Nonlinear thermal gradients shape broad-scale patterns in geographic range size and can reverse Rapoport's rule

Aim: Species living at latitudes that have greater annual temperature variations are expected to achieve broader geographic ranges than species living at latitudes that have smaller annual temperature variations, generating a positive relationship between range size and latitude (Rapoport's rule). However, this prediction fails to take into account the greater latitudinal extent of tropical temperatures relative to those at higher latitudes. Here we model the contributions of the broader latitudinal extent of equal-temperature habitats at low latitudes and the greater annual temperature variation at high latitudes to the range size-latitude relationship, and test whether the latitudinal variation in geographic range size in marine bivalves can be explained by models that account for both annual temperature variation and the steepness of latitudinal thermal gradients. Location: Western Pacific, eastern Pacific and western Atlantic. Methods: We use a null model where geographic ranges are placed on the ocean surface independently of thermal gradients, and a range-expansion model where the minimum and maximum temperatures encompassed by the geographic range of a species (macroecological thermal ranges) are positively related to annual temperature minima and maxima at the location where the species originated. We compare results with a database containing 40,820 occurrences of 4760 marine bivalve species. Result: Models incorporating temperature-limited range expansion along realistic thermal gradients predict an inverse relationship between range size and latitude, in opposition to Rapoport's rule. The distribution patterns of marine bivalves match this prediction. Main conclusions: The poleward trend in latitudinal range size is determined by the nonlinearity of the latitudinal gradient of temperature minima and maxima and less by the latitudinal gradient of the local seasonal range in temperatures. Although tropical species do have narrower macroecological thermal ranges than high-latitude species, the nearly constant temperatures over wide areas of the tropics allow tropical species to achieve broad latitudinal ranges.