Dispersal behaviour in fragmented landscapes: Deriving a practical formula for patch accessibility
Dispersal has been shown to be a key determinant of spatially structured populations. One crucial aspect is predicting patch accessibility: the probability rij of a certain patch j being reached by individuals starting at another patch i. Patch accessibility rij depends on both the landscape structure and the individuals’ dispersal behaviour. To investigate the effects of these factors on rij, we developed a simulation model focusing on animal dispersal. Our model analyses show that there is an important intrinsic effect of the interplay between landscape structure and dispersal behaviour on patch accessibility: the competition between patches for migrants. We derive a formula for patch accessibility. This formula is very simple because it just takes distances into account: not only the distance between start patch and target patch, but also between the start patch and all the other patches in the landscape. Despite its simplicity, the formula is able to cover effects such as the competition for migrants. The formula was found to have high predictive power for a variety of movement behaviours (random walk with various degrees of correlation, Archimedean spirals and loops) in any given landscape. The formula can be interpreted as a generic function for patch accessibility for further population dynamics analyses. It also delivers insights into the consequences of dispersal in fragmented landscapes.