Background/Question/Methods   Roads can have major impacts on wildlife populations. They fragment the landscape, thus reducing the dispersal ability and gene flow of species, and they are also a major source of mortality due to road killings. Thus, roads are responsible for the reduction of population sizes, and can even lead to the extinction of a given population. Therefore, the assessment of the impact that roads have on wildlife, especially in densely human populated areas, is a major concern for conservation efforts. Here, based on Skellam's diffusion model, we develop an analytical framework and simulation tools to assess this impact. Our model treats space explicitly and consists of a periodic landscape where the basic patch has a rectangular shape. Its analytical solution is only possible in simple situations, such as when populations have exponential growth or when individuals necessarily die when crossing a road. In order to deal with more realistic problems we used numerical simulations based on a discretized version of the original model.

Results/Conclusions   We exemplify the application of our methods by studying, first, how minimum patch size and its geometrical shape relate to the survival of a population, and, second, how the size of nonviable patch relates to time to extinction of a population. Concerning patch size and shape, our model highlights the negative relationship between diffusion and persistence of populations, and how it is influenced by the layout of the roads. Specifically, we show that the distance between roads and the shape of the area are determining factors. For instance, populations are at higher risk of extinction in a rectangular than a square patch because the former has a larger contact region with roads. Concerning patch size and time to extinction, we show analytically and via simulations that time to extinction increases as a function of fragment area, almost like a power law (with exponent larger than one). We anticipate that our simulation approach can be used as a first tool to assess the impact of road fragmentation on wildlife populations and can be used to study the applicability of mitigation measures, such as, corridors and fences.