TheInfoList

Population genetics is a subfield of
genetics Genetics is a branch of biology Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemistry, chemical processes, Molecular biology, molecular interactions, Physiology, ...

that deals with genetic differences within and between
population Population typically refers the number of people in a single area whether it be a city or town, region, country, or the world. Governments typically quantify the size of the resident population within their jurisdiction by a process called a ...

s, and is a part of
evolutionary biology Evolutionary biology is the subfield of biology Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemistry, chemical processes, Molecular biology, molecular interacti ...
. Studies in this branch of
biology Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemistry, chemical processes, Molecular biology, molecular interactions, Physiology, physiological mechanisms, Development ...

examine such phenomena as
adaptation In , adaptation has three related meanings. Firstly, it is the dynamic evolutionary process that fits s to their environment, enhancing their . Secondly, it is a state reached by the population during that process. Thirdly, it is a or adapti ...
,
speciation Speciation is the evolution Evolution is change in the Heredity, heritable Phenotypic trait, characteristics of biological populations over successive generations. These characteristics are the Gene expression, expressions of genes that are ...

, and population structure. Population genetics was a vital ingredient in the
emergence In philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and Philosophy of language, ...

of the modern evolutionary synthesis. Its primary founders were
Sewall Wright Sewall Green Wright FRS(For) H FRSE (December 21, 1889March 3, 1988) was an American geneticist known for his influential work on evolutionary theory Evolutionary thought, the recognition that species change over time and the perceived unde ...

, and
Ronald Fisher Sir Ronald Aylmer Fisher (17 February 1890 – 29 July 1962) was a British polymath A polymath ( el, πολυμαθής, , "having learned much"; la, homo universalis, "universal human") is an individual whose knowledge spans a subs ...
, who also laid the foundations for the related discipline of
quantitative genetics Quantitative genetics deals with phenotype right , Here the relation between genotype and phenotype is illustrated, using a Punnett square, for the character of petal color in pea plants. The letters B and b represent genes for color, and t ...
. Traditionally a highly mathematical discipline, modern population genetics encompasses theoretical, laboratory, and field work. Population genetic models are used both for
statistical inference Statistical inference is the process of using data analysis Data analysis is a process of inspecting, Data cleansing, cleansing, Data transformation, transforming, and Data modeling, modeling data with the goal of discovering useful information ...
from DNA sequence data and for proof/disproof of concept. What sets population genetics apart from newer, more phenotypic approaches to modelling evolution, such as
evolutionary game theory Evolutionary game theory (EGT) is the application of game theory to evolving populations in biology. It defines a framework of contests, strategies, and analytics into which Darwinism, Darwinian competition can be modelled. It originated in 1973 wit ...
and adaptive dynamics, is its emphasis on such genetic phenomena as dominance,
epistasis File:Epistasis.png, Example of epistasis in coat colour genetics: If no pigments can be produced the other coat colour genes have no effect on the phenotype, no matter if they are dominant or if the individual is homozygous. Here the genotype "c ...

, the degree to which
genetic recombination Genetic recombination (also known as genetic reshuffling) is the exchange of genetic material between different organism In biology Biology is the natural science that studies life and living organisms, including their anatomy, ph ...
breaks
linkage disequilibrium In population genetics, linkage disequilibrium (LD) is the non-random association of allele An allele (, ; ; modern formation from Greek ἄλλος ''állos'', "other") is one of two, or more, forms of a given gene In biology, a gene (fr ...
, and the random phenomena of
mutation In biology Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemistry, chemical processes, Molecular biology, molecular interactions, Physiology, physiological mechan ...
and
genetic drift Genetic drift (allelic drift or the Sewall Wright effect) is the change in the frequency of an existing gene In biology Biology is the natural science that studies life and living organisms, including their anatomy, physical stru ...

. This makes it appropriate for comparison to population genomics data.

# History

Population genetics began as a reconciliation of
Mendelian inheritance Mendelian inheritance is a type of biological Biology is the natural science Natural science is a branch of science Science (from the Latin word ''scientia'', meaning "knowledge") is a systematic enterprise that Scientific me ...

and
biostatistics Biostatistics (also known as biometry) are the development and application of statistical Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data are units of in ...
models.
Natural selection Natural selection is the differential survival and reproduction of individuals due to differences in phenotype right , Here the relation between genotype and phenotype is illustrated, using a Punnett square, for the character of peta ...
will only cause evolution if there is enough
genetic variation thumb File:Genetic Variation and Inheritance.svg, Parents have similar gene coding in this specific situation where they reproduce and variation in the offspring is seen. Offspring containing the variation also reproduce and passes down traits t ...

in a population. Before the discovery of
Mendelian genetics Mendelian inheritance is a type of biological inheritance Inheritance is the practice of passing on private property, titles A title is one or more words used before or after a person's name, in certain contexts. It may signify either ...
, one common hypothesis was
blending inheritance Blending inheritance is an Superseded scientific theories, obsolete theory in biology from the 19th century. The theory is that the progeny inheritance (biology), inherits any characteristic as the average of the parents' values of that characteris ...

