Multistability in an open recruitment food web model

A general model for three species food web found in marine systems is analyzed. Following single-species approaches to model the dynamics of marine organisms, we relaxed the assumption of closed population structure and examine the behavior of webs in which some or all the component populations have completely open dynamics, that is, there is no connection between the arrival of new individuals and local reproductive output. Recent reviews have shown that coexistence among species with self-recruitment with those with completely open-recruitment is the norm in marine habitats. As part of a study of tri-trophic food web models with combinations of self-versus open-recruitment, we describe here the stability properties of a food web with omnivory where the basal and the intermediate predator species have open populations and the top predator reproduces locally. This system can have a maximum of four critical points and at least one corresponding to the omnivore-free equilibrium point. In this case our system reduces to a two level food web without omnivory. This equilibrium point has stability properties that depend on the capacity of invasion of the omnivore species. If the omnivore succeeds in invading the community then a three level food web can be established but with more complex stability properties. When the equilibrium point without the top predator is unstable, then there may exist three more critical points, at least one of which is asymptotically stable. The exact number of critical points that may exist depends on the food web parameter space. We speculate that the restrictive conditions for three-species stability could explain the scarcity of this particular combination of dispersal abilities in natural communities.