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

Abstract

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.

Global attractivity of Leslie–Gower predator-prey model incorporating prey cannibalism

“…During the last decades, mathematics biology has become one of the important research areas . Specially, many scholars investigated the dynamic behaviors of the ecosystem with cannibalism (see [28][29][30][31][32][33][34] and the references cited therein). Cannibalism often occurs in plankton, fishes, spiders [28], and social insect populations [29].…”

“…Sufficient conditions which ensure the global stability of the positive equilibrium and the existence of a unique limit cycle have been obtained, respectively. In 2016, Basheer et al [31] proposed the prey-predator model with prey cannibalism as follows:…”

“…It brings to our attention that the authors only investigated the local stability property of the equilibrium and did not investigate the global stability property of the positive equilibrium, nor did they investigate the uniqueness of the limit cycle. Recently, stimulated by the works of Basheer et al [31,32], based on the traditional Lotka-Volterra type predator prey system, Deng et al [33] investigated the dynamic behaviors of the following predator-prey model with cannibalism for predator:…”

“…Also, unlike Basheer et al [31,32], by constructing some suitable Lyapunov function, Deng et al [33] showed that if system (1.7) has a positive equilibrium, it then is globally asymptotically stable. Stimulated by the works of Basheer et al [31,32] and Deng et al [33], based on model (1.2), we propose the Leslie-Gower predator prey model with prey cannibalism, i.e., system (1.1). As far as system (1.1) is concerned, two interesting issues are proposed: Can we obtain sufficient conditions to ensure the existence of a unique globally stable positive equilibrium?…”

The Effects of Invasive Epibionts on Crab–mussel Communities: A Theoretical Approach to Understand Mussel Population Decline

“…= 0.1, e 1 = 0.9, e 2 = 0.5, h 1 = 2.0, h 2 = 1.0, b = 0.2, δ 1 = 0.1, a = 0(A) Solid curves are the density change for each species of the system (129)-(132) under e = K and the dashed line are the optimal state of the control system (43)-(46) for the objective function J 1 (u 1 , u 2 ) (B) Optimal controls of J 1 (u 1 , u 2 ) with the above parameter set (73).…”