Does heat tolerance actually predict animals' geographic thermal limits?

The "climate extremes hypothesis" is a major assumption of geographic studies of heat tolerance and climatic vulnerability. However, this assumption remains vastly untested across taxa, and multiple factors may contribute to uncoupling heat tolerance estimates and geographic limits. Our dataset includes 1000 entries of heat tolerance data and maximum temperatures for each species' known geographic limits (hereafter, Tmax). We gathered this information across major animal taxa, including marine fish, terrestrial arthropods, amphibians, non-avian reptiles, birds, and mammals. We first tested if heat tolerance constrains the Tmax of sites where species could be observed. Secondly, we tested if the strength of such restrictions depends on how high Tmax is relative to heat tolerance. Thirdly, we correlated the different estimates of Tmax among them and across species. Restrictions are strong for amphibians, arthropods, and birds but often weak or inconsistent for reptiles and mammals. Marine fish describe a non-linear relationship that contrasts with terrestrial groups. Traditional heat tolerance measures in thermal vulnerability studies, like panting temperatures and the upper set point of preferred temperatures, do not predict Tmax or are inversely correlated to it, respectively. Heat tolerance restricts the geographic warm edges more strongly for species that reach sites with higher Tmax for their heat tolerance. These emerging patterns underline the importance of reliable species' heat tolerance indexes to identify their thermal vulnerability at their warm range edges. Besides, the tight correlations of Tmax estimates across on-land microhabitats support a view of multiple types of thermal challenges simultaneously shaping ranges' warm edges for on-land species. The heterogeneous correlation of Tmax estimates in the ocean supports the view that fish thermoregulation is generally limited, too. We propose new hypotheses to understand thermal restrictions on animal distribution.