**Culturing and experimental conditions**

Experimental cultures were grown with a semi-continuous culturing method at 28 degrees C in autoclave-sterilized artificial seawater medium with nutrients added in concentrations equivalent to the recipe for the Aquil medium (except for NO3-), as in Garcia et al. (2011) and originally described by Morel et al. (1979). The total P concentration was altered in the P-light-CO2 manipulation experiment by adding P as H2NaPO4 in aqueous solution.

**P-light-CO2 experiment and cellular growth rates**

In the P-light-CO2 experiment, triplicate cultures were diluted every two days to 5 x 103 cells per mL with medium that contained treatment concentrations of PO43- ranging from 0.1 - 4.0 umol per L. Cells were counted microscopically in each replicate culture with a hemocytometer at the end of each dilution period, and steady state growth rates were calculated from an increase in culture cell number per unit volume between 2-3 dilution periods (4-6 days) after cultures were acclimated to treatment conditions for 7-10 generations.

A low cell biomass was necessary to control CO2 concentrations in cultures and a consistent dilution period reduced variations in growth rates between dilutions. In the P-light-CO2 experiment cultures were grown in 1 L polycarbonate bottles at 40 or 150 umol quanta per square meter per second and bubbled with 19 Pa or 81 Pa pCO2 pre-mixed air supplied and certified by Gilmore Liquid Air Company. Culture pH was measured with a pH meter using the National Bureau of Standards (NBS) scale for seawater pH measurements (model: Orion 5 star, Thermo Scientific). For the P-light-CO2 experiment seawater was bubbled and pre-equilibrated with treatment concentrations of pCO2 before measuring pH and adding nutrients. This was essential to maintain high pH values in the 19 Pa pCO2 treatments. The investigators excluded data from the high light, 19-Pa pCO2 treatment where the pH was >0.05 units lower than the expected pH range of 8.45-8.49 (specifically, the 0.4, 0.8, 2.0 umol total P per L treatments).

Light was supplied on a 12:12 light:dark cycle with cool white fluorescent bulbs. The investigators terminally sampled each replicate culture 24 hours after the last dilution for N2-fixation rates and CO2-fixation rates, and at this point they also sampled for P-uptake rate measurements and cellular P content from each replicate in the P-light-CO2 experiment. To acclimate cultures to low P conditions in the P-light-CO2 experiment, the investigators consecutively reduced the concentration of P by transferring cultures acclimated to neighboring P concentrations in the experimental matrix. Steady-state growth was not achievable in treatments with the lowest P concentrations because growth rates continuously declined when the concentration of P was reduced to those concentrations. In these cases, the investigators sampled cultures before growth rates became negative, except for the low-light, low-P, low-pCO2 treatment, which did have a negative growth rate.

**Nitrogen fixation rates**

Nitrogen-fixation rates were determined with the acetylene reduction method as described in Garcia et al. (2013). Briefly, duplicate 50 mL culture samples were collected from experimental replicates and 4 mL of acetylene was injected into 30 mL headspace at the beginning of the dark period of the light cycle. Samples were gently agitated to equilibrate gas concentrations between the headspace and culture samples after injecting acetylene and before measuring ethylene concentrations. The investigators used a Bunsen coefficient for ethylene of 0.082 (Breitbarth et al. 2004) and an ethylene production:N2 fixation rate ratio of 3:1 and they calculated N2-fixation rates over 14 h (this included the 12 h dark cycle and the first 2 h of the light cycle).

**Total CO2**

Samples for measurements of total CO2 (TCO2) were preserved with 0.05% mercuric chloride (final concentration) in glass bottles without headspace and determined using a carbon coulomb meter (model: CM 140, UIC inc.). For these analyses, the investigators acidified 5 mL with a 10% phosphoric acid solution (1-2% final concentration), quantified the CO2 trapped in an acid sparging column, and calculated TCO2 with reference material provided by Andrew Dickson’s laboratory (batch 95). PCO2 was calculated with the CO2 System Calculations program using K1 and K2 constants from Mehrbach et al. (1973), refit by Dickson and Millero (1987) and the NBS pH scale (Lewis and Wallace 1998; see Table 1 of Garcia et al. (2013) for TCO2 measurements and PCO2 calculations in the P-light-CO2 experiment).

**CO2 fixation rates**

CO2-fixation rates were determined using a Multi-purpose Scintillation Counter (model: LS-6500, Beckman Coulter) similar to the method described by Garcia et al. (2011). Briefly, the investigators inoculated 40 mL samples from each treatment replicate with 0.925 KBq mL-1 H14CO3-. The concentration of H14CO3- added to the sample was negligible in comparison with the TCO2 concentration of the sample. Samples were incubated for 12 h under treatment-specific conditions of irradiance and temperature, and then filtered onto Whatman GF/F filters and rinsed 3 times with ~5 mL filtered seawater to remove extracellular H14CO3-. The incubation was initiated at the beginning of the light period and terminated at the end of the 12 h light period. Total CO2 concentrations were multiplied by the ratio of radioactivity of cellular incorporation of 14C to the total radioactivity of H14CO3-. For CO2-fixation rate calculations in the P-light-CO2 experiment, the investigators pooled ~25 mL from each of 3 treatment replicates into one sample for TCO2 measurements. Non-photosynthetically driven 14C incorporation was determined by incubating replicate culture samples (40 mL) for 12 h during the same time period in opaque bottles at 28 degrees C with the same concentration of H14CO3-; these values were subtracted from measured total 14C incorporation to estimate photosynthetic incorporation. The total radioactivity of H14CO3- was determined by stabilizing 50 uL of the 37 MBq H14CO3- with 100 mL of a basic solution of phenylethylamine (99%) before adding 4 mL of Ultima Gold® XR (PerkinElmer).

**Other measurements**

The investigators calculated the light compensation point (Ec, where net rates are zero) and the minimum concentration (Cmin) of total P for growth, CO2- and N2-fixation rates using the hyperbolic function [y=(a•x)/(b+x)] with the software program Sigma Plot 10. All 3 replicates in the 0.15 umol total P per L low-light, low-PCO2 treatment had slightly negative growth rates, so the investigators assumed net growth rates of zero in those replicates as was done in a prior study of phytoplankton growth kinetics (Hutchins et al. 2007). Next, the values of ‘a’ (the maximum rate) and ‘b’ (the half-saturation concentration, K½) were calculated after aligning the data set as a whole along the x-axis, with respect to the origin, to yield the highest r2 value. The investigators then realigned the data to their original values along with the best-fit hyperbolic functions. The Cmin and Ec are equivalent to the origin before the realignment. This method yields realistic Monod hyperbolic maximum rates, K½, and Cmin or Ec values. The investigators also calculated 95% confidence bands on the hyperbolic functions using Sigma Plot 10. For the light experiment the hyperbolic function of CO2- and N2-fixation rates were fitted to irradiance without including the rates measured at 100 umol quanta per square meter per second due to problems with an altered light level for this treatment just prior to sampling for CO2- and N2-fixation rates.

**References:**

Garcia, N. S., F.-X. Fu, , C. L. Breene, P. W. Bernhardt, M. R. Mulholland, J. A. Sohm, and D. A. Hutchins. 2011. Interactive effects of irradiance and CO2 on CO2- and N2 fixation in the diazotroph Trichodesmium erythraeum (Cyanobacteria). J. Phycol. 47: 1292-1303. DOI: 10.1111/j.1529-8817.2011.01078.x

Garcia, N. S., F.-X. Fu, C. L. Breene, E. K. Yu, P. W. Bernhardt, M. R. Mulholland, and D. A. Hutchins. 2013. Combined effects of CO2 and light on large and small isolates of the unicellular N2-fixing cyanobacterium Crocosphaera watsonii from the western tropical Atlantic Ocean. Eur. J. Phycol. 48: 128-139. DOI: 10.1080/09670262.2013.773383

Hutchins, D. A., F.-X. Fu, Y. Zhang, M. E. Warner, Y. Feng, K. Portune, P. W. Bernhardt, and M. R. Mulholland. 2007. CO2 control of Trichodesmium N2-fixation, photosynthesis, growth rates, and elemental ratios: Implications for past, present, and future ocean biogeochemistry. Limnol. Oceanogr. 52: 1293-1304. DOI: 10.4319/lo.2007.52.4.1293

Morel, F. M. M., J. G. Rueter, D. M. Anderson, and Guillard, R. R. L. 1979. Aquil: Chemically defined phytoplankton culture medium for trace metal studies. J. Phycol. 15:135-141. DOI: 10.1111/j.1529-8817.1979.tb02976.x