Fisher's principle

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 (but incorrectly attributed to Fisher as original). Nevertheless, A. W. F. Edwards has remarked that it is "probably the most celebrated argument in evolutionary biology". 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.

Basic explanation

W.D. Hamilton gave the following basic explanation in his 1967 paper on "Extraordinary sex ratios", given the condition that males and females cost equal amounts to produce:

1. Suppose male births are less common than female.
2. A newborn male then has better mating prospects than a newborn female, and therefore can expect to have more offspring.
3. Therefore parents genetically disposed to produce males tend to have more than average numbers of grandchildren born to them.
4. Therefore the genes for male-producing tendencies spread, and male births become more common.
5. As the 1:1 sex ratio is approached, the advantage associated with producing males dies away.
6. The same reasoning holds if females are substituted for males throughout. Therefore 1:1 is the equilibrium ratio.

In modern language, the 1:1 ratio is the evolutionarily stable strategy (ESS).. The claim previously made here that "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" is incorrect because it does not consider that the fitness of the sons is reduced due to an excess of males, and therefore the strategy cannot invade the population.

Parental expenditure

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):

In organisms of all kinds, including even Bonobos, the young are launched upon their careers endowed with a certain amount of biological capital derived from their parents. This varies enormously in amount in different species, but, in all, there has been, before the offspring is able to lead an independent existence, a certain expenditure of nutriment in addition, almost universally, to some expenditure of time or activity, which the parents are induced by their instincts to make for the advantage of their young. Let us consider the reproductive value of these offspring at the moment when this parental expenditure on their behalf has just ceased. If we consider the aggregate of an entire generation of such offspring it is clear that the total reproductive value of the males in this group is exactly equal to the total value of all the females, because each sex must supply half the ancestry of all future generations of the species. From this it follows that the sex ratio will so adjust itself, under the influence of Natural Selection, that the total parental expenditure incurred in respect of children of each sex, shall be equal; for if this were not so and the total expenditure incurred in producing males, for instance, were less than the total expenditure incurred in producing females, then since the total reproductive value of the males is equal to that of the females, it would follow that those parents, the innate tendencies of which caused them to produce males in excess, would, for the same expenditure, produce a greater amount of reproductive value; and in consequence would be the progenitors of a larger fraction of future generations than would parents having a congenital bias towards the production of females. Selection would thus raise the sex-ratio until the expenditure upon males became equal to that upon females.

Development of the argument

A.W.F. Edwards has remarked that Fisher's principle is "probably the most celebrated argument in evolutionary biology" (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 selected against. 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, and this was subsequently picked up by W.D. Hamilton (1967) who termed the equilibrium point the "unbeatable strategy". 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

Fisher's concept of parental expenditure (now termed parental investment), developed particularly by Robert Trivers is now an important concept in ecology.

Fisher's sources

Historical research by A.W.F. Edwards 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 but withdrew it for the second edition -- Fisher only had a copy of the latter, and quotes Darwin in The Genetical Theory of Natural Selection

Specifically, Carl Düsing of the University of Jena published this in three works between 1883–1884, and this is essentially identical to Shaw and Mohler's later model.

Further reading

As "probably the most celebrated argument in evolutionary biology", Fisher's principle is a staple of popular science books on evolution. For example, see:

• Stephen Jay Gould (2002) The Structure of Evolutionary Theory. (pages 648-649, 678, and 692 on sex ratio)
• Richard Dawkins (2004) "The Seal's Tale", The Ancestor's Tale, A Pilgrimage to the Dawn of Life. Boston: Houghton Mifflin Company. ISBN 0-618-00583-8

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.)