Eco-evolutionary cyclic dominance among predators, prey, and parasites

Predator-prey interactions are one of ecology's central research themes, but with many interdisciplinary implications across the social and natural sciences. Here we consider an often-overlooked species in these interactions, namely parasites. We first show that a simple predator-prey-parasite model, inspired by the classical Lotka-Volterra equations, fails to produce a stable coexistence of all three species, thus failing to provide a biologically realistic outcome. To improve this, we introduce free space as a relevant eco-evolutionary component in a new mathematical model that uses a game-theoretical payoff matrix to describe a more realistic setup. We then show that the consideration of free space stabilizes the dynamics by means of cyclic dominance that emerges between the three species. We determine the parameter regions of coexistence as well as the types of bifurcations leading to it by means of analytical derivations as well as by means of numerical simulations. We conclude that the consideration of free space as a finite resource reveals the limits of biodiversity in predator-prey-parasite interactions, and it may also help us in the determination of factors that promote a healthy biota.

Automated summary

Predator-prey interactions are a central research theme in ecology, but the role of parasites in these interactions is often overlooked. Using a predator-prey-parasite model inspired by classical equations, we demonstrate that a stable coexistence of all three species is not biologically realistic. To improve this, we introduce the concept of free space as a relevant eco-evolutionary component in a new mathematical model, which describes a more realistic setup using a game-theoretical payoff matrix. By considering free space, we stabilize the dynamics between the three species through cyclic dominance, determining the parameter regions of coexistence and the types of bifurcations leading to it.