Population dynamics with multiple Allee effects induced by fear factors – A mathematical study on prey-predator interactions

Abstract

• Mathematical models on effect of fear and strong Allee mechanism have been proposed and analysed. • We have shown how fear can significantly reduce the per-capita growth rate of prey with generalised predator. • We have shown that fear has no role in the stability of prey-predator system, with linear functional response. • Fear effect can stabilize the eco-epidemiological system and promote the coexistence of all the three populations. • Finally, fear may be a cause of the Allee effect/multiple Allee effects at low population density. In the present, ecologists generally consider the interactions, which are directly related to the density effects, that species have on each other, like predation, mutualism, refuge, etc. However, some experimental studies showed that apart from the direct killing, predation fears itself can reduce the prey growth rate by 40%. Therefore, in the present study, we have considered a trait effect, which is characterized by the reduction of prey growth rate due to fear of predator, where the prey is already suffered by the mating induced strong Allee effects, in the reproduction process. First, we developed and analyzed the single-species model and showed that how the fear effect can significantly reduce the per-capita growth rate (pgr) and may be a possible cause of the multiple Allee effects at low population density. Next, we consider a prey-predator model with linear functional response and showed that fear does not affect the equilibrium stability, but the time scale difference among two populations has a positive effect. It will help the system to converge to the stable steady states faster than before. Finally, we study an eco-epidemiological model with the same assumptions, where prey is being suffered by the disease. We showed that in eco-epidemiological systems fear can greatly affect the system stability. Fear can stabilize the system at the interior equilibrium, where all the three population coexists, or it can create the oscillatory coexistence of all the three populations. In the presence of fear, system shows bi-stability among different equilibria. We have also shown the basin stability at multiple stable parameter regions, which yields the probability of convergence of each equilibrium for a given set of different initial conditions. All these findings may have potential impacts in population management and conservation biology.