Modeling the Allee effects induced by cost of predation fear and its carry-over effects

Predation driven Allee effects play an important role in the dynamics of small population, however, such predation-driven Allee effects cannot occur for the model with type I functional response. It generally occurs when a generalist predator targets some specific prey. However, apart from the lethal effects of predation, there are some non-lethal effects in the presence of predator. Due to the fear of predation, positive density dependence growth may be observed at low population density, because of reduced foraging activities. Moreover, this non-lethal effect can be carried over generations. In the present manuscript, we investigate the role of predation fear and its carry-over effects in prey-predator model. First, we study the single species model in global perspective. We have shown that depending on the birth rate, our single species model describes three types of growth dynamics, namely, strong Allee dynamics, weak Allee dynamics and logistic dynamics. Then we consider the explicit dynamics of predator, with type I functional response. Basic dynamical properties, as well as global stability of each equilibria have been discussed. From our analysis, we can observe that both the fear and its carry-over effects have significant role in the stability of the coexistence equilibrium, even if for the model with type I functional response. The phenomenon paradox of enrichment can be observed in our model, which cannot be observed in the classical prey-predator model with type I functional response. However, we can see that such phenomenon can be ruled out by choosing suitable non-lethal effect parameters. Therefore, our study shows how non-lethal effects change the dynamics of a competition model, and has important biological insights, specially for the understanding of the dynamics of small populations.