Recent theories regarding the evolution of predator-prey interactions is reviewed. This includes theory about the dynamics and stability of both populations and traits, as well as theory predicting how predatory and anti-predator traits should respond to environmental changes. Evolution can stabilize or destabilize interactions; stability is most likely when only the predator evolves, or when traits in one or both species are under strong stabilizing selection. Stability seems least likely when there is coevolution and a bi-directional axis of prey vulnerability. When population cycles exist, adaptation may either increase or decrease the amplitude of those cycles. An increase in the defensive ability of prey is less likely to produce evolutionary counter- measures in its partner than is a comparable increase in attack ability of the predator. Increased productivity may increase or decrease offensive and defensive adaptations. The apparent predominance of evolutionary responses of prey to predators over those of predators to prey is in general accord with equilibrium theory, but theory on sta- bility may be difficult to confirm or refute. Recent work on geographically structured populations promises to advance our understanding of the evolution of predator-prey interactions.
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