Fisher's fundamental theorem of natural selection is an idea about genetic variance [1] [2] in population genetics developed by the statistician and evolutionary biologist Ronald Fisher. The proper way of applying the abstract mathematics of the theorem to actual biology has been a matter of some debate, however, it is a true theorem. [3]
It states:
Or in more modern terminology:
The theorem was first formulated in Fisher's 1930 book The Genetical Theory of Natural Selection . [4] Fisher likened it to the law of entropy in physics, stating that "It is not a little instructive that so similar a law should hold the supreme position among the biological sciences". The model of quasi-linkage equilibrium was introduced by Motoo Kimura in 1965 as an approximation in the case of weak selection and weak epistasis. [6] [7]
Largely as a result of Fisher's feud with the American geneticist Sewall Wright about adaptive landscapes, the theorem was widely misunderstood to mean that the average fitness of a population would always increase, even though models showed this not to be the case. [8] In 1972, George R. Price showed that Fisher's theorem was indeed correct (and that Fisher's proof was also correct, given a typo or two), but did not find it to be of great significance. The sophistication that Price pointed out, and that had made understanding difficult, is that the theorem gives a formula for part of the change in gene frequency, and not for all of it. This is a part that can be said to be due to natural selection. [9]
Due to confounding factors, tests of the fundamental theorem are quite rare though Bolnick in 2007 did test this effect in a natural population. [10]
Evolution is the change in the heritable characteristics of biological populations over successive generations. It occurs when evolutionary processes such as natural selection and genetic drift act on genetic variation, resulting in some characteristics becoming more or less common within a population over successive generations. The process of evolution has given rise to biodiversity at every level of biological organisation.
Genetic drift, also known as random genetic drift, allelic drift or the Wright effect, refers to random fluctuations in the frequency of an existing gene variant (allele) in a population.
The modern synthesis was the early 20th-century synthesis of Charles Darwin's theory of evolution and Gregor Mendel's ideas on heredity into a joint mathematical framework. Julian Huxley coined the term in his 1942 book, Evolution: The Modern Synthesis. The synthesis combined the ideas of natural selection, Mendelian genetics, and population genetics. It also related the broad-scale macroevolution seen by palaeontologists to the small-scale microevolution of local populations.
Sir Ronald Aylmer Fisher was a British polymath who was active as a mathematician, statistician, biologist, geneticist, and academic. For his work in statistics, he has been described as "a genius who almost single-handedly created the foundations for modern statistical science" and "the single most important figure in 20th century statistics". In genetics, Fisher was the one to most comprehensively combine the ideas of Gregor Mendel and Charles Darwin, as his work used mathematics to combine Mendelian genetics and natural selection; this contributed to the revival of Darwinism in the early 20th-century revision of the theory of evolution known as the modern synthesis. For his contributions to biology, Richard Dawkins declared Fisher to be the greatest of Darwin's successors. He is also considered one of the founding fathers of Neo-Darwinism. According to statistician Jeffrey T. Leek, Fisher is the most influential scientist of all time based off the number of citations of his contributions.
Population genetics is a subfield of genetics that deals with genetic differences within and among populations, and is a part of evolutionary biology. Studies in this branch of biology examine such phenomena as adaptation, speciation, and population structure.
In evolutionary biology, sympatric speciation is the evolution of a new species from a surviving ancestral species while both continue to inhabit the same geographic region. In evolutionary biology and biogeography, sympatric and sympatry are terms referring to organisms whose ranges overlap so that they occur together at least in some places. If these organisms are closely related, such a distribution may be the result of sympatric speciation. Etymologically, sympatry is derived from Greek συν (sun-) 'together', and πατρίς (patrís) 'fatherland'. The term was coined by Edward Bagnall Poulton in 1904, who explains the derivation.
The Genetical Theory of Natural Selection is a book by Ronald Fisher which combines Mendelian genetics with Charles Darwin's theory of natural selection, with Fisher being the first to argue that "Mendelism therefore validates Darwinism" and stating with regard to mutations that "The vast majority of large mutations are deleterious; small mutations are both far more frequent and more likely to be useful", thus refuting orthogenesis. First published in 1930 by The Clarendon Press, it is one of the most important books of the modern synthesis, and helped define population genetics. It is commonly cited in biology books, outlining many concepts that are still considered important such as Fisherian runaway, Fisher's principle, reproductive value, Fisher's fundamental theorem of natural selection, Fisher's geometric model, the sexy son hypothesis, mimicry and the evolution of dominance. It was dictated to his wife in the evenings as he worked at Rothamsted Research in the day.
George Robert Price was an American population geneticist. Price is often noted for his formulation of the Price equation in 1967.
In evolutionary biology, inclusive fitness is one of two metrics of evolutionary success as defined by W. D. Hamilton in 1964:
Evolvability is defined as the capacity of a system for adaptive evolution. Evolvability is the ability of a population of organisms to not merely generate genetic diversity, but to generate adaptive genetic diversity, and thereby evolve through natural selection.
