Harvesting in discrete-time predator-prey systems

Fisheries for assemblages of interacting species with seasonal recruitment occur throughout temperate and boreal regions of the world ocean. Such systems are conveniently modeled within a difference-equation framework. Here, we examine the dynamic behavior of discrete-time models for an exploited predator-prey system. We contrast the dynamic properties of an aggregate production model and an age-structured model in which recruitment and mortality are explicitly considered. The joint effects of harvesting and interspecific interactions on the stability of the system are defined and contrasted with results for single species systems. We demonstrate that harvesting is a potentially stabilizing factor in the production model and in an age-structured model in which juveniles are harvested and that the relative magnitude of the interaction between predator and prey strongly affects the exploitation levels at which stabilization occurs. In contrast, harvesting is potentially destabilizing (i.e., results in complex dynamics) in an age-structured model with harvesting of adults only; again, the magnitude of the interaction determines the stability boundaries, with stronger interactions leading to a broader range of stable parameter space. In both the aggregate production model and the age-structured model with harvesting of juvenile predator and prey, exploitation effectively reduces the intrinsic rate of increase of the populations; for prey, this effect is amplified by high predation mortality rates. Sustainable levels of exploitation for both predators and prey are lower for the case where juveniles are harvested. Predators and resource harvesters can be viewed as competitors for the prey, and sustainable harvest levels are directly affected by the magnitude of predation mortality. These considerations expand the scope of issues to be resolved in fishery management to include factors such as trade-offs between mean yield and the potential for intrinsic variability and the role of predator-prey interactions in shaping the dynamics of exploited systems.