Supporting Information Figure Legends Figure S1. Effect of temperature on the size scaling of growth rate for the whole dataset from Thomas et al.’s (2012). Similar to Fig. 3 but without restricting to only those species that have been sequenced. Panels on the left show the size scaling of growth (log10 transformed) for predicted growth rates at (a) 30ºC and (b) 12ºC. Grey dots show all data points whereas colors dots show the corresponding averaged growth rates for each size bin as used in the colour matrix plot (c). The black solid line corresponds to a linear fit. The black dashed line corresponds to a quadratic fit. Linear fit in (a): log10() = 0.04 x log10(BV) -0.51; ANOVA: r2= 0.003, n = 100, p-value = 0.57. Linear fit in (b): log10() = -0.11 x log10(BV) -0.13; ANOVA: r2= 0.09, n = 141, p-value < 0.001. Quadratic fits are shown in the panels. (c) The colour matrix shows for each temperature from 2 to 33ºC (y axis) the averaged growth rate at each cell size bin (x axis). The p-value column shows the degree of significance of the quadratic fit for the log10- log10 relationship between growth rate and cell size using all data points (no data binning). When the quadratic term is not significant, i.e. p-value>0.05 the box appears empty. (*) indicates p-value<0.05, (**) indicates p-value<0.01 and (***) pvalue<0.001. The right panel shows the ratio between the r-squared of the quadratic term and the r-squared of the linear term for the different fits at each temperature, i.e., the proportional increase in explained variance of the quadratic fit in relation to the linear fit. Figure S2. Size scaling of growth rate for those species with optimum temperatures between 23 and 28ºC in Thomas et al.’s (2012) data (big grey dots). The black solid line corresponds to a linear fit (log10() = 0.005 x log10(BV) -0.41 ANOVA: r2= 0.001, n = 43, p-value = 0.83). The black dashed line correspond to a quadratic fit (log10() = -0.04 x [log10(BV)]2 + 0.14 x log10(BV) -0.38; ANOVA: r2= 0.22, n = 43, p-value < 0.005). Small grey dots on the background show the whole dataset. 1 Figure S3. Size scaling of growth rate for López-Urrutia et al.’s (2006) data (as used by Chen and Liu (2011)) to demonstrate the existence of unimodal scaling. Here several measurements of growth rate at different temperatures are provided for each species together with cell volume. The difference between Thomas et al. (2012) and López-Urrutia et al. (2006) is that the latter only considers the exponential part of the growth response to temperature and includes also the effects of irradiance. Following the same procedure as for Thomas et al. (2012), we restricted the dataset to only those species that have been sequenced and averaged thermal responses were calculated for each strain in the case we had several thermal growth response curves recorded. Hence, the dataset was reduced from 1063 to 49 data points, one for each sequenced strain. Black solid line is the linear fit (log10() = -0.03 x log10(BV) + 5.10; ANOVA: r2 = 0.04, n = 49, p-value = 0.17), black dashed line is quadratic fit (log10() = -0.02 x [log10(BV)]2 +0.10 x log10(BV) +4.97; ANOVA: r2 = 0.17, n = 49, p-value < 0.01), grey solid line is the linear PGLS fit (log10() = -0.06 x log10(BV) + 4.96, p-value < 0.01, λ=0.92) and grey dashed line is the quadratic PGLS fit (log10() = -0.02 x [log10(BV)]2 + 0.06 x log10(BV) +4.95, p-value =0.06 ,λ=0.91). Grey dots show species composing the picophytoplankton. Figure S4. Phylogenetic tree for Thomas et al.’s (2012) data. Figure S5. Phylogenetic tree for López-Urrutia