To predict the niche, model colonization and extinction.

Ecologists frequently try to predict the future geographic distributions of species. Most studies assume that the current distribution of a species reflects its environmental requirements (i.e., the species' niche). However, the current distributions of many species are unlikely to be at equilibrium with the current distribution of environmental conditions, both because of ongoing invasions and because the distribution of suitable environmental conditions is always changing. This mismatch between the equilibrium assumptions inherent in many analyses and the disequilibrium conditions in the real world leads to inaccurate predictions of species' geographic distributions and suggests the need for theory and analytical tools that avoid equilibrium assumptions. Here, we develop a general theory of environmental associations during periods of transient dynamics. We show that time-invariant relationships between environmental conditions and rates of local colonization and extinction can produce substantial temporal variation in occupancy-environment relationships. We then estimate occupancy-environment relationships during three avian invasions. Changes in occupancy-environment relationships over time differ among species but are predicted by dynamic occupancy models. Since estimates of the occupancy-environment relationships themselves are frequently poor predictors of future occupancy patterns, research should increasingly focus on characterizing how rates of local colonization and extinction vary with environmental conditions.