Supplementary Materials for

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1 Supplementary Materials for Direct quantification of energy intake in an apex marine predator suggests physiology is a key driver of migrations Rebecca E. Whitlock, Elliott L. Hazen, Andreas Walli, Charles Farwell, Steven J. Bograd, David G. Foley, Michael Castleton, Barbara A. Block This PDF file includes: Published 11 September 2015, Sci. Adv. 1, e (2015) DOI: /sciadv Fig. S1. Spatial plot of the data set analyzed in this paper by month. Fig. S2. Raw data (visceral temperature, red line; ambient temperature, blue line) trace from an archival tagged Pacific bluefin tuna. Fig. S3. Raw data (visceral temperature, red line; ambient temperature, blue line) trace from a second archival tagged Pacific bluefin tuna. Fig. S4. Tracks with estimated median HIF (kcal day 1 ) for two archival tagged Pacific bluefin tuna. Fig. S5. Correlates of average daily energy intake (kcal) in tagged Pacific bluefin tuna. Fig. S6. HIF in relation to SST, latitude, and chl-a. Fig. S7. Predicted values for weekly mean thermal excess ( C) plotted by quarter from the final GAMM fitted to thermal excess data between 2002 and 2009 (data from 144 archival tagged Pacific bluefin tuna with 5961 weekly values of thermal excess). Fig. S8. Patterns of habitat use and energy intake by length for archival tagged Pacific bluefin tuna between 2002 and Fig. S9. Physiological responses to ambient temperature with mean energy intake. Fig. S10. Boxplot of posterior predictive probability distributions for estimated energy intake (kcal) for three archival tagged Pacific bluefin tuna in the feeding experiment (22). Fig. S11. Histograms of HIF magnitude observations. Fig. S12. Estimated smooth terms from the GAMM for feeding success in archival tagged Pacific bluefin tuna.

2 Fig. S13. Predicted feeding success between September 2002 and August 2003 from the binomial GAMM for a subset of archival tagged Pacific bluefin tuna (23 tagged individuals, 6705 observations) released in August Fig. S14. Predicted HIF magnitude (conditional on feeding on a given day) between September 2002 and August 2003 from the Gamma GAMM for a subset of archival tagged Pacific bluefin tuna (23 tagged individuals, 6212 observations) released in August Fig. S15. GAMM-predicted values from the delta-gamma model for HIF magnitude (combining predictions of feeding success and HIF magnitude) between September 2002 and August 2003 for a subset of archival tagged Pacific bluefin tuna (23 tagged individuals, 6212 observations) released in August Table S1. Proximate analysis of sardine and anchovy used as feeds for captive tuna, reproduced from Farwell (43). Table S2. Priors in the hierarchical Bayesian regression model. Table S3. Wilcoxon rank sums (from two-sided tests) for size-based differences in latitude, SST, and HIF. Table S4. Correlates of thermal excess. References (36 43)

3 Supplementary Figures Figure S1. Spatial plot of the data set analyzed in this paper by month. Each yellow circle marks one daily geolocation point for an archival-tagged Pacific bluefin tuna.

4 Figure S2. Raw data (visceral temperature, red line; ambient temperature, blue line) trace from an archival tagged Pacific bluefin tuna. Panels A-C show one year of data (1 st January to 31 st December 2003), while panels D-F show one week of data from the corresponding 4-month period plotted in A-C. The green line shows the model predicted baseline visceral temperature (i.e. with no feeding), while the grey shaded area indicates HIF area as quantified by the model. This individual was at approximately 29 N at during the first period with few feeding events (8 th to 25 th August); it reached a latitude of 38 N in mid-september, having been at 23 N in early June. The second period with little feeding is associated with a southward movement the individual was at 38 N on 28 th October, and moved south to N, where few feeding events were observed (13 th -30 th November) after this, it moved north again, reaching 34 N by mid-december.

