Eco-Evolutionary Cyclic Dominance Among Predators, Prey, and Parasites

13 Pages Posted: 29 Nov 2022

See all articles by Sayantan Nag Chowdhury

Sayantan Nag Chowdhury

University of California, Davis

Jeet Banerjee

Think & Learn Pvt. Ltd. - BYJUS

Matjaz Perc

Faculty of Natural Sciences and Mathematics, University of Maribor

Dibakar Ghosh

Indian Statistical Institute, New Delhi - Indian Statistical Institute

Abstract

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.

Keywords: self-organization, coevolution, Mathematical Modeling, coexistence, oscillations

Suggested Citation

Nag Chowdhury, Sayantan and Banerjee, Jeet and Perc, Matjaz and Ghosh, Dibakar, Eco-Evolutionary Cyclic Dominance Among Predators, Prey, and Parasites. Available at SSRN: https://ssrn.com/abstract=4276362

Sayantan Nag Chowdhury

University of California, Davis ( email )

Jeet Banerjee

Think & Learn Pvt. Ltd. - BYJUS ( email )

Matjaz Perc

Faculty of Natural Sciences and Mathematics, University of Maribor ( email )

Koroska cesta 160
Maribor, SI-2000
Slovenia

HOME PAGE: http://www.matjazperc.com/

Dibakar Ghosh (Contact Author)

Indian Statistical Institute, New Delhi - Indian Statistical Institute ( email )

New Delhi
New Delhi, 110016
India

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