2026/07/13 by Manon Costa, Madeleine Kubasch, Nicolas Loeuille
#math.DS #q-bio.PE
We are interested in the long-time behaviour of the ecological dynamics of two competing species in a spatially heterogeneous environment consisting of two habitat types. Our goal is to provide conditions for the persistence of the two populations. First, we consider a spatially continuous model, formalized as an infinite-dimensional system of integro-differential equations. We show that if each species would persist if it were alone, then mutual invasibility of each other's monospecific equilibrium is a sufficient condition for long time survival of both species. Second, we introduce a finite-dimensional system of ordinary differential equations which approximate the spatial dynamics by averaging over a finite number of habitat types. We derive an analogous sufficient condition for stable coexistence, and show that in this case, there exists a positive coexistence equilibrium. Finally, we complete our theoretical result using a simulation study. Our results indicate that mutual invasibility also is a necessary condition for stable coexistence in both models. In addition, we show that the finite-dimensional model underestimates species' persistance, which indicates that spatial heterogeneity promotes survival.