Allee effect driven by predation: A study of Gause type predator-prey model

Abstract Reduced population growth at low population density has important implications for conservation, colonization success, and wildlife management. In this context, the Allee effect, i.e., the positive relationship between per capita growth rate and biomass at small population density, is a crucial biological phenomenon since it is directly related to population extinction. The present paper deals with a two-species interacting model with predator-prey relationship, where prey population experiences mate finding Allee effect caused by predator. Here we assume that an individual's searching efficiency decreases linearly with predator density due to predation, and investigate how predation intensity affects predator-prey dynamics. Moreover, we consider the Monod-Haldane type functional response for predator-prey interactions, which shows group defense of prey against the predator. We provide a detailed mathematical analysis, including positivity and boundedness of solutions, all biologically feasible equilibria, and their local and global stabilities. From our detailed mathematical analysis, we can observe that when the system carrying capacity is low, at most one interior equilibrium exists, and system dynamics is simple, compared to the case with high carrying capacity, in which multiple coexistence equilibria may exist. We discuss three co-dimension one bifurcations mathematically, e.g., Hopf-bifurcation, transcritical bifurcation, saddle-node bifurcation. We notice multi-stability in our system, where the system can be bi-stable when there are two-interior equilibria with high carrying capacity. However, a unique attractor exists when there is only a single interior equilibrium, and both populations persist. We perform extensive numerical simulations by varying two parameters simultaneously and explore how system dynamics are complex when carrying capacity is high compared to low carrying capacity. Moreover, in the numerical section, we discuss other important biological phenomena, e.g., the paradox of enrichment, bubbling, etc.