Rule-based models for evaluating mechanisms of distributional change

Viability models assume that particular mechanisms (e.g., decreased probability of colonization in isolated habitats) drive the pattern of population invasion and extinction. Although authors often provide evidence supporting the inclusion or exclusion of a mechanism, there has been no means of rigorously comparing different factors for a given species. We present a method of evaluating alternative mechanisms of distributional change that relies on two or more surveys of species presence-absence across a large number of sites, a dataset often available (or at least attainable) for many taxa. The key idea of our approach is to use hypotheses to specify rules for dividing sites into classes. Our model estimates class-specific probabilities of invasion and extinction and then uses these rates to assign invasions and extinctions to sites in multiple stochastic simulations. The output of the model is a frequency distribution of mistakes generated by comparing predicted distributions with the actual distributions. As a first attempt to apply the approach we modeled invasions and extinctions of 14 amphibian species across 32 ponds in Michigan. We compared hypotheses that amphibian distributions changed as a result of the spatial arrangement of sites, as a result of succession, or randomly. Overall, the spatial approach provided a poor explanation of distributional changes, performing no better than the random model for all species. In contrast, the succession model, based on temporal changes in breeding sites, performed better than the null model for at least three species. These results were surprising as spatial effects are thought to be important to the dynamics of pond-breeding amphibians. Our results say little about the general importance of fragmentation and other spatial effects, but do suggest that alternative mechanisms of change can be important. Because of their ability to assess the importance of different mechanisms, rule based models could provide useful input into the design of biodiversity management strategies.