5 Figure S3. Raw data (visceral temperature, red line; ambient temperature, blue line) trace from a second archival tagged Pacific bluefin tuna. Panels A-C show one year of data (1 st January to 31 st December 2003), while panels D-F show one week of data from the corresponding 4-month period plotted in A-C. The green line shows the model predicted baseline visceral temperature (i.e. with no feeding), while the grey shaded area indicates HIF area as quantified by the model. Periods with few feeding events occurred between 9 th and 22 nd August, when the fish was migrating northwards (between 30 N and 32 N) and between 1 st and 16 th November, again between approximately 30 N and 32. Prior to this (mid-october) the fish was at 35 N; it moved northwards again in late November, reaching 33 N by the end of November.

6 Figure S4. Tracks with estimated median HIF (kcal day -1 ) for two archival tagged Pacific bluefin tuna. Panels A and B show daily median HIF (kcal) between April and October in 2003 (A) and 2004 (B) for the same individual. Panels C and D show daily median HIF (kcal) between April and October in 2003 (C) and 2004 (D) for a second tagged individual. Latitudes for the first HIF in April are between 24.6 N and 24.8 N in all panels (i.e. fish are moving northwards). The radius of the

7 circles is proportional to estimated median HIF magnitude on a given day. HIF magnitude is also indicated by the colour scale. Figure S5. Correlates of average daily energy intake (kcal) in tagged Pacific bluefin tuna. Estimated response curves (smooth terms) and year effects from the final generalized additive mixed model. Panel (A) eddy kinetic energy; (B) relative light level; (C) day of the year; (D) year. Dashed lines represent 95% confidence limits. Vertical axes in A-D are partial responses (estimated, centered smooth functions) on the scale of the linear predictor.

8 Figure S6. HIF in relation to SST, latitude, and chl-a. (A) Latitudinal distribution of tagged bluefin tuna in the California Current. Top, latitude versus date with mean daily SST ( C) recorded by the tags indicated by the colour scale. Centre, Hovmöller plot for predicted daily energy intake (kcal) from 2003 to Bottom, Hovmöller plot for the logarithm of the median daily chlorophyll-a concentration (mg m -3 ) from the SeaWifs and MODIS sensors. The solid black line in each panel denotes median latitude, while the dashed lines show the 2.5th and 97.5th percentiles for the latitudinal distribution. (B) Median plus 2.5 and 97.5 percentiles for SST (obtained from archival tags) over the course of the year.

9 Figure S7. Predicted values for weekly mean thermal excess ( C) plotted by quarter from the final GAMM fitted to thermal excess data between 2002 and 2009 (data from 144 archival tagged Pacific bluefin tuna with 5961 weekly values of thermal excess). (A) September to November (B) December to February (C) March to May (D) June to August.

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11 Figure S8. Patterns of habitat use and energy intake by length for archival tagged Pacific bluefin tuna between 2002 and (A) Utilisation densities for archival tagged Pacific bluefin tuna in the California Current in February - solid line, 50% density contour; dashed lines, 10% and 90% density contours. (B) Observed energy intake (interpolated and smoothed for visualisation) by time and latitude in January and February. (C) Utilisation densities for archival tagged Pacific bluefin tuna in the California Current in October - solid line, 50% density contour; dashed lines, 10% and 90% density contours. (D) Observed energy intake (interpolated and smoothed for visualisation) by time and latitude October and November. In each panel, age increases from left to right: left, age 2.5 years and younger; centre, age years; right older than 3.5 years.

12 Figure S9. Physiological responses to ambient temperature with mean energy intake. Black, rate of oxygen consumption, MO2, of bluefin tuna swimming at a constant speed of 1.0 body length per second (mg kg -1 h -1, mean ± 1 SD, N=6); grey (with dashed line), heart rate [beats min -1, mean ± 1 SE, N=4 (10, 20, 25 ), N=6 (15 )]; orange, energy intake (kcal) in wild bluefin tuna, mean +/- 1 SE. The histogram shows the number of days spent by archival tagged Pacific bluefin tuna in each 1 C temperature bin (N=39,387 days).

