The Effects of Predation and Inbreeding Depression on the Viability of a Small Population: Analysis of a Mathematical Model

The model of Hartt and Haefner (1995) which represents the combined effects of predation and inbreeding depression on a population is re-analysed. It is demonstrated that the system has two trivial equilibria with one or both species extinct and one non-trivial equilibrium with both species present. Conditions on parameter values for the existence of these equilibria are obtained explicitly. The effect of varying parameter values on the size of the two populations at non-trivial equilibrium is also obtained analytically. Local stability analysis is used to obtain an expression for the conditions under which this equilibrium will be stable or oscillatory. Inbreeding depression does not affect the stability of the model predator–prey system. These results are used to speculate on the static and dynamic effects of plausible modifications to the model structure. The principle conclusion is that inbreeding depression decreases the size of the predator population but not that of the prey. The practical implication of this result is that managers should be aware that the effect of inbreeding depression in one species may not be obvious in population changes in that species but may have a major impact in another species within the ecosystem.