1 2 3 4 5 6 7 8 9 10 11 Supporting Information Appendix: Supplementary Statistical Methods Table S1: Sources for trait values Figure S1: Times series of nitrate and PAR at L4 Figure S2: Distribution of densities at L4 Figure S3: Observed and predicted probability of presence vs. PAR Figure S4: Partial residuals vs. nitrate Figure S5: Partial residuals vs. nitrate*par Figure S6: Time series of biovolumes at L4 Figure S7: Evaluation of autocorrelated residuals for occurrence model Figure S8: Evaluation of autocorrelated residuals for abundance model 12 13 14 15 16 17 18 19 20 21 22 23 1
24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 Supplementary Statistical Methods In both the occurrence and abundance models, there are four species-level random effects: b!!!!!, b!"#, b!"#, and b!!. We initially allowed these effects to covary according to a multivariate normal distribution. These analyses showed large uncertainty in the correlations among random effects, i.e. all values from -1 to 1 were supported by the posterior distribution. Consequently, we used a simpler formulation of these models in which the random effects were modeled as being independently distributed, as this formulation converged faster and had very similar parameter estimates. The parameters b!, b!"#, b!"#, b!!, γ!, γ!!", γ!"#$, γ!!"!, γ!"#!"#$, γ!"#!!", γ!"#!"#$, and γ!!!"#$ were assigned normally distributed priors with zero mean and variance of 10 4. In the occurrence model, ρ was assigned a normally distributed prior with zero mean and variance of 10 4, and in the abundance model ρ was assigned a uniform prior on [-1,1]. Following Gelman and Hill (2007), the random effect variances σ!, σ!"#, σ!"#, and σ!! were assigned half-cauchy prior distributions with scale 25 and 1 degree of freedom. The residual variance σ! in the abundance model was assigned a uniform prior on [0,100]. We obtained very similar results using other common prior distributions for the random effect variances. Both models were run long enough to ensure mixing of 2 independent chains, and no auto-correlation in sequential posterior samples. To quantify the interspecific variation in slopes explained by functional traits, we define a partial R 2 for µ 10 and N saff respectively as γ PAR μ10 var(μ 10 ) γ PAR μ10 var μ 10 +σ PAR 2 and 45 γ nit N var(n saff ) γ nit N var(n saff )+σ nit 2, where var(μ!") is the variance across species in µ 10 and var(n!"## ) is the 2
46 47 48 variance across species in N saff. These are partial R 2 estimates because quantify the proportion of variance in slopes explained by the focal traits, after removing the variance explained by the lower-order µ max interaction terms. R 2 for µ max is calculated as 49 γ n P μmax var(μ max ) γ n P μmax var μ max +σ n P 2. 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 3
Table S1. Sources for functional traits. Species Data sources Asterionellopsis glacialis 7,23,26,27 Alexandrium tamarense 5,16,20,28,29 Coscinodiscus wailesii 7,25,35 Ditylum brightwellii 6,7,30,31 Emiliania huxleyi 7,8,12,19,22,32 Eucampia zodiacus 11,21,24,33 Gymnodinium catenatum 18,34 Nitzschia closterium 1,2,15,38 Prorocentrum micans 13,37 Pseudo-nitzschia pungens 3,36 Skeletonema costatum 4,7,9,10,14,15,16,17,27,28,39,40 Trait Source References 1. Admiraal, W., & Werner, D. Utilization of limiting concentrations of ortho-phosphate and production of extracellular organic phosphates in cultures of marine diatoms. J. Plankton Res. 5, 495-513, (1983). 2. Carpenter, E. J., Phosphorus requirements of two planktonic diatoms in steady state culture. J. Phycol. 6, 28-30 (1970). 3. Cheng, Z., & Jingzhong, Z. Nutrient uptake kinetics and growth under nutrient limitation of Pseudo-nitzschia. Oceanol. Limnol. Sinica 28, 599-603 (1997). 4. Conway, H.L., & Harrison P.J., Marine diatoms grown in chemostats under silicate or ammonium limitation. 4. Transient response of Chaetoceros debilis, Skeletonema costatum, and Thalassiosira gravida to a single addition of limiting nutrient. Mar. Biol. 43, 33-43 (1977). 4