. But with blending inheritance, genetic variance would be rapidly lost, making evolution by natural or sexual selection implausible. The
Hardy–Weinberg principle In population genetics, the Hardy–Weinberg principle, also known as the Hardy–Weinberg equilibrium, model, theorem, or law, states that allele An allele (, ; ; modern formation from Greek ἄλλος ''állos'', "other") is one of two, o ...
provides the solution to how variation is maintained in a population with Mendelian inheritance. According to this principle, the frequencies of alleles (variations in a gene) will remain constant in the absence of selection, mutation, migration and genetic drift. The next key step was the work of the British biologist and statistician
Ronald Fisher Sir Ronald Aylmer Fisher (17 February 1890 – 29 July 1962) was a British polymath A polymath ( el, πολυμαθής, , "having learned much"; la, homo universalis, "universal human") is an individual whose knowledge spans a subs ...
. In a series of papers starting in 1918 and culminating in his 1930 book ''
The Genetical Theory of Natural Selection ''The Genetical Theory of Natural Selection'' is a book by Ronald Fisher Sir Ronald Aylmer Fisher (17 February 1890 – 29 July 1962) was a British statistician, geneticist, and academic. For his work in statistics, he has been describ ...
'', Fisher showed that the continuous variation measured by the biometricians could be produced by the combined action of many discrete genes, and that natural selection could change allele frequencies in a population, resulting in evolution. In a series of papers beginning in 1924, another British geneticist, , worked out the mathematics of allele frequency change at a single gene
locus Locus (plural loci) is Latin for "place". It may refer to: Entertainment * Locus (comics), a Marvel Comics mutant villainess, a member of the Mutant Liberation Front * Locus (magazine), ''Locus'' (magazine), science fiction and fantasy magazine ...
under a broad range of conditions. Haldane also applied statistical analysis to real-world examples of natural selection, such as
peppered moth evolution The evolution of the peppered moth is an evolutionary instance of directional colour change in the moth population as a consequence of air pollution during the Industrial Revolution The Industrial Revolution was the transition to new man ...
and
industrial melanism Industrial melanism is an evolution Evolution is change in the Heredity, heritable Phenotypic trait, characteristics of biological populations over successive generations. These characteristics are the Gene expression, expressions of genes ...
, and showed that
selection coefficient In population genetics, a selection coefficient, usually denoted by the letter ''s'', is a measure of differences in relative Fitness (biology), fitness. Selection coefficients are central to the quantitative description of evolution, since fitness ...
s could be larger than Fisher assumed, leading to more rapid adaptive evolution as a camouflage strategy following increased pollution. The American biologist
Sewall Wright Sewall Green Wright FRS(For) H FRSE (December 21, 1889March 3, 1988) was an American geneticist known for his influential work on evolutionary theory Evolutionary thought, the recognition that species change over time and the perceived unde ...

, who had a background in
animal breeding Animal breeding is a branch of animal science Animal science (also bioscience) is described as "studying the biology Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Bioch ...
experiments, focused on combinations of interacting genes, and the effects of
inbreeding Inbreeding is the production of offspring In biology, offspring are the young creation of living organisms, produced either by a Asexual reproduction, single organism or, in the case of sexual reproduction, two organisms. Collective offspri ...
on small, relatively isolated populations that exhibited genetic drift. In 1932 Wright introduced the concept of an adaptive landscape and argued that genetic drift and inbreeding could drive a small, isolated sub-population away from an adaptive peak, allowing natural selection to drive it towards different adaptive peaks. The work of Fisher, Haldane and Wright founded the discipline of population genetics. This integrated natural selection with Mendelian genetics, which was the critical first step in developing a unified theory of how evolution worked.
John Maynard Smith John Maynard Smith (6 January 1920 – 19 April 2004) was a British theoretical and mathematical evolutionary biologist Evolutionary biology is the subfield of biology that studies the evolutionary processes ( natural selection, commo ...

was Haldane's pupil, whilst W. D. Hamilton was influenced by the writings of Fisher. The American George R. Price worked with both Hamilton and Maynard Smith. American
Richard Lewontin Richard Charles Lewontin (March 29, 1929 – July 4, 2021) was an American evolutionary biologist Evolutionary biology is the subfield of biology that studies the evolutionary processes ( natural selection, common descent, speciation) that ...
and Japanese
Motoo Kimura (November 13, 1924 – November 13, 1994) was a Japanese Japanese may refer to: * Something from or related to Japan , image_flag = Flag of Japan.svg , alt_flag = Centered deep red circle on a white r ...
were influenced by Wright and Haldane.

