Stabilizing effect of intra-specific competition on prey-predator dynamics with intraguild predation

¹ Osaka Prefecture University, Graduate School of Science, Department of Biological Science, Gakuen-cho 1-1, Naka-ku, Sakai 599-8531, Japan
² College of Science and Engineering, Aoyama Gakuin University, Kanagawa, Japan
³ Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur 208016, India

^* Corresponding author: malayb@iitk.ac.in

Received: 14 December 2017
Accepted: 8 March 2018

Abstract

Multi-species population models with various types of interactions are important to understand the stable coexistence of prey and predator species and the role of various factors leading to complex dynamics and extinction of one or more species. Models of two predators sharing one prey population are analyzed by some researchers and the role of nonlinear functional responses and interaction strengths are reported to be responsible for the stable coexistence of three species. However, one-prey-two-predator models with intraguild predation have received relatively less attention from researchers. Recent literature on this topic mainly focused on the study of local and global stability properties of possible equilibria and appearance of various types of bifurcations. Intra-specific competition among predator species is an important factor for coexistence of more than one predator species competing for one shared prey. Hence it is quite essential to understand the role of intra-specific competition on the stability and bifurcation behavior. In this work we wish to demonstrate the stabilizing role of intra-specific competition among intermediate and top predators when the growth rate of prey species is adequate to support both the predator species. With the help of stability and bifurcation analysis we show the stabilizing role of intra-specific competition among predators. Moreover, strong self-regulation in intraguild predator prevents extinction of intraguild prey at high productivity and resolve the contradiction between empirical and previous theoretical results on the fate of intraguild prey at high productivity. To establish our claim we present, apart from analytical results, extensive numerical simulation results and couple of bifurcation diagrams.