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 generalised 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 low degree, a pattern commonly observed in real ecosystems. Further, the average abundance of the neighbours 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 neighbours. More precisely, we find that highly-connected species tend to benefit from their neighbours more than their neighbours benefit from them. These correlations are not present in the initial pool of species and are a result of the dynamics.