) and knob (non-porous) regions of *O. ammonoides* from the Gulf of Eilat (sample Eil 19; Fig. 2). In addition, we investigated Mg/Ca, Na/Ca and Sr/Ca to compare the variability in their elemental ratios in these two regions of the shell, to understand whether trace element data from this species is sensitive to the region analysed. While we do observe ±20% K/Ca variability between individual laser spots (Fig. 2), the K/Ca ratio of the knobs (0.199±0.004 mmol mol⁻¹) and marginal cord (0.205±0.005 mmol mol⁻¹) are statistically indistinguishable based on a Student's t-test at the 95% confidence interval. The difference in the average value of Sr/Ca in both regions was 3.2%, whereas the average Na/Ca and Mg/Ca values were about 4.6% and 7.8% higher along the marginal cord, respectively (Fig. 2). Marginally higher values of Mg/Ca along the marginal cord have been previously reported (Evans et al., 2015). While this demonstrates that a consistent choice regarding the part of the shell to be analysed should be made in the case of Na, Mg, and Sr, the same is not true in the case of K/Ca. Hence, we performed all measurements on the non-porous knob region in all modern LBF to minimise possible contamination.
<figure><img src="image_4.png" /><figcaption>**Fig. 3.** a) Variation in K/Ca values during repeated cleaning steps (step 1: 10% NaOCl + methanol + deionised water; step 2-5: methanol + deionised water). The relationship of K/Ca in modern *Operculina* sp. with b) Al/Ca and c) Mn/Ca following the final cleaning process (see Methods).</figcaption></figure>

The K/Ca measurements performed on *Operculina* sp. were repeated 3-5 times after repeated cleaning procedures (in addition to those described in the Methods section) to assess whether the initial cleaning steps were sufficient to remove all contaminant phases from the shell. This additional cleaning step consisted solely of a further ~10-15 minute ultrasonication in methanol followed by several deionised water (18.2 MΩcm) rinses. Further oxidative cleaning steps were not conducted because we suspect that possible remnant contaminant phases are sedimentary particles that require physical removal, rather than the result of (e.g.) incomplete oxidation of organic material.
Al/Ca and Mn/Ca were monitored to determine contamination-free measurements after each cleaning step, and the overall change in K/Ca after each sequential step was used to determine whether incomplete removal of possible contaminant phases during this process biased the mean sample values. We observe a decrease in measured K/Ca in the first three cleaning steps in four out of the seven samples investigated here, indicating that a single oxidative cleaning step followed by several deionised water rinses is unlikely to be sufficient to remove K contamination in the majority of cases, even when analysing non-porous regions of the shell. Specifically, samples Pd 2801, Pd 2805, and Eil 19 were characterised by no significant change in K/Ca with further cleaning, whereas SS 07G14, KKE 30 and SER 33 needed three additional cleaning steps (Fig. 3a). The K/Ca of *Operculina* from NE Kalimantan (BBx 49A) continued to decrease even after the third cleaning step (Fig. 3a). The decrease in the K/Ca after cleaning step-2 represents possible clay contamination. Even after five cleaning steps the K/Ca of BBx 49A and SS 07G14 remained substantially elevated compared to the other larger benthic foraminifera samples, but we retain both in our data analysis because there is no reason to treat these data points as outliers. After the final cleaning step, all samples that were considered in this study were characterised by Al/Ca and Mn/Ca lower than 0.5 mmol mol⁻¹ and 0.3 mmol mol⁻¹, respectively (Fig. 3b,c). Due to higher Al/Ca, we had to remove one foraminifera each from Pd 2805, Pd 2801, and BBx 49A.

Within the subset of samples that were unambiguously not affected by remnant contamination, K/Ca in modern *Operculina* sp. varied between 0.15±0.01 mmol mol⁻¹ to 0.31±0.01 mmol mol⁻¹ (Tab. S4). The relationship between K/Ca in modern *Operculina* sp. and key oceanographic parameters is shown in Fig. 4. These data demonstrate that there is no clear relationship between K/Ca in modern *Operculina* and temperature, salinity, [CO₃²⁻] or pH (R² of K/Ca
versus temperature, salinity, [CO3²⁻] and pH were 0.07, 0.02, 0.00, and 0.00, respectively), implying no resolvable influence of these seawater parameters on K incorporation in *Operculina* species, although we note that the addition of further modern data is a priority, given the relatively small sample number.