13 Figure S10. Boxplot of posterior predictive probability distributions for estimated energy intake (kcal) for 3 archival tagged Pacific bluefin tuna in the feeding experiment 22. Each box summarises the posterior predictive distribution for one feeding; horizontal lines through the centre of each box denote the median, while the ends of the box denote the upper and lower quartiles. Whiskers denote the 95% probability interval. Feedings are shown in order of ascending estimated energy intake. Blue boxes, normal observation model 22 ; black boxes, lognormal observation model (this study). Supplementary Methods Hierarchical Bayesian regression model (HBM) We apply a slightly modified version of the hierarchical Bayesian model (HBM) to quantify the relationship between meal energy and HIF area 22 that uses a lognormal observation model to estimate daily HIF magnitude as a function of peritoneal and ambient temperature in wild Pacific bluefin tuna. Prior distributions (summarising knowledge about the parameter before making

14 experimental observations) for parameters whose prior is not given below can be found in Supplementary Table S2. In the equations that follow, Normal distributions are parameterized in terms of mean and variance. Equations are given on a logarithmic scale unless otherwise stated. Vague normal priors were placed on the means of the population level priors for regression coefficients for squid and sardine feeds at 20 C: S [20] ~ Normal (0,5 ), S [20] ~ Normal (0,5 ), where ~ means is distributed as, 1 [20] denotes the mean of the population level prior for squid feeds at 20 C and 2 [20] denotes the mean of the population level prior for sardine feeds at 20 C. Individual level regression coefficients at 20 C were assumed to arise from a common (population level) normal distribution with means given above and food type-specific standard deviations: 2 S3. 1,i Normal [20] 1 [20] 1, [20] ~ (, ), 2 S4. 2, i Normal [20] 2 [20] 2 [20] ~ (, ),

15 where 1, i[20] is the squid feed regression coefficient for individual i at 20 C and 2, i [20] is the 2 2 sardine feed regression coefficient for individual i at 20 C. and are the variances of the [20] [ 20] population level priors for log-scale regression coefficients at 20 C, for squid and sardine feeds respectively. 1, 2, A vague normal prior was placed on the mean of the population level prior for the ratio of the slope of kcal/hif magnitude at 20 C to the slope of kcal/hif magnitude at 15 for squid feeds, : 1,1 2 S5. ~ Normal (0,3.16 ), 1,1 Log-scale individual level priors for temperature effect parameters for squid feeds (slopes at 15 C relative to 20 C), i,1,1, were assumed to arise from a common (population level) normal distribution with mean given above:, 2 S6. i,1,1 ~ Normal (, ) 1,1 where i,1,1 is the temperature effect parameter for individual i for squid feeds at 15 C relative to 2 20 C and is the variance of the population level prior for the temperature effect parameter for squid feeds at 15 C relative to 20 C. Priors for the individual level temperature effect parameters for squid feeds at 22 C relative to 20 C were specified relative to those for 15 C relative to 20 C as:

16 , S7. i,1,2 i,1,1 where i,1,2 is the temperature effect parameter for individual i for squid feeds at 22 C relative to 20 C and: S8. 2 ~ Normal (0,31.62 ). Similarly, priors for log-scale temperature effect parameters for sardine feeds were specified relative to the log-scale temperature effect parameters for squid feeds:, S9. i,2,1 i,1,1 1, S10. i,2,2 i,1,2 2 where i,1,2 is the temperature effect parameter for individual i for sardine feeds at 15 C relative to 20 C and i,2,2 is the temperature effect parameter for individual i for sardine feeds at 22 C relative to 20 C. γ parameters were given vague normal priors (Table S2). Priors for log-scale individual level regression coefficients at 15 C and 22 C were expressed relative to the log-scale individual level coefficient priors at 20 C (equations S11 to S14):

