  Many theoretical models have been formulated to better understand the
coevolutionary patterns that emerge from antagonistic interactions. These
models usually assume that the attacks by the exploiters are random, so the
effect of victim selection by exploiters on coevolutionary patterns remains
unexplored. Here we analytically studied the payoff for predators and prey
under coevolution assuming that every individual predator can attack only a
small number of prey any given time, considering two scenarios: (i) predation
occurs at random; (ii) predators select prey according to phenotype matching.
We also develop an individual based model to verify the robustness of our
analytical prediction. We show that both scenarios result in well known similar
coevolutionary patterns if population sizes are sufficiently high: symmetrical
coevolutionary branching and symmetrical coevolutionary cycling (Red Queen
dynamics). However, for small population sizes, prey selection can cause
unexpected coevolutionary patterns. One is the breaking of symmetry of the
coevolutionary pattern, where the phenotypes evolve towards one of two
evolutionarily stable patterns. As population size increases, the phenotypes
oscillate between these two values in a novel form of Red Queen dynamics, the
episodic reversal between the two stable patterns. Thus, prey selection causes
prey phenotypes to evolve towards more extreme values, which reduces the
fitness of both predators and prey, increasing the likelihood of extinction.
