Appendix 3 - Evolutionarily stable strategies and nonequilibrium

Abstract

Games Theory was developed by John von Neumann and Oskar Morgenstern (1944), although the French mathematician Antoine Augustin Cournot studied some aspects (1838, later further developed by John Forbes Nash) in the nineteenth century. Its most important contribution to evolutionary biology is the concept of evolutionarily stable strategy (ESS). It is central to modern evolutionary ecology, and Richard Dawkins (1976) suggests that it may be "one of the most important advances in evolutionary theory since Darwin". It was introduced into ecology by John Maynard Smith and George R. Price (1973). It can be derived from the concept of Nash Equilibrium (John Nash 1950), according to which none of a number of players in a game can gain by changing her/his strategy unilaterally. John Maynard Smith (1982) gave a detailed account of applications of Game Theory to evolutionary theory including ESS. However, parts of his book rely heavily on mathematics. Richard Dawkins' (1976) The Selfish Gene contains a discussion of ESS and many examples, clearly explained without any mathematics. According to Maynard Smith (1982), "An 'ESS' or 'evolutionarily stable strategy' is a strategy such that, if all the members of a population adopt it, no mutant strategy can invade". A strategy is a genetically determined behavioural "policy" ("course of action"). There may be more than one ESS for a population, and the type(s) of ESS depend on many characteristics of the members of a population, such as the genetic relatedness of the members in the population, population size, whether members of a population can learn from previous experience, whether populations reproduce asexually or sexually, whether contests are symmetric or asymmetric, etc. A symmetric game is one in which the adversaries start in similar situations and can choose the same strategies with the same potential payoffs (the changes in reproductive success due to the strategy). The game using dove-hawk strategies discussed below is an example of a symmetric game. It is important to realize that an ESS is not necessarily a strategy that is "best" for all the members of the population, i.e. guarantees the greatest fitness (reproductive success) for them in the long term. The reason is that genes (any proportion of genetic material potentially lasting long enough for natural selection to act on it as a unit) have no "foresight". They are selected on the basis of the present conditions in their environment.