A Holling's predator-prey model with handling and searching predators

TL;DR

This paper derives the classical Rosenzweig-MacArthur predator-prey model from a predator population divided into searching and handling groups, demonstrating convergence through analysis and simulations.

Contribution

It introduces a predator model with separate handling and searching groups, linking it to the classical model and enabling potential extensions like age or size structure.

Findings

The model converges to the Rosenzweig-MacArthur model under rescaling.

Numerical simulations confirm the convergence behavior.

The model provides a framework for adding predator age or size structure.

Abstract

The goal of this paper is to explain how to derive the classical Rosenzweig-MacArthur's model by using a model with two groups of predators in which we can separate the vital dynamic and consumption of prey to describe the behavior of the predators. This will be especially very convenient if we want to add an age or size structure to the predator population. As mentioned by Holling (without mathematical model), we divide the population of predators into the searching and the handling predators. In this article we study some properties of this model and conclude the paper proving that the model converges to the classical Rosenzweig-MacArthur's model by using an appropriate rescalling. This convergence property is observed by using numerical simulations.