5. Davidson, K., & Gurney, W.S.C., An investigation of non-steady-state algal growth. II. Mathematical modelling of co-nutrient-limited algal growth. J. Plankton Res. 21, 839-858 (1999). 6. Eppley, R.W., & Coatsworth, J.l. Uptake of nitrate and nitrite by Ditylum brightwellii: kinetics and mechanisms. J. Phycol. 4, 151-156 (1968). 7. Eppley, R.W., Rogers J.N., & Mccarthy J.J., Half-saturation constants for uptake of nitrate and ammonium by marine phytoplankton. Limnol. Oceanogr. 14, 912-920 (1969). 8. Flynn, K.J., Page S., Wood G., & Hipkin C.R., Variations in the maximum transport rates for ammonium and nitrate in the prymnesiophyte Emiliania huxleyi and the raphidophyte Heterosigma carterae. J. Plankton Res. 21, 355-371 (1999). 9. Harrison, P.J., Conway, H.L., & Dugdale, R.C., Marine diatoms grown in chemostats under silicate or ammonium limitation. 1. Cellular chemical composition and steady-state growth kinetics of Skeletonema ostatum. Mar. Biol. 35, 177-186 (1976). 10. Harrison, P.J., Conway, H.L., Holmes, R.W., & Davis, C.O., Marine diatoms grown in chemostats under silicate or ammonium limitation. 3. Cellular chemical composition and morphology of Chaetoceros debilis, Skeletonema costatum, and Thalassiosira gravida. Mar. Biol. 43, 19-31 (1978). 11. Nishikawa, T., Tarutani, K. & Yamamoto, T., Nitrate and phosphate uptake kinetics of the harmful diatom Eucampia zodiacus Ehrenberg, a causative organism in the bleaching of aquacultured Porphyra thalli. Harmful Algae 8, 513-517 (2009). 12. Page, S., Hipkin, C.R., & Flynn, K.J., Interactions between nitrate and ammonium in Emiliania huxleyi. J. Exp. Mar. Biol. Ecol. 236, 307-319 (1999). 5
13. Qi, Y.Z., & Zhu, C.J., A comparative study of nitrate uptake kinetics by two red tide causative algae. Asian Mar. Biol. 11, 103-106 (1994). 14. Romeo, A.J., & Fisher, N.J., Intraspecific comparisons of nitrate uptake in three marine diatoms. J. Phycol. 18, 220-225 (1982). 15. Shuter, B.J. Size dependence of phorphorus and nitrogen subsistence quotas in unicellular microorganisms. Limnol. Oceanogr 23, 1248-1255 (1978). 16. Smayda, T.J. Harmful algal blooms: Their ecophysiology and general relevance to phytoplankton blooms in the sea. Limnol. Oceanogr. 42, 1137-1153 (1997). 17. Tarutani, K., & Yamamoto, T., Phosphate uptake and growth kinetics of Skeletonema costatum isolated from Hiroshima Bay. Journal of the Faculty of Applied Biological Science Hiroshima University 33, 59-64 (1994). 18. Yamamoto, T., Oh, S.J., & Kataoka Y., Growth and uptake kinetics for nitrate, ammonium and phosphate by the toxic dinoflagellate Gymnodinium catenatum isolated from Hiroshima Bay, Japan. Fish. Science 70, 108-115 (2004). 19. Benson, B.C., & Rusch, K.A., Investigation of the light dynamics and their impact on algal growth rate in a hydraulically integrated serial turbidostat algal reactor (HISTAR). Aquacultural Engineering 35,122-134 (2006) 20. Johnston, A.M., The effect of environmental variables on 13C discrimination by two marine phytoplankton. Mar. Ecol. Progr. Series. 132, 257-263 (1996). 21. Lewis, N.I., Bates, S.S., Mclachlan, J.L., & Smith, J.C. Temperature effects on growth, domoic acid production, and morphology of the diatom Nitzschia pungens f. multiseries, p. 601-606. In Toxic Phytoplankton Blooms in the Sea [eds. Smayda, T.J., & Shimizu, Y.]. Elsevier Science (1993). 6
