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Role of prey dispersal and refuges on predator-prey dynamics. (English) Zbl 1242.92056
The authors explore the population dynamics of predator-prey systems when their interactions are mediated by a prey population with access to a refuge. The emphasis is on situations when differences in prey abundance between refuge and nonrefuge habitats are the drivers of prey dispersal. It is shown that as dispersal between the prey-refuge and the predator-prey habitats increases, the system typically experiences transitions from predator extinction (for all initial conditions) to predator-prey oscillatory coexistence, to predator-prey non-oscillatory coexistence (outcomes depend on initial conditions). The possibility of bistability and tristability all leading to distinct outcomes is discussed. Differential outcomes (highly distinct joint predator-prey dynamics) turn out to be purely a function of the initial conditions. That is, the analyses in this paper show that diversity in predator-prey life-history dynamics must not necessarily be the result of sophisticated intrinsic biological mechanism like, for example, those responsible for genotypic differences. The variability may in fact be the result of random variation on the initial conditions of a system.
34C60Qualitative investigation and simulation of models (ODE)