<figure><img src="image_5.png" /><figcaption>**Fig. 4.** K/Ca in modern *Operculina* sp. as a function of temperature, salinity, pH, and [CO3²⁻]. All error bars are 1SD. The solid line represents the 95% confidence interval on the linear regressions. Sample site details are given in Tab. 1.</figcaption></figure>

### 3.3. Incorporation of K in cultured *Operculina ammonoides* grown in seawater with variable [Ca²⁺]sw and variable pH

O. ammonoides were cultured at three different temperatures and four different [Ca²⁺]sw (12 experiments in total, (see Hauzer et al., (2018)). The K/Ca of O. ammonoides grown at elevated [Ca²⁺]sw were broadly reproducible irrespective of the culture temperature. For example, at the highest [Ca²⁺]sw value investigated here (18 mmol kg⁻¹), K/Ca = 0.180±0.016, 0.193±0.017, and
0.195±0.013 mmol mol⁻¹ at 28, 25, and 22°C respectively (Fig. 5a; Tab. S7). The exception to this was the lowest [Ca²⁺]sw experiment (10.7 mmol kg⁻¹, equivalent to modern seawater at salinity = 37), in which K/Ca was 0.189±0.018, 0.210±0.010, and 0.261±0.009 mmol mol⁻¹ at 28, 25, and 22°C respectively (Fig. 5a). However, the K/Ca of cultured foraminifera overall falls within the range of the modern field samples described above, in which we find no clear relationship between K incorporation and seawater temperature, salinity, or carbonate chemistry. As such, we pool the data together from the three temperature experiments conducted for each [Ca²⁺]sw (Tab. S5), treating the three experiments as replicate cultures at a given [Ca²⁺]sw to examine the overall relationship between seawater and shell K/Ca. The average K/Ca<sub>LFB</sub> values are tightly correlated with [Ca²⁺]sw, albeit with a very shallow slope (the least squares linear regression has m = 0.072±0.013). Because the shell K/Ca ratio must equal 0 at K/Ca<sub>sw</sub> = 0, we fit a distribution function through the data (see Hauzer et al., (2018) for terminology). This yields a power relationship (y=ax<sup>b</sup>) with K/Ca<sub>sw</sub> (b = 0.29, R<sup>2</sup> = 0.93, p = 0.04), again, with a shallow slope compared to other major/trace elements (Na/Ca: b = 0.54; Mg/Ca: b = 0.72; Evans et al., (2015); Hauzer et al., (2018)).

The Na/Ca data of this study are a test of analytical external reproducibility, given that Na/Ca of the same samples was previously reported by Hauzer et al. (2018), measured in a different laboratory and using a different type of mass spectrometer. Our LA-SF-ICPMS results agree well with the previously reported LA-Q-ICPMS Na/Ca data (Fig. 5b), demonstrating that a power function between Na/Ca<sub>sw</sub>-Na/Ca<sub>shell</sub> best describes the culture experiment. This adds confidence to the inter-laboratory comparability of laser ablation trace element data using different mass spectrometers (note that the data reported here use NIST SRM610 as a primary calibration standard, whereas Hauzer et al. (2018) used NIST SRM612 for Na/Ca quantification).
<figure><img src="image_6.png" /><figcaption>**Fig. 5.** a) The relationship between *Operculina ammonoides* and seawater K/Ca. b) The relationship between *Operculina ammonoides* and seawater Na/Ca. Error bars represent 2SE. The solid line represents the 95% confidence interval on the power regressions. The seawater Ca<sub>sw</sub> values are taken from Hauzer et al., (2018)</figcaption></figure>

Measured K/Ca values in foraminifera grown at different pH (constant DIC) are shown in Fig. 5.6, with the data reported in Tab. S6. Although we find no resolvable relationship between K/Ca and pH in the modern *O. ammonoides* samples (Fig. 4), K/Ca and pH shows significant relationship in this culture experiment (R² = 0.96; *p* = 0.01), conducted over a much larger pH range (~7.5 to 8.3) (Fig. 6a). The saturation state (Ω<sub>c</sub>) of the experimental seawaters was estimated using the Matlab program CO2SYS.m (Van Heuven et al., 2011) using the total alkalinity (TAlk) and pH measurements made during experimental period. This exercise demonstrates that a significant relationship exists between *O. ammonoides* K/Ca and seawater saturation state (Ω<sub>c</sub>) (R² = 0.96; *p* = 0.01; Fig. 6b), with a slope of 0.0067 mmol mol<sup>-1</sup> per unit change in Ω<sub>c</sub>.
<figure><img src="image_7.png" /><figcaption>**Fig. 6.** The relationship between K/Ca in cultured *O. ammonoides* and a) pH and b) saturation state (Ωc). The equation represents the York-fit linear regression line (solid line), accounting for the uncertainties in both axes (York et al., 2004). R² and *p* values represents least square fit line. Error bars are 2SE.</figcaption></figure>

# 4. Discussion

## 4.1. Controls on modern high-Mg benthic and low-Mg planktonic foraminifera K/Ca

We investigated the effect of a wide range of seawater carbonate chemistry and physical parameters on K/Ca in both the shallow dwelling, warm water high-Mg calcite larger benthic foraminifera (*Operculina sp.*) and the low-Mg calcite planktonic foraminifera (*G. ruber*). The contrasting mineralogy of these species, as well as the wide range of ambient conditions investigated here in both laboratory culture and the natural environment, means that the sample set is well-placed to identify whether any of these factors drive changes in K incorporation.

