Antipredator Behavior and the Population Dynamics of Simple Predator-Prey Systems

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Abstract
We derive a model that has one predator and one prey species and includes antipredator behavior. The prey are allowed to increase their investment in antipredator behavior, thereby decreasing their chance of being captured by the predator. However, they must pay for this protection by a cost exacted through decreased fecundity or increased mortality caused by factors other than predation. The population-dynamic consequences of antipredator behaviors are explored by comparing systems in which the efficiencies of the antipredator behavior differ; as the antipredator behavior becomes more efficient, the prey need to invest less in order to achieve the same level of protection from the predator. We assume that for any degree of efficiency, the prey choose their level of investment in antipredator behavior in order to optimize their expected reproductive fitness. By assuming only that the predators and prey coexist and that there is a stable equilibrium, we show that increased efficiency of antipredator behaviors increases prey densities and decreases the ratio of predator-to-prey densities. This is true even though the prey''s level of investment in antipredator behavior initially increases and then decreases with increasing efficiency of the antipredator behavior. Consequently, the effect of antipredator behaviors on population densities cannot be inferred from the level of prey investment in these behaviors. A specific model is used to illustrate the second result of the paper, that antipredator behaviors tend to decrease the oscillatory dynamics inherent in model predator-prey systems.