Abstract
Coccolithophores, a group of unicellular calcifying phytoplankton, have been major contributors to marine carbonate production since the calcite plates that they produce (coccoliths) first appeared in the fossil record over 200 million years ago (Ma). The response of this process to changes in environment on evolutionary timescales remains poorly understood, particularly in warm climates. Here we integrate a dataset consisting of carbon isotope ratios of size-separated coccolith calcite from marine sediments with a cell-scale model to interrogate cellular carbon fluxes and \(p_{{\mathrm{CO}}_2}\) through the Eocene (~55–34 Ma), Earth’s hottest interval of the past 100 million years. We show that the large coccolithophores that rose to dominate the oceans through the Eocene have higher calcification-to-carbon fixation ratios than their predecessors while the opposite is true for smaller coccolithophores. These changes, which occurred in the context of increasing ocean alkalization, may have played a role in an apparent positive carbon cycle feedback to decreasing \(p_{{\mathrm{CO}}_2}\). Our approach also provides independent support of multiproxy-based evidence for general \(p_{{\mathrm{CO}}_2}\) decline through the Eocene in step with temperature. Together, this challenges the emerging view that a general decline in \(p_{{\mathrm{CO}}_2}\) reduces calcification on evolutionary timescales.
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Coccolith production and export removes alkalinity from the surface ocean, reducing its capacity to buffer changes in \(p_{{\mathrm{CO}}_2}\) (ref. 1). On geologic timescales, coccolith burial in deep-sea sediments removes carbon from the ocean–atmosphere system2. From a biogeochemical perspective, carbon fixation in the surface ocean is limited by nutrient availability3,4, temperature5 and light levels6; the amount of calcite produced is then dictated by the particulate inorganic carbon (PIC) to particulate organic carbon (POC) ratio (PIC/POC) of biogenic material. PIC and POC are, respectively, the time-integrated rates of calcite precipitation (Rcalc) and carbon fixation (Rfix). Rcalc/Rfix (conceptually distinct from PIC/POC but equivalent at steady state) varies between species of coccolithophore, so changes in species composition through time can alter the amount of calcite transported to the deep ocean7,8,9,10,11. At the cellular level, Rcalc/Rfix is a physiologically important parameter because calcification and carbon fixation fluxes have opposing effects on intracellular chemistry. These fluxes also drive the carbon isotope ratio of dissolved inorganic carbon (DIC) in the intracellular environment in opposite directions, which lays the foundation for reconstructing this ratio in ancient coccolithophores through the carbon isotope compositions of their intracellularly formed coccoliths12.
The prevailing view, based largely on the morphometry and weight of fossil coccoliths, is that coccolithophore calcification decreased during periods of lowered \(p_{{\mathrm{CO}}_2}\) in the icehouse Neogene and glacial periods10,13,14,15,16,17 (although there are counter-examples11,18,19; Supplementary Table 1). There is a degree of ambiguity in the meaning of ‘calcification’, whether this refers to the amount of calcite per cell, production rates or the rate of calcite precipitated per unit carbon fixed. In this Article, we target the last of these explicitly by constraining Rcalc/Rfix. We take an approach that integrates carbon isotopes and morphometric data, with a cellular carbon flux model, to simultaneously constrain Rcalc/Rfix across different taxonomic groups and CO2 levels. The fossil record captures how communities change on evolutionary timescales, and the Eocene in particular, characterized by high but declining temperature20 and \(p_{{\mathrm{CO}}_2}\) (refs. 21,22), provides a unique opportunity to gain this insight in a hothouse climate.
For decades, carbon isotope ratios of coccolith calcite were ignored in the field of palaeoclimatology because they exhibited large and variable deviations from calcite precipitated at equilibrium in the same environment, making them an unreliable target to reconstruct the carbon isotopic composition of DIC. More recently, these deviations, or carbon isotope vital effects (CIVEs), have themselves been shown to contain information regarding rates of calcification12. CIVEs are a function of coccolithophore physiology and ambient carbonate chemistry12,13,23. Coccolith calcite enriched (depleted) in 13C compared with equilibrium calcite possesses a positive (negative) CIVE24,25,26,27. CIVE expression is driven by the molar ratio of carbon demand to carbon supply and the partitioning of carbon between calcification and carbon fixation12. The direction of the CIVE is largely set by Rcalc/Rfix, which differs by a factor of around four in modern species (Rcalc/Rfix is approximately 0.5 in Emiliania huxleyi and 2.0 in Calcidiscus leptoporus8). A high Rcalc/Rfix (typically greater than 1) produces a negative CIVE, while a low Rcalc/Rfix (typically less than 1) produces a positive CIVE12. This difference is due to the effect of photosynthesis, which discriminates against 13C, leaving the residual intracellular pool enriched in 13C (ref. 12). The magnitude of the CIVE is set by the molar ratio of carbon demand to supply (carbon utilization), which increases with cell size and growth rate and decreases with ambient CO2(aq). Intracellular allocation of HCO3– (ref. 28) and variations associated with changing light conditions23 impose secondary controls.
