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 …
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