## Modern synthesis

The mathematics of population genetics were originally developed as the beginning of the
modern synthesis Modern synthesis or modern evolutionary synthesis refers to several perspectives on evolutionary biology, namely: * Modern synthesis (20th century), the term coined by Julian Huxley in 1942 to denote the synthesis between Mendelian genetics and s ...
. Authors such as Beatty have asserted that population genetics defines the core of the modern synthesis. For the first few decades of the 20th century, most field naturalists continued to believe that
Lamarckism Lamarckism, also known as Lamarckian inheritance or neo-Lamarckism, is the notion that an organism In biology, an organism (from Ancient Greek, Greek: ὀργανισμός, ''organismos'') is any individual contiguous system that embodies ...

and
orthogenesis Orthogenesis, also known as orthogenetic evolution, progressive evolution, evolutionary progress, or progressionism, is the biological hypothesis that organism In biology, an organism (from Ancient Greek, Greek: ὀργανισμός, '' ...
provided the best explanation for the complexity they observed in the living world. During the modern synthesis, these ideas were purged, and only evolutionary causes that could be expressed in the mathematical framework of population genetics were retained. Consensus was reached as to which evolutionary factors might influence evolution, but not as to the relative importance of the various factors.
Theodosius Dobzhansky Theodosius Grygorovych Dobzhansky ( uk, Теодо́сій Григо́рович Добжа́нський; russian: Феодо́сий Григо́рьевич Добржа́нский; January 25, 1900 – December 18, 1975) was a prominent Ukr ...
, a postdoctoral worker in T. H. Morgan's lab, had been influenced by the work on
genetic diversity Genetic diversity is the total number of genetic characteristics in the genetic makeup of a species, it ranges widely from the number of species to differences within species In biology, a species is the basic unit of biological classificati ...
by Russian geneticists such as . He helped to bridge the divide between the foundations of
microevolution Microevolution is the change in allele frequencies that occurs over time within a population. This change is due to four different processes: mutation, selection (natural selection, natural and artificial selection, artificial), gene flow and ge ...
developed by the population geneticists and the patterns of
macroevolution Macroevolution in the modern sense is evolution that is guided by selection among interspecific variation, as opposed to selection among intraspecific variation in microevolution Microevolution is the change in allele frequencies that occurs ...
observed by field biologists, with his 1937 book ''
Genetics and the Origin of Species ''Genetics and the Origin of Species'' is a 1937 book by the Ukrainian-American evolutionary biologist Theodosius Dobzhansky Theodosius Grygorovych Dobzhansky ( uk, Теодо́сій Григо́рович Добжа́нський; russian: Ф ...
''. Dobzhansky examined the genetic diversity of wild populations and showed that, contrary to the assumptions of the population geneticists, these populations had large amounts of genetic diversity, with marked differences between sub-populations. The book also took the highly mathematical work of the population geneticists and put it into a more accessible form. Many more biologists were influenced by population genetics via Dobzhansky than were able to read the highly mathematical works in the original. In Great Britain E. B. Ford, the pioneer of
ecological genetics Ecological genetics is the study of genetics in natural populations. Traits in a population can be observed and quantified to represent a species adapting to a changing environment. This contrasts with classical genetics, which works mostly o ...
, continued throughout the 1930s and 1940s to empirically demonstrate the power of selection due to ecological factors including the ability to maintain genetic diversity through genetic polymorphisms such as human
blood type A blood type (also known as a blood group) is a classification of blood Blood is a body fluid Body fluids, bodily fluids, or biofluids are liquid A liquid is a nearly incompressible In fluid mechanics or more generally continuum ...
s. Ford's work, in collaboration with Fisher, contributed to a shift in emphasis during the modern synthesis towards natural selection as the dominant force.

## Neutral theory and origin-fixation dynamics

The original, modern synthesis view of population genetics assumes that mutations provide ample raw material, and focuses only on the change in frequency of alleles within
population Population typically refers the number of people in a single area whether it be a city or town, region, country, or the world. Governments typically quantify the size of the resident population within their jurisdiction by a process called a ...

s. The main processes influencing allele frequencies are
natural selection Natural selection is the differential survival and reproduction of individuals due to differences in phenotype right , Here the relation between genotype and phenotype is illustrated, using a Punnett square, for the character of peta ...
,
genetic drift Genetic drift (allelic drift or the Sewall Wright effect) is the change in the frequency of an existing gene In biology Biology is the natural science that studies life and living organisms, including their anatomy, physical stru ...

