Exclusion and spatial segregation in the apparent competition between two hosts sharing macroparasites.

In this paper we investigate the spatial dynamics of a deterministic model describing two host species that partially share a common spatial domain, experiencing apparent competition mediated by macroparasites. The aim of this work is to understand the mechanisms underlying apparent competition processes in a spatially structured environment, which have been generally overlooked up to now. First, we analyse the behaviour of a single-host macroparasite partial differential equation (PDE) model, both in the cases of uniform or spatially-dependent vital rates of the host, focusing on the role of spatial diffusion on parasite persistence and host abundance. We obtained the threshold condition for parasite persistence, and (in contrast to what occurs in reaction-diffusion models for an isolated population) we found that, in the case of spatially-dependent vital rates, increasing the host diffusion coefficient results in an increase of the overall host population. Then, a PDE model featuring spatial diffusion and apparent competition mediated via shared macroparasites between two species is analysed in order to understand the role of spatial heterogeneity in host coexistence. We assumed a partial overlap among the habitats of the two species and found that the shared parasites could cause, depending on the values of the diffusion coefficients and differences in induced mortality among host species, a decrease of the realized habitat and, eventually, the extinction of the species less tolerant to parasite infection. This shows that the presence of regulating parasites complicates the effect of dispersal on population dynamics and that the dynamics of apparent competition cannot be adequately understood from spatially-independent models.