Cells of different sizes, and characterized by different values of Rcalc/Rfix, express distinct CIVEs under the same CO2(aq) regime. Coccolith size scales with cell size, so size separation of coccoliths enables the study of different-sized cells29,30,31. Analysis of multiple size fractions from the same sample also allows us to define a new parameter, CIVEmean, which is the isotopic composition of coccolith calcite of a specific size fraction minus the mean isotopic composition of all coccolith size fractions from that sample of sediment. This parameter is independent of equilibrium compositions and so can place constraints on Rcalc/Rfix and CO2(aq), two key drivers of CIVEs, without independent knowledge of the carbon isotope composition of equilibrium calcite. We present a new coccolith calcite isotope dataset comprising isotope measurements from five size fractions of coccoliths across 37 depths from the Eocene section of Ocean Drilling Program (ODP) leg 208, site 1263, 1,300 km off the coast of southern Namibia (see Methods for site description). The carbon isotope ratios of the individual size fractions reveal rich variability compared with the bulk carbonate record (Fig. 1a). To explore the data, we used a cell-scale carbon isotopic flux model to find the optimal combination of Rcalc/Rfix and CO2(aq) that provides the best fit to measured isotopic CIVEmean. Our isotopic data for the Eocene exhibit large deviations from the bulk record at approximately 46 million years ago (Ma) (Fig. 1a). After optimizing for values of Rcalc/Rfix and CO2(aq), we were able to successfully model the distribution of measured CIVEmean (Fig. 1b).
a, Measured δ13C across all five size fractions and coeval foraminifera measurements. Coeval foraminifera are composed of the genus Acarinina, which probably had symbionts, hence leaving the foraminifera calcite enriched in 13C; we investigate vital effects associated with foraminifera in the Supplementary Information. Also shown are contemporaneous bulk sediment δ13C values, which track the total sum of coccolith and foraminifera calcite and changes depending on their proportion, vital effects and mixed-layer whole-ocean signals. Covariation between the fine fractions and bulk is interpreted to imply that the bulk is largely composed of coccoliths and so their calcite dominates the geochemistry, although we cannot rule out some overgrowth (Supplementary Information). b, δ13C values of each sediment size fraction relative to their age interval mean (CIVEmean). Points are measurements; lines are fitted model values. The error bars on the points represent uncertainty introduced through contamination of neighbouring size fractions (Methods). The coloured envelope surrounding each line represents 95% of model runs over 10,000 Monte Carlo simulations. The coloured vertical regions represent important periods during the Eocene, including the Palaeocene–Eocene Thermal Maximum (PETM), ETM2, early Eocene Climatic Optimum (EECO) and MECO.
Calcification across the Eocene
Eocene coccolithophores were some of the largest of the entire Cenozoic era32. Compared with modern, glacial and Miocene periods, Eocene coccolithophores grew under higher temperatures and higher \(p_{{\mathrm{CO}}_2}\) (refs. 21,22). In our study, we identified four dominant genera across the Eocene: Coccolithus, Chiasmolithus, Discoaster and Reticulofenestra (Fig. 2). We found that Rcalc/Rfix ratios across size ranges and genera were similar to those of modern-day coccolithophores8; however, the existence of substantially larger cells29,30 means that more calcite was produced per cell7,29,30,33 (Fig. 2). On the basis of our modelled values of Rcalc/Rfix and coccolith size measurements from microscopic analysis, we infer that a cell belonging to the Eocene Coccolithus genus (radius ~10 μm) would have consisted of ~1.3 times more calcite per cell than an equivalently sized large modern-day Coccolithus braarudii34. We have also been able to place constraints on the Rcalc/Rfix of extinct genus Discoaster, which we conclude was surprisingly low. Nevertheless, owing to the apparently large size of these cells, they may have produced 2.8 times more calcite per cell than modern-day Coccolithus braarudii (Supplementary Information). Until now, attempts to reconstruct Rcalc/Rfix for Discoaster with morphometric approaches have been hampered by a lack of intact coccospheres in the fossil record and the uniqueness of their star-shaped coccoliths, which have no modern analogue (Supplementary Fig. 1). Isotopic compositions are determined by cellular chemical and isotopic disequilibrium that depends on relative rates of calcification to photosynthesis and thus circumvents these difficulties.