,
gene flow In population genetics Population genetics is a subfield of that deals with genetic differences within and between s, and is a part of . Studies in this branch of examine such phenomena as , , and . Population genetics was a vital ingredient ...

and recurrent
mutation In biology Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemistry, chemical processes, Molecular biology, molecular interactions, Physiology, physiological mechan ...
. Fisher and Wright had some fundamental disagreements about the relative roles of selection and drift. The availability of molecular data on all genetic differences led to the
neutral theory of molecular evolution The neutral theory of molecular evolution holds that most evolutionary changes occur at the molecular level, and most of the variation within and between species are due to random genetic drift Genetic drift (allelic drift or the Sewall Wright ...
. In this view, many mutations are deleterious and so never observed, and most of the remainder are neutral, i.e. are not under selection. With the fate of each neutral mutation left to chance (genetic drift), the direction of evolutionary change is driven by which mutations occur, and so cannot be captured by models of change in the frequency of (existing) alleles alone. The origin-fixation view of population genetics generalizes this approach beyond strictly neutral mutations, and sees the rate at which a particular change happens as the product of the mutation rate and the fixation probability.

# Four processes

## Selection

Natural selection Natural selection is the differential survival and reproduction of individuals due to differences in phenotype right , Here the relation between genotype and phenotype is illustrated, using a Punnett square, for the character of peta ...
, which includes
sexual selection Sexual selection is a mode of natural selection Natural selection is the differential survival and reproduction of individuals due to differences in phenotype right , Here the relation between genotype and phenotype is illustrat ...
, is the fact that some
traits Trait may refer to: * Phenotypic trait in biology, which involve genes and characteristics of organisms * Trait (computer programming), a model for structuring object-oriented programs (a template class in the C++ programming language) * Trait the ...
make it more likely for an
organism In biology Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemistry, chemical processes, Molecular biology, molecular interactions, Physiology, physiological ...

to survive and
reproduce Reproduction (or procreation or breeding) is the biological process Biological processes are those processes that are vital for an organism In biology, an organism (from Ancient Greek, Greek: ὀργανισμός, ''organismos'') is ...

. Population genetics describes natural selection by defining fitness as a propensity or probability of survival and reproduction in a particular environment. The fitness is normally given by the symbol w=1-s where s is the
selection coefficient In population genetics, a selection coefficient, usually denoted by the letter ''s'', is a measure of differences in relative Fitness (biology), fitness. Selection coefficients are central to the quantitative description of evolution, since fitness ...
. Natural selection acts on
phenotype In genetics Genetics is a branch of biology Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemistry, chemical processes, Molecular biology, molecular inter ...

s, so population genetic models assume relatively simple relationships to predict the phenotype and hence fitness from the
allele An allele (, ; ; modern formation from Greek ἄλλος ''állos'', "other") is one of two, or more, forms of a given gene In biology, a gene (from ''genos'' "...Wilhelm Johannsen coined the word gene to describe the Mendelian_inheritance ...
at one or a small number of loci. In this way, natural selection converts differences in the fitness of individuals with different phenotypes into changes in allele frequency in a population over successive generations. Before the advent of population genetics, many biologists doubted that small differences in fitness were sufficient to make a large difference to evolution. Population geneticists addressed this concern in part by comparing selection to
genetic drift Genetic drift (allelic drift or the Sewall Wright effect) is the change in the frequency of an existing gene In biology Biology is the natural science that studies life and living organisms, including their anatomy, physical stru ...

. Selection can overcome genetic drift when s is greater than 1 divided by the
effective population size The effective population size (''N'e'') is the number of individuals that an idealised population would need to have in order for some specified quantity of interest to be the same in the idealised population as in the real population. Idealised ...
. When this criterion is met, the probability that a new advantageous mutant becomes
fixed Fixed may refer to: * Fixed (EP), ''Fixed'' (EP), EP by Nine Inch Nails * ''Fixed'', an upcoming 3D adult animated film directed by Genndy Tartakovsky * Fixed (typeface), a collection of monospace bitmap fonts that is distributed with the X Window ...
is approximately equal to 2s. The time until fixation of such an allele depends little on genetic drift, and is approximately proportional to log(sN)/s.

