In biology

Biology

Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...

, the idea of an unbeatable strategy was proposed by W.D. Hamilton in his 1967 paper on sex ratio

Sex ratio

Sex ratio is the ratio of males to females in a population. The primary sex ratio is the ratio at the time of conception, secondary sex ratio is the ratio at time of birth, and tertiary sex ratio is the ratio of mature organisms....

s in Science

Science (journal)

Science is the academic journal of the American Association for the Advancement of Science and is one of the world's top scientific journals....

. In this paper Hamilton discusses sex ratios as strategies

Strategy (game theory)

In game theory, a player's strategy in a game is a complete plan of action for whatever situation might arise; this fully determines the player's behaviour...

 in a game

Game theory

Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...

, and cites Verner as using this language in his 1965 paper which "claims to show that, given factors causing fluctuations of the population's primary sex ratio, a 1:1 sex-ratio production proves the best overall genotypic strategy".

"In the way in which the success of a chosen sex ratio depends on choices made by the co-parasitizing females, this problem resembles certain problems discussed in the "theory of games." In the foregoing analysis a game-like element, of a kind, was present and made necessary the use of the word unbeatable to describe the ratio finally established. This word was applied in just the same sense in which it could be applied to the "minimax" strategy of a zero-sum two-person game. Such a strategy should not, without qualification, be called optimum because it is not optimum against -although unbeaten by- any strategy differing from itself. This is exactly the case with the "unbeatable" sex ratios referred to." Hamilton (1967).

"[...] But if, on the contrary, players of such a game were motivated to outscore, they would find that is beaten by a higher ratio, ; the value of which gives its player the greatest possible advantage over the player playing , is found to be given by the relationship and shows to be the unbeatable play." Hamilton (1967).

The concept can be traced through R.A. Fisher

Ronald Fisher

Sir Ronald Aylmer Fisher FRS was an English statistician, evolutionary biologist, eugenicist and geneticist. Among other things, Fisher is well known for his contributions to statistics by creating Fisher's exact test and Fisher's equation...

 (1930) to Darwin (1859); see Edwards (1998). Hamilton did not explicitly define the term "unbeatable strategy" or apply the concept beyond the evolution of sex-ratios, but the idea was very influential. George R. Price

George R. Price

George Robert Price was an American population geneticist. Originally a physical chemist and later a science journalist, he moved to London in 1967, where he worked in theoretical biology at the Galton Laboratory, making three important contributions: first, rederiving W.D...

 generalised the verbal argument, which was then formalised mathematically by John Maynard Smith

John Maynard Smith

John Maynard Smith,His surname was Maynard Smith, not Smith, nor was it hyphenated. F.R.S. was a British theoretical evolutionary biologist and geneticist. Originally an aeronautical engineer during the Second World War, he took a second degree in genetics under the well-known biologist J.B.S....

, into the evolutionarily stable strategy

Evolutionarily stable strategy

In game theory and behavioural ecology, an evolutionarily stable strategy , which is sometimes also called an evolutionary stable strategy, is a strategy which, if adopted by a population of players, cannot be invaded by any alternative strategy that is initially rare. An ESS is an equilibrium...

(ESS).

External links

• http://www.iiasa.ac.at/Publications/Documents/IR-02-019.pdf