17 S11. 1, [15] 1,i [20],1,1 log( ), i i S12. 1, [22] 1,i [20],1,2 log( ), i i S13. 2,i [15] 2,i [20] i,2,1 log( ), S14. 2,i [22] 2,i [20] i,2,2 log( ), Predicted meal energy (kcal) for squid and sardine feeds, respectively, is then given by: yˆ log( ), S15. 1, i, j, k 1, i, k 1, i, j, k yˆ log( ), S16. 2, i, j, k 2, i, k 2, i, j, k where 1, i, j, k is HIF magnitude ( C hours) for squid feed j for individual i at temperature level k and y ˆ1, i, j, k is the log-scale predicted meal energy in kcal for squid feed j for individual i at temperature level k (equation S15) and analogously for sardine feeds (equation S16). k=1 denotes feedings at 15 C;. k=2 denotes feedings at 20 C and k=3 denotes feedings at 22 C. Log-transformed measured meal energy values (kcal) for squid and sardine were assumed to be normally distributed around the predicted energetic value for a given individual, food type and tank temperature:

18 S17. log( y ) ~ Normal ( yˆ, ), 2 1, i, j, k 1, i, j, k obs,1 S18. log( y ) ~ Normal ( yˆ, ), 2 2, i, j, k 2, i, j, k obs,2 where y 1, i, j, k is the measured caloric value of squid feed j for fish i at temperature level k, and y 2, i, j, k is the measured caloric value of sardine feed j for fish i at temperature level k. 2 obs,2 are observation error variances for squid and sardine feeds, respectively. 2 obs,1 and To obtain an estimate of energy intake in a wild juvenile Pacific bluefin tuna for which no experimental observations are available, the posterior predictive distribution is used. The posterior predictive distribution can be obtained by sampling random effect parameters from their respective distributions, given the posteriors for hyperpriors, e.g. assuming a diet of sardine: 2 S19. 2, i Normal [20] 2 [20] 2 [20] ' ~ (, ), 2 S20. ' i,1,1 ~ Normal (, ) 1,1, ' ', S21. i,2,1 i,1,1 1 ' ', S22. i,2,2 i,1,1 2 where the prime sign indicates a new individual i. The resulting sampled parameters can then be used to obtain the regression coefficient for a given measured SST:

19 ' ' (1 I ) ' (19.9 SST ) I ' ( SST 19.9), S23. 2, i SST 2, i [20] T i,2,1 T i,2,2 where IT is an indicator variable taking a value of 0 for SST 19.9 C and 1 for SST> 19.9 C. The SSTspecific regression coefficient for a new individual ( 2, i used to predict (log) energy intake (kcal) for HIF event j: ' SST ) and the observed HIF magnitude are yˆ ' log( ). S24. 2, i, j SST 2, i SST i, j The posterior predictive distribution for energy intake (kcal) (assuming a diet of sardine) takes into 2 account the estimated observation error variance, obs,2: S25. log( y ) ~ Normal ( yˆ, ). 2 2, i, j SST 2, i, j SST obs,2 Assumptions about diet in wild Pacific bluefin tuna The results presented in this paper assume a diet of sardines (Sardinops sagax) or forage fish of similar nutritional composition 22,36. While the use of one food type is a simplification, sardines have been found to comprise the main food item for Pacific bluefin tuna in the eastern Pacific Ocean in an earlier study 36. Analysis of the stomach contents of 650 Pacific bluefin tuna