### Dominance

Dominance means that the phenotypic and/or fitness effect of one allele at a locus depends on which allele is present in the second copy for that locus. Consider three genotypes at one locus, with the following fitness values s is the
selection coefficient In population genetics, a selection coefficient, usually denoted by the letter ''s'', is a measure of differences in relative Fitness (biology), fitness. Selection coefficients are central to the quantitative description of evolution, since fitness ...
and h is the dominance coefficient. The value of h yields the following information:

### Epistasis

Epistasis File:Epistasis.png, Example of epistasis in coat colour genetics: If no pigments can be produced the other coat colour genes have no effect on the phenotype, no matter if they are dominant or if the individual is homozygous. Here the genotype "c ...

means that the phenotypic and/or fitness effect of an allele at one locus depends on which alleles are present at other loci. Selection does not act on a single locus, but on a phenotype that arises through development from a complete genotype. However, many population genetics models of sexual species are "single locus" models, where the fitness of an individual is calculated as the product of the contributions from each of its loci—effectively assuming no epistasis. In fact, the genotype to fitness landscape is more complex. Population genetics must either model this complexity in detail, or capture it by some simpler average rule. Empirically, beneficial mutations tend to have a smaller fitness benefit when added to a genetic background that already has high fitness: this is known as diminishing returns epistasis. When deleterious mutations also have a smaller fitness effect on high fitness backgrounds, this is known as "synergistic epistasis". However, the effect of deleterious mutations tends on average to be very close to multiplicative, or can even show the opposite pattern, known as "antagonistic epistasis". Synergistic epistasis is central to some theories of the purging of mutation load and to the
evolution of sexual reproduction Sexual reproduction is an adaptive feature which is common to almost all multi-cellular organisms (and also some single-cellular organisms) with many being incapable of asexual reproduction, reproducing asexually. Prior to the advent of sexual ...
.

## Mutation

Mutation is the ultimate source of
genetic variation thumb File:Genetic Variation and Inheritance.svg, Parents have similar gene coding in this specific situation where they reproduce and variation in the offspring is seen. Offspring containing the variation also reproduce and passes down traits t ...

in the form of new alleles. In addition, mutation may influence the direction of evolution when there is mutation bias, i.e. different probabilities for different mutations to occur. For example, recurrent mutation that tends to be in the opposite direction to selection can lead to
mutation–selection balance Mutation–selection balance is an equilibrium in the number of deleterious alleles in a population that occurs when the rate at which deleterious alleles are created by mutation equals the rate at which deleterious alleles are eliminated by Natural ...
. At the molecular level, if mutation from G to A happens more often than mutation from A to G, then genotypes with A will tend to evolve. Different insertion vs. deletion mutation biases in different taxa can lead to the evolution of different genome sizes. Developmental or mutational biases have also been observed in morphological evolution. For example, according to the phenotype-first theory of evolution, mutations can eventually cause the
genetic assimilation Genetic assimilation is a process described by Conrad H. Waddington by which a phenotype right , Here the relation between genotype and phenotype is illustrated, using a Punnett square, for the character of petal color in pea plants. The let ...
of traits that were previously induced by the environment. Mutation bias effects are superimposed on other processes. If selection would favor either one out of two mutations, but there is no extra advantage to having both, then the mutation that occurs the most frequently is the one that is most likely to become fixed in a population. Mutation can have no effect, alter the product of a gene, or prevent the gene from functioning. Studies in the fly '''' suggest that if a mutation changes a protein produced by a gene, this will probably be harmful, with about 70 percent of these mutations having damaging effects, and the remainder being either neutral or weakly beneficial. Most loss of function mutations are selected against. But when selection is weak, mutation bias towards loss of function can affect evolution. For example,
pigment A pigment is a colored material that is completely or nearly insoluble in water. In contrast, dyes are typically soluble, at least at some stage in their use. Generally dyes are often organic compound , CH4; is among the simplest organic compou ...
s are no longer useful when animals live in the darkness of caves, and tend to be lost. This kind of loss of function can occur because of mutation bias, and/or because the function had a cost, and once the benefit of the function disappeared, natural selection leads to the loss. Loss of
sporulation )'', growing on a thinned hybrid black poplar ''(Populus x canadensis)''. The last stage of the moss lifecycle is shown, where the sporophytes are visible before dispersion of their spores: the calyptra (1) is still attached to the capsule ( ...
ability in a
bacterium Bacteria (; common noun bacteria, singular bacterium) are ubiquitous, mostly free-living organisms often consisting of one biological cell The cell (from Latin ''cella'', meaning "small room") is the basic structural, functional, and ...

