This article uses several models to explore the potential indirect evolutionary interaction between two prey species that share one or more predator species. It asks how the antipredator adaptations of a focal prey species are likely to evolve following the introduction of a second prey species that shares one or more of the same predator species. The interactions are represented by differential equation models of homogeneous populations, and evolutionary change occurs in a single quantitative trait within each prey species. Models differ in assumptions about the number of predator types, the costs of antipredator traits, and in how predator and prey traits combine to determine a per capita capture rate. Parallel change in the antipredator characteristics of two species usually occurs when the general risk of predation is changed by the introduction of the second prey. This may be a parallel increase or decrease, depending on whether the ecological interaction is apparent competition or apparent mutualism. Divergence in trait values is most often associated with the presence of two or more distinct types of predators with some form of trade-off in the prey's ability to avoid different predators. Divergence may also occur with a single predator type, when two or more strategies exist for reducing predation risk. Convergence is a possible outcome when there are two or more predator types. Coevolution may also produce trait and population cycles in models, and the nature of character displacement is often changed markedly by such instability. The limited evidence for evolutionary indirect effects mediated by shared predation is reviewed. Possible reasons for the disparity between theory and observation are discussed.
Keywords: adaptive divergence; antipredator traits; apparent competition; character displacement; coevolution; indirect effects.