To accurately identify optimal conditions, tipping points and sensitivities of rates in response to changing CO2, light and temperature, a broad range of experimental conditions are required. Hence, monospecific cultures of the coccolithophore E. huxleyi (strain PML B92/11 morphotype A isolated from Bergen, Norway) were grown in artificial seawater (ASW) at 20 ∘C and a salinity of 35 across a pCO2 (partial pressure of CO2) gradient from ∼ 25 to 7000 µatm. Light intensities were set to 50, 400 and 600 µmol photons m-2 s-1 of photosynthetically active radiation (PAR) on a 16:8 h light–dark cycle in a Panasonic versatile environmental test chamber (MLR-352-PE). An additional set of cultures was also incubated at 1200 µmol photons m-2 s-1 under a Philips SON-T HPS 600W light in a water bath set to 20 ∘C. Light intensities at each bottle position for all experiments were measured using a LI-193 spherical sensor (LI-COR). Cells were pre-acclimated to experimental conditions for 8–12 generations. To account for differences in growth rate between the extreme high/low CO2 treatments and the intermediate CO2 treatments, initial cell densities were chosen between 20 and 80 cells mL-1. Treatments were run using a dilute-batch culture setup, mixed daily and harvested before dissolved inorganic carbon (DIC) consumption exceeded 10 %.

ASW with a salinity of 35 was prepared according to . ASW was enriched with f/8 trace metals (ethylenediaminetetraacetic acid (EDTA)-bound Fe, Cu, Mo, Zn, Co, Mn) and vitamins (thiamine, biotin, cyanocobalamin) according to , 64 µmol kg-1 nitrate (NO3-), 4 µmol kg-1 phosphate (PO43-), 10 nmol kg-1 SeO2 and 1 mL kg-1 of coastal seawater (collected at Shelly Beach, Ballina, NSW, Australia) to prevent possible limitation by trace elements during culturing which had not been added to the artificial seawater mix. ASW medium was sterile filtered (0.2 µm pore size, Whatman^™ Polycap 75 AS) directly into autoclaved acclimation (0.5 L) or experimental (2 L) polycarbonate bottles (Nalgene^®), leaving a small headspace for the adjustment of carbonate chemistry conditions.

Carbonate chemistry, i.e. total alkalinity (TA) and DIC, for each treatment was adjusted through calculated additions of hydrochloric acid (certified 3.571 mol L-1 HCl, Merck) and Na2CO3 (Sigma-Aldrich, TraceSELECT^® quality, dried for 2 h at 240 ∘C). Samples for TA and DIC measurements were taken at the end of the experiment. TA samples were filtered through GF/F filters, stored in the dark at 4 ∘C and processed within 7 days (; SOP 1). TA samples were measured by potentiometric titration using a Metrohm Titrino Plus automatic titrator with 0.05 mol kg-1 HCl as the titrant, adjusted to an ionic strength of 0.72 mol kg-1 with NaCl (; SOP 3b).

DIC samples were sterile filtered by gentle pressure filtration with a peristaltic pump (0.2 µm pore size polycarbonate, Sartorius) into glass stoppered 100 mL bottles (Schott Duran) with overflow of at least 50 % of bottle volume similar to , sealed without headspace and stored in the dark at 4 ∘C until processing within 7 days. To determine DIC, 2 mL of sample was analysed on a Marianda AIRICA system by acidification with 10 % phosphoric acid to convert all DIC into CO2, followed by extraction with N2 (5.0) and concomitant CO2 analysis with an IR detector (LI-COR LI-7000 CO2 / H2O analyser). Both TA and DIC measurements were calibrated against certified reference materials (batches 139, 141 and 150) following . Initial DIC and TA concentrations were estimated by adding measured total particulate carbon build-up during incubations to measured final DIC and double the particulate inorganic carbon build-up during incubations to measured final TA concentrations. Carbonate chemistry speciation for each treatment was calculated from mean TA, mean DIC, measured temperature, salinity and [PO43-] using the program CO2SYS , the dissociation constants for carbonic acid determined by , KS for sulfuric acid determined by and KB for boric acid following .