during laboratory evolution appears to have been caused by mutation bias, rather than natural selection against the cost of maintaining sporulation ability. When there is no selection for loss of function, the speed at which loss evolves depends more on the mutation rate than it does on the
effective population size The effective population size (''N'e'') is the number of individuals that an idealised population would need to have in order for some specified quantity of interest to be the same in the idealised population as in the real population. Idealised ...
, indicating that it is driven more by mutation bias than by genetic drift. Mutations can involve large sections of DNA becoming duplicated, usually through
genetic recombination Genetic recombination (also known as genetic reshuffling) is the exchange of genetic material between different organism In biology Biology is the natural science that studies life and living organisms, including their anatomy, ph ...
copy-number variation Copy number variation (CNV) is a phenomenon in which sections of the genome are repeated and the number of repeats in the genome varies between individuals. Copy number variation is a type of structural variation: specifically, it is a type of Ge ...
within a population. Duplications are a major source of raw material for evolving new genes. Other types of mutation occasionally create new genes from previously noncoding DNA.

## Genetic drift

''Genetic drift'' is a change in allele frequencies caused by
random sampling In statistics, quality assurance, and Statistical survey, survey methodology, sampling is the selection of a subset (a statistical sample) of individuals from within a population (statistics), statistical population to estimate characteristics o ...
. That is, the alleles in the offspring are a random sample of those in the parents. Genetic drift may cause gene variants to disappear completely, and thereby reduce genetic variability. In contrast to natural selection, which makes gene variants more common or less common depending on their reproductive success, the changes due to genetic drift are not driven by environmental or adaptive pressures, and are equally likely to make an allele more common as less common. The effect of genetic drift is larger for alleles present in few copies than when an allele is present in many copies. The population genetics of genetic drift are described using either
branching process In probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressi ...
es or a
diffusion equation The diffusion equation is a parabolic partial differential equation. In physics, it describes the macroscopic behavior of many micro-particles in Brownian motion, resulting from the random movements and collisions of the particles (see Fick's law ...
describing changes in allele frequency. These approaches are usually applied to the Wright-Fisher and Moran models of population genetics. Assuming genetic drift is the only evolutionary force acting on an allele, after t generations in many replicated populations, starting with allele frequencies of p and q, the variance in allele frequency across those populations is :$V_t \approx pq\left\left(1-\exp\left\\right\right).$
Ronald Fisher Sir Ronald Aylmer Fisher (17 February 1890 – 29 July 1962) was a British polymath A polymath ( el, πολυμαθής, , "having learned much"; la, homo universalis, "universal human") is an individual whose knowledge spans a subs ...
held the view that genetic drift plays at the most a minor role in evolution, and this remained the dominant view for several decades. No population genetics perspective have ever given genetic drift a central role by itself, but some have made genetic drift important in combination with another non-selective force. The
shifting balance theory Image:fitness-landscape-cartoon.png, Sketch of a fitness landscape. The arrows indicate the preferred flow of a population on the landscape. The red ball indicates a population that moves from an adaptive valley to the top of an adaptive peak. Unde ...
of
Sewall Wright Sewall Green Wright FRS(For) H FRSE (December 21, 1889March 3, 1988) was an American geneticist known for his influential work on evolutionary theory Evolutionary thought, the recognition that species change over time and the perceived unde ...

held that the combination of population structure and genetic drift was important.
Motoo Kimura (November 13, 1924 – November 13, 1994) was a Japanese Japanese may refer to: * Something from or related to Japan , image_flag = Flag of Japan.svg , alt_flag = Centered deep red circle on a white r ...
's
neutral theory of molecular evolution The neutral theory of molecular evolution holds that most evolutionary changes occur at the molecular level, and most of the variation within and between species are due to random genetic drift Genetic drift (allelic drift or the Sewall Wright ...
claims that most genetic differences within and between populations are caused by the combination of neutral mutations and genetic drift. The role of genetic drift by means of
sampling errorIn statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a ...
in evolution has been criticized by John H Gillespie and Will Provine, who argue that selection on linked sites is a more important stochastic force, doing the work traditionally ascribed to genetic drift by means of sampling error. The mathematical properties of genetic draft are different from those of genetic drift. The direction of the random change in allele frequency is autocorrelated across generations.