22. Litchman, E., Growth rates of phytoplankton under fluctuating light. Freshwater Biology 44, 223-235 (2000). 23. Müller, V.H., Wachstum und phosphatbedarf von Nitzschia actinastroides (Lemm.) v. Goor statischer und homokontinuierlicher kultur unter phosphatlimitierung. Archiv für Hydrobiologie. Supplement 38, 399-484 (1971). [Growth and phosphate needs of Nitzschia actinastroides (Lemm.) v. Under static and homogeneous continuous culture under phosphate limitation] 24. Seguel, M.R. Interactive effects of temperature-light and temperature-salinity on growth of five phytoplanktonic species isolated from a shallow-water embayment of Nova Scotia. M.Sc. thesis, Acadia University, Wolfville, NS (1991). 25. Nishikawa, T., Tarutani, K., & Yamamoto, T., Nitrate and phosphate uptake kinetics of the harmful diatom Coscinodiscus wailesii, a causative organism in the bleaching of aquacultured Porphyra thalli. Harmful Algae 9, 563-567 (2010). 26. Kain, J.M., & Fogg, G.E., Studies on the growth of marine phytoplankton. J. Mar. Biol. Ass. U.K., 37, 397-413 (1958). 27. Shikata, T., et al., Effects of temperature, salinity and light irradiance on phytoplankton growth in the Yatsushiro Sea. Nippon Suisan Gakkaishi 76, 34-45 (2010). 28. Langon, C., On the causes of interspecific differences in the growth-irradiance relationship for phytoplankton. Part I. A comparative study of the growth-irradiance relationship of three marine phytoplankton species: Skeletonema costatum, Olisthodiscus luteus, and Gonyaulax tamarensis. J. Plankton Res. 9, 459-482 (1987). 7
29. Parkhill, J., & Cembella, A.D., Effects of salinity, light, and inorganic nitrogen on growth an toxigenicity of the marine dinoflagellate Alexandrium tamarense from northeastern Canada. J. Plankton Res., 21, 939-955 (1999). 30. Brussaard, C.P.D., Noordeloos, A.A.M., & Riegman, R., Autolysis kinetics of the marine diatom Ditylum brightwellii (Bacillariophyceae) under nitrogen and phosphorus limitation and starvation. J. Phycol. 33, 980-987 (1997). 31. Brand, L.E., & Guillard, R.R.L., The effects of continuous light and light intensity on the reproduction rates of twenty-two species of marine phytoplankton. J. exp. Mar. Biol. Ecol. 50, 119-132 (1981). 32. Nielsen, M.V., Growth, Dark respiration and photosynthetic parameters of the coccolithophorid Emiliania huxleyi (Prymnesiophyceae) acclimated to different day length-irradiance combinations. J. Phycol. 33, 818-822 (1997). 33. Nishikawa, T., & Yamaguchi, M., Effect of temperature on light-limited growth of the harmful diatom Eucampia zodiacus Ehrenberg, a causative organisms in the discoloration of Porphyra thalli. Harmful Algae, 5, 141-147 (2006). 34. Yamamoto, T., Oh, S.J., & Kataoka, Y., Effects of temperature, salinity and irradiance on the growth of the toxic dinoflagellate Gymnodinium catenatum (Dinophyceae) isolated from Hiroshima Bay, Japan. Fish. Science, 68, 356-363 (2002). 35. Nishikawa, T., & Yamaguchi. M., Effect of temperature on light-limited growth of the harmful diatom Coscinodiscus wailesii, a causative organism in the bleaching of aquacultured Porphyra thalli. Harmful Algae 7, 561-566 (2008). 36. Xu, N., et al., Effects of temperature, salinity and irradiance on the growth of the harmful dinoflagellate Prorocentrum donghaiense Lu. Harmful Algae, 9, 13-17 (2010). 8
37. Falkowski, P.G., Dubinsky, Z., & Wyman, K., Growth-irradiance relationships in phytoplankton. Limnol. Oceanogr., 30, 311-321 (1985). 38. Maddux, W.S., & Jones, R.F., Some interactions of temperature, light intensity, and nutrient concentration during the continuous culture of Nitzschia closterium and Tetraselmis sp. Limnol. Oceanogr. 9, 79-86 (1964). 39. Yoder, J.A., Effect of temperature on light-limited growth and chemical composition of Skeletonema costatum (Bacillariophyceae). J. Phycol. 15, 362-370 (1979). 40. Oh, S.J., et al., Effects of irradiance of various wavelengths from light-emitting diodes on the growth of the harmful dinoflagellate Heterocapsa circularisquama and the diatom Skeletonema costatum. Fish. Science 74, 137-145 (2008). 9