a–e, Stack plots represent coccolith counts for the 15–20 μm (a), 10–15 μm (b), 8–10 μm (c), 5–8 μm (d) and 3–5 μm (e) size fractions. Each stack plot represents a normalized closed sum of the four genera. Also shown to the right of each plot is the distribution of associated Rcalc/Rfix values (for full species percentage abundance counts, see Extended Data). Reconstructed Rcalc/Rfix values are shown for each of the four dominant genera across all sediment size fractions. Rcalc/Rfix is not presented for Chiasmolithus in d or e and Reticulofenestra is not show in a due to a lack of coccolith contribution to the respective size fractions resulting in an underconstrained value. Presented Rcalc/Rfix represent the values that minimize the error between measured and modelled CIVEmean. Error bars represent 95% of Monte Carlo realizations. The solid black line associated with each stack plot represents the abundance-weighted average of each size fraction Rcalc/Rfix. Dashed lines bound 95% of calculated weighted Rcalc/Rfix values. The weighted Rcalc/Rfix values are on an equivalent scale to the subplots on the right-hand side. Also shown in a–e are key periods during the Eocene, including the ETM2, EECO and MECO.
The 3–5 μm size fraction shows a continuous negative CIVE from 56 to 50 Ma (Fig. 1b). Previous studies also noted the presence of the largest negative CIVE in the smallest size fraction during the Eocene28; however, this behaviour has previously proved difficult to interpret. In laboratory cultures, smaller species tend to show more positive CIVEs compared with larger species owing to their lower carbon demand and generally lower Rcalc/Rfix (refs. 12,25,26). Our microscopic analysis shows that from 56 to 50 Ma, the smallest size fraction consisted mostly of Coccolithus while the largest size fraction was dominated by the genus Discoaster (Fig. 2). Given our modelled Rcalc/Rfix values for the measured genera distribution and CIVEmean pattern during the early Eocene, we suggest that this negative CIVEmean in the 3–5 μm size fraction was probably the result of the smallest size fraction having a larger Rcalc/Rfix than other size fractions (Fig. 2) as Coccolithus was heavily calcified relative to cell volume.
Our results show that there was a large shift in community composition from Discoaster to dominance by Coccolithus, Chiasmolithus and Reticulofenestra, and that the timing of this coincides with a decline in both CO2 and temperature35. Our inverse modelling efforts suggest that the community shift corresponded to a change from coccolithophores with a low apparent Rcalc/Rfix to those with a higher apparent Rcalc/Rfix in the largest size fraction. Yet in the smallest size fraction, the community shift corresponds to a change from the genus Coccolithus to Reticulofenestra and a shift from high to low apparent Rcalc/Rfix. There is a relative lack of studies that have focused on reconstructing Rcalc/Rfix across the Eocene epoch, although a morphometric study focused on the PETM suggests that species such as Coccolithus pelagicus possessed ratios of ~2 (ref. 7), similar to our findings for the Coccolithus genus Rcalc/Rfix.
It is additionally important to understand how our results fit into the wider context of the global carbon cycle. Evidence suggests that across the Eocene, the calcite compensation depth (CCD) deepened36, ocean pH rose22 and an increase in global weathering37,38,39,40 probably drove an increased flux of alkalinity to the oceans. Carbonate mass accumulation rates at site 1263 and at other sites across the ocean appear to have declined41,42 (Supplementary Table 1). The putative deepening of the CCD implies an increase in the saturation state of the deep ocean, which suggests that there was either a whole-ocean decrease in calcite production rates or an increase in delivery of alkalinity to the deep ocean reservoir, possibly via increased respiration-driven dissolution of exported carbonate. Resolving the intensity of respiration dissolution during the Eocene could be addressed in future work by assessing the history of decoupling between the lysocline and CCD.
Implications of temperature, light and nutrients on growth rate and calcification
Growth rate is a key parameter in all phytoplankton δ13C-based investigations of palaeo-CO2 but is notoriously difficult to constrain12,23,25,26,27. In our model, growth rate was assumed to scale allometrically. On million-year timescales, the effects of variations in nutrient conditions, light and temperature on cellular growth rate, photosynthesis and calcification43 are difficult to predict because of evolutionary change and species succession. We therefore assume that growth rate is constant for individual cell sizes across genera and incorporate uncertainties within our model (Methods). A constant growth rate is qualitatively supported by strontium-to-calcium ratios (Supplementary Information). Lab-based studies have shown that coccolithophores probably exhibit a species-specific optimum-like response to variations in temperature5, light and carbonate chemistry44. For an observed CIVE, a net decrease (increase) in the growth rate of a size fraction would require a correspondingly lower (higher) predicted ambient CO2 concentration. Future improvements may be made with an allometric formulation of growth-rate relationship that includes coefficients for temperature, light and nutrient conditions, which would allow for such variations to be quantitatively investigated within our model. Within our sensitivity analysis (Supplementary Fig. 2), we found that, although variations to assumed growth rate altered absolute values of Rcalc/Rfix and relative CO2, given here as the ratio of modelled output CO2(aq) to modelled input CO2(aq) (see Methods for further derivation of relative CO2 and reasoning for its use over absolute values), trends remained the same.
In our study, we assume that Rcalc/Rfix is constant for each genus and size fraction throughout our record. Predicted Rcalc/Rfix values therefore reflect the best fit for the entire Eocene. This is a limitation to our approach: the long-term environmental change across the Eocene may be associated with variations to Rcalc/Rfix within a genus and size fraction, which, due to our assumption that Rcalc/Rfix is constant across our interval, cannot be captured. Previous culture studies on multiple species have found complex responses for variations in Rcalc/Rfix given changes to environmental parameters45, but the translations of these results to evolutionary timescales is not clear. Changes in Rcalc/Rfix within a genus and size fraction could potentially be constrained if this modelling approach were paired with an independent high-quality CO2(aq) record as an input and high-resolution record of δ13CDIC.
Eocene CO2 levels
Our model implies that relative CO2(aq) was higher in the early Eocene and decreased across the epoch as CIVEmean emerge and increase in magnitude, in line with previous data21 (Fig. 3). Given site 1263 was probably close to equilibrium with the atmosphere (Methods), modelled CO2(aq) can be assumed to reflect atmospheric \(p_{{\mathrm{CO}}_2}\). Unlike the use of other carbon isotope-based \(p_{{\mathrm{CO}}_2}\) proxies46,47,48, the use of mean-normalized model predictions fitted to mean-normalized measurements makes our approach internally dependent on the isotopic composition of coccolith calcite and independent of seawater carbon isotopic values. Independence comes at the cost of one degree of freedom per depth interval (total of 37) and results in a solution that is non-unique in absolute CO2(aq) but robust with respect to relative change in CO2(aq) and Rcalc/Rfix (Supplementary Fig. 3). Loose constraints on the absolute value and change in \(p_{{\mathrm{CO}}_2}\) are provided by estimates of seawater carbon isotopic values from foraminiferal calcite (Supplementary Fig. 4). When carbon utilization is low (particularly at high external CO2(aq)) the effect of CO2(aq) on CIVE expression is small. During Eocene hyperthermals (for example ~40 Ma), the model therefore results in a greater spread of possible CO2(aq) values.
a, Relative CO2, defined as model output CO2(aq) relative to model input CO2, is derived from our optimized model with size-differentiated isotopic constraints (see Methods for detailed explanation of relative CO2). The coloured markers represent previously published pCO2 data21,22 across the Eocene (right-hand y axis). The black circles represent the median relative CO2(aq) over 10,000 iterations of our Monte Carlo optimization (left-hand y axis), with error bars representing plus and minus 2-sigma of all realisations for each age point (95% of realizations). The black line represents a three-point moving average of our output, with the grey shaded region representing the moving average of plus 2 sigma and minus 2 sigma. Our modelled low relative CO2(aq) during the middle Eocene coincides with a step-wise increase in proxies linked to an increase in the rate of chemical weathering and therefore CO2 draw-down37,38,39,40. The dashed black line during the MECO joins points without a moving average. Using a moving average at this time greatly skews the trend line given the large, and uncertain, deviation to higher relative CO2. Also shown is the approximate interval of the EECO. b, The five-point moving average of relative CO2(aq) is plotted against the five-point moving average of δ18Obenthic. The five-point moving average was used to avoid noise in the data and evaluate the longer-term trend. Error bars represent one sigma uncertainty on reconstructed CO2(aq) values. The equation of the line has been overlaid on the figure. The four points in red represent the points from the MECO and younger, which have been excluded from the P-value calculation (P < 0.001). Without the MECO data included, our relative CO2(aq) and δ18Obenthic show a robust negative correlation. The warmer early Eocene, characterized by more negative values of δ18Obenthic, has on average higher values of relative CO2(aq). c, The slope of relative CO2(aq) with δ18Obenthic for each of the 10,000 Monte Carlo simulations was calculated and plotted as a histogram. Only one value was greater than zero.
Qualitatively, the convergence of CIVEmean at 53.5–54.0 Ma indicates higher \(p_{{\mathrm{CO}}_2}\), given reduced CIVEs are observed at higher [CO2(aq)] in culture experiments12, which is supported by our modelled predictions (Figs. 1 and 3). Long-term temperature change across the Eocene was considered when calculating \(p_{{\mathrm{CO}}_2{\mathrm{atm}}}\) across the interval via Henry’s law (Supplementary Fig. 4). Previous estimates of Eocene CO2 vary between ~500 and 2,000 ppm (refs. 20,21,22,49,50,51) but agree on the presence of a long-term decline, with substantial departures at 40 Ma and 54 Ma (refs. 21,22), in line with our results (Fig. 3). Our predicted peak in relative CO2(aq) during the early Eocene approximately 53.5–54.0 Ma may be attributed to Eocene Thermal Maximum 2 (ETM2), a rapid period of warming52,53,54. Further, high relative CO2(aq) at ~40 Ma is probably associated with the middle Eocene Climatic Optimum (MECO55). The MECO is believed to represent a period of elevated volcanic outgassing, decreased silicate weathering due to a decreased weatherability after the extended warm Eocene56 and rapid shallowing of the CCD36. Before the MECO, our relative CO2(aq) curve shows a highly significant (P < 0.001) negative correlation with global δ18Obenthic data (Fig. 3b), a widely accepted proxy for deep-sea temperature (in the absence of ice sheets) in the Eocene that reflects longer-term climatic change. The observed covariance between reconstructed CO2(aq) and global δ18Obenthic data supports the robustness of our findings. From 41.5 Ma to 38.5 Ma, we find that the relative CO2(aq) curve shows no correlation to global δ18Obenthic. Data from 41.5 Ma to 38.5 Ma (4 of 37 data points) were excluded from the regression analysis. The exclusion is justified given the potential decoupling between δ18Obenthic, atmospheric CO2 and carbonate storage within the ocean during the MECO owing to an unstable nascent cryosphere50. Variations in ice volume at high latitudes and altitudes from 41.5 to 38.5 Ma rather than temperature could cause a deviation in the relationship between δ18Obenthic and CO2.
The question thus remains: what parameters drive long-term adaptive changes in calcification? In addition to declining temperature and CO2(aq), the Eocene was probably characterized by an increase in ocean alkalinity37,38,40, nutrients and pH22. These conditions appear to have selected for large cells with higher Rcalc/Rfix, with the inverse being true for the smallest cells. For the largest cells, whose small surface-area-to-volume ratios may make them particularly vulnerable to self-acidification of the cytosol by calcification, increasing surface ocean pH22 may have resulted in a more favourable gradient for the efflux of H+ ions and thus enabled the emergence of large, more heavily calcified coccolithophores57,58. This effect may have been less pronounced in the small cells, which may therefore have been limited by other environmental parameters. To fully elucidate the environmental drivers of calcification change in coccolithophores, further work to understand why coccolithophores calcify will be necessary58.
Methods
Sample selection and preparation
The sediment samples were from ODP leg 208, site 1263. Site 1263 has remained at a relatively constant latitude for most of the Cenozoic59. Ocean general circulation models suggest reduced Atlantic upwelling during the Eocene, with the Walvis ridge probably outside of any significant zones of upwelling60,61. We thus posit that site 1263 was in equilibrium with the atmosphere. Site 1263 was drilled from a current water depth of 2,717 m, with the palaeodepth during the Eocene believed to be around 1,500 m (ref. 59). Thirty-seven samples were selected at approximately 0.5 Myr intervals through the early and middle Eocene.
Sediment samples were placed in 100 ml of pH-neutral de-ionized water and placed on an orbital shaker overnight for disaggregation. Samples were then filtered through 64 μm, 38 μm and 20 μm sieves to remove large particles such as foraminifera and their fragments. The <20 μm fraction was separated into four smaller fractions with microfiltration62: 3–5 μm, 5–8 μm, 8–10 μm and 10–20 μm. The 10–20 μm fraction was further separated into 10–15 μm and 15–20 μm fractions via the settling method63. Through size separation and microscopic analysis, we constrained the average coccolith length for each genus across all size fractions. The coccolith length was subsequently used to determine cell size through established morphometric relationships (Supplementary Information)7,29. Nannofossil counts were conducted over a gridded 400 μm2 area. Nannofossil relative abundance is presented as percentage contribution of coccoliths to total counted and averaged across two counts. The microfiltration technique was assumed to be imperfect; we therefore ascribed an uncertainty to the measured coccolith carbon isotopic values relative to an international standard (δ13C) assuming contamination from neighbouring size fractions. The 15–20 μm fraction and the 3–5 μm fraction were assumed to have a 25% contamination from the 10–15 μm fraction and the 5–8 μm fraction, respectively, in line with previous studies64. The remaining size fractions were assumed to have a 12.5% contamination from the bounding size fractions. Scanning electron microscope images show good preservation of coccolith material; however, we address the possibility of slight overgrowth on individual coccoliths/nannoliths in the Supplementary Information.
Age model
The age of each sample has been calculated on the basis of three astronomically tuned age models for site 1263 that best represent the middle and late Eocene65,66,67. The age model from 56 Ma to 50 Ma is based on a regression model of the biostratigraphic datums to best fit the data around the PETM, with our oldest point believed to be during peak PETM, given its isotopic signature.
Isotopic measurements
The δ13Clith was determined from ~150 μg of size-separated sedimentary material. In total, 178 samples were processed (5 size fractions × 37 depths = 185, minus 7 samples lost due to machine error). Material was analysed via a Delta V Advantage isotope mass spectrometer fitted with a Gas Bench II in the Department of Earth Sciences at the University of Oxford. An isotopic measurement was made for each of the five size fractions from each time interval. Samples were calibrated to PeeDee Belemnite via the international NBS-19 standard. All measurements are expressed relative to the Vienna PeeDee Belemnite standard, and the analytical precision was better 0.04‰ across repeat measurements for δ13C (1σ). The final error on isotopic measurements encompasses both analytical error and error introduced from the microfiltration technique (Fig. 1).
Development of the forward model
We developed a forward model that used coccolithophore taxonomic abundance (resolved to genus level) and a previously published cellular isotopic flux model12 to generate abundance-weighted predictions of size-fraction-specific CIVEmean, with individual taxon-specific CIVEmean calculated as a function of Rcalc/Rfix and CO2(aq). Our approach separates the dependence of the CIVE from the isotopic composition of DIC by subtracting the mean CIVE for each depth (age point) from both the modelled predictions and the data. We use an iterative optimization approach to search parameter space for 20 size- and genus-specific values of Rcalc/Rfix (5 size fractions within the 4 dominant genera) and 37 (age- or depth-specific) values of CO2(aq) to maximize the fit of model predictions to the mean-normalized CIVE record (See Supplementary Fig. 5 for full work flow). Our approach allowed changes in relative CO2, modelled output CO2(aq) relative to model input CO2(aq), to be constrained independent of δ13CDIC. We also used a foraminiferal record of δ13CDIC to place additional constraints on absolute \(p_{{\mathrm{CO}}_2}\) (Supplementary Information). We used a Monte Carlo approach to explore the sensitivity of constrained values to model inputs (Supplementary Information).
The forward model predicts the δ13C of each size fraction as a weighted sum of the predicted δ13C for taxa that contribute to each size fraction and their observed relative abundances. Predicted δ13C values for each size and taxon-specific unit (STU; 4 genera across 5 size fractions giving 20 in total) were calculated from a previously published model as a function of ambient carbonate chemistry (all STUs are assumed to experience the same ambient environment at each time point) and STU-specific parameters: Rcalc/Rfix, cell size and growth rate (assumed constant for each STU throughout the studied interval). Growth rate was assumed to follow an allometric scaling relationship with cell size8, cell size was determined from coccolith size7,29,33 and abundances were counted directly (model inputs are summarised in Supplementary Table 2). The assumption of constant growth rate for each STU is supported by Sr/Ca data (Supplementary Fig. 6). Parameters fitted to culture data in the original paper remain unchanged12. Carbon speciation in ambient seawater was calculated via the Seacarb package for R68 with an assumed constant calcite saturation state. The remaining parameters, CO2(aq) and Rcalc/Rfix (referred to as RR in the following mathematical representation), defined the parameter space to be explored. Initial values for CO2(aq) and Rcalc/Rfix were initialized from a random uniform distribution (Selecting initial CO2 and Rcalc/Rfix).
For each STU-specific RRi (\(i \in 1:\) I, I = 20 STUs) and each age-specific CO2(aq)j (\(k \in 1:K\), K = 37 depths), the isotopic flux model was used to calculate a δ13C value, Dij (I × K = 740 in total). Modelled estimates of size-fraction-specific δ13C, Ejk (\(j \in 1:J\), J = 5 size fractions) then involved weighting each age and STU combination by its relative contribution to the analysed calcite for each size fraction. To do this, D was combined with a matrix of the fractional abundance of each genus in each size fraction (B, with elements Bik) on the basis of data from microscope counts, a matrix of genus coccolith weight (C, with elements Cik) calculated from previously published morphometric relationships7,33 and a sorting matrix to produce a J × K (5 × 37) matrix of age- and size-fraction-specific δ13C values (E):
A, B, C, D and E are all matrices; ⊙ represents the mathematical operation of element-wise multiplication and ⊘ represents element-wise division, and A (5 × 20) is given by:
The overall result is to transform D (STU-specific δ13C I × K matrix) to E (a J × K matrix that represents the weighted δ13C values for each size fraction that would have been measured at each time interval).
The modelled δ13C mean for each time interval was then subtracted from each size fraction δ13C at the corresponding time interval to remove the dependence on absolute isotopic compositions and generate a mean-centred value of CIVE (F) for each size fraction:
where \(\overline {E_{1:J,k}}\) is the mean for modelled δ13C across all five size fractions at each age point; F represents a J × K matrix of mean-centred model-predicted δ13C values subsequently used for the fitting of Rcalc/Rfix and CO2.
Optimization
The measured data were treated similarly to remove the dependence on δ13CDIC and generate a mean-corrected measured isotope matrix, H:
where Gjk is the absolute δ13Ccalcite measured for each size fraction at each depth and \(\overline {G_{1:J,k}}\) is the mean δ13Ccalcite across all five size fractions at each age point. The misfit function between the mean-corrected data (H) and the mean-corrected model-predicted values (F) is given by:
where n is the total number of measured and modelled pairs (J × K minus any missing values). There were 7 missing values across 185 size and depth combinations, giving a total of 178 data points to constrain 57 parameter values (20 Rcalc/Rfix + 37 CO2).
An iterative optimization approach was taken to find the best CO2(aq) and Rcalc/Rfix combination to generate model predictions (F) that fit the measured mean-centred CIVE data (H). We used a two-step iterative optimization to minimize the offset: step one consisted of optimizing for Rcalc/Rfix given an initial constant CO2(aq); step two consisted of optimizing for CO2(aq) using the values of Rcalc/Rfix determined in step one. Taking the fitted values of CO2(aq) for the new initial value, the optimization process was repeated until Rcalc/Rfix and CO2(aq) were stable. An unconstrained Nelder–Mead optimizer (fminsearch, Matlab) was used to determine fitted values of CO2(aq) and Rcalc/Rfix that reduced the misfit between the measured and modelled CIVEmean (according to equation (4)) for each iteration. Both CO2(aq) and Rcalc/Rfix were allowed to be only positive values.
Selecting initial CO2 and R calc/R fix
The model outputs of Rcalc/Rfix and CO2(aq) using CIVEmean are dependent on their initial values. However, relative change is robust across depths and across STUs (Supplementary Fig. 3). These parameters described a valley of stability in parameter space whereby the average output CO2(aq) trades off against the average output Rcalc/Rfix. We therefore present CO2 as a relative change where relative CO2 is given by the optimized CO2(aq) output divided by the initial prescribed CO2(aq) value. Differences in the trends in CO2 between different initial values were minor; however, to non-arbitrarily choose initial values of CO2 and Rcalc/Rfix, we introduced an additional optimization step that used an independent estimate of δ13CDIC derived from coeval planktic foraminifera (Supplementary Fig. 4).F
From a log-uniform distribution between 0.5 and 10, 10,000 initial values of Rcalc/Rfix were selected, while an initial 10,000 CO2(aq) values were selected from a uniform distribution between 20 and 150 μmols kg−1, with external carbon conditions allowed to reach concentrations as low as 5 μmols kg−1. The optimization outlined in equations (1)–(3) was undertaken for each of the 10,000 combinations, and a fitted array of CO2(aq) and Rcalc/Rfix values was generated for each combination. The fitted values of CO2 and Rcalc/Rfix were then passed to the forward model to generate 10,000 E matrices of modelled absolute CIVEs.
The δ13C of planktic foraminifera were analysed for ten depths with the associated δ13CDIC determined assuming a constant vital effect (P; Supplementary Information). The δ13CDIC was added onto Ej:J for the corresponding depths, and the misfit between the mean raw size fraction data (G) and the predicted mean of the E matrices + δ13CDIC were calculated:
where foram depths is a set where each value is the depth at which planktic foraminifera were picked and measured, P is the vector of δ13CDIC values and N is the total number of size-fraction-specific δ13C values from the ten samples where we analysed coeval foraminifera.
