The role of predator overlap in the robustness and extinction of a four species predator–prey network

Predators and preys often form species networks with asymmetric patterns of interaction. We study the dynamics of a four species network consisting of two weakly connected predator–prey pairs. We focus our analysis on the effects of the cross interaction between the predator of the first pair and the prey of the second pair. This is an example where the predator overlap, which is the proportion of predators that a given prey shares with other preys, is not uniform across the network due to asymmetries in patterns of interaction. We explore the behavior of the system under different interaction strengths and study the dynamics of survival and extinction. In particular, we consider situations in which the four species have initial populations lower than their long-term equilibrium, simulating catastrophic situations in which their abundances are reduced due to human action or environmental change. We show that, under these reduced initial conditions, and depending on the strength of the cross interaction, the populations tend to oscillate before re-equilibrating, disturbing the community equilibrium and sometimes reaching values that are only a small fraction of the equilibrium population, potentially leading to their extinction. We predict that, contrary to one’s intuition, the most likely scenario is the extinction of the less predated preys