Fragmentation creates landscape-level spatial heterogeneity which in turn influences population dynamics of the resident species. This often leads to declines in abundance of the species as the fragmented landscape becomes more susceptible to edge effects between the remnant habitat patches and the lower quality “matrix” surrounding these focal patches. In this study, we formalize the connection between small-scale movement and patch-level predictions of persistence through a mechanistic model based on the reaction-diffusion framework. The model is capable of incorporating essential information about edge-mediated effects such as patch preference, movement behavior, and matrix-induced mortality at the patch/matrix interface. A major advantage of this framework is that the model involved contains explicit parameters that can be estimated through empirical studies and used to predict critical population metrics like persistence and minimum patch size under the context of changing landscape structure. We mathematically analyze the model's predictions of persistence with a general logistic-type growth term and explore their sensitivity to demographic attributes both in the patch and matrix, as well as patch size and geometry. Finally, we illustrate the utility of this framework with a well-studied planthopper species (Prokelisia crocea) living in a highly fragmented landscape.
Results/Conclusions
Our mathematical analysis of the model provides bounds on demographic attributes and patch size in order for the model to predict persistence of a species in a given patch based on assumptions on the patch/matrix interface. In fact, we provide exact mathematical descriptions of these bounds that can be numerically calculated given a particular patch geometry. As an example, we provide an analysis of the model’s predictions of persistence for a disk-shaped patch. Also, through application of a variance-based sensitivity analysis to our model, we suggest a ranking of the most important model parameters based on which parameter will cause the largest output variance. Our results indicate that for disk-shaped patches, the most important parameter in determining persistence of a species is the patch intrinsic growth rate, followed by patch diffusion rate, and probability of remaining in the patch upon reaching the boundary. This ranking could be employed to prioritize resources in future empirical studies to ensure a greater degree of accuracy. Finally, we used experimentally derived data for P. crocea from various sources to parameterize the model. We show that, qualitatively, the model results are in accord with experimental predictions regarding minimum patch size of P. crocea.