
In
population genetics
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 (biology), adaptation, s ...
, the Hardy–Weinberg principle, also known as the Hardy–Weinberg equilibrium, model, theorem, or law, states that
allele
An allele is a variant of the sequence of nucleotides at a particular location, or Locus (genetics), locus, on a DNA molecule.
Alleles can differ at a single position through Single-nucleotide polymorphism, single nucleotide polymorphisms (SNP), ...
and genotype frequencies in a population will remain constant from generation to generation in the absence of other evolutionary influences. These influences include ''
genetic drift
Genetic drift, also known as random genetic drift, allelic drift or the Wright effect, is the change in the Allele frequency, frequency of an existing gene variant (allele) in a population due to random chance.
Genetic drift may cause gene va ...
'', ''
mate choice
Mate choice is one of the primary mechanisms under which evolution can occur. It is characterized by a "selective response by animals to particular stimuli" which can be observed as behavior.Bateson, Paul Patrick Gordon. "Mate Choice." Mate Choi ...
'', ''
assortative mating'', ''
natural selection
Natural selection is the differential survival and reproduction of individuals due to differences in phenotype. It is a key mechanism of evolution, the change in the Heredity, heritable traits characteristic of a population over generation ...
'', ''
sexual selection
Sexual selection is a mechanism of evolution in which members of one sex mate choice, choose mates of the other sex to mating, mate with (intersexual selection), and compete with members of the same sex for access to members of the opposite sex ...
'', ''
mutation
In biology, a mutation is an alteration in the nucleic acid sequence of the genome of an organism, virus, or extrachromosomal DNA. Viral genomes contain either DNA or RNA. Mutations result from errors during DNA or viral replication, ...
'', ''
gene flow
In population genetics, gene flow (also known as migration and allele flow) is the transfer of genetic variation, genetic material from one population to another. If the rate of gene flow is high enough, then two populations will have equivalent ...
'', ''
meiotic drive'', ''
genetic hitchhiking
Genetic hitchhiking, also called genetic draft or the hitchhiking effect, is when an allele changes frequency not because it itself is under natural selection, but because it is near another gene that is undergoing a selective sweep and that is ...
'', ''
population bottleneck
A population bottleneck or genetic bottleneck is a sharp reduction in the size of a population due to environmental events such as famines, earthquakes, floods, fires, disease, and droughts; or human activities such as genocide, speciocide, wid ...
'', ''
founder effect
In population genetics, the founder effect is the loss of genetic variation that occurs when a new population is established by a very small number of individuals from a larger population. It was first fully outlined by Ernst Mayr in 1942, us ...
,'' ''
inbreeding
Inbreeding is the production of offspring from the mating or breeding of individuals or organisms that are closely genetic distance, related genetically. By analogy, the term is used in human reproduction, but more commonly refers to the genet ...
and
outbreeding depression
In biology, outbreeding depression happens when crosses between two genetically distant groups or populations result in a reduction of fitness. The concept is in contrast to inbreeding depression, although the two effects can occur simultaneously o ...
''.
In the simplest case of a single locus with two
allele
An allele is a variant of the sequence of nucleotides at a particular location, or Locus (genetics), locus, on a DNA molecule.
Alleles can differ at a single position through Single-nucleotide polymorphism, single nucleotide polymorphisms (SNP), ...
s denoted ''A'' and ''a'' with frequencies and , respectively, the expected genotype frequencies under random mating are for the AA
homozygote
Zygosity (the noun, zygote, is from the Greek "yoked," from "yoke") () is the degree to which both copies of a chromosome or gene have the same genetic sequence. In other words, it is the degree of similarity of the alleles in an organism.
Mos ...
s, for the aa homozygotes, and for the
heterozygote
Zygosity (the noun, zygote, is from the Greek "yoked," from "yoke") () is the degree to which both copies of a chromosome or gene have the same genetic sequence. In other words, it is the degree of similarity of the alleles in an organism.
Mos ...
s. In the absence of selection, mutation, genetic drift, or other forces, allele frequencies ''p'' and ''q'' are constant between generations, so equilibrium is reached.
The principle is named after
G. H. Hardy
Godfrey Harold Hardy (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis. In biology, he is known for the Hardy–Weinberg principle, a basic principle of pop ...
and
Wilhelm Weinberg, who first demonstrated it mathematically. Hardy's paper was focused on debunking the view that a
dominant allele would automatically tend to increase in frequency (a view possibly based on a misinterpreted question at a lecture). Today, tests for Hardy–Weinberg genotype frequencies are used primarily to test for
population stratification
Population structure (also called genetic structure and population stratification) is the presence of a systematic difference in allele frequencies between subpopulations. In a randomly mating (or ''panmictic'') population, allele frequencies ar ...
and other forms of non-random mating.
Derivation
Consider a population of
monoecious
Monoecy (; adj. monoecious ) is a sexual system in seed plants where separate male and female cones or flowers are present on the same plant. It is a monomorphic sexual system comparable with gynomonoecy, andromonoecy and trimonoecy, and contras ...
diploids, where each organism produces male and female gametes at equal frequency, and has two alleles at each gene locus. We assume that the population is so large that it can be treated as infinite. Organisms reproduce by random union of gametes (the "
gene pool
The gene pool is the set of all genes, or genetic information, in any population, usually of a particular species.
Description
A large gene pool indicates extensive genetic diversity, which is associated with robust populations that can survi ...
" population model). A locus in this population has two alleles, A and a, that occur with initial frequencies and , respectively. The allele frequencies at each generation are obtained by pooling together the alleles from each
genotype
The genotype of an organism is its complete set of genetic material. Genotype can also be used to refer to the alleles or variants an individual carries in a particular gene or genetic location. The number of alleles an individual can have in a ...
of the same generation according to the expected contribution from the homozygote and heterozygote genotypes, which are 1 and 1/2, respectively:
The different ways to form genotypes for the next generation can be shown in a
Punnett square
The Punnett square is a square diagram that is used to predict the genotypes of a particular cross or breeding experiment. It is named after Reginald C. Punnett, who devised the approach in 1905. The diagram is used by biologists to determine ...
, where the proportion of each genotype is equal to the product of the row and column allele frequencies from the current generation.
The sum of the entries is , as the genotype frequencies must sum to one.
Note again that as , the binomial expansion of gives the same relationships.
Summing the elements of the Punnett square or the binomial expansion, we obtain the expected genotype proportions among the offspring after a single generation:
These frequencies define the Hardy–Weinberg equilibrium. It should be mentioned that the genotype frequencies after the first generation need not equal the genotype frequencies from the initial generation, e.g. . However, the genotype frequencies for all ''future'' times will equal the Hardy–Weinberg frequencies, e.g. for . This follows since the genotype frequencies of the next generation depend only on the allele frequencies of the current generation which, as calculated by equations () and (), are preserved from the initial generation:
:
For the more general case of
dioecious
Dioecy ( ; ; adj. dioecious, ) is a characteristic of certain species that have distinct unisexual individuals, each producing either male or female gametes, either directly (in animals) or indirectly (in seed plants). Dioecious reproduction is ...
diploids rganisms are either male or femalethat reproduce by random mating of individuals, it is necessary to calculate the genotype frequencies from the nine possible matings between each parental genotype (''AA'', ''Aa'', and ''aa'') in either sex, weighted by the expected genotype contributions of each such mating. Equivalently, one considers the six unique diploid–diploid combinations:
: