How do species interactions affect species distribution models?

One of the most promising recent advances in biogeography has been the increased interest and understanding of species distribution models estimates of the probability that a species is present given environmental data. Unfortunately, such analyses ignore many aspects of ecology, and so are difficult to interpret. In particular, we know that species interactions have a profound influence on distributions, but it is not usually possible to incorporate this knowledge into species distribution models. What is needed is a rigorous understanding of how unmeasured biotic interactions affect the inferences generated by species distribution models. To fill this gap, we develop a general mathematical approach that uses probability theory to determine how unmeasured biotic interactions affect inferences from species distribution models. Using this approach, we reanalyze one of the most important classes of mechanistic models of competition: models of consumer resource dynamics. We determine how measurements of one aspect of the environment a single environmental variable can be used to estimate the probability that an environment is suitable with species distribution models. We show that species distribution models, which ignore numerous facets of consumer resource dynamics such as the presence of a competitor or the dynamics of depletable resources, can furnish useful predictions for the probability that an environment is suitable in some circumstances. These results provide a rigorous link between complex mechanistic models of species interactions and species distribution models. In so doing they demonstrate that unmeasured biotic interactions can have strong and counterintuitive consequences on species distribution models.