Macroecology, geographic range size-body size relationship and minimum viable population analysis for new world carnivora

Macroecology deals with variation and covariation of complex variables, such as body size, population density and geographic range size (GRS), measured across species at broad spatial scales. Despite the increasing number of papers in this field, little attention has been given to the links between patterns at different scales. In this paper, we analysed the constraint envelope formed by the macroecological relationship between GRS and body size for 70 species of New World terrestrial Carnivora. The lower-right constraint line of this envelope is usually interpreted as the minimum viable GRS that keeps extinction risks relatively low across evolutionary time, and in this paper we fitted this line by multiplying average home range size (established by allometric equations) by different minimum viable population sizes, establishing a minimum viable GRS. Then we estimated the difference between actual geographical range size and minimum viable geographical range size, in log scale (ΔA), which indicates how large is the geographic range of a species in relation to the minimum necessary to its long-term persistence. These ΔA values are significantly correlated with extinction risk defined by IUCN threat categories, even after keeping geographical range size constant and after taking into account phylogenetic structure in data. This gives support to the minimum viable population model explaining the relationship between GRS and body size and highlights a way to use constraint envelopes to evaluate the influence of complex variables to predict extinction risks.