Explosive predator and mutualistic preys: A comparative study

Abstract

Mutualism is a powerful strategy by which species can assist each other to survive in various harsh environments. These will often take the form of anti-predator strategies. In the current manuscript we consider two preys that mutually benefit each other in the presence of a sexually reproductive generalist predator. In the absence of the predator, the prey grow logistically, and there is no mutualism between them. However, in the presence of the predator the prey will begin to cooperate. We formulate five different models according to their functional responses which are either prey dependent (Holling type-III, IV and Hassel Varley functional responses) or predator–prey dependent (Beddington–DeAngelis and Crowley–Martin functional responses). We perform dynamical analysis of these five models, and also establish the mathematical restrictions under which the species can blow up at a finite time. Interestingly it is observed that the prey populations will blow-up before the predator can. We use our results to comment on a certain paradox in ecological theory, as well as provide further insight into the nature of predator interference and exploding populations of invasive species.