20 caught off southern California and Baja Califonia between 1968 and 1969 showed that forage fish constitute 91.8% by number and 93.1% by volume of all food consumed 36. Northern anchovy (Engraulis mordax) was the most important food item, comprising 86.6% by number and 80.0% by volume of the bluefin diet 36, while cephalopods comprised 3.88% by number and 2.16% by volume. S. Sagax and E. mordax are comparable in terms of their nutritional compositions (Table S1). A study from 2007 hypothesized that Pacific bluefin tuna in the eastern Pacific would primarily have consumed S. sagax in recent years 9. This was based on observations from a tagging cruise in 2002, which revealed that most of the bluefin tuna had Pacific sardines in their stomachs 9. In a more recent study Pacific bluefin tuna were found to show a high degree of omnivory, with a trophic group containing S. sagax making up around a third of the diet, although the seasonal and spatial coverage of this study was more limited 36,37. Assuming a fixed proportion of squid (or other prey items with differing nutritional values) and sardine in the diet across regions and seasons would not be expected to lead to different predictions about relative energy intake in time and space, although absolute values would change. More problematic is the possibility that juvenile bluefin exploit different prey resources in different areas of their distribution. Differences in prey energy content alone would not be expected to lead to marked differences in predictions, as we accounted for the caloric densities of food items in the laboratory experiments used to estimate the relationship between energy intake and HIF 22. However, if Pacific bluefin switch between prey items with markedly differing protein contents in different areas of their distribution, our model may under- or over- estimate HIF in some regions. Seasonal collection of stomach content samples at a range of locations would allow development of the model to accommodate this behavior.

21 GAMM for daily HIF Appropriate error distributions for response variables (estimated daily energy intake and thermal excess) were selected by plotting histograms and then using maximum likelihood methods to select among suitable candidate distributions for the resulting frequency distribution. Inspection of the daily HIF data revealed a fairly high proportion of days with no feeding (i.e. zero-inflated data, Figure S11), suggesting that a two-step modeling approach was appropriate. We chose to combine a Bernoulli model for the presence or absence of HIF on a given day with a suitable model for HIF magnitude (conditional on a non-zero observation). For purposes of analysis, days with total HIF of 50 kcal or less were also counted as non-feeding days or zeros. A gamma density was found to be a suitable error distribution for positive-valued HIFs on the basis of likelihoods computed for different parametric distributions (Figure S11), so that the overall model for the distribution is a Delta-Gamma model 38. The likelihood for all HIF observations is given by (equation S26): S26. L(y) (1 p) n m p m y 0 y e ( r)( / r) r 1 ry/ r where Ly ( ) denotes the likelihood of the data, n denotes the total number of data, and m denotes the number of successes in the binomial distribution (here, the number of days with HIF events). The gamma density is expressed in term of its mean and shape parameter r. To implement this error structure in Generalized Additive Mixed Models, a binomial GAMM with logit link was used to model the numbers of zero and non-zero data, and a GAMM with Gamma

22 distributed error and a log link was used to model positive valued data. Fitted mean values for a given set of covariates can then be obtained by multiplying the probability of feeding (p) from the binomial GAMM with predicted HIF magnitude, conditional on feeding ( ) from the Gamma GAMM Figure S11. Histograms of HIF magnitude observations. (A) all observations. (B) positive-valued observations, with parametric distributions fitted by maximum likelihood indicated; red, gamma distribution; blue, lognormal distribution. We applied GAMMs to the daily feeding success and HIF magnitude data for a subset of archival tagged juvenile Pacific bluefin tuna released in August 2002 (those with tracks of at least 300 days)

23 over their first year at large (n=6705; 23 tagged individuals). We used R package gamm4 (version ) to fit the binomial model for feeding success as it offers better performance for binary data. R package mgcv (version ) was used to fit GAMMS for the magnitude of positive valued HIFs. Supplementary Results Over their first year at large, juvenile Pacific bluefin tuna released in August 2002 fed on 92% of days (SE 0.3%). Feeding success was higher on days when successful feeding had occurred on the previous day (lag 1 autocorrelation =0.35; Durbin Watson test statistic=1.29; P < 0.01). A GAMM for daily feeding success during the first year at large of archival tagged Pacific bluefin tuna released in August 2002 with individual as a random effect, binomial error and a logit link function explained 23% of the total variation (adjusted R-squared) in feeding success. The final model included SST, relative light level, ILD and day of the year as predictors of feeding success (Figure S12). Seasonal and spatial variation in GAMM predicted feeding success is shown in Figure S13. On average, feeding success was predicted to be highest in spring (0.97 ± (SE) and summer (0.92 ± 0.007), with lower feeding success in autumn (0.90 ± 0.008) and winter (0.91 ± 0.006). In winter, lower feeding success was predicted off northern Baja California and north of Cedros Island (Figure S13). By spring, feeding success was predicted to be high in all areas of the tuna s distribution. Slightly lower feeding success was predicted in the southern California Bight and off northern Baja California in summer, while in autumn, the highest feeding success was predicted in the northern part of the tuna s range off central and northern California (Figure S13).