## Gene flow

Because of physical barriers to migration, along with the limited tendency for individuals to move or spread ( vagility), and tendency to remain or come back to natal place (philopatry), natural populations rarely all interbreed as may be assumed in theoretical random models (panmixy). There is usually a geographic range within which individuals are more closely coefficient of relatedness, related to one another than those randomly selected from the general population. This is described as the extent to which a population is genetically structured. Genetic structuring can be caused by migration due to historical climate change (general concept), climate change, species range expansion or current availability of habitat. Gene flow is hindered by mountain ranges, oceans and deserts or even man-made structures such as the Great Wall of China, which has hindered the flow of plant genes. Gene flow is the exchange of genes between populations or species, breaking down the structure. Examples of gene flow within a species include the migration and then breeding of organisms, or the exchange of pollen. Gene transfer between species includes the formation of Hybrid (biology), hybrid organisms and horizontal gene transfer. Population genetic models can be used to identify which populations show significant genetic isolation from one another, and to reconstruct their history. Subjecting a population to isolation leads to inbreeding depression. Migration into a population can introduce new genetic variants, potentially contributing to evolutionary rescue. If a significant proportion of individuals or gametes migrate, it can also change allele frequencies, e.g. giving rise to Genetic load#Migration load, migration load. In the presence of gene flow, other reproductive isolation, barriers to hybridization between two diverging populations of an outcrossing species are required for the populations to speciation, become new species.

### Horizontal gene transfer

Horizontal gene transfer is the transfer of genetic material from one organism to another organism that is not its offspring; this is most common among prokaryotes. In medicine, this contributes to the spread of antibiotic resistance, as when one bacteria acquires resistance genes it can rapidly transfer them to other species. Horizontal transfer of genes from bacteria to eukaryotes such as the yeast ''Saccharomyces cerevisiae'' and the adzuki bean beetle ''Callosobruchus chinensis'' may also have occurred. An example of larger-scale transfers are the eukaryotic Bdelloidea, bdelloid rotifers, which appear to have received a range of genes from bacteria, fungi, and plants. Viruses can also carry DNA between organisms, allowing transfer of genes even across domain (biology), biological domains. Large-scale gene transfer has also occurred between the ancestors of eukaryote, eukaryotic cells and prokaryotes, during the acquisition of chloroplasts and Mitochondrion, mitochondria.

If all genes are in linkage equilibrium, the effect of an allele at one locus can be averaged across the gene pool at other loci. In reality, one allele is frequently found in
linkage disequilibrium In population genetics, linkage disequilibrium (LD) is the non-random association of allele An allele (, ; ; modern formation from Greek ἄλλος ''állos'', "other") is one of two, or more, forms of a given gene In biology, a gene (fr ...
with genes at other loci, especially with genes located nearby on the same chromosome. Recombination (biology), Recombination breaks up this linkage disequilibrium too slowly to avoid genetic hitchhiking, where an allele at one locus rises to high frequency because it is genetic linkage, linked to an allele under selection at a nearby locus. Linkage also slows down the rate of adaptation, even in sexual populations. The effect of linkage disequilibrium in slowing down the rate of adaptive evolution arises from a combination of the Hill–Robertson effect (delays in bringing beneficial mutations together) and background selection (delays in separating beneficial mutations from deleterious genetic hitchhiking, hitchhikers). Linkage is a problem for population genetic models that treat one gene locus at a time. It can, however, be exploited as a method for detecting the action of
natural selection Natural selection is the differential survival and reproduction of individuals due to differences in phenotype right , Here the relation between genotype and phenotype is illustrated, using a Punnett square, for the character of peta ...
via selective sweeps. In the extreme case of an asexual reproduction, asexual population, linkage is complete, and population genetic equations can be derived and solved in terms of a travelling wave of genotype frequencies along a simple fitness landscape. Most microorganisms, microbes, such as bacteria, are asexual. The population genetics of their adaptation have two contrasting regimes. When the product of the beneficial mutation rate and population size is small, asexual populations follow a "successional regime" of origin-fixation dynamics, with adaptation rate strongly dependent on this product. When the product is much larger, asexual populations follow a "concurrent mutations" regime with adaptation rate less dependent on the product, characterized by clonal interference and the appearance of a new beneficial mutation before the last one has Fixation (population genetics), fixed.

# Applications

## Explaining levels of genetic variation

neutral theory of molecular evolution, Neutral theory predicts that the level of nucleotide diversity in a population will be proportional to the product of the population size and the neutral mutation rate. The fact that levels of genetic diversity vary much less than population sizes do is known as the "paradox of variation". While high levels of genetic diversity were one of the original arguments in favor of neutral theory, the paradox of variation has been one of the strongest arguments against neutral theory. It is clear that levels of genetic diversity vary greatly within a species as a function of local recombination rate, due to both genetic hitchhiking and background selection. Most current solutions to the paradox of variation invoke some level of selection at linked sites. For example, one analysis suggests that larger populations have more selective sweeps, which remove more neutral genetic diversity. A negative correlation between mutation rate and population size may also contribute. Life history affects genetic diversity more than population history does, e.g. r/K selection theory, r-strategists have more genetic diversity.

