We 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 in 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 increase, the system typically experiences transitions from predator extinction (for all initial conditions) to predator-prey oscillatory coexistence, to predator-prey nonoscillatory coexistence (outcomes depend on initial conditions). The possibility of bistability and tristability all leading to distinct outcomes is discussed. We argue that the impact of evolution is enhanced by the availability of refuges, the dispersal of fragile prey populations (strong Allee effect), and the existence of habitat-specific predators. 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 lifehistory 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.
|Number of pages||19|
|Journal||SIAM Journal on Applied Mathematics|
|State||Published - 27 Apr 2010|
- Allee's effects
- Dynamical system