Effects of Topology and Spatial Heterogeneity on Dispersal in Dendritic Systems

We apply an evolutionary game theoretic approach to the evolution of dispersal in explicitly spatial metacommunities, using a flexible parametric class of dispersal kernels, namely 2Dt kernels, and study the resulting evolutionary dynamics and outcomes.  We observe strong selective pressure on mean dispersal distance (i.e., the first moment), and weaker, but significant, one on the shape of dispersal kernel (i.e., higher moments).  We investigate the effects of landscape topology and spatial heterogeneity on the resulting "optimal" dispersal kernels.  The shape--importantly the tail structure--and stability of evolutionarily optimal dispersal strategies are strongly affected by landscape topology.  Specifically, the results suggest that the optimal dispersal kernels in the river network topology have heavier tails and are stable, while those in the direct topology, where organisms are allowed to travel directly from one location to another, have relatively thin tails and may be unstable.  We also find that habitat spatial heterogeneity enables coexistence and controls spatial distribution of distinct groups of dispersal strategies and that alteration in topology alone may not be sufficient to change such coexistence.  This work provides a tool to translate environmental changes such as global climate change and human intervention into changes in dispersal behavior.  Such changes can in turn lead to important alterations of biodiversity and biological invasion patterns and thus have important conservation implications.