With regards to the effect of mineralogy, we observe Na/Ca 2-3 times higher in the high-Mg foraminifera than the low-Mg foraminifera, as previously reported (e.g. Delaney et al., 1985; Evans et al., 2015; van Dijk et al., 2017; Bertlich et al., 2018). This has been previously ascribed to Mg-induced lattice distortion (Evans et al., 2015; Hauzer et al., 2018), while the presence of Na at relatively high concentration in organic-rich layers within the shell has also been described (Bonnin et al., 2019; Branson et al., 2016). In contrast to Na (and Sr; Mucci and Morse, 1983); Evans et al., (2015)), we
observe that the average value of K/Ca in modern high-Mg foraminifera *Operculina* sp. (0.21±0.02 mmol mol⁻¹) falls in the same range as the average of all modern low-Mg planktonic species *G. ruber* (0.23±0.03 mmol mol⁻¹). This possibly suggests a similar incorporation mechanism of K in these foraminifera and/or no effect of mineralogy on the K distribution coefficient.

Previous work has shown that salinity exerts a control on the incorporation of alkali ions (i.e., Na and Li) in both biogenic marine carbonates and inorganic calcite (Allen et al., 2016; Hauzer et al., 2021; Marriott et al., 2004; Wit et al., 2013). For example, the effect of salinity on alkali element incorporation in *O. ammonoides* was observed to be 1.38% per salinity unit in the case of Na/Ca and 2.05% for Li/Ca (Hauzer et al., 2021). The effect of salinity on *G. ruber* Na/Ca appears to differ between plankton-tow and core-top samples, and/or depending on how the samples are analysed (laser ablation versus solution ICPMS). For example, Allen et al., (2016) report a 1.09% change in Na/Ca per salinity unit in laboratory culture measured by solution ICPMS, whereas Mezger et al., (2016) report a slope of 0.57 (plankton-tow samples measured by LA). In this study, we observed no relationship between K/Ca and salinity in *O. ammonoides* and *G. ruber*. While we cannot rule out that a salinity control exists, e.g., if a wider range of salinities were to be investigated, this – at least – indicates that other factors readily mask any salinity control on K incorporation in foraminifera.

We find no significant relationship between pH or [CO₃²⁻] and K/Ca in modern (sediment trap/core-top) *G. ruber* or *O. ammonoides*. Laboratory culture experiments have previously demonstrated no carbonate system control on Li/Ca and Na/Ca in *G. ruber* (Allen et al., 2016), suggesting that seawater carbonate chemistry is not a first-order control on alkali element incorporation in any of these foraminifera in their natural environment. In contrast, we do find a positive relationship between K/Ca and pH in laboratory cultures of *O. ammonoides* conducted over
a much wider pH range than that of the modern ocean (Fig. 6a), and some previous studies have
demonstrated a Li/Ca sensitivity to the carbonate system in other species (Roberts et al., 2018; Vigier
et al., 2015). There is also a significant relationship between K/Ca and the seawater saturation state,
discussed in more detail below (Sec. 4.3).

Overall, we show that the K/Ca ratio of modern *Operculina* sp. and *G. ruber* is similar, and in
both cases not resolvably driven by any key oceanographic parameters or the carbonate chemistry
of seawater, to the extent that these vary in the modern (sub)tropics.

Finally, we note that the absolute K/Ca ratios that we report for *G. ruber* are ~0.1 mmol mol⁻¹ higher than the four planktonic foraminifera samples reported by Li et al., (2021); further data will be required to understand whether this represents real variability in natural samples greater than that reported here, or if it is an artefact of the different analytical or sample preparation procedures.

