Supporting information 2 Respirometry methods The acclimation time needed to obtain resting levels of oxygen consumption in the 4 species examined here, 90 min., is shorter thanwhat is necessary forother species, especially larger fishes or those that are more active. The damselfishes and cardinalfishes investigated 6 here, and in other recent studies (Nilsson et al., 2009; Gardiner et al., 2010; Couturier et al., 2013;Rummer et al., 2013;) exhibit minimal handling stress and quickly become accustomed 8 to the respirometry chamber. We conducted pilot studies to determine how long it takes for ṀO2Restvalues to stabilize after fish were placed in the respirometry chamber. Even after a 10 fish had been chased to exhaustion, which would be far more stressful and energetically costly than handling stress, ṀO2 values stabilized earlier than 2h. See Fig. S1 for chase and 12 post-chase ṀO2 values for three C. atripectoralisindividuals (Rummer, unpublished data). The pilot data show that the fish return to a low, very stable rate of oxygen 14 consumptionrapidly following disturbance (Fig. S1). We could not detect significant differences between the average ṀO2Maxand average 16 ṀO2Restof two of our species (D. melanurus and C. quinquelineatus) acclimated to 34°C and, over the course of the entire study, we observed 5 individual fish that had a ṀO2Max value that 18 was numerically, albeit only slightly below their ṀO2Rest value. We note that resting rates increased significantly upon acclimation to34°C, if not by 33°C, in all except for one of the 20 species investigated, and thatṀO2Maxvalues had already peaked and fallen in all except for twospecies. The patterns of change resulted in a very low aerobic scope nearing zero at 34°C. 22 We believe this was the result of the fish being unable to exhibit a maximum swimming performance and the overall stress of high temperatures. This interpretationisfurther 24 supported by the variability around the means; which is small across all species and temperatures for both ṀO2Max and ṀO2Rest, except at the highest temperature where the error 1 26 bars are noticeably larger. 28 Latitudinal comparisons and reanalysis of data It was necessary to re-analyze data from the two previous studies (Nilsson et al., 2009; 30 Gardiner et al., 2010) becauseone higher acclimation temperature (at 33C) was added for the Heron Island populations andadditional replicates were obtained for the other temperatures to 32 make the latitudinal comparisons more robust. After incorporating the additional replicates and the additional acclimation temperature for the Heron Island populations, we found that 34 the overall patterns were retained. However, there was less variability around the means, and with the addition of33°Cdata, it was clear that performance was starting to fall at the higher 36 temperatures, which could be due to an increase in ṀO2Rest, a decrease in ṀO2Max, or both. Both sets of reanalyzed data – plotted in the same way as we did for the PNG populations – in 38 addition to aerobic scopes for the PNG populations are summarized in Fig. S2. Re-analysis of the previously published data with the inclusion of the additional 40 replicates and temperature group was also necessary in the present study in order to more appropriately make comparisons across the three separate data sets. In particular, we aimed to 42 compare the temperatures at which the representatives from each population performed best, not directly compare values of absolute scope among populations, because the magnitude of 44 the absolute aerobic scope may not be what dictates performance. Therefore,we estimated the temperatures at which performance is the greatest within populations and then compared those 46 temperaturesamong the different sites. 48 Local adaptation While we found no evidence for a consistent pattern of local adaptation of aerobic 50 scope to the average and maximum temperatures among the populations we studied, this does 2 not mean that adaptation is irrelevant. High latitude populations may be adapted to the greater 52 range of seasonal temperatures that they experience when compared with low latitude populations, leading to improved capacity to perform at a range of temperatures, including 54 higher temperatures outside the normal range experienced. This could produce an apparent mismatch between the average temperatures experienced in high latitude populations and the 56 temperatures where aerobic scope is the greatest. Consequently, our results could indicate that reef fish populations are more closely adapted to seasonal temperature variation than they are 58 to the average temperatures they experience. There could also be other traits that provide evidence for local thermal adaptation (e.g. reproductive timing). Furthermore, despite no 60 obvious adaptation of aerobic scope to different temperatures across latitudes, it does not follow that local adaptation of aerobic scope could not occur once temperatures exceed the 62 natural range. The magnitude of selection and trade-offs in genetic correlations among traits(Mundayet al., 2013) may be very different at temperatures outside the normal range 64 when compared with temperatures within the normal range. As a consequence, there could be adaptation to rapid climate change in the future, even in cases where there is no strong 66 evidence for local adaptation to existing natural temperature variation (Mundayet al., 2013). 68 Fig. S1Representative traces from three individual C. atripectoralis chased to exhaustion and then immediately placed into respirometry chambers where ṀO2 could be monitored until 70 recovery, which was sooner than 2h (Rummer, unpublished data). 72 Fig. S2Absolute aerobic scope (ṀO2Max - ṀO2Rest) for five coral reef fish species from three populations (see legend for symbols) investigated upon acclimation to 27, 29, 31, 32, 33, 74 and/or 34°C. Note: D. melanurus was only investigated at the equatorial site; whereas,D. 3 aruanus was investigated only at Lizard and Heron Islands.All data are means ±S.E.M., n≥8 76 for each species and each temperature. 78 Supporting References(not cited in main text) Couturier CS, Stecyk JAW, Rummer JL, Munday PL, Nilsson GE (2013) Species-specific effects of 80 near-future CO2 on the respiratory performance of two tropical prey fish and their predator. Comparative Biochemistry and Physiology, Part A: Molecular and Integrative 82 Physiology,166, 482-489. Rummer JL, Stecyk JAW, Couturier CS, Watson S-A, Nilsson GE, Munday PL (2013) Elevated CO2 84 enhances aerobic scope of a coral reef fish. Conservation Physiology,1. Munday PL, Warner RR, Munro K, Pandolfi JM, Marshall DJ (2013) Predicting evolutionary 86 responses to climate change in the sea. Ecology Letters, doi: 10.1111/ele.12185. 4