Asymmetric dispersal is a common trait among populations, often attributed to heterogeneity and stochasticity in both environment and demography. Dispersal ability is an important characteristic that often influences the ability of a population to persist. The cumulative effects of population dispersal in space and time have been described with some success by Van Kirk and Lewis's (1997) average dispersal success approximation, but this approximation was designed to model symmetric dispersal, and has been demonstrated to perform poorly when applied to asymmetric dispersal. Here we provide a comparison of different characterizations of dispersal success, and introduce a method called geometric symmetrization, that accurately captures the effects of asymmetric dispersal. We apply these different methods to a variety of integrodifference equation population models with asymmetric dispersal, and examine the methods' effectiveness in approximating key ecological traits of the models, such as the critical patch size and the critical speed of climate change for population persistence.
Results/Conclusions
Our results indicate that presently available dispersal success approximations consistently overestimate the ability of a population with asymmetric dispersal to persist. In contrast, geometric symmetrization provides extremely accurate estimates of persistence criteria for a variety of growth functions, dispersal kernels, and model parameters. We conclude that geometric symmetrization provides the best method for describing the persistence of populations with asymmetric dispersal.