## 4.2. Sensitivity of foraminiferal K/Ca to seawater K/Ca

The laboratory culture experiments were conducted at [Ca²⁺]sw of 10.7, 12.7, 15.3, and 18.0 mmol kg⁻¹, with repetitions of each experiment at three temperatures (22°C, 25°C, and 28°C). We observed similar K/Ca for all temperature experiments in the three experiments with elevated [Ca²⁺]sw, whereas in the control experiment with normal [Ca²⁺]sw, K/Ca of *O. ammonoides* grown at 22°C was higher than that at 25°C and 28°C. It is not clear why the lower temperature and low [Ca²⁺]sw favoured the higher incorporation of K/Ca in this foraminifera. Although foraminifera in this experiment were characterised by the lowest growth rates of the set overall (Hauzer *et al.*, 2018) such that this may relate to physiological stress. The modern *ammonoides* sp. datasets presented here suggest that temperature is unlikely to play a substantial role in K incorporation given that, if
temperature were the controlling factor, we would also expect to see this effect at cultures conducted under elevated [Ca²⁺]sw.

Averaging the results of the three temperature experiments together (Fig. 5), results in a significant but extremely shallow relationship between K/Caₜell-K/Caₜw; to our knowledge, shallower than other trace element reported so far for the surface-dwelling foraminifera (e.g. Li, Mg, Sr, Ba; Delaney et al., 1985; Hönisch et al., 2013; Allen et al., 2015; Evans et al., 2015; Hauzer et al., 2018). The insensitivity of shell K/Ca to seawater K/Ca most likely results either from a biological vital effect, acting to increase the [K⁺] of the calcification site as [Ca²⁺]sw increases to drive a much shallower relationship between shell-seawater K/Ca than would otherwise be expected, or from a kinetic effect on K incorporation into calcite driven by the differential [Ca²⁺]sw. We first briefly explore the former possibility here, and the latter in more detail in Sec. 4.3.

Transmembrane alkali element pumps are ubiquitous (e.g. Nakao and Gadsby, 1986; Skou and Esmann, 1992; Gouaux and MacKinnon, 2005). In foraminifera, proton pumping is known to accompany calcification (Bentov et al., 2009; Toyofuku et al., 2017). Li-proton pumps have been implicated in controlling the carbonate chemistry of the calcification site (Vigier et al., 2015), with Na-proton pumps another likely candidate given the abundance of Na⁺ in seawater (see e.g. Erez, 2003; McNicholl et al., 2019). Given that K⁺ is present at a concentration of 10.2 mmol kg⁻¹ in seawater and at much higher concentrations in the cytosol of marine cells (>100 mM; Eppley, 1958; Dodd et al., 1966; Thompson and MacLeod, 1974), the use of a K-proton pump as a means of regulating vacuole or calcification site pH may be a likely possibility. At face value, the shallow slope resulting in elevated K/CaₐBF at higher [Ca²⁺]sw would imply a greater degree of proton elevation and therefore a higher [K⁺] at the calcification site in experiments with a higher-than-natural [Ca²⁺]sw. This may seem
unintuitive, given that at higher $[Ca^{2+}]_{sw}$, the saturation state of seawater ($\Omega_c$) is higher, thus requiring a lower degree of pH elevation to achieve a similar degree of calcite precipitation. However, an alternative possibility is that a greater $[Ca^{2+}]_{sw}$ means that the organism can continue to precipitate calcite from the same package of seawater for longer, because more $Ca^{2+}$ is available for calcification.

If so, this continued precipitation would require a greater degree of proton pumping given that calcification releases protons, in order to maintain an elevated pH through this process to promote precipitation and CO$_2$ diffusion from the cytosol to the calcification site (as calcification is carbon limited in unmodified seawater). However, while calcification from seawater with an elevated $[Ca^{2+}]$ may well be associated with a greater degree of Li/Na/K pumping, as the organism makes use of the extra $Ca^{2+}$ available, the high concentration of $K^+$ in seawater ($K^+/H^+ \approx 10^6$) means that the calcification site $[K^+]$ is likely to be negligibly modified by this process (in contrast to Li; Vigier et al., 2015, we note that the same logic also applies to the calcification site $[Na^+]$). Thus, we argue that the highly nonlinear seawater-shell K/Ca relationship that we observe is perhaps more likely to represent a kinetic effect, driven by the control that $[Ca^{2+}]_{sw}$ has on the rate of mineral precipitation.

### 4.3. Evidence for a kinetic effect on K incorporation

The seawater $[Ca^{2+}]$ in the culture experiments utilised here was varied independently of all other parameters. As a result, the saturation state of these seawaters with respect to calcite ($\Omega_c$) covaried with $[Ca^{2+}]_{sw}$, as $[CO_3^{2-}]$ remained constant. Because the carbonate chemistry of seawater is known to be an important control on both inorganic calcite precipitation and the calcification of foraminifera (e.g. Erez, 2003; Wolthers et al., 2012; Oron et al., 2020), it is possible that the experimental design could have affected not only the growth rate of the foraminifera (Hauzer et al., 2018), but also the crystal growth rates at the calcification site. Here, we explore whether this
phenomenon could explain the observed shallow slope of the relationship between seawater-shell K/Ca, i.e., if the elevated [Ca²⁺]sw drove higher surface-area normalised crystal growth rates and therefore higher shell K/Ca for a given [Ca²⁺]sw than would otherwise be expected if Ωc had remained constant in these experiments.

