Contrasting effects of prey refuge on biodiversity of species

Abstract

Abstract Refugia have been perceived as a major role in structuring species biodiversity, and understanding the impacts of this force in a community assembly with prey–predator species is a difficult task because refuge process can interact with different ecological components and may show counterintuitive effects. To understand this problem, we used a simple two-species model incorporating a functional response inspired by a Holling type-II equation and a prey refuge mechanism that depends on prey and predator population densities (i.e., density-dependent prey refuge). We then perform the co-dimension one and co-dimension two bifurcation analysis to examine steady states and its stability, together with the bifurcation points as different parameters change. As the capacity of prey refuge is varied, there occur critical values i.e., saddle-node and supercritical Hopf bifurcations. The interaction between these two co-dimension one bifurcations engenders distinct outcomes of ecological system such as coexistence of species, bistability phenomena and oscillatory dynamics. Additionally, we construct a parameter space diagram illustrating the dynamics of species interactions as prey refuge intensity and predation pressure vary; as the two saddle-node move nearer to one another, these bifurcations annihilate tangentially in a co-dimension two cusp bifurcation. We also realised several contrasting observations of refuge process on species biodiversity: for instance, while it is believed that some refuge processes (e.g., constant proportion of prey refuge) would result in exclusion of predator species, our findings show that density-dependent prey refuge is beneficial for both predator and prey species, and consequently, promotes the maintenance of species biodiversity.