Evolutionary Stability of Aposematic Coloration and Prey Unprofitability: A Theoretical Analysis

Abstract

Species that have evolved some defense against predators, here called unprofitable prey, often show aposematic (warning) coloration. The process whereby a predator learns not to attack unprofitable prey is an essential ingredient in the interaction between predators and such prey. Using learning theory and evolutionary game theory, we develop a model of predator-prey interactions, focusing on two characters: prey unprofitability and prey coloration. Both these characters are treated as one-dimensional variables, and it is assumed that variation in coloration causes variation in the rate at which prey are detected by predators. Regarding the two characters as strategies used by prey individuals, we determine evolutionarily stable strategies (ESS's). The coloration yielding the smallest possible rate of detection is called cryptic, and colorations yielding higher rates of detection are called aposematic. Two aspects of predator behavior are shown to be important for the stability of an aposematic strategy: a reluctance to attack prey more conspicuously colored than those so far encountered, and faster avoidance learning vis-a-vis prey with more conspicuous coloration. At least one of these factors must be present for an aposematic strategy to be an ESS. Similarly, two factors are important for the evolution of prey unprofitability: increased survival of attacks by a predator, and faster avoidance learning vis-a-vis more-unprofitable prey. If there is a nonpredatory cost associated with unprofitability, at least one of these factors must be present for an unprofitable strategy to be an ESS. The first factor mentioned, both for coloration and unprofitability, results in individual selection. The second factor, variation in the rate of avoidance learning caused by variation in the character, produces a selection pressure only if there is a correlation between prey phenotypes encountered by the predator. Such correlation may be the result of relatedness among prey individuals (resulting in kin selection) or repeated encounters with the same prey individual.