Interaction networks in persistent Lotka-Volterra communities

A central concern of community ecology is the interdependence between interaction strengths and the underlying structure of the network upon which species interact. In this work we present a solvable example of such a feedback mechanism in a generalized Lotka-Volterra dynamical system. Beginning with a community of species interacting on a network with arbitrary degree distribution, we provide an analytical framework from which properties of the eventual "surviving community" can be derived. We find that highly connected species are less likely to survive than their poorly connected counterparts, which skews the eventual degree distribution towards a preponderance of species with lower degrees. Furthermore, the average abundance of the neighbors of a species in the surviving community is lower than the community average (reminiscent of the famed friendship paradox). Finally, we show that correlations emerge between the connectivity of a species and its interactions with its neighbors. More precisely, we find that highly connected species tend to benefit from their neighbors more than their neighbors benefit from them. These correlations are not present in the initial pool of species and are a result of the dynamics.