Populations on Fragmented Landscapes with Spatially Structured Heterogeneities: Landscape Generation and Local Dispersal

The goal of this investigation was to study the effects of spatially structured habitat heterogeneities on locally dispersing single-species populations. In this investigation, the environmental heterogeneities were not randomly distributed, but rather were clustered by specifying probabilities of small local configurations of the landscape, as in local structure or pair approximations. This allows the study of landscapes with the same amount of habitat loss but different levels of fragmentation or clustering. I describe a simple algorithm for generating such structured landscapes. Spatially explicit simulations of population models on these landscapes were performed using stochastic cellular automata and compared to predictions from mean-field and pair approximations, for which detailed derivations are presented. For populations with local dispersal, I show that the spatial correlations of habitat types completely determine equilibrium population density on suitable sites and that the amount of suitable habitat has no effect, precisely the opposite of what the mean-field approximation predicts. When habitat types are randomly distributed on the landscape, the two approximations do almost equally well, and thus the additional complexity of the pair approximation is not justified. However, when habitat types are not randomly distributed, the mean-field approximation gives qualitatively incorrect predictions for population response to varying habitat heterogeneity. Thus, pair approximations combine some of the best features of spatially explicit and implicit models and serve as a useful supplement to those methods for understanding spatially structured ecological systems, especially where environmental heterogeneities are spatially correlated.