Fisher's principle is an evolutionary model that explains why the sex ratio of most sexual species is approximately 1:1. It was famously outlined by Ronald Fisher in his 1930 book The Genetical Theory of Natural Selection[1] (but incorrectly attributed to Fisher as original[2]). Nevertheless, A. W. F. Edwards has remarked that it is "probably the most celebrated argument in evolutionary biology".[2][3] Specifically, Fisher couched his argument in terms of parental expenditure, and predicted that parental expenditure on both sexes should be equal. Sex ratios that are 1:1 are hence known as "Fisherian", and those that are not 1:1 are "non-Fisherian" or "extraordinary" and occur because they break the assumptions made in Fisher's model.[4]
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W.D. Hamilton gave the following basic explanation in his 1967 paper on "Extraordinary sex ratios",[4] given the condition that males and females cost equal amounts to produce:
Strictly speaking, this is not an evolutionarily stable strategy (ESS), since all strategies have equal fitness when the sex ratio is 1:1 (i.e. an individual who produces strictly sons has just as many offspring as an individual producing sons and daughters with equal probability), and thus can invade the population.[5]
Specifically, Fisher frames his argument in terms of parental expenditure. In Chapter 6 "Sexual Reproduction and Sexual Selection" under the heading "Natural Selection and the sex-ratio" (p141)[1]:
A.W.F. Edwards has remarked that Fisher's principle is "probably the most celebrated argument in evolutionary biology"[2] (though this seems debatable; if Darwin's original arguments are arbitrarily excepted from consideration, W.D. Hamilton's concept of inclusive fitness at least rivals it), and has significance beyond merely finding an equilibrium value in the sex ratio.
Fisher's principle is an early example of a model in which genes for greater production of either sex become equalized in the population, because each sex supplies exactly half the genes of all future generations.
Fisher's principle is rooted in the concept of frequency-dependent selection, though Fisher's principle is not frequency-dependent selection per se. Frequency-dependent selection, in this scenario, is the logic that the probability of an individual being able to breed is dependent on the frequency of the opposite sex in relation to its own sex. It was first described by Darwin in 1871.
Fisher's principle extends frequency dependence to explain how natural selection can act on genes that affect the frequency of an individual's grandchildren without affecting the frequency of their children. Fisher predicted that parents will invest their resources equally between each sex of offspring, because each sex supplies exactly half the genes of all future generations. As a result, those genes that cause parents to invest unequally in the sexes will tend to be deselected. Fisher was aware that in humans, more boys are born, whilst boys are also more likely to die in infancy. As a consequence, he reasoned that because parents tend to invest less in boys - because more boys die before the end of the period of parental care - there is a higher rate of male births to equalise parental investment in each sex.
Fisher's principle is also the precursor to evolutionary game theory. R.H. MacArthur (1965) first suggested applying to sex ratios the language of game theory,[6] and this was subsequently picked up by W.D. Hamilton (1967) who termed the equilibrium point the "unbeatable strategy".[4] Hamilton's unbeatable strategy was refined by John Maynard Smith and George R. Price (1973) into their concept of the evolutionarily stable strategy, i.e. one which cannot be invaded by a mutant strategy[5]
Fisher's concept of parental expenditure (now termed parental investment), developed particularly by Robert Trivers is now an important concept in ecology.
Historical research by A.W.F. Edwards[2][7] has shown that the argument is incorrectly attributed to Fisher (the name is in common use and is unlikely to change). Charles Darwin had originally formulated a similar but somewhat confused argument in the first edition of The Descent of Man[8] but withdrew it for the second edition[9] -- Fisher only had a copy of the latter, and quotes Darwin in The Genetical Theory of Natural Selection[1]
Specifically, Carl Düsing of the University of Jena published this in three works between 1883–1884,[7] and this is essentially identical to Shaw and Mohler's later model.[10]
As "probably the most celebrated argument in evolutionary biology",[2] Fisher's principle is a staple of popular science books on evolution. For example, see:
For those wishing more advanced treatment, see the 2002 book Sex Ratios: Concepts and Research Methods edited by Ian C.W. Hardy, (chapters 1 and 2 by Ido Pen and Franz J. Weissing.)