Species’ observed ranges for key environmental factors were defined by the maximum and minimum value obtained from matching up the species’ raw observations with sea surface temperature (48), sea surface wind stress (49), MLD (40), and additional factors, at monthly 1° resolution (Fig. 2B and fig. S6). Species’ latitudinal ranges corresponded to the maximum and minimum latitude of raw observations (Fig. 2C). We assessed the expected maximum species richness over the full range of each environmental variable in the ocean based on species’ observed presence ranges. At each environmental value (Fig. 2, B and C, and fig. S6), maximum richness is defined as the sum of the species’ ranges that overlapped, and range size is defined as the species’ mean range size.

To denote parts of the environmental gradients where edge effects likely distorted species’ observed range patterns, we created a null model of the environmental response in expected maximum richness and average range size. To this end, we randomized the species’ presences in the observational data (n = 100 runs) and derived species’ range limits and expected richness/mean range size based on these randomized data. Thus, our null model represents the expected maximum richness/mean range size in absence of any environmental sorting of species’ ranges. We identified areas with likely edge effects as those areas where the null model values deviated significantly (using the 95% confidence interval range) from the null model value obtained in the center (i.e., not affected by edge effects) of the environmental gradient studied. In Fig. 2 (B and C) and fig. S6, we only show estimates of maximum richness (red line) and range size (blue line) for areas unaffected by edge effects.

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