Sampling started approximately 2 h after the onset of the light period and lasted no longer than 3 h. Duplicate samples for total and particulate organic carbon (TPC and POC) were filtered (-200 mbar) onto GF/F filters (Whatmann, precombusted at 500 ∘C for 4 h) and stored in glass petri dishes (precombusted at 500 ∘C for 4 h) at -20 ∘C until analysis. POC filters were placed in a desiccator above fuming (37 %) HCl for 2 h to remove all particulate inorganic carbon (PIC). All filters were dried overnight at 60 ∘C and analysed for carbon content and corresponding isotopic signature according to on an elemental analyser (Flash EA, Thermo Fisher) coupled to an isotope ratio mass spectrometer (IRMS, Delta V plus, Thermo Fisher). PIC was calculated by subtracting measured POC from TPC.

Cell densities were measured every 3–4 days after the commencement of the experiment using a flow cytometer (Becton Dickinson FACSCalibur) on high flow settings (58 µL min-1) for 2 min per measurement. Living cells were detected by their red autofluorescence in relation to their orange fluorescence in scatter plots (FL3 vs. FL2). At both the extreme low and high CO2 treatments, carbonate chemistry at the end of the pre-incubation phase can significantly deviate from initial and hence experimental treatment conditions due to enhanced air/water CO2 gas exchange during regular cell abundance monitoring. As a result, at some extreme CO2 levels, there was an initial lag phase, and therefore growth rates were calculated from densities only during the exponential part of the growth phase. After disregarding lag-phase measurements, the majority of treatments had only two to three data points in the exponential phase. As a result, specific growth rates were calculated as μ=ln⁡(Cf)-ln⁡(C0)d, where Cf represents cell densities at time of sampling, C0 represents cell densities at the beginning of the exponential growth phase, and d is the duration of the exponential phase in days. Calcification and photosynthetic rates were calculated by multiplying cellular PIC and POC quotas with respective growth rates.

Coccolithophore metabolic rate (MR) responses of growth, calcification and photosynthetic carbon fixation to combined changes in temperature, light and carbonate chemistry speciation can be described as follows : MR(T,I,S,H)=k1SITk2HT+k3SHT+k4I+k5SI+SIT+k6SHI2T2, where k1 (pg C cell-1 d-1 or d-1), k2 (µmol photons m-2 s-1), k3 (kg mol-1 µmol photons m-2 s-1), k4 (mol kg-1 ∘C), k5 (∘C), k6 (kg mol-1 µmol photons-1 m2s ∘C-1) are fit coefficients, and MR (T, I, S, H) is the metabolic rate of photosynthesis, calcification or growth dependent on temperature (T), light intensity (I), substrate (S= [CO2] + [HCO3-]) and [H+] (H). Inputs to the equation consisted of calculated CO2, HCO3- and H+ (H in total scale) concentrations, as well as measured metabolic rates, and light (I) and temperature (T) levels of all treatments (please see below for information on temperature and light transforms).

Data from this study (Tables S1, S2) and were fitted to Eq. () using the non-linear regression fit procedure nlinfit in MATLAB (MathWorks). The reason only these studies were chosen, from the multitude of E. huxleyi datasets, is because (1) they use the same strain (PML B92/11), (2) they have the same nutrient conditions, and (3) they use the same carbonate chemistry manipulation methods. Nevertheless, the two chosen studies provided light (six levels) and temperature (three levels) interactions over a broad carbonate chemistry speciation range. It is noted that in both studies the carbonate chemistry system is coupled, meaning that a change in CO2 results in a change in pH. This method reflects the changes in carbonate chemistry speciation due to ongoing ocean acidification . However, some studies have examined the effects of decoupled carbonate chemistry where CO2 is changed at a constant pH. This approach is used to tease apart the independent effects of H+ and CO2 on physiological responses (see ). While Eq. () can also be used to explain responses under decoupled carbonate chemistry conditions (see for details), the fit obtained here is only valid for coupled CO2/pH changes as no data from decoupled experiments (i.e. ) have been used. The reason for this is that does not contain data of temperature, light and carbonate chemistry interactions.

To reduce skew and to better accommodate certain features (i.e. light and temperature inhibition and limitation), both temperature and light data were transformed. Light data were square root transformed with light (I)=PFD, where PFD is the photon flux density (µmol photons m-2 s-1) of an incubation. To accommodate for known temperature inhibition below 2 and above 30 ∘C at a much narrower experimental range (10–20 ∘C), the upper and lower limits for E. huxleyi growth were added into the equation with a general transform of T=(Tt-2)×(30-Tt), where Tt is the temperature of an incubation. To accurately express the onset of high temperature inhibition, the transform was further modified with a square root transform to give T=(Tt-2)×(30-Tt). This transform produces reasonable results when compared to the Eppley temperature envelope curve and the Norberg model (see ).

Equation () was used to assess the combined effects of carbonate chemistry, temperature and light on growth, calcification and photosynthetic carbon fixation rates, with a focus on general physiological features, such as limitation and inhibition, as well as how much variability could be explained. For growth, photosynthetic carbon fixation and calcification rates of optimum CO2 concentrations for maximum production rates (Vmax⁡) and half-saturation values were calculated at each experimental light and temperature level. K12 values consisted of K12CO2 sat which is the CO2 concentration (at certain T and I) at which rates are saturated to half the maximum, and K12CO2 inhib, which is the CO2 concentration (at certain T and I) at which high proton concentrations reduce physiological rates to half the maximum. Fitting results (R2, fit coefficients, p values, F values and degrees of freedom), as well as Vmax⁡, K12 and CO2 optima are presented in Tables , and . Species-specific differences in response to changing carbonate chemistry, temperature and light were assessed by comparing the above fit to that recently produced for Gephyrocapsa oceanica .

To examine the potential of ongoing ocean change to influence realised niches, and hence individual success, ranges for light and temperature where both Emiliania huxleyi and Gephyrocapsa oceanica might be expected to coexist were selected (i.e. 50–1000 µmol photons m-2 s-1 and 8–30 ∘C). E. huxleyi and G. oceanica were chosen for comparison as they are currently the only two species with response data over a range of carbonate chemistry, temperature and light conditions. Growth rates were selected as the point of comparison because they can be used as a measure of relative abundance and therefore dominance of a species, and because growth rates largely control carbon fixation rates. To assess competitive ability, and the potential realised niche, the difference in growth rates between the species was visualised using contour plots.

The effect of temperature on growth rates and hence potential dominance was then compared to phytoplankton community data from global surface sediment samples above the lysocline . As E. huxleyi and G. oceanica have similar average numbers of coccoliths per cells, 28 and 21, respectively , the abundance ratio of E. huxleyi to G. oceanica coccoliths was here assumed to be a suitable proxy for species dominance. It is noted that E. huxleyi has been found to produce excess coccoliths towards the end of blooms when inorganic nutrients become limiting for cellular growth , which would result in an overestimate of E. huxleyi dominance in our study. Nevertheless, given that the coccoliths' ratio varies orders of magnitude in modern marine sediments, none of our general conclusions should be affected. Temperature for each sampling site was retrieved from the National Oceanic and Atmospheric Administration (NOAA) 1∘ resolution annual temperature climatology .

While our fit equation has previously explained variability in lab experiments quite well , natural systems are much more complex, with the interactions of dozens of variables including temperature, light, nutrients, predation and competition all influencing productivity . As such, we wanted to examine how projections of productivity using our relatively simple equation compared to coccolithophorid productivity patterns observed in natural systems. Productivity can be defined in a few ways; traditionally, changes in cellular calcification rates, in response to ocean change, have been used as indicator for the potential success of coccolithophores in the future ocean. However, the exponential nature of phytoplankton growth amplifies even small differences in cellular growth rates, when applied on the community level. For instance, a phytoplankton bloom occurring over 1 week at a growth rate of 1.0 d-1 and a starting cell density of 50 cells mL-1 would lead to a peak density of about 55 000 cells mL-1. This is in stark contrast to conditions where growth is only 10 % lower as peak cell densities, and hence biomass and PIC standing stock, will only be half.

Recently, a new metric was proposed, the CaCO3 production potential (CCPP), which (1) should be a better representation of potential coccolithophore success on the community level and (2) can be tested against modern observations of surface ocean CaCO3 distribution . CCPP is defined as the amount of CaCO3 produced within a week by a coccolithophore community (with a set starting cell count) for a certain environmental condition, calculated from Eq. () derived growth rates and inorganic carbon quotas. Inorganic carbon quotas are calculated as the quotient of calcification and growth rates. As CCPP is calculated from calcification and growth rates, it accounts for the individual effects of temperature, light and carbonate chemistry on growth rates and on carbon production. It was for these reasons that CCPP was the metric chosen for comparison.

Provided values for temperature, light, substrate (CO2 + HCO3-) and hydrogen ion concentrations (H) for the surface mixed layer, coccolithophore CaCO3 production potential can be projected for the world oceans. CCPP can then be cautiously evaluated against and compared to satellite-derived global particulate inorganic carbon concentration estimates (PICs). As inorganic nutrients are a critical factor influencing phytoplankton abundance, and especially bloom formation, in the ocean , nitrate concentrations were also included in the analysis (for details, see below). As a result, climatological datasets consisted of World Ocean Atlas (WOA) 2013 v2 nitrate concentrations at 1∘ resolution ; SeaWiFS mixed layer depth (MLD 2∘ resolution) from ; surface photosynthetically available radiation (PAR µmol photons m-2 s-1 9 km resolution) from the Moderate Resolution Imaging Spectroradiometer (MODIS)-Aqua ; diffuse attenuation coefficients at 490 nm (9 km resolution) from ; and NOAA dissolved inorganic carbon, pCO2, pH (total scale), [CO32-], temperature and salinity (4 × 5∘ resolution) from . A 9 km resolution climatology for particulate inorganic carbon (PICs) concentration (mol PIC m-3) was also retrieved from MODIS-Aqua . Once acquired, all datasets were interpolated to a 1∘ resolution.

Hydrogen ion concentrations were calculated as 10-pH, CO2, after conversion of pCO2 to fCO2 as described in CO2SYS , as [fCO2] × K0 (with K0 being the temperature- and salinity-dependent Henry's constant), HCO3- as [HCO3-] = DIC - ([CO2] + [CO32-]) and substrate (S) as the sum of CO2 and HCO3- concentrations. Mean mixed layer nitrate concentrations were calculated by determining concentrations for each depth and averaging from the surface to the mixed layer depth for each grid cell. Mean mixed layer irradiance was calculated in 1 m depth increments for each grid cell as I=∑i=1MLD=exp⁡-kd(i)×I0, where I is the average PAR (µmol photons m-2 s-1), kd is the attenuation coefficient (m-1), MLD denotes the mixed layer depth in metres, and I0 is the incident PAR at the surface (µmol photons m-2 s-1).

Global coverage of oceanic nutrient concentrations is often limited to only a few macronutrients (nitrate, silicate, phosphate). However, concentrations of these nutrients are often strongly correlated (e.g. phosphate and nitrate in ). To ensure there were sufficient nutrients to support the level of production estimated by CCPP, we opted to use a single nutrient, i.e. nitrate, in combination with a simple scaling metric. We first assumed a Redfieldian ratio of 106 : 16 C : N to determine the maximum POC production possible from the amount of available nitrate. We then calculated the amount of PIC which would be co-produced based on a mean PIC : POC. The average PIC : POC of E. huxleyi and G. oceanica was calculated as the average of all treatments between 300 and 1000 µatm from , and this study. Based on these averages (PIC : POC of 0.8 and 1.35 for E. huxleyi and G. oceanica, respectively), and assuming Redfieldian production, a corresponding PIC : PON of 5.3 and 8.94 was calculated. Hence, maximum CaCO3 production potential (CCPPmax) in a grid cell would be 5.3 and 8.94 times the nitrate concentration for E. huxleyi and G. oceanica, respectively. If estimated CCPP for a cell exceeded CCPPmax, and therefore the nitrate required to produce that much PIC, then it was replaced with the CCPPmax value. If CCPP was less than Cmax, then no further changes were applied.

To ensure that mean global CCPP and mean global PICs would be of the same magnitude, starting cell counts for CCPP calculations were set at 1 mL-1 for E. huxleyi alone, 0.25 mL-1 for G. oceanica alone and 0.25 mL-1 for each species when combined. To allow comparison, CCPP and PICs were both converted to units of µmol PIC L-1. All data were then averaged for austral summer/boreal winter (December–February) and austral winter/boreal summer (June–August). Austral summer/boreal winter and austral winter/boreal summer were chosen as they provide prominent differences between minimum and maximum PIC, while spring and autumn do not. A direct comparison between PICs and CCPP was achieved by splitting results into major ocean biogeographical provinces following with the single change of adjusting the Antarctic and the north ocean regions to start at 45∘ as in rather than 40∘ (see Sect. ). For each major province, the total amount of PICs and CCPP for all comparable grid cells was calculated for austral summer/boreal winter and austral winter/boreal summer. For comparison, values for each basin and season were then converted into percentages of annual global (global summer plus global winter) PICs or CCPP production. Agreement between the satellite and CCPP estimates was then assessed using a linear correlation. While three CCPP scenarios are presented above, only the results with the highest correlation to satellite PIC are shown and discussed below.

Based on fits of Eq. (), growth, calcification and photosynthetic carbon fixation rates all had a similar optimum curve response to the broad changes in carbonate chemistry speciation (Fig. ) regardless of temperature and light intensities. Growth, calcification and photosynthetic carbon fixation rates required similar CO2 concentrations, with differences of less than 3 µmol kg-1 under comparable temperature and light conditions, to stimulate rates to half the maximum, K12CO2 sat (Tables , ). Optimum CO2 concentrations for calcification (8.4–19.1 µmol kg-1) were slightly lower than for photosynthesis (9.9–52.1 µmol kg-1) or growth (15–29.1 µmol kg-1 Tables , ). At CO2 concentrations beyond the optimum, a much higher sensitivity to increasing [H+], i.e. K12CO2 inhib, was observed for calcification (47.4–118.5 µmol kg-1) than for photosynthesis (73.0–250 µmol kg-1) or growth rates (157.7–250 µmol kg-1; Tables , and Figs. , ).

The effect of temperature on rates was dependent upon CO2, with the greatest effect observed at optimum CO2 concentrations (Fig. ). Increasing temperature increased maximum growth rates (Vmax⁡) up to 2-fold, photosynthetic rates up to 43 % and calcification rates up to 52 % (Fig. , Table ) under optimal CO2 concentrations. CO2 half-saturation concentrations (K12CO2 sat) were insensitive to temperature (Table ). However, under increasing temperatures, CO2 concentrations for both optimal growth and for inhibition of rates to half the maximum (K12CO2 inhib) decreased (Table ).

Light intensities affected all physiological rates, with the greatest effect generally being observed at CO2 concentrations at or above the optimum (Fig. ). Between 50 and 1200 µmol photons m-2 s-1, calcification rates doubled, photosynthetic rates tripled and growth rates increased around 36 % (Fig. , Table ). Both optimum CO2 and CO2 concentrations at which rates were half saturated (K12CO2 sat) increased slightly with increasing light intensity (Table ). CO2 concentrations required to inhibit rates to half of the maximum (K12CO2 inhib) for calcification and photosynthesis increased with increasing light intensity, while those for growth increased from 50 to 150 µmol photons m-2 s-1 before decreasing with further increases in light (Table ).

Rates of photosynthesis, calcification and growth in coccolithophores are strongly influenced by CO2 . Increasing CO2 concentrations resulted in enhanced rates up to an optimum level beyond which they then declined again. This pattern in growth, photosynthetic carbon fixation and calcification rates has been observed previously for several coccolithophore species . The availability of substrate (CO2 and HCO3-) was suggested as the factor influencing the increase in rates on the left side of the optimum, while the proton concentration ([H+]) was the factor most likely driving declines to the right side of the optimum .

Of the two species, E. huxleyi has a higher CO2 optimum than G. oceanica (Tables , and S3; ) for all rates and under most conditions. This could suggest that E. huxleyi has a slightly higher substrate requirement than G. oceanica. However, considering that G. oceanica has both a larger cell size and higher carbon quotas per cell, the opposite would be expected . An explanation for achieving maximum rates only at higher CO2 concentrations in E. huxleyi, in comparison to G. oceanica despite a lower inorganic carbon demand, might be a less efficient or capable carbon uptake/concentrating mechanism. Alternatively, a decreased sensitivity to high [H+] in E. huxleyi, in comparison to G. oceanica (see below), would lead to a shift in the optimum towards higher CO2 as well and might be a more likely explanation.

Of the three rates, calcification in E. huxleyi had both the lowest CO2 requirement and the highest sensitivity to increasing [H+] (Tables  and ). This is a pattern previously observed for G. oceanica under varying temperature and light conditions (; see also Table S3 in the Supplement). As evidenced by higher K12CO2 inhib values for all processes, E. huxleyi also appears less sensitive to the inhibiting effects of increasing [H+] than G. oceanica (i.e. K12CO2 inhib is 47–250 µmol kg-1 versus 25–99 µmol kg-1 for G. oceanica depending on light intensities or K12CO2 inhib is 62–250 µmol kg-1 versus 25–130 µmol kg-1 for G. oceanica depending on temperature) (Tables , , S3; ). This also supports earlier results in a model analysis by where E. huxleyi reacted less sensitively to higher CO2 (and [H+]) than G. oceanica.

A lower sensitivity of rates to changes in carbonate chemistry speciation, in particular calcification rates, could be explained by the lower degree of calcification in E. huxleyi (PIC : POC ratios 0.24–1.38) when compared to G. oceanica (PIC : POC ratios 0.84–2.44) . Higher rates of calcification result in greater production of intracellular H+ (Ca2+ + HCO3- ⇌ CaCO3 + H+), potentially decreasing [CO32-] in the coccolith-producing vesicle and hence the CaCO3 saturation state . Furthermore, increased [H+] has been found to result in declines in [HCO3-] uptake, the primary carbon source for calcification .

Temperature was observed to have few modulating effects on CO2 responses in E. huxleyi. Changes in temperature produced little (< 1 µmol kg-1) change in CO2 substrate half-saturation (K12CO2 sat) levels, at least within the measured range (Fig. , Table ). CO2 requirements for optimum rates tended to slightly decrease with warming temperatures. Similar results were observed for G. oceanica . This indicates that while overall rates change, carbon uptake mechanisms appear to scale to maintain internal substrate concentrations and thus cellular requirements regardless of temperature conditions.

In contrast, the inhibition of rates by rising [H+], i.e. K12CO2 inhib, was more sensitive to temperature. The CO2 concentration at which rates were reduced to half the maximum increased with decreasing temperatures (Table ). These results were also observed for G. oceanica which had a lower sensitivity to increasing [H+] at the lowest tested temperature . This also agrees with in which a greater decline in calcification rate was observed with increasing CO2 at 18 ∘C than at 13 ∘C. These results indicate that at least some coccolithophores may be less sensitive to high CO2 levels at lower temperatures. As a result, both G. oceanica and E. huxleyi may become more vulnerable to the negative effects of ocean acidification as ocean temperatures increase due to climate change.

The sensitivity of all rates in E. huxleyi to changing carbonate chemistry, in particular increasing [H+], was clearly modulated by light intensity (Fig. ), agreeing with earlier findings . CO2 half saturation (K12CO2 sat) for all rates was insensitive to increasing light intensities (Table S3). This agrees with results for G. oceanica which also displayed little change in CO2 half-saturation concentrations with increasing light (Table S3). Increasing light intensity induced increases in CO2 optima in all rates; however, these changes were small (< 10 µmol kg-1) for calcification and growth rates. This contrasts with G. oceanica for which a distinct decrease in optimal CO2 concentrations for growth rates with increasing light intensities was observed (Table S3). However, G. oceanica projections are based on a dataset with only three CO2 concentrations (∼ 16, 31, 45 µmol kg-1). As such, it is difficult to determine how robust the estimates of CO2 optima and half-saturation requirements may be for this species .

