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Compilation of acidification experiments.

A search of the Web of Science was conducted using the phrase ‘(coccolith^∗ OR diatom^∗ OR prochloroc^∗ OR synechoc^∗ OR trichodes^∗ OR crocosphae^∗ OR diazotroph^∗) AND (CO₂ or ‘carbon dioxide’ OR ‘ocean acidification’) AND (‘growth rate’)’. Each paper that mentioned a comparison between ambient and elevated CO₂ conditions in the abstract was downloaded. Additional papers were selected based on reference lists from the above papers and personal communications with researchers. We further curated these papers by excluding any (Supplementary Table 3) that: did not actually compare growth rates at different CO₂ concentrations; did not specify the CO₂ levels examined; used CO₂ concentrations outside the range 250–1,100 μatm; attempted to separately manipulate CO₂ concentration and pH using organic buffers; manipulated CO₂/pH in such a way as to radically change alkalinity; presented data in such a way that it was impossible to calculate a ratio of elevated:ambient growth rates; included only freshwater species; or had been retracted. Results were divided into single species short-term laboratory studies, long-term (evolutionary) laboratory studies, and field experiments with mixed communities (Fig. 1). Values were collected from tabulated data in papers where possible; otherwise values were estimated visually from figures. No attempt was made to extract information about replication level, variance, or significance level of data; only experimental means were collected. Many papers examined the response to CO₂ enrichment under a variety of environmental conditions (for example, different light or nutrient levels). In this study, each environment was considered as a unique experiment, and no attempt was made to examine covariance or synergy between any other parameter and response to CO₂. Such synergy is probably important, but as yet there is too little data to make these distinctions.

To compare laboratory studies to field studies, we considered a number of field CO₂-enrichment experiments. Unfortunately, only one of these papers, Lomas et al.¹⁵, provided sufficient data to allow calculation of GRR for specific functional groups. Supplementary Table 2 summarizes our re-analysis of the data set in Table 3 of Lomas and colleagues¹⁵. In four out of five paired experiments, Prochlorococcus cell density decreased during multi-day incubations at elevated p_CO2. We note that growth rate reponses to elevated p_CO2 (GRR) values are meaningless when the test organism’s numbers do not increase under one or both CO₂ treatments, and represent this case with no number in Supplementary Table 2. In contrast, Synechococcus cell density always increased, with GRR > 1 in three out of five experiments. We note that the authors of the original paper¹⁵ concluded, owing to the large variability and apparent contradictions between their treatments, that there were ‘small or nonsignificant effects of pH’ on the two genera. However, we nevertheless include these data in Fig. 1 for three reasons: the overall lack of relevant field observations in our meta-analysis; the overall lack of observations of Synechococcus and Prochlorococcus responses to elevated p_CO2; and the fact that none of our other data points from the meta-analysis considered either the authors’ intent or the statistical significance of their conclusions. Our study shows that any change, even small, can be important, especially relative to competitors (see Fig. 3). We suggest that further experiments are needed on the competition between these two species at elevated p_CO2.

Finally, we considered a number of evolution experiments with phytoplankton cultures^{11, 12, 13, 14} to determine whether long-term adaptation to elevated p_CO2 could push strains outside of the range observed in short-term studies. We considered only experiments where single strains of marine phytoplankton belonging to one of the six functional groups considered in our simulation were adapted to high p_CO2 for at least 100 generations.

The full data set compiled from our meta-analysis, including many more observations than the growth rates reported here, is available for download via BCO-DMO: http://www.bco-dmo.org/dataset/554221.

Climate model.

The MIT Integrated Global Systems Model (IGSM) framework^{5, 16} was used in this study. In this earth system model of intermediate complexity, the three-dimensional ocean circulation³¹ had a horizontal resolution of 2° × 2.5° and 22 vertical levels ranging from 10 m in the surface to 500 m at depth. Ocean boundary layer physics and the effects of mesoscale eddies not captured at this coarse resolution are parameterized^{32, 33}. The ocean is coupled to a two-dimensional (latitude and height) atmospheric physical³⁴ and chemical module, and a terrestrial component³⁵ with hydrology³⁶, vegetation³⁷ and natural emissions³⁸. The coupled system was spun up for 2000 years (using 1860 conditions) before simulating 1860 to 2100 changes. Atmospheric greenhouse gas and volcanic observations were specified from 1860 to 2000; for the twenty-first century, human emissions for a ‘business as usual’ scenario were predicted from an economics module¹⁶ (similar to the IPCC AR5 RCP8.5 scenario⁷). In both the spin-up, historical and future simulation phases, the three-dimensional ocean was forced with prescribed wind fields. These fields had variability as provided by NCEP (ref. 39) re-analysis (de-trended winds over the period 1948 to 2007 were employed; these winds were ‘recycled’ for years outside this period), which produced interannual variability in the ocean model. An El Niño Southern Oscillation (ENSO)-type signal was apparent. For simplicity, we did not allow changes to the wind patterns and intensity in the future period. Although some clear patterns of changes in wind stress emerged from analysis of the archived results from coupled runs⁴⁰, considerable model uncertainty remained^{41, 42}. This aspect of physical changes to the system is beyond the scope of this work.