In the culture experiment, population-scale calcification rate was calculated based on measurements of alkalinity depletion (Hauzer et al., 2018). However, population-scale calcification rates may not necessarily represent crystal-precipitation rates for two reasons: i) not all foraminifera in our experiments calcified at the same rate. Because it is not practically feasible to weigh individual foraminifera to estimate the growth rate that is characteristic of the calcifying specimens (e.g. approximately 20% of foraminifera did not add any new chambers in culture), the overall calcification rate is biased downwards by specimens that did not grow in culture, and/or ii) irrespective of this complication, bulk calcification rate could be decoupled from surface area normalised precipitation rate at the calcification site because calcification is almost certainly a discontinuous process; chamber formation usually takes place at discrete intervals every few days. This is important because it is surface area-normalised precipitation rates that ultimately exert a large control on trace element incorporation into the growing mineral (Watson, 2004). To avoid these issues, and given that Ωc and [Ca²⁺]sw covaried in the culture experiment with varying CaSW (Fig. 5), we alternatively explore the extent to which Ωc-driven crystal growth rate effect could impact our results by deriving an empirical relationship between Ωc and K/Ca in O. ammonoides from the culture experiment in which O. ammonoides was grown at variable pH/Ωc but constant DIC. In the supplementary materials we additionally formulate a theoretical relationship to account for the effect of variable [Ca²⁺]sw on crystal growth rate and thus EI/CaLBF (based on empirical growth rate equations and information from
478 inorganic precipitation experiments regarding the rate control on alkali element incorporation),
479 demonstrating that the direction of this effect is the same in both inorganic and foraminiferal calcite.
480 We stress that a precipitation rate-driven kinetic effect on K incorporation is not the only potential
481 explanation for the strong deviation of the data from a constant apparent distribution coefficient.
482 For example, differences in the degree of Ca utilization within the pool at the calcification site may
483 also be important (Elderfield et al., 1996), as may be large degrees of K⁺ transport or leakage.
484 However, we focus on a kinetic effect here because our data demonstrate an impact of seawater
485 carbonate chemistry on foraminiferal K/Ca.

486 The results of this exercise are shown in Fig. 7. Here, a correction was applied to the seawater-
487 shell Na-K/Ca data using a relationship between shell El/Ca and Ωc based on culture experiment at
488 varying pH (details in supplementary material). The results of this correction suggest that a
489 substantial portion of the apparent insensitivity of shell K/Ca to K/Ca<sub>sw</sub> (Fig. 5) is mechanistically
490 explicable via a growth-rate driven kinetic control on K incorporation into calcite. Given that rate has
491 been shown to impact the incorporation of the alkali elements to a much greater degree than the
492 alkali earth elements in calcite (e.g. Lorens, 1981; Nehrke et al., 2007; Füger et al., 2019), Ωc-driven
493 rate effect on K/Ca in our [Ca<sup>2+</sup>]<sub>sw</sub> laboratory culture data should be accounted for before using these
494 results to understand the relationship between seawater and shell K/Ca. We note that even following
495 this correction, to our knowledge, the power relationship between seawater-shell K/Ca has a lower
496 power coefficient than any trace element studied so far, which could relate to a biological vital effect
497 (e.g. a higher [K<sup>+</sup>] of the calcification site driven by processes other than alkali-proton pumps), or
498 further kinetic effects (e.g. if the calcification site Ωc is not characterised by a 1:1 relationship to
499 seawater Ωc, when saturation state changes are driven by [Ca<sup>2+</sup>]<sub>sw</sub>.
In terms of using the laboratory culture calibration as a potential tool to reconstruct changes in [Ca²⁺]sw, we advocate for the use of the Ω_c-corrected equation (Fig 7). This is because Ω_c varied by 3.74 units in the seawater [Ca²⁺]sw experiment, but is not thought to have undergone substantial variation in the (sub)tropical surface ocean through the Cenozoic (e.g. (Anagnostou et al., 2016; Tyrrell and Zeebe, 2004)). Therefore, if the notion that [K⁺]sw was constant throughout the Cenozoic, as suggested by Horita et al., (2002) is correct, then the K/Ca calibration established in this study may be used for direct reconstruction of [Ca²⁺]sw.

<figure><img src="image_8.png" /><figcaption>**Fig. 7.** The relationship between K/Ca<sub>LBF</sub> and K/Ca<sub>sw</sub>. A growth rate correction, explored here because [Ca²⁺]sw in these culture experiments covaried with Ω_c is shown using the relationship between K/Ca and Ω_c from the experiment in which pH was varied at constant (modern) Ω_c. Error bars are 2SE. Solid lines depict the 95% confidence intervals of the least-squares power regressions. The equations given in the panels are those through the corrected K/Ca data.</figcaption></figure>

### 4.4. Incorporation of K in CaCO₃

A better understanding of the processes by which marine carbonates incorporate trace elements from seawater is important in improving the accuracy of reconstructions based on shell geochemistry. Given that there is a limited amount of previous work on K incorporation in marine carbonates, we summarise most of the data published so far and place it in the context of inorganic
precipitation work in an attempt to identify the broad controls on K incorporation into biogenic CaCO₃.

**Inorganic CaCO₃:** Several studies have investigated the influence of various solution chemistry and physical parameters on alkali metal incorporation into calcite and aragonite. Ishikawa and Ichikuni (1984) examined the uptake of Na and K in inorganically precipitated calcite primarily as a function of solution [Na⁺] and [K⁺] and observed a clear control of solution El/Ca on their incorporation, demonstrating that both trace elements have a distribution coefficient in both CaCO₃ polymorphs. White (1977) investigated the mechanism of K incorporation in inorganically precipitated aragonite and observed that Na and K incorporation decreases with decreasing pH and increasing temperature, in addition to demonstrating an inhibition of K incorporation in the presence of high concentrations of Na, implying competition between these elements for certain sites or spaces within the lattice (although the range of solution alkali metal/Ca ratios investigated were far higher than those of our study). While we also observe a clear Na and K distribution coefficient (function) into biogenic high-Mg calcite, the overall much larger parameter space investigated in the inorganic experimental work conducted to-date likely explains why we do not observe many of these factors in marine biogenic CaCO₃.

**Calcitic organisms:** The nummulitid larger benthic foraminifer *Operculina* sp. analysed in the present study are formed of high-Mg calcite (Blackmon and Todd, 1959; Cotton et al., 2020). To the best of our knowledge, our data represent the first report of K/Ca in high-Mg calcite. These foraminifera have K/Ca = 0.21±0.100 (2SD) and D<sub>K</sub> =2.2×10<sup>-4</sup> (averaged across all of our field and culture data) which is similar to the range of *G. ruber* reported here (0.23±0.097 (2SD); D<sub>K</sub> =2.3×10<sup>-4</sup>) and other low-Mg calcitic marine organisms (deep sea corals, brachiopods; (Li et al., (2021) Fig. 8)
with only the bivalves offset to significantly lower values. As such, there is no evidence for a
mineralogical control on K incorporation, in contrast to Na and Sr, and possibly other trace elements
(Evans et al., 2015; van Dijk et al., 2017). The *O. ammonoides* culture experiment presented here is the
first time that the relationship between K/Ca<sub>shell</sub> and K/Ca<sub>sw</sub> has been assessed for a foraminifer
species, demonstrating that K/Ca<sub>shell</sub> is governed by K/Ca<sub>sw</sub>, albeit with a shallow slope. Interestingly,
this relationship is substantially shallower that those that have been described between Na/Ca<sub>shell</sub>
and Na/Ca<sub>sw</sub> (Hauzer et al., 2018; Le Houedec et al., 2021; Zhou et al., 2021; Fig. 9). If the shallow slope
of the seawater-shell K/Ca ratio in this experiment is indeed driven in part by kinetic processes (Sec.
4.3), this may imply a greater sensitivity of K incorporation to factors such as growth rate. Curiously,
this is intuitively difficult to reconcile with the relative constancy between K/Ca across multiple groups
of marine calcitic organisms, while the incorporation of other trace elements differs widely between
these groups (Raja et al., 2007; Ulrich et al., 2021; Van Dijk et al., 2017); further work will be required
to understand why this is the case. While it is beyond the scope of this study to investigate this in
more detail, we note that the commonality of the power relationship between Na/Ca with Na/Ca<sub>sw</sub>
in all foraminifera studied so far, and a similar observation for K/Ca in biogenic calcite (Fig. 9a,b),
suggests – at least – that the mechanism of Na and K incorporation may be similar in low-Mg planktic
foraminifera and high-Mg large benthic foraminifera.

Aragonitic organisms: As is the case for the calcitic organisms, the K/Ca of a number of
biogenic aragonites (corals, bivalves, gastropods) is characterised by a relatively narrow range (K/Ca:
0.20 to 0.25 mmol mol⁻¹), and absolute values that are indistinguishable from most biogenic calcites.
This is in contrast to Na/Ca, which is a factor of ~2 higher in biogenic aragonite compared to biogenic
low-Mg calcite (Schleinkofer et al., 2019). Thus, there is no evidence for a first-order mineralogical
control on K incorporation into CaCO₃, potentially implying that the calcification site K/Ca and K distribution coefficient may be similar across a large range of marine calcifying organisms, if shell K/Ca is alternatively primarily determined by K/Ca<sub>sw</sub>. A review of the limited amount of existing research indicates that this assumption of a primary K/Ca<sub>sw</sub> control is the case for some aragonitic organisms but not others. K/Ca measured in the aragonitic shells of gastropods showed no relationship with fluid K/Ca (Rosenthal and Katz, 1989), although this study reported data for a freshwater species. In contrast, K/Ca and Na/Ca of aragonitic scleractinian corals follow a near linear relationship with El/Ca<sub>sw</sub> (Ram and Erez, 2021), which has similarly been shown to be the case for inorganically precipitated K/Ca and Na/Ca (at least up to seawater-like K-Na/Ca ratios; Okumura and Kitano, 1986).

<figure><img src="image_9.png" /><figcaption>**Fig. 8.** The D<sub>K</sub> in a) calcitic biogenic marine carbonates, b) aragonitic marine carbonates and c) inorganic calcite. The D<sub>K</sub> estimations are based on solution K and Ca concentrations, except in the case of the inorganic calcite study of I&I84, in which the D<sub>K</sub> values are based on K activity. The symbols denote: this study (triangles; open triangles indicate specimens from different locations and culture study), Li et al., 2021 (circle; open circles indicate different species); Bell et al., 2018 (square; open squares indicate different specimens); Ram and Erez, 2021 (diamond) and inverted triangles (I&I84: Ishikawa and Ichikuni, 1984; O&K, 86: Okumura and Kitano, 1986). Solid symbols are average values. In all cases error bars denote the 2SD of each dataset, but note that each dataset represents a wide range of sample collection types (multiple/single species, culture/natural populations etc., see brackets in the earlier part of the figure caption for brief descriptions).</figcaption></figure>

572
<figure><img src="image_10.png" /><figcaption>**Fig. 9.** a,b) The relationship between K/Ca and Na/Ca of different marine carbonates and El/Ca<sub>sw</sub>. c,d) The relationship between the apparent distribution coefficient of K (D<sub>K</sub>) and Na (D<sub>Na</sub>) with their El/Ca<sub>sw</sub>. All error bars are 2SE.</figcaption></figure>

Both our work and a previous study (Ram and Erez, 2021) demonstrate that the partition of K in marine carbonates is governed to large degree by the K/Ca<sub>sw</sub> ratio. The apparent distribution coefficient of K in *O. ammonoides*, calculated as D<sub>El</sub> = (El/Ca)<sub>shell</sub>/(El/Ca)<sub>sw</sub>, decreases with increasing K/Ca<sub>sw</sub>, a behaviour which is similar to that of Na (Fig. 9c,d) and Mg in a wide range of biogenic calcites (Hasiuk and Lohmann, 2010) and inorganic calcite (Mucci and Morse, 1983). To facilitate the comparison of K and Na distribution coefficients presented here to other marine carbonates, we compile apparent distribution coefficient data as a function of the respective seawater ratio (Fig. 9c,d). The D<sub>Na</sub> of both planktonic foraminifera and larger benthic foraminifera showed a decreasing trend with increasing seawater Na/Ca, whereas the D<sub>K</sub> and D<sub>Na</sub> of two aragonitic scleractinian corals
is characterised by a shallow positive slope with $E_1/C_{sw}$ (Ram and Erez, 2021). As we discuss above, this is perhaps most parsimoniously explained by a kinetic (growth rate) effect on the incorporation of K and Na in the foraminifera which results in higher $D_{E1}$ with increasing $C_{sw}$, although we again note that understanding the degree of Rayleigh fractionation at the calcification site of calcifying organisms is also key in terms of understanding bulk calcite trace element geochemistry (Elderfield et al., 1996; Evans et al., 2018b). Culture experiments that vary $[K^+]_{sw}$ rather than $[Ca^{2+}]_{sw}$ would be one way in which this hypothesis could be tested. In addition, inorganic precipitation experiments focusing on both calcite and aragonite are required to understand why this affect does not seem to have biased the coral data, given that the foraminifera $[Ca^{2+}]_{sw}$ experiment discussed here was experimentally similar to that of Ram and Erez, (2021).

