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Hardy–Weinberg principle
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Hardy–Weinberg principle
In population genetics, the Hardy–Weinberg principle, also known as the Hardy–Weinberg equilibrium, model, theorem, or law, states that allele 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, mate choice, assortative mating, natural selection, sexual selection, mutation, gene flow, meiotic drive, genetic hitchhiking, population bottleneck, founder effect, inbreeding and outbreeding depression.
In the simplest case of a single locus with two alleles denoted A and a with frequencies f(A) = p and f(a) = q, respectively, the expected genotype frequencies under random mating are f(AA) = p2 for the AA homozygotes, f(aa) = q2 for the aa homozygotes, and f(Aa) = 2pq for the heterozygotes. 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 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 and other forms of non-random mating.
Consider a population of monoecious 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" population model). A locus in this population has two alleles, A and a, that occur with initial frequencies f0(A) = p and f0(a) = q, respectively. The allele frequencies at each generation are obtained by pooling together the alleles from each genotype 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, 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 p2 + 2pq + q2 = 1, as the genotype frequencies must sum to one.
Note again that as p + q = 1, the binomial expansion of (p + q)2 = p2 + 2pq + q2 = 1 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:
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Hardy–Weinberg principle
In population genetics, the Hardy–Weinberg principle, also known as the Hardy–Weinberg equilibