Predator–prey ecological system with group defense and anti-predator traits of the preys: Synergies between two important ecological actions

Abstract

During smart anti-predator adaptations, preys use their size, fleeing capability and herd in their evolutionary tug-of-war with the predators. Predator–prey ecology is teeming with such examples where predators can be defeated or even killed by the group of victims, that is, preys, banding together. In this paper, we focus on a stage-structured predator–prey model with herd behavior and anti-predator phenomenon that results in the lesser ecological opportunities for predation in the presence of the smart anti-predatory constraints. It is our purpose in this paper to illustrate the combined effects of the herd behavior and anti-predator strategy on the predator–prey ecology. By constructing the model equations, we present an analytical study of the system and the occurrence of Hopf and transcritical bifurcation for the anti-predator rate as a bifurcation parameter. Conditions for co-existence under global stable interior equilibrium as well as permanence region for the survival of all species is adequately discussed. Also, the extinction of predators is explored via numerical simulations, that is, the prey population survives successfully in the habitat due to their defense mechanism and anti-predator behavior. In order to better understand the role of anti-predator traits in predator–prey system with square root functional response, we compare the theoretical and numerical results of the proposed model with a similar predator–prey system having Holling type-I functional response. Our findings show that the predator–prey dynamics under prey’s herd behavior and anti-predator tactics can have large influence on shifting the paradigm of predator–prey relationship by turning the predator–prey dynamics into the prey dominant dynamics, which is indeed, due to the smart synergy between both ecological actions. When underdog, sticking together, fights back, that would be a headache to deal with, no matter how menacing the predator is.