On the dynamics of predator–prey models with role reversal

Abstract

We present a novel mathematical model that incorporates role reversal in predator–prey interactions. In particular, we consider the case where adult preys attack and kill juvenile predators. The model is derived from the McKendrick–Von Foerster equation and includes a maturation delay for juvenile predators. We prove that the initial value problem of the modeling framework is globally wellposed and establish conditions for the existence of positive equilibrium points. The model is compared with a version without role reversal, and we use the implicit function theorem to analyze the impact of weak role reversal on the equilibrium points of the model. This approach is necessitated as finding explicit expressions for the equilibrium points in the model with role reversal is particularly challenging. Phase portraits and bifurcation diagrams are used to illustrate our theoretical findings. Our results suggest that the maturation delay of predators and the handling time are the key factors in the dynamics of the model with role reversal, thus highlighting the importance of considering these phenomena in predator–prey interactions. This study provides a novel theoretical observation that the role reversal mechanism in predator–prey interactions has the potential to prevent cyclic population dynamics. The model outcome has been validated with the help of available data for the forage-piscivore fish trade-offs. Experimental studies are needed to validate model predictions and determine its relevance in real-world ecological systems.