Comparison of the modelled CIVEs with δ13CDIC provides constraints on the absolute magnitude of Rcalc/Rfix and CO2(aq) (and \(p_{{\mathrm{CO}}_2}\); Supplementary Fig. 4). However, estimating δ13CDIC from planktic foraminifera relies on poorly constrained vital effects, which compromises the elegance of our approach. We thus present relative CO2(aq) changes based on an internally consistent analysis of coccolith calcite (independent of δ13CDIC) and consider estimates of absolute CO2(aq) to be only loosely constrained by the additional consideration of the δ13C of foraminiferal calcite.
Monte Carlo exploration of model output
A Monte Carlo approach was employed to further explore how uncertainties in growth rate, coccolith abundance data, coccolith weight and external carbonate saturation state impact the results over 10,000 runs. For each iteration, values were resampled from their uncertainties (Supplementary Table 2). In addition, the initial target value for H was selected from the uncertainty ascribed due to contamination during the filtration process (Sample selection and preparation). The distribution was assumed normal around its mean. Initial Rcalc/Rfix was fixed at 1.45, and the initial [CO2(aq)] at 29 μmol kg−1, the values that provided the best fit of measured CIVEs with modelled CIVEs relative to δ13CDIC. Assuming an average \(p_{{\mathrm{CO}}_2}\) of 1,000 ppm, pH of 7.7 and temperature of 25 °C across our time interval21,22, the corresponding average [CO2(aq)] calculated via Seacarb in R68 would be ~29 μmol kg−1, which further validates our choice. Final values of Rcalc/Rfix and relative CO2(aq) presented in Figs. 2 and 3 represent the output of Rcalc/Rfix from the Monte Carlo simulation over 10,000 iterations.
We also performed a sensitivity analysis on our Monte Carlo simulation to determine the degree of uncertainty that each of our input variables had on our final predicted values of CIVE, relative CO2(aq) and Rcalc/Rfix over 100 iterations (Supplementary Fig. 2). For each of the sensitivity analyses, uncertainty on all but the target variable was assumed to be 0, while the uncertainty on the target variable was ascribed as listed in Supplementary Table 2. We found the model similarly sensitive to all parameters within the ranges investigated. The robustness of our outputs to variations in our model assumptions such as the validity of an allometrically scaled growth rate and an assumed constant Rcalc/Rfix was also investigated. Our results show that the trends in CO2(aq) and Rcalc/Rfix were robust across growth rates and that the model is unable to fit measured CIVEmean given a constant Rcalc/Rfix (Supplementary Fig. 7). When growth rate was fixed at one for all sizes, much larger values of relative CO2(aq) were required to fit the modelled data. Finally, we investigated the effect of changes in carbonate chemistry parameter space given variations in Ca2+ concentration across the Eocene (Supplementary Fig. 7). While marginal differences were apparent, the trends in CO2(aq) and Rcalc/Rfix were robust. We opted not to include the change in Ca2+ over time to avoid imposing trends into our data that were not internally derived from the measured values.
The model produced a narrow range of fitted values of Rcalc/Rfix when the genus contributed a large proportion to the total sediment size fraction (Fig. 2). If a genus is underrepresented in a specific size fraction, the possible range of Rcalc/Rfix is much wider since it contributes minimal carbonate within the size-fraction δ13C signal. The Rcalc/Rfix values of Chiasmolithus in the 3–5 μm and the 5–8 μm size fractions and Reticulofenestra in the 15–20 μm size fraction are poorly constrained and thus not presented.
Data availability
Supplementary data have been made available via EarthChem online repository (https://doi.org/10.26022/IEDA/112365).
Code availability
Code is available via GitHub at https://github.com/hmcclelland/Coccolith_CIVEs.
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Acknowledgements
This study was conducted at the University of Oxford, Department of Earth Sciences. L.M.C. was funded by NERC PhD studentship NE/L002612/1. We thank the International Ocean Discovery Program (IODP) for providing the samples and C. Day for conducting the isotopic analysis.
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L.M.C. and R.E.M.R. conceived the study. L.M.C. conducted the sedimentary analysis with guidance from M.H. H.L.O.M. and L.M.C. wrote the optimization and Monte Carlo procedures. L.M.C. interpreted the results and wrote the paper with comments and guidance from H.L.O.M., M.H. and R.E.M.R.
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Claxton, L.M., McClelland, H.L.O., Hermoso, M. et al. Eocene emergence of highly calcifying coccolithophores despite declining atmospheric CO2. Nat. Geosci. 15, 826–831 (2022). https://doi.org/10.1038/s41561-022-01006-0
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DOI: https://doi.org/10.1038/s41561-022-01006-0
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