In E. huxleyi, the relationship between H+ sensitivity and light intensity was the same for the three rates. Calcification and photosynthetic carbon fixation and growth rates were most sensitive to H+ at the lowest (50 µmol photons m-2 s-1) and growth rates were also slightly more sensitive at the highest (1200 µmol photons m-2 s-1) light intensities (Table ). This result is in part due to an underestimation of growth rates by the fitting equation under high CO2 conditions at 50 µmol photons m-2 s-1 light (Fig. ). However, it may be that sub-optimal light intensities add additional stress to the cells resulting in them having less resources with which to handle the stress of increasing high [H+]. Hence, rates are lower but also appear more sensitive to changing carbonate chemistry. These findings agree with findings by where a diploid E. huxleyi strain became insensitive to the effects of rising CO2 (380 vs. 1000 µatm) when light intensities were increased from 50 to 300 µmol photons m-2 s-1. However, this differs from G. oceanica which, with rising light intensities, had no change in sensitivity for calcification rates, a decrease in sensitivity for photosynthesis and an increase in sensitivity for growth rates (Table S3). Again, although this could be indicative of species-specific differences in sensitivity, it may also be a result of the low number of CO2 treatments used in the light data of G. oceanica (see ).

In the future ocean CO2, temperature and light availability are all expected to change . Levels of fCO2 are expected to reach as high as 985 µatm by the end of the century with concomitant rise in global ocean temperature of up to 4.8 ∘C (RCP8.5 scenario, ). Light intensities in the surface ocean are also expected to increase as a result of mixed layer depth shoaling . By calculating and comparing growth rates for E. huxleyi and G. oceanica over a range of environmental conditions, it is possible to differentiate between the fundamental (physiological) niche of a species and its potentially realised niche when in competition with others. For this purpose, light, temperature and CO2 ranges were restricted to those where both species would be expected to co-occur, i.e. 20–1000 µmol photons m-2 s-1, 8–30 ∘C and 25–4000 µatm, respectively. The calculated difference in growth rates in response to CO2 and temperature does not significantly change with light intensity (Figs.  and ). It should be noted, however, that light intensity might modify observed growth rate differences for other strains of the same species than used here as they can possess different sensitivities and requirements (i.e. ).

The CCPP is based on cellular CaCO3 quotas and growth rates calculated for a given set of temperature, light and carbonate chemistry conditions (see Sect. ). Here, we test how this measure for productivity compares to estimated surface ocean CaCO3 content observed by satellite imaging (PICs). At this point, it is important to remember that CCPP does not account for top-down controls such as grazing or viral attack , and bottom-up controls such as competition for macro- or micronutrients . Thus, a potential for high CaCO3 production is not necessarily realised when exposed to different top-down and bottom-up pressures.

Calculated CCPP of E. huxleyi alone (Fig. ) for the global ocean visually reproduces the midlatitude production belts, however at lower latitudes than satellite PIC estimates. This agrees with the NEMO and OCCAM models of coccolithophore dominance and the chlorophyll a NASA Ocean Biogeochemical Model (NOBM) model for the Southern Hemisphere and central North Atlantic provinces . CCPP also estimates seasonal changes with higher productivity during summer in both hemispheres (see Fig. a and d vs. b and e). This pattern is driven mainly by temperature, which influences the latitudinal location of the bands, and light intensity, which influences whether the northern or southern band of productivity is stronger in a season. Nutrients are an essential, and in the ocean often limiting, requirement for biological productivity . As such, it would be expected that nutrients should also be strongly influencing seasonal patterns of PIC production. However, with the starting cell concentrations for the CCPP calculations chosen here, there was sufficient nitrate to support the projected production in most ocean regions (Fig. c and f). High temperatures drove relatively low productivity in the equatorial regions in agreement with satellite PIC. Similar low levels of coccolithophores are estimated in in the equatorial Pacific and Atlantic with the mixed phytoplankton functional group dominating with or without coccolithophores due to low iron and moderate phosphate concentrations, and in for the equatorial Indian and Atlantic provinces. CCPP underestimates production at cold high latitudes, in particular in the Southern Ocean, when compared to the satellite. Similar low levels of coccolithophores have been projected in the Southern Ocean in (very low coccolithophore chlorophyll a), (growth rates at or close to zero which equates to low to zero CCPP) and (high nutrients resulting in coccolithophores being dominated by diatoms). For the Southern Ocean, it has been suggested that satellite PIC concentrations in subantarctic waters are overestimated by a factor of 2–3 while those in Antarctic waters may be even more so . The fact that three other global estimates, based on different sets of environmental parameters, all estimate very little PIC productivity in the Southern Ocean seems to support this theory. However, there are also specifically cold-adapted strains of Emiliania huxleyi found at high latitudes which at least partially could explain discrepancies between the mentioned model projections and satellite-derived PIC concentrations (see also below).