et al.’s (2006) data. 2 Table 1: Cell size references for the species used in the study for the compilation of Thomas et al. (2012). Species Name Akashiwo sanguinea Alexandrium catenella Alexandrium fundyense Alexandrium minutum Alexandrium monilatum Alexandrium ostenfeldii Alexandrium tamarense Amphiprora sp. Apedinella radians Asterionellopsis glacialis Calcidiscus leptoporus Chaetoceros didymus Chaetoceros lorenzianus Bermuda Chaetoceros pseudocurvisetus Chaetoceros sp. Chattonella marina Chattonella marina var. antiqua Chlamydomonas Chlorella sp. Chrysochromulina polylepis Coccolithus pelagicus ssp. Braarudii Cochlodinium polykrikoides Conticribra guillardii Corethron pennatum Cryptomonas sp. Cylindrotheca closterium Dactyliosolen fragilissimus Detonula confervacea Dunaliella tertiolecta Emiliania huxleyi Eucampia zodiacus Eutreptiella gymnastica Fibrocapsa japonica Fragilariopsis cylindrus Fragilariopsis kerguelensis Gephyrocapsa oceanica Gephyrocapsa oceanica var. typica Gymnodinium aureolum Gymnodinium catenatum Gymnodinium corollarium Gymnodinium (probably G. simplex) Helicotheca tamesis Heterocapsa rotundata Heteromastix pyriformis Heterosigma akashiwo Isochrysis galbana Isochrysis sp. Karenia brevis Source Olenina et al. (2006) http://species-identification.org http://species-identification.org Marañón et al. (2013) http://species-identification.org Olenina et al. (2006) Marañón et al. (2013) Olenina et al. (2006) Olenina et al. (2006) Olenina et al. (2006) Marañón et al. (2013) Olenina et al. (2006) Olenina et al. (2006) Leblanc et al. Leblanc et al. (2012) http://www.eos.ubc.ca/research/phytoplankton Band-Schmidt et al. (2012) Band-Schmidt et al. 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Neoceratium furca Neoceratium fusus Neoceratium lineatum Neoceratium tripos Nitzschia frigida Nitzschia paleacea Odontella mobiliensis Olisthodiscus luteus Peridinium sp. Phaeocystis antarctica Phaeocystis globosa Phaeocystis pouchetii Phaeodactylum tricornutum Prochlorococcus marinus Prorocentrum gracile Prorocentrum micans Prorocentrum minimum Prymnesium parvum f. patelliferum Prymnesium parvum Pseudo-nitzschia multiseries Pseudopedinella pyriformis Pyramimonas disomata Pyrodinium bahamense var. compressum Rhizosolenia setigera Scrippsiella trochoidea Skeletonema ardens Skeletonema costatum Skeletonema japonicum Skeletonema marinoi dohrnii complex Skeletonema menzelii Skeletonema pseudocostatum Skeletonema tropicum Stellarima microtrias Stephanopyxis palmeriana Stichococcus (possibly S. cylindricus) Synechococcus Synedra sp. Tetraselmis sp. Thalassionema nitzschioides Thalassiosira nordenskioeldii Thalassiosira pseudonana Thalassiosira rotula Trichodesmium erythraeum Source http://nordicmicroalgae.org Galimany et al. (2007) Škaloud (2006) http://nordicmicroalgae.org http://nordicmicroalgae.org https://ncma.bigelow.org http://nordicmicroalgae.org http://nordicmicroalgae.org http://nordicmicroalgae.org http://nordicmicroalgae.org Olenina et al. (2006) Olenina et al. (2006) Olenina et al. (2006) Leadbeater (1969) http://diatom.ansp.org/taxaservice/ShowList.aspx Zingone (1999) Olenina et al. (2006) Olenina et al. (2006) Marañón et al. (2013) Marañón et al. (2013) Marañón et al. (2013) Olenina et al. (2006) Olenina et al. (2006) Green et al. (1982) Green et al. (1982) http://diatom.ansp.org/taxaservice/ShowList.aspx http://www.smhi.se http://www.smhi.se http://species-identification.org Olenina et al. (2006) Olenina et al. (2006) https://ncma.bigelow.org Marañón et al. 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