Prey cannibalism alters the dynamics of Holling-Tanner type predator-prey models

TL;DR

This paper investigates the effects of prey and predator cannibalism on the stability and pattern formation in Holling-Tanner predator-prey models, revealing that prey cannibalism can destabilize equilibria and induce Turing patterns.

Contribution

It extends existing models by analyzing prey cannibalism effects, showing its destabilizing influence and potential to generate spatial patterns in predator-prey dynamics.

Findings

Predator cannibalism stabilizes the system as expected.

Prey cannibalism can destabilize stable equilibria.

Prey cannibalism induces Turing patterns in spatial models.

Abstract

Cannibalism, which is the act of killing and at least partial consumption of conspecifics, is ubiquitous in nature. Mathematical models have considered cannibalism in the predator primarily, and show that predator cannibalism in two species ODE models provides a strong stabilizing effect. There is strong ecological evidence that cannibalism exists among prey as well, yet this phenomenon has been much less investigated. In the current manuscript, we investigate both the ODE and spatially explicit forms of a Holling-Tanner model, with ratio dependent functional response. We show that cannibalism in the predator provides a stabilizing influence as expected. However, when cannibalism in the prey is considered, we show that it cannot stabilise the unstable interior equilibrium in the ODE case, but can destabilise the stable interior equilibrium. In the spatially explicit case, we show that in certain parameter regime, prey cannibalism can lead to pattern forming Turing dynamics, which is an impossibility without it. Lastly we consider a stochastic prey cannibalism rate, and find that it can alter both spatial patterns, as well as limit cycle dynamics.