| Abstract: | Abstract Classical models for biological invasions were single-species models in
homogeneous landscapes, but most invasions happen in the presence of interacting
species and in heterogeneous environments. The combination of spatial variation
and species interaction could alter the spreading process significantly. For example,
the ‘environmental heterogeneity hypothesis of invasions’ posits that heterogeneity
offers more opportunities for invaders and reduces the negative impact on native
species. Environmental heterogeneity offers an obvious coexistence mechanism on
the regional scale if two or more competing species have different spatial niches,
i.e., if the local competitive advantage changes in space. We consider a more subtle
mechanism of space use through individual movement behavior when the local
competitive advantage remains with the same species. Specifically, we model the
densities of two species, diffusing and competing in an infinite landscape consisting
of two types of patches. We include individual behavior in terms of movement
rate and patch preference. We consider the scenario that one of the species is
the stronger local competitor in both patch types. We then uncover a number
of mechanisms – based solely on movement behavior – through which these two
species can coexist regionally, how the inferior competitor can replace the superior
competitor globally, or how a bistable situation can arise between the two. We
calculate mutual invasion conditions as well as mutual spatial spread rates, and
we show that spread rates may depend on movement parameters in unexpected
ways. |