A predator-prey model with age-structured role reversal

TL;DR

This paper introduces an age-structured predator-prey model that incorporates role reversal and ontogenetic niche shifts, analyzing its dynamics and stability through mathematical and computational methods.

Contribution

It develops a novel age-structured predator-prey model with role reversal, linking it to existing differential equations and analyzing its complex dynamics.

Findings

Age structure promotes instability of coexistence equilibrium.

Long-term dynamics depend heavily on predator maturation age and juvenile predation rate.

Model reduction to ODE and DDE captures key stability features.

Abstract

We propose a predator-prey model with an age-structured predator population that exhibits a functional role reversal. The structure of the predator population in our model embodies the ecological concept of an "ontogenetic niche shift," in which a species' functional role changes as it grows. This structure adds complexity to our model but increases its biological relevance. The time evolution of the age-structured predator population is motivated by the Kermack-McKendrick Renewal Equation (KMRE). Unlike KMRE, the predator population's birth and death rate functions depend on the prey population's size. We establish the existence, uniqueness, and positivity of the solutions to the proposed model's initial value problem. The dynamical properties of the proposed model are investigated via Latin Hypercube Sampling in the 15-dimensional space of its parameters. Our Linear Discriminant Analysis suggests that the most influential parameters are the maturation age of the predator and the rate of consumption of juvenile predators by the prey. We carry out a detailed study of the long-term behavior of the proposed model as a function of these two parameters. In addition, we reduce the proposed age-structured model to ordinary and delayed differential equation (ODE and DDE) models. The comparison of the long-term behavior of the ODE, DDE, and the age-structured models with matching parameter settings shows that the age structure promotes the instability of the Coexistence Equilibrium and the emergence of the Coexistence Periodic Attractor.