Fisher's principle
Encyclopedia
Fisher's principle explains why the sex ratio
of most 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.
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.
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
, 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
.
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.
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.)
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....
of most species is approximately 1:1. It was famously outlined by Ronald 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...
in his 1930 book The Genetical Theory of Natural Selection
The Genetical Theory of Natural Selection
The Genetical Theory of Natural Selection is a book by R.A. Fisher first published in 1930 by Clarendon. It is one of the most important books of the modern evolutionary synthesis and is commonly cited in biology books.-Editions:...
(but incorrectly attributed to Fisher as original). Nevertheless, A. W. F. Edwards
A. W. F. Edwards
Anthony William Fairbank Edwards is a British statistician, geneticist, and evolutionary biologist, sometimes called Fisher's Edwards. He is a Life Fellow of Gonville and Caius College and retired Professor of Biometry at the University of Cambridge, and holds both the ScD and LittD degrees. A...
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:-
- Suppose male births are less common than female.
- A newborn male then has better mating prospects than a newborn female, and therefore can expect to have more offspring.
- Therefore parents genetically disposed to produce males tend to have more than average numbers of grandchildren born to them.
- Therefore the genes for male-producing tendencies spread, and male births become more common.
- As the 1:1 sex ratio is approached, the advantage associated with producing males dies away.
- The same reasoning holds if females are substituted for males through-out. Therefore 1:1 is the equilibrium ratio.
Strictly speaking, this is not an 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), 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.
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 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 fitnessInclusive fitness
In evolutionary biology and evolutionary psychology, the inclusive fitness of an organism is the sum of its classical fitness and the number of equivalents of its own offspring it can add to the population by supporting others...
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
Charles Darwin
Charles Robert Darwin FRS was an English naturalist. He established that all species of life have descended over time from common ancestry, and proposed the scientific theory that this branching pattern of evolution resulted from a process that he called natural selection.He published his theory...
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
Evolutionary game theory
Evolutionary game theory is the application of Game Theory to evolving populations of lifeforms in biology. EGT is useful in this context by defining a framework of contests, strategies and analytics into which Darwinian competition can be modelled. It originated in 1973 with John Maynard Smith...
. R.H. MacArthur
Robert MacArthur
Robert Helmer MacArthur was an American ecologist who made a major impact on many areas of community and population ecology....
(1965) first suggested applying to sex ratios the language of game theory
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 this was subsequently picked up by W.D. Hamilton (1967) who termed the equilibrium point the "unbeatable strategy
Unbeatable strategy
In biology, the idea of an unbeatable strategy was proposed by W.D. Hamilton in his 1967 paper on sex ratios in Science. In this paper Hamilton discusses sex ratios as strategies in a game, and cites Verner as using this language in his 1965 paper which "claims to show that, given factors causing...
". Hamilton's unbeatable strategy was refined 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....
and 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...
(1973) into their concept of 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...
, i.e. one which cannot be invaded by a mutant strategy
Fisher's concept of parental expenditure (now termed parental investment
Parental investment
In evolutionary biology, parental investment is any parental expenditure that benefits one offspring at a cost to parents' ability to invest in other components of fitness...
), developed particularly by Robert Trivers
Robert Trivers
Robert L. Trivers is an American evolutionary biologist and sociobiologist and Professor of Anthropology and Biological Sciences at Rutgers University. Trivers is most noted for proposing the theories of reciprocal altruism , parental investment , facultative sex ratio determination , and...
is now an important concept in ecology
Ecology
Ecology is the scientific study of the relations that living organisms have with respect to each other and their natural environment. Variables of interest to ecologists include the composition, distribution, amount , number, and changing states of organisms within and among ecosystems...
.
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 DarwinCharles Darwin
Charles Robert Darwin FRS was an English naturalist. He established that all species of life have descended over time from common ancestry, and proposed the scientific theory that this branching pattern of evolution resulted from a process that he called natural selection.He published his theory...
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
The Genetical Theory of Natural Selection
The Genetical Theory of Natural Selection is a book by R.A. Fisher first published in 1930 by Clarendon. It is one of the most important books of the modern evolutionary synthesis and is commonly cited in biology books.-Editions:...
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 sciencePopular science
Popular science, sometimes called literature of science, is interpretation of science intended for a general audience. While science journalism focuses on recent scientific developments, popular science is broad-ranging, often written by scientists as well as journalists, and is presented in many...
books on evolution. For example, see:
- Stephen Jay GouldStephen Jay GouldStephen Jay Gould was an American paleontologist, evolutionary biologist, and historian of science. He was also one of the most influential and widely read writers of popular science of his generation....
(2002) The Structure of Evolutionary TheoryThe Structure of Evolutionary TheoryThe Structure of Evolutionary Theory is a technical book on macroevolutionary theory by the Harvard paleontologist Stephen Jay Gould, published only two months before his death. The volume is divided into two parts. The first is a historical study and exegesis of classical evolutionary thought,...
. (pages 648-649, 678, and 692 on sex ratio) - Richard DawkinsRichard DawkinsClinton Richard Dawkins, FRS, FRSL , known as Richard Dawkins, is a British ethologist, evolutionary biologist and author...
(2004) "The Seal's Tale", The Ancestor's TaleThe Ancestor's TaleThe Ancestor's Tale is a 2004 popular science book by Richard Dawkins, with contributions from Dawkins' research assistant Yan Wong. It follows the path of humans backwards through evolutionary history, meeting humanity's cousins as they converge on common ancestors...
, 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.)