A theoretical framework for multi-species range expansion in spatially heterogeneous landscapes

Range expansion is the spatial spread of a population into previously unoccupied regions. Understanding range expansion is important for the study and successful manipulation and management of ecosystems, with applications ranging from controlling bacterial biofilm formation in industrial and medical environments to large scale conservation programmes for species undergoing climate-change induced habitat disruption. During range expansion, species typically encounter competitors. Moreover, the environment into which expansion takes place is almost always heterogeneous when considered at the scale of the individual. Despite the ubiquitous nature of these features, the impact of competition and spatial landscape heterogeneities on range expansion remains understudied. In this paper we present a theoretical framework comprising two competing generic species undergoing range expansion and use it to investigate the impact of spatial landscape heterogeneities on range expansion with a particular focus on its effect on competition dynamics. We reveal that the area covered by range expansion during a fixed time interval is highly variable due to the fixed landscape heterogeneities. Moreover, we report significant variability in competitive outcome (relative abundance of a focal species) but determine that this is induced by low initial population densities, independent of landscape heterogeneities. We further show that both area covered by range expansion and competitive outcome can be accurately predicted by a Voronoi tessellation with respect to an appropriate metric, which only requires information on the spatial landscape and the response of each species to that landscape. Finally, we reveal that if species interact antagonistically during range expansion, the dominant mode of competition depends on the initial population density. Antagonistic actions determine competitive outcome if the initial population density is high, but competition for space is the dominant mode of competition if the initial population density is low.