24 Figure S12. Estimated smooth terms from the GAMM for feeding success in archival tagged Pacific bluefin tuna. (A) sea surface temperature (B) mixed layer depth (C) relative light level (D) day of the year. Dashed lines represent 95% confidence limits. Vertical axes are partial responses (estimated, centered smooth functions) on the scale of the linear predictor. A GAMM for daily HIF magnitude when successful feeding occurred with individual as a random effect explained 23% of the total variation in the magnitude of positive-valued HIFs. The final model included relative light level, ILD, day of the year, location (latitude-longitude smooth) and length of the individual as predictors of HIF magnitude. An AR1 error structure (nested within

25 individual) was also found to provide a better fit to the daily HIF magnitude data (lower AIC value) compared with a model without correlation in errors. The correlation parameter estimate for daily HIF was 0.42 (interval ). Considering only days on which feeding occurred (results from the Gamma GAMM), the highest energy intake was predicted in summer (June to August) followed by winter (December to February), Figure S14. Accounting for feeding success too (by combining predictions from the binomial and Gamma GAMMs), the highest average energy intake was predicted in summer, followed by spring (March to May). In winter and spring, when feeding occurred, higher energy intake was predicted at the northern end of the tuna s distribution, off central California and to a lesser extent, off Punta Eugenia in spring (Figure S14). Some individuals made westward movements in winter or spring before moving east again to rejoin the main area of aggregation (Figure S1). These movements often appeared to be associated with high caloric intake (Figures S14, S15). In summer, predicted energy intake was highest in areas closest to the coast in the southern California Bight and off northern Baja California. By autumn, higher energy intake was again predicted at the northern end of the tuna s distribution, off northern California. A similar pattern was obtained from the Delta-Gamma model, when predictions of feeding success and HIF magnitude (conditional on feeding) were combined (Figure S15).

26 Figure S13. Predicted feeding success between September 2002 and August 2003 from the binomial GAMM for a subset of archival tagged Pacific bluefin tuna (23 tagged individuals, 6705 observations) released in August (A) September to November (B) December to February (C) March to May (D) June to August.

27 Figure S14. Predicted HIF magnitude (conditional on feeding on a given day) between September 2002 and August 2003 from the Gamma GAMM for a subset of archival tagged Pacific bluefin tuna (23 tagged individuals, 6212 observations) released in August (A) September to November (B) December to February (C) March to May (D) June to August.

28 Figure S15. GAMM-predicted values from the Delta-Gamma model for HIF magnitude (combining predictions of feeding success and HIF magnitude) between September 2002 and August 2003 for a subset of archival tagged Pacific bluefin tuna (23 tagged individuals, 6212 observations) released in August (A) September to November (B) December to February (C) March to May (D) June to August.

29 Abbreviations CCLME CFL GAM GAMM HIF HBM ILD SD SE SST California Current Large Marine Ecosystem Curved fork length Generalised additive model Generalised additive mixed model Heat increment of feeding Hierarchical Bayesian model Isothermal layer depth Standard deviation Standard error Sea surface temperature Supplementary References 36. Pinkas, L., Oliphant, M. S. & Iverson, I. L. K. Food habits of Albacore, Bluefin tuna, and Bonito in California Waters. California Department of Fish and Game Fish Bulletin 152 (1971). 37. Madigan, D.J. et al. Stable isotope analysis challenges wasp-waist food web assumptions in an upwelling pelagic ecosystem. Sci.Rep. 2, DOI: /srep00654 (2012). 38. Stefánsson, G. Analysis of groundfish surey abundance data: combining the GLM and delta approaches. ICES J. Mar. Sci. 53, (1996). 39. Pennington, M. Efficient estimators of abundance, for fish and plankton surveys. Biometrics, 39, (1963).

