Effects of Patch–Matrix Composition and Individual Movement Response on Population Persistence at the Patch Level

James T. Cronin, Louisiana State University
Jerome Goddard, Auburn University at Montgomery
Ratnasingham Shivaji, The University of North Carolina at Greensboro


© 2019, Society for Mathematical Biology. 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 due to increased susceptibility to edge effects between the remnant habitat patches and the lower quality “matrix” surrounding these focal patches. In this paper, we formalize a framework to facilitate the connection between small-scale movement and patch-level predictions of persistence through a mechanistic model based on reaction–diffusion equations. The model is capable of incorporating essential information about edge-mediated effects such as patch preference, movement behavior, and matrix-induced mortality. We mathematically analyze the model’s predictions of persistence with a general logistic-type growth term and explore their sensitivity to demographic attributes in both the patch and matrix, as well as patch size and geometry. Also, we provide 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. Finally, we illustrate the utility of this framework with a well-studied planthopper species (Prokelisia crocea) living in a highly fragmented landscape. Using experimentally derived data 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. Through application of a sensitivity analysis to the model, we also suggest a ranking of the most important model parameters based on which parameter will cause the largest output variance.