## Detecting selection

Population genetics models are used to infer which genes are undergoing selection. One common approach is to look for regions of high
linkage disequilibrium In population genetics, linkage disequilibrium (LD) is the non-random association of allele An allele (, ; ; modern formation from Greek ἄλλος ''állos'', "other") is one of two, or more, forms of a given gene In biology, a gene (fr ...
and low genetic variance along the chromosome, to detect recent selective sweeps. A second common approach is the McDonald–Kreitman test which compares the amount of variation within a species (Polymorphism (biology), polymorphism) to the divergence between species (substitutions) at two types of sites; one assumed to be neutral. Typically, synonymous substitution, synonymous sites are assumed to be neutral. Genes undergoing positive selection have an excess of divergent sites relative to polymorphic sites. The test can also be used to obtain a genome-wide estimate of the proportion of substitutions that are fixed by positive selection, α. According to the
neutral theory of molecular evolution The neutral theory of molecular evolution holds that most evolutionary changes occur at the molecular level, and most of the variation within and between species are due to random genetic drift Genetic drift (allelic drift or the Sewall Wright ...
, this number should be near zero. High numbers have therefore been interpreted as a genome-wide falsification of neutral theory.

## Demographic inference

The simplest test for population structure in a sexually reproducing, diploid species, is to see whether genotype frequencies follow Hardy-Weinberg proportions as a function of allele frequencies. For example, in the simplest case of a single locus with two
allele An allele (, ; ; modern formation from Greek ἄλλος ''állos'', "other") is one of two, or more, forms of a given gene In biology, a gene (from ''genos'' "...Wilhelm Johannsen coined the word gene to describe the Mendelian_inheritance ...
s denoted A and a at frequencies ''p'' and ''q'', random mating predicts freq(AA) = ''p''2 for the AA homozygotes, freq(aa) = ''q''2 for the aa homozygotes, and freq(Aa) = 2''pq'' for the heterozygotes. In the absence of population structure, Hardy-Weinberg proportions are reached within 1-2 generations of random mating. More typically, there is an excess of homozygotes, indicative of population structure. The extent of this excess can be quantified as the F-statistics, inbreeding coefficient, F. Individuals can be clustered into ''K'' subpopulations. The degree of population structure can then be calculated using Fixation index, FST, which is a measure of the proportion of genetic variance that can be explained by population structure. Genetic population structure can then be related to geographic structure, and genetic admixture can be detected. Coalescent theory relates genetic diversity in a sample to demographic history of the population from which it was taken. It normally assumes neutral theory of molecular evolution, neutrality, and so sequences from more neutrally-evolving portions of genomes are therefore selected for such analyses. It can be used to infer the relationships between species (Computational phylogenetics, phylogenetics), as well as the population structure, demographic history (e.g. population bottlenecks, population growth), biological dispersal, source–sink dynamics and introgression within a species. Another approach to demographic inference relies on the allele frequency spectrum.

## Evolution of genetic systems

By assuming that there are loci that control the genetic system itself, population genetic models are created to describe the evolution of dominance and other forms of robustness (evolution), robustness, the
evolution of sexual reproduction Sexual reproduction is an adaptive feature which is common to almost all multi-cellular organisms (and also some single-cellular organisms) with many being incapable of asexual reproduction, reproducing asexually. Prior to the advent of sexual ...
and recombination rates, the evolution of mutation rates, the evolution of evolutionary capacitance, evolutionary capacitors, the evolution of Signalling theory, costly signalling traits, the evolution of ageing, and the evolution of co-operation (evolution), co-operation. For example, most mutations are deleterious, so the optimal mutation rate for a species may be a trade-off between the damage from a high deleterious mutation rate and the metabolism, metabolic costs of maintaining systems to reduce the mutation rate, such as DNA repair enzymes. One important aspect of such models is that selection is only strong enough to purge deleterious mutations and hence overpower mutational bias towards degradation if the selection coefficient s is greater than the inverse of the
effective population size The effective population size (''N'e'') is the number of individuals that an idealised population would need to have in order for some specified quantity of interest to be the same in the idealised population as in the real population. Idealised ...
. This is known as the drift barrier and is related to the nearly neutral theory of molecular evolution. Drift barrier theory predicts that species with large effective population sizes will have highly streamlined, efficient genetic systems, while those with small population sizes will have bloated and complex genomes containing for example introns and transposable elements. However, somewhat paradoxically, species with large population sizes might be so tolerant to the consequences of certain types of errors that they evolve higher error rates, e.g. in Transcription (genetics), transcription and Translation (biology), translation, than small populations.