30 40. Barry, S.C., Welsh, A.H. Generalized additive modeling and zero-inflated count data. Ecol. Model. 157, (2002). 41. Wood, S., Scheipl, F. gamm4: Generalized additive mixed models using mgcv and lme4. R package version (2013). 42. Wood, S.N. Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models. J. Royal Stat. Soc. B 73, 3-36 (2011). 43. Block, B. A. and Stevens, E. D. Tuna: Physiology, Ecology, and Evolution, San Diego: Academic Press (2001).

31 Table S1. Proximate analysis of sardine and anchovy used as feeds for captive tuna, reproduced from Farwell (43). Species Sardinops sagax Engraulis mordax Size Small (35g) Large (75g) Small (11g) Large (34g) Percent protein Percent fat kcal/100g

32 Table S2. Priors in the hierarchical Bayesian regression model. Parameter Description Prior Hyperprior mean for the per degree proportion of the 1,1 slope of kcal/hif magnitude at 20 C the slope of Normal (0,10) kcal/hif magnitude at 15 C represents (squid feeds) Hyperprior standard deviation for the per degree proportion of the slope of kcal/hif magnitude at 20 C the slope of kcal/hif magnitude at 15 C represents Uniform(0.0001, 2) (squid feeds) Multiplier for the temperature effect between 20 C to 22 C relative to 15 C to 20 C for squid feeds. Normal (0,1000) Multiplier for the temperature effect between 15 C 1 and 20 C for sardine feeds relative to the temperature Normal (0,1000) effect for squid feeds. Multiplier for the temperature effect between 20 C 2 and 22 C for sardine feeds relative to the temperature Normal (0,1000) effect for squid feeds. 1 [20] Hyperprior standard deviation for the squid feed coefficient at 20 C. Uniform(0.0001, 2)

33 2 [ 20] Hyperprior standard deviation for the sardine feed coefficient at 20 C. Uniform(0.0001, 2) obs,1 Observation error standard deviation for logtransformed meal energy (kcal), squid feeds Uniform(0.0001,1) obs,2 Observation error standard deviation for logtransformed meal energy (kcal), sardine feeds Uniform(0.0001,1) Parameters of normal distributions are mean and variance.

34 Table S3. Wilcoxon rank sums (from two-sided tests) for size-based differences in latitude, SST, and HIF. Latitude Temperature HIF magnitude Month Age 2 and younger vs. age 3 Age 3 vs. age 4 and older Age 2 and younger vs. age 3 Age 3 vs. age 4 and older Age 2 and younger vs. age 3 Age 3 vs. age 4 and older *** *** *** *** *** * *** *** ** ** ** ** *** *** *** *** *** *** *** *** *** *** *** * *** *** *** *** *** * *** ** 75761*** *** ** *** * *** *** *** *** *** *** *** *** *** *** ** *** *** *** *** * ** * *** ***

35 The significance of comparisons of the distributions of latitude ( ), SST ( C) and the magnitude of the heat increment of feeding (kcal) is denoted by asterisks: * P < 0.05; **P<0.01; ***P< The colour of the cell indicates the direction of significant differences: red indicates a higher value of the variable in question for the younger age class, while blue indicates a lower value for the younger age class. See Methods for age class definitions.

36 Table S4. Correlates of thermal excess. GAMM term Approximate percentage deviance explained Approximate significance level s(sea surface temperature, C) 59% p<0.001 s(isothermal layer depth, m) 3% p<0.001 s(eddy kinetic energy, cm 2 s -2 ) 3% p<0.001 s(sea surface height anomaly, cm) 3% p<0.001 s(relative light level) 3% p<0.001 s(length, cm) 12% p<0.001 s(day of the year) 12% p<0.001 Entries are approximate percentage deviance explained by term (of the total deviance explained by the model) for the final Generalized Additive Mixed Model for mean daily thermal excess ( C), adjusted R 2 =50%.