Figure S1. Time series of (A) nitrate, at ~weekly or biweekly intervals; (B) nitrate, averaged by month; (C) incident PAR, at daily intervals, (D) mixed layer depth, at ~weekly or biweekly intervals, and (E) mean mixed-layer PAR, averaged by month. Nitrate (µmol L 1 ) 15 10 5 0 A 2002 2004 2006 2008 2010 Nitrate (µmol L 1 ) 10 8 6 4 2 0 B Date 2002 2004 2006 2008 2010 Einsteins m 2 d 1 50 40 30 20 10 C Index 2002 2004 2006 2008 2010 10 D Index Meters 30 50 2002 2004 2006 2008 2010 Einsteins m 2 d 1 30 25 20 15 10 5 0 E Date 2002 2004 2006 2008 2010 10
Figure S2. Distribution of mean density for all species in the L4 dataset (A), and for the 11 species in the current analysis (B). 11
Figure S3. Observed and predicted probabilities of occurrence as a function of PAR, for the 11 species in the occurrence model. PAR is divided into five equal quantiles, on a log scale. Black points are empirical proportions of occurrence in each quantile. Blue points are model predictions for the probability of occurrence in each quantile; for each sampling date in the model, predicted probability of presence is calculated using eqns. 3 and 4, and the posterior means for each parameter. These predictions are then divided according to the PAR quantiles and averaged to produce the blue points. The same procedure is used with 1,000 MCMC samples to calculated a 95% HPD credible interval, shown with error bars. 12
Figure S4. Scatterplots of partial residuals vs. nitrate for the 8 species in the abundance model. Partial residuals are calculated as r!! = ν!!!! + β!"# nit!, where r! is the partial residual for species i at time t, ν!! is the posterior mean of the autocorrelation-corrected! residual for species i at time t, β!"# is the posterior mean of the slope vs. nitrate for species i (see eqn. 3), and nit! is nitrate at time t. The partial residual plots show the relationship between a species abundance and nitrate, including residual variation, while accounting for the other predictors in the model. Blue lines are 100 samples from the! posterior distribution of β!"#. 13
Figure S5. Scatterplots of partial residuals vs. nitrate*par for the 8 species in the abundance model. Partial residuals are calculated as r!! = ν!!!! + β!! nitpar!, where r! is the partial residual for species i at time t, ν!! is the posterior mean of the autocorrelation-! corrected residual for species i at time t, β!! is the posterior mean of the slope vs. nitrate*par for species i (see eqn. 3), and nitpar! is nitrate*par at time t. The partial residual plots show the relationship between a species abundance and nitrate*par, including residual variation, while accounting for the other predictors in the model. Blue! lines are 100 samples from the posterior distribution of β!!. 14
Figure S6. Time series of biovolume, averaged by month, for the 11 species in the analysis. Vertical dotted lines are at January 1 in each year. 15
Figure S7. Autocorrelation of Pearson residuals at lags 0-3 for the occurrence model. (A) without a term for lag-1 presence, and (B) with a term for lag-1 presence. Error bars are 95% HPD credible intervals. 16
Figure S8. Autocorrelation of adjusted residuals at lags 0-3 for the abundance model. (A) using the uncorrected residuals, ε!! in eqn. 4; (B) using the residuals accounting for autocorrelation, ν!! in eqn. 4. Error bars are 95% HPD credible intervals. 17