Spatially continuous modeling approach for population persistence in road-fragmented landscapes

The paper addresses the characteristics of landscape fragmentation caused by roads and their consequences on movement/dispersal and persistence of species. We propose a mathematical model, sufficiently general to enable inclusion of the effects of fragmentation by roads, assuming that the continuity of habitats across road-fragmented landscapes cannot be strictly defined. The mathematical formalization of the colonization–extinction dynamics is given, respecting the fact that both inter-patch and intra-patch processes matter in road-fragmented landscapes. Using the technique of integral operators, we define a population persistence capacity, indicating at what point the landscape is prone to be functionally disconnected for the species of interest. Population persistence capacity derived from the model, responds monotonically to fragmentation processes. The explicit inequalities relating population persistence capacity to other relevant fragmentation metrics are established.