Additional food supplements as a tool for biological conservation of predator-prey systems involving type III functional response: A qualitative and quantitative investigation

Abstract

Provision of additional food supplements for the purpose of biological conservation in ecosystems has of late been intensely researched by agriculturalists, biologists and mathematicians. The study of these ecosystems is usually done using the predator-prey systems. In these ecological studies it has been observed that the quality and quantity of additional food supplements provided play a crucial role in the growth of the predators and thereby influence the eventual state of the ecosystem. Also, in some of the ecological experiments it has been observed that predators exhibit non-optimal foraging behaviour in the presence of additional food. Findings also show that the predators exhibit a Holling type II response towards a target prey with predation highest at low prey densities. The results suggest that predation by predators is unlikely to stabilize low density prey populations. This can be attributed to the prey detectability independent nature of the type II response. In nature, sigmoidal functional responses such as the Holling type III response, have been documented in organisms from various taxa. In this kind of type III response the predators exhibit low detectability nature at low prey densities. Due to this the ecosystem tends to get stabilized at low prey densities avoiding the oscillations encountered in type II response. Motivated by these studies, in this paper, we consider a predator-prey system provided with additional food where the predator is assumed to exhibit Holling type III functional response towards the available food and the additional food supplements provided are assumed to be of constant density. We also assume that the predators are not optimal foragers. The model is analyzed in the control parameter space using the control parameters, quality and quantity of additional food. It is observed that the system exhibits apparent competition only when the predators are provided with high quality additional food supplements. Further, it has been shown that the ecosystem tends to get stabilized at low prey densities and the system can be steered to a desired state by a suitable choice of additional food supplements. Provision of low quality additional food supplements can result in completely opposite results to the expected ones.