Landscape structure and boundary effects determine the fate of mutations occurring during range expansions

The interplay between the spatial dynamics of range expansion and evolutionary processes is receiving considerable attention. Recent theory has demonstrated that mutations occurring towards the front of a spatially expanding population can sometimes 'surf' to high frequency and spatial extent. Here, we extend this work to consider how the fate of a novel mutation is influenced by where and when it occurs. Specifically, we are interested in establishing how the origin of a mutation relative to a habitat edge influences its dynamics, and in understanding how this is mediated by the behaviour of individuals at those boundaries. Using a coupled-map lattice model, we demonstrate that the survival probability, abundance and spatial extent of surviving mutants can depend on their origin. An edge effect is often observed and can be quite different both qualitatively and quantitatively depending on the behavioural rules assumed. Mutations, especially those that are deleterious, that arise at a habitat edge with reflective boundary conditions can be many more times likely to survive for substantial periods of time than those that arise away from the edge. Conversely, with absorbing boundary conditions, their survival is greater when they arise well away from the edge. Our results clearly illustrate that landscape structure, habitat edges and boundary conditions have a considerable influence on the likely fate of mutations that occur during a period of range expansion.