In austral winter/boreal summer, CCPP (for E. huxleyi) and satellite PIC estimates closely match (R2 of 0.73, F of 26.78, p < 0.01, slope of 1.03) with low PIC in the south and central south provinces, very low PIC in the equatorial, north Indian and Antarctic provinces and higher PIC in the north central Pacific, North Pacific and North Atlantic provinces (Fig. a). In austral summer/boreal winter, CCPP (for E. huxleyi) and satellite PIC estimates in individual ocean provinces are also generally of overall good agreement but with a much lower slope (R2 of 0.85, F of 50.01, p < 0.01, slope of 0.32). Both CCPP and satellite PIC estimates for austral summer/boreal winter are low in all equatorial and north ocean provinces with slightly higher CCPP and satellite PIC production for the north central provinces and higher production in the south and central south provinces (Fig. b). The reason for the relatively small slope of 0.32 in austral summer, meaning that CCPP overestimates the total production by a factor of 3, is the high values of satellite-derived PIC in the Antarctic province. To rectify this issue, a simple scaling factor could be introduced.

Despite having similar PIC patterns, overall PIC estimates can differ significantly between CCPP and PICs in some provinces. These provinces can be divided into two groups characterised by either greater or lesser PIC estimates than those observed by satellite (Fig. ). The midlatitude provinces of central south and central North Pacific and Atlantic and central south Indian Ocean in the summer season belong to the former, with higher CCPP than PICs. Recently, low phytoplankton biomass in these subtropical gyre systems has been hypothesised to be the result of strong grazing pressure despite high cellular growth rates , lending an explanation of why CCPP is higher than satellite PIC standing stocks. The lower PIC standing stocks estimated from the satellite could also be the result of other phytoplankton functional groups, such as diatoms, taking a comparatively bigger nutrient share , thereby leaving less for PIC production by coccolithophores.

In contrast, in austral summer/boreal winter in the Antarctic and austral winter/boreal summer in the North Pacific, CCPP is smaller than satellite PIC estimates (Fig. ). E. huxleyi, which our projections are based off, has been found to dominate assemblages in polar areas, particularly in the Southern Hemisphere . The strains of E. huxleyi found here are special cold-adapted ones which can survive at temperatures as low as -1.7 ∘C in the Antarctic and -0.9 ∘C in the Arctic . As our CCPP is based on a temperate coccolithophore strain, lacking the cold-adapted ones, our projections underestimate coccolithophore productivity in these areas. Additionally, differences in CCPP and satellite PIC in the Southern Ocean may also be connected to satellite overestimation of PIC at high southern latitudes (see above).

Comparing satellite PIC and CCPP in different oceanic provinces (Fig. c) E. huxleyi alone provided the greatest agreement between both. The addition of G. oceanica to CCPP calculations negatively affected correlations with satellite PIC. This is counterintuitive as one would expect increasing correlation of CCPP with satellite PIC as more species are used for the projection of the former. Indeed, estimates based on a combination of E. huxleyi and G. oceanica in austral summer/boreal winter were similar to those for E. huxleyi alone. However, in austral winter/boreal summer, estimates based on a combination of E. huxleyi and G. oceanica resulted in much lower agreement between CCPP and satellite PIC when compared to E. huxleyi alone. This difference is driven by greatly increased CCPP estimates in the central North Pacific and Atlantic, combined with greatly decreased CCPP estimates in the North Pacific and Atlantic, relative to the E. huxleyi fit alone. Being a warm-adapted species including G. oceanica would result in more productivity in the subtropical zones. However, these zones are also regions of potentially significant top-down control (see above for details). Meanwhile, the North Pacific and Atlantic are likely dominated by cold-adapted species (see above for details), so including the warm-adapted G. oceanica in CCPP calculations would further reduce estimates in these regions. As a result, the inclusion of G. oceanica does not assist in making global estimates of coccolithophore PIC production.