Locally dispersing populations in heterogeneous dynamic landscapes with spatiotemporal correlations. I. Block disturbance.

Locally dispersing populations are generally favorably affected by increasing the scale of habitat heterogeneity because they can exploit contiguous patches of suitable habitat. Increasing the spatial scale of landscape disturbances (such as by applying a pesticide to control an unwanted species) drives down population density because of reasons including dispersal-limited recolonization and the resulting increase in temporal variability. Here, we examine how population density changes as the spatial scale of landscape disturbance increases: does it increase due to increases in spatial correlations in landscape habitat type, or does it decrease due to the various spatial and temporal effects of larger-scale disturbances? We use simulations, mean field approximations, pair approximations, landscape-improved pair approximations (LIPA), and block probabilities to investigate a model of a locally dispersing species on a dynamic landscape with spatiotemporally structured heterogeneous habitat. Pesticide is applied at a given spatial scale, leaving habitat unsuitable for some time before dissipating and allowing the habitat to revert to a suitable state. We found that increasing the spatial scale of disturbances (while keeping the overall disturbance rate fixed) can increase population density, but generally only when landscape turnover is slow relative to population dynamics and when the population is somewhat close to its extinction threshold. Applying control measures at larger spatial scales may allow them to be more effective with the same overall treatment rate. The optimal spatial strategy for applying disturbances depends on both habitat availability as well as the turnover rate of the control measure being used. For the large-scale habitat dynamics in our model, it is possible to analytically calculate spatial correlations in habitat types over arbitrary scales. However, including exact habitat correlations at the triplet scale but approximating population correlations at that scale still neglects information needed to accurately predict simulation results, showing that larger-scale correlations in the population distribution have an important effect on dynamics.