I have published a detailed discussion of games theory (Nash equilibria) applied to ecology as an electronic Appendix to my book Nonequilibrium Ecology, Cambridge University Press 2005 . For copyright reasons I include here only some excerpts, parts of the first and the second paragraph, as well as the summary. For the complete text please see the website of the book, “Resources and Solutions…free online support material, Appendix 3. “
The most important contribution of games theory“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.”………….
“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”).
“Types of ESS”
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.”An ESS is not necessarily best for all participants in the 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.”………….
“In summary, evolutionarily stable strategies are most likely in populations of animals belonging to the same species, when conditions remain relatively unchanged, and in the tropics. They are likely to structure predator-prey and host-parasite systems, but less likely to structure multi-species communities by interspecific competition, when conditions tend to change significantly over relatively short time spans, and at high latitudes. Even under long-term environmental stability, nonlinear evolutionary dynamics may prevent establishment of ESS’s and may even lead away from them.
This contribution contains some very brief excerpts from an electronic appendix to my book Nonequilibrium Ecology, Cambridge University Press, Cambridge (2005), for which I own copyright.