Ecosystem model.

The ocean physical fields (velocities, mixing and temperature) from the climate model were used to drive a modified version of the marine ecosystem model⁵. Inorganic and organic forms of carbon, nitrogen, phosphorus, iron and silica, as well as 96 phytoplankton types and two grazers were transported in the three-dimensional ocean. The biogeochemical and biological tracers interacted through the formation, transformation and remineralization of organic matter. Iron chemistry included explicit complexation with an organic ligand, scavenging by particles⁴³ and representation of aeolian⁴⁴ and sedimentary⁴⁵ sources.

Phytoplankton growth rates were parameterized as functions of the maximum photosynthesis rate, local light, nutrients temperature, as in previous studies⁵, as well as p_CO2.

Nutrient limitation of growth was determined by the most limiting resource,

where the nutrients (N_i) considered were phosphate, iron, silicic acid and dissolved inorganic nitrogen, and j represents phytoplankton type j (j = 1–96). The effect on growth rate of ambient phosphate, iron or silicic acid concentrations was represented by a Michaelis–Menten function:

where the k_ij were half-saturation constants for phytoplankton type j with respect to the ambient concentration of nutrient i. We resolved three potential sources of inorganic nitrogen (ammonia, nitrite and nitrate). Phytoplankton preferentially used ammonia.

Each functional group had different values of maximum photosynthesis rate, nutrient half-saturation constant, and potentially had different nutrient needs, as in our previous studies^{5, 46, 47}. For instance, diatoms were parameterized to have the highest maximum photosynthesis, but also a high nutrient half-saturation and silicate requirements. Prochlorococcus had the lowest growth rate, but also the lowest half-saturation. These differences allowed each functional group to have a distinct and plausible spatial and temporal niche within our model^{5, 46, 47} (Supplementary Fig. 4).

Temperature modulation of growth was represented by a non-dimensional factor (Supplementary Fig. 1a). This factor⁴⁸ was a function of ambient temperature, T(K):

Coefficient τ_T normalized the maximum value, whereas A_T, B_T, T_N and b regulated the sensitivity envelope. T_oj sets the optimum temperature specific to each of the 16 types in each functional group. There was an increase in maximum growth rate for types with higher optimum temperature, as suggested by observations^{19, 49}, and a specific temperature range over which each type could grow, as suggested by observations^{17, 18}. We test other assumptions on the temperature growth function (Supplementary Figs 1b, c and 13; discussed later).

The unique feature of this model was the inclusion of a modification to growth rate by the ambient p_CO2 (Fig. 2 and Supplementary Fig. 2a):

where δ_j was a randomly assigned coefficient from the range of responses seen in each functional group from the meta-analysis (that is, GRR, Fig. 1, Table 1). If δ_j = 0, then there was no change in growth rate with increased p_CO2, if δ_j = 0.2 then the phytoplankton grew 20% faster when p_CO2 reached 1,000 μatm.

Because the meta-analysis focused on elevated p_CO2 and not the effects of pre-industrial low p_CO2, we assumed that p_CO2 had no effect on growth rate until 400 μatm, and that there was a linear change from 400 to 1,000 μatm (Fig. 2). This simplest linear description was chosen as the majority of laboratory experiments conducted only present day and ‘elevated’ p_CO2. Experiments conducted over a wider range of p_CO2 values suggested a hyperbolic Michaelis–Menten response for nitrogen fixation rates for Trichodesmium and Crocosphaera⁸, but the GRR in that study (and others) appeared more complex. We do test how more complex p_CO2 growth functions (Supplementary Fig. 2b, c) alter the results (Supplementary Section 4, Supplementary Fig. 12,) finding that the func