## 5. Summary

In this study, we investigated the influence of a wide range of seawater parameters on the incorporation of K into the planktonic foraminifer, *Globigerinoides ruber* (white) and larger benthic foraminifer, *Operculina* sp.. In both cases, no significant correlation of K/Ca with temperature, salinity, pH, or $[CO_3^{2-}]$ was observed, which suggests that the incorporation of K is independent of these seawater parameters, or that other factors act to easily mask these effects. The similar K/Ca of low-Mg planktonic foraminifera and high-Mg benthic foraminifera suggest no major effect of mineralogy on K incorporation, which also appears to be more broadly the case (i.e. between calcite and aragonite) based on a compilation of published data.

In addition, we investigated K/Ca in marine carbonate as a potential proxy for the seawater K/Ca ratio, based on laboratory cultures of *Operculina ammonoides*. Given that previous work has suggested that large changes in $[K^+]_{sw}$ have not occurred (Horita et al., 2002), this may be an
additional tool for understanding past changes in [Ca²⁺]ₛw. We show that a power relationship best describes seawater-shell K/Ca, implying a variable apparent distribution coefficient. Indeed, the slope of the K/Ca - K/Caₛw relationship is very shallow, indicating another major control on K incorporation into foraminifera. We suggest that this shallow relationship is, at least in part, the result of a kinetic growth rate effect on K incorporation in O. ammonoides cultured at elevated [Ca²⁺]ₛw, although further work will be required to conclusively rule out other possibilities such as K transport into the calcifying fluid. The mechanistic basis of this could be that in the laboratory culture experiment reported here, [Ca²⁺]ₛw was varied in isolation, which means that [Ca²⁺]ₛw and the saturation state of seawater (Ωc) covaried. Because Ωc is one of the dominant controls on surface area-normalised precipitation rate, we propose that a crystal growth rate effect may explain the shallow seawater-shell K/Ca relationship, driving K/Ca to higher ratios at elevated [Ca²⁺]ₛw. We corrected for this using a relationship between Ωc and K/Ca derived from a second culture experiment in which O. ammonoides was grown at different seawater pH values, which has the effect of increasing the slope of the seawater-shell K/Ca relationship. Given that surface ocean Ωc has likely not varied to a large degree over the Cenozoic (e.g. Tyrrell and Zeebe, 2004; Ridgwell and Zeebe, 2005), we argue that this corrected relationship should be applied in the geologic past, and that the slope of this curve is sufficiently steep to make K/Ca a potentially useful tool for unravelling past changes in seawater major ion chemistry. Given that other seawater parameters show no resolvable influence on K incorporation into foraminifera, and if the notion that the seawater [K⁺] has remained constant through the Phanerozoic Eon is correct (Horita et al., 2002), this calibration could therefore be used as a tool to reconstruct [Ca²⁺]ₛw. Ultimately, combining Na/Ca (Hauzer et al., 2018; Zhou et al., 2021) and K/Ca data from the same specimens may be a potential means of further improving the accuracy
639 of reconstructions of the history of seawater [Ca²⁺] variability, or could be used to determine whether
640 seawater [Na⁺] and [K⁺] have indeed remained within narrow bounds. Because *O. ammonoides* are
641 a close relative of the nummulitid foraminifera which were abundant during the Paleogene (Hallock,
642 1985; Holzmann et al., 2003), this group, and the calibration presented here, may represent a good
643 target for the reconstruction of Cenozoic seawater chemistry, opening up new possibilities in terms
644 of understanding the processes that govern the seawater Ca cycle.

645 Acknowledgments

646 This work is part of the VeWA consortium funded by the Hessen State Ministry for
647 Higher Education, Research, and the Arts through the LOEWE program. MJH gratefully acknowledges
648 the provision of sample materials by Michal Kucera and Helen Bostock. The foraminifera culture work
649 of HH and DE was carried out in the laboratory of J.Erez and funded by ISF grant # 1886/20. FIERCE
650 is financially supported by the Wilhelm and Else Heraeus Foundation and by the Deutsche
651 Forschungsgemeinschaft (DFG: INST 161/921-1 FUGG, INST 161/923-1 FUGG and INST 161/1073-1
652 FUGG), which is gratefully acknowledged. This is FIERCE contribution No. 126. We gratefully thank
653 the associate editor Tom Marchitto, as well as Sambuddha Misra and an anonymous reviewer for
654 their thoughtful consideration of this work.

655 Appendix A. Supplementary material

656 The supplementary table contains detail information on the analytical setup, analytical
657 performance, the El/Ca data of all foraminifera from modern seawater, and the culture experiments
658 investigated in this study. The supplementary PDF file includes further discussion on the analytical
659 performance, carbonate chemistry culture experiment, and the growth rate correction of the K/Ca<sub>LBF</sub>-
660 K/Ca<sub>sw</sub> relationship.

661

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