RESEARCH ARTICLE Spatio-temporal impacts of roads on the persistence of populations: analytic and numerical approaches Luı ´s Borda-de-A ´ gua • Laetitia Navarro • Catarina Gavinhos • Henrique M. Pereira Received: 20 April 2010 / Accepted: 5 October 2010 / Published online: 20 October 2010 Ó Springer Science+Business Media B.V. 2010 Abstract Roads can have drastic impacts on wild- life 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 distribu- tion 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 anthropo- genically disturbed landscape. Keywords Skellam’s model  Reaction–diffusion equations  Dispersal  Road mortality  Mitigation measures  Fences  Spatially explicit model  Minimum patch size  Patch shape Introduction Roads, being associated with human well being and development, tend to occupy a growing percentage of landscapes worldwide. They now cover an average density of 1.2 km/km 2 in the United States (Forman 2000), over 2 km/km 2 in some European countries (Carr et al. 2002), and one can expect that road density will increase in developing countries since Electronic supplementary material The online version of this article (doi:10.1007/s10980-010-9546-2) contains supplementary material, which is available to authorized users. L. Borda-de-A ´ gua (&)  L. Navarro  H. M. Pereira Centro de Biologia Ambiental, Faculdade de Cie ˆncias da Universidade de Lisboa, 1749 016 Lisbon, Portugal e-mail: lbagua@gmail.com C. Gavinhos Escola Agra ´ria, Instituto Polite ´cnico de Castelo Branco, Quinta da Sra de Mercules, Apartado 119, 6001 909 Castelo Branco, Portugal C. Gavinhos  H. M. Pereira Departamento de Engenharia Civil e Arquitectura, Instituto Superior Te ´cnico, 1049 001 Lisbon, Portugal 123 Landscape Ecol (2011) 26:253–265 DOI 10.1007/s10980-010-9546-2