A probabilistic approach to dispersal in spatially explicit meta-populations.

Meta-population and -community models have extended our understanding regarding the influence of habitat distribution, local patch dynamics, and dispersal on species distribution patterns. Currently, theoretical insights on spatial distribution patterns are limited by the dominant use of deterministic approaches for modeling species dispersal. In this work, we introduce a probabilistic, network-based framework to describe species dispersal by considering inter-patch connections as network-determined probabilistic events. We highlight important differences between a deterministic approach and our dispersal formalism. Exemplified for a meta-population, our results indicate that the proposed scheme provides a realistic relationship between dispersal rate and extinction thresholds. Furthermore, it enables us to investigate the influence of patch density on meta-population persistence and provides insight on the effects of probabilistic dispersal events on species persistence. Importantly, our formalism makes it possible to capture the transient nature of inter-patch connections, and can thereby provide short term predictions on species distribution, which might be highly relevant for projections on how climate and land use changes influence species distribution patterns.