Spatio-temporal impacts of roads on the persistence of populations: analytic and numerical approaches

Roads can have drastic impacts on wildlife populations. Although there is wide recognition of the negative impacts caused by roads and a wealth of practical studies, there is a lack of theoretical work that can be used to predict the impact of road networks or to implement mitigation measures. Here, using Skellam's diffusion model, we develop analytic and numerical approaches to analyze the impact of road networks on the survival of populations. Our models show that the viability of a population is determined not only by road density but also by the size and shape of patches. Accordingly, we studied the minimum size of a patch to sustain a population with given diffusion and growth parameters. We provide simple formulas to estimate the minimum patch size, and illustrate the importance of shape with square and rectangular patches. Our models also allow the estimation of time to extinction after road construction for a population in a patch smaller than that of the minimum size. Finally, using numerical computations we illustrate how the spatial arrangement of fences strongly affects both the equilibrium density and the spatial distribution of populations, and that not all fence layouts are equally effective. We anticipate that our methods provide a tool to assess the impact of geometrical features of road networks on wildlife and that they can be used to design mitigation measures to prevent the decline and extinction of populations in an anthropogenically disturbed landscape.