In the theory of evolution and natural selection, the Price equation describes how a trait or allele changes in frequency over time. The equation uses a covariance between a trait and fitness, to give a mathematical description of evolution and natural selection. It provides a way to understand the effects that gene transmission and natural selection have on the frequency of alleles within each new generation of a population. The Price equation was derived by George R. Price, working in London to re-derive W.D. Hamilton's work on kin selection. Examples of the Price equation have been constructed for various evolutionary cases. The Price equation also has applications in economics.
Genetic load is the difference between the fitness of an average genotype in a population and the fitness of some reference genotype, which may be either the best present in a population, or may be the theoretically optimal genotype. The average individual taken from a population with a low genetic load will generally, when grown in the same conditions, have more surviving offspring than the average individual from a population with a high genetic load. Genetic load can also be seen as reduced fitness at the population level compared to what the population would have if all individuals had the reference high-fitness genotype. High genetic load may put a population in danger of extinction.
Enquiry into the evolution of ageing, or aging, aims to explain why a detrimental process such as ageing would evolve, and why there is so much variability in the lifespans of organisms. The classical theories of evolution suggest that environmental factors, such as predation, accidents, disease, and/or starvation, ensure that most organisms living in natural settings will not live until old age, and so there will be very little pressure to conserve genetic changes that increase longevity. Natural selection will instead strongly favor genes which ensure early maturation and rapid reproduction, and the selection for genetic traits which promote molecular and cellular self-maintenance will decline with age for most organisms.
In population genetics, the Hill–Robertson effect, or Hill–Robertson interference, is a phenomenon first identified by Bill Hill and Alan Robertson in 1966. It provides an explanation as to why there may be an evolutionary advantage to genetic recombination.
The shifting balance theory is a theory of evolution proposed in 1932 by Sewall Wright, suggesting that adaptive evolution may proceed most quickly when a population divides into subpopulations with restricted gene flow. The name of the theory is borrowed from Wright's metaphor of fitness landscapes, attempting to explain how a population may move across an adaptive valley to a higher adaptive peak. According to the theory, this movement occurs in three steps:
Genetic variance is a concept outlined by the English biologist and statistician Ronald Fisher in his fundamental theorem of natural selection. In his 1930 book The Genetical Theory of Natural Selection, Fisher postulates that the rate of change of biological fitness can be calculated by the genetic variance of the fitness itself. Fisher tried to give a statistical formula about how the change of fitness in a population can be attributed to changes in the allele frequency. Fisher made no restrictive assumptions in his formula concerning fitness parameters, mate choices or the number of alleles and loci involved.
Reinforcement is a process of speciation where natural selection increases the reproductive isolation between two populations of species. This occurs as a result of selection acting against the production of hybrid individuals of low fitness. The idea was originally developed by Alfred Russel Wallace and is sometimes referred to as the Wallace effect. The modern concept of reinforcement originates from Theodosius Dobzhansky. He envisioned a species separated allopatrically, where during secondary contact the two populations mate, producing hybrids with lower fitness. Natural selection results from the hybrid's inability to produce viable offspring; thus members of one species who do not mate with members of the other have greater reproductive success. This favors the evolution of greater prezygotic isolation. Reinforcement is one of the few cases in which selection can favor an increase in prezygotic isolation, influencing the process of speciation directly. This aspect has been particularly appealing among evolutionary biologists.
In evolutionary biology, developmental bias refers to the production against or towards certain ontogenetic trajectories which ultimately influence the direction and outcome of evolutionary change by affecting the rates, magnitudes, directions and limits of trait evolution. Historically, the term was synonymous with developmental constraint, however, the latter has been more recently interpreted as referring solely to the negative role of development in evolution.
The infinitesimal model, also known as the polygenic model, is a widely used statistical model in quantitative genetics and in genome-wide association studies. Originally developed in 1918 by Ronald Fisher, it is based on the idea that variation in a quantitative trait is influenced by an infinitely large number of genes, each of which makes an infinitely small (infinitesimal) contribution to the phenotype, as well as by environmental factors. In "The Correlation between Relatives on the Supposition of Mendelian Inheritance", the original 1918 paper introducing the model, Fisher showed that if a trait is polygenic, "then the random sampling of alleles at each gene produces a continuous, normally distributed phenotype in the population". However, the model does not necessarily imply that the trait must be normally distributed, only that its genetic component will be so around the average of that of the individual's parents. The model served to reconcile Mendelian genetics with the continuous distribution of quantitative traits documented by Francis Galton.
Mark A. Kirkpatrick is a theoretical population geneticist and evolutionary biologist. He currently holds the T. S. Painter Centennial Professorship in Genetics in the Department of Integrative Biology at the University of Texas at Austin. His research touches on a wide variety of topics, including the evolution of sex chromosomes, sexual selection, and speciation. Kirkpatrick is the co-author, along with Douglas J. Futuyma, of a popular undergraduate evolution textbook. He is a member of the United States National Academy of Sciences.