A generalized predator- prey model: Uncertainty and management

Abstract

Predators that compete with humans for the harvest of prey often create a demand for predator-control programs. However, give that habitat reduction and a history of predator control may have already reduced the predator population on a local, national, continental, or even global basis, there may also be a demand to ensure the predator population's continued existence. In such cases it is important to consider the stability of the predator-prey system and how it might be affected by a predator-management program. The stability of the system depends upon its parameters, estimates of which may be uncertain. Hence the stability of the system may be uncertain and extinction may be a possibility. Improved estimates of the parameters would provide better information on system stability, and the Arrow-Fisher-Henry concept of option value becomes relevant in decisions regarding predator-control programs. This paper investigates stability conditions for a fairly general predator-prey model which exhibits self-limiting density effects and minimum viable population levels for both the predator and the prey. The intrinsic rates of increase in the two populations are assumed to be known only with error. Reductions in the variance of these parameters constitute improved information. Given that extinction is irreversible, a decision maker, who ignores the possibility of improving information about these parameters, will to some degree undervalue the social costs of a destablizing strategy. In the example used, wolves are predators, and a recreationally harvested ungulate (moose or caribou) is the prey.