Are comparisons of species distribution models biased? Are they biologically meaningful

A major problem in ecology is to understand how environmental requirements change over space and time. To this end, numerous authors have attempted to use comparisons of species distributions as a surrogate for comparisons of environmental requirements. Unfortunately, it is currently unclear when comparisons of species distributions produce reliable inferences about changes in environmental requirements. To address this problem, I develop an analytic model that identifies the conditions under which a comparison of species distribution models can serve as surrogate for a comparison of environmental requirements. This work demonstrates that 1) comparisons of species distributions typically produce biased comparisons of environmental requirements, 2) assuming distribution models are fit appropriately, it is possible to compare environmental requirements of distinct taxa, 3) there are multiple biologically relevant questions we can address using comparisons of distribution models, with each question corresponding to a distinct measure of the difference between distribution models. By developing an analytic model for comparisons of species distributions this work helps to clarify and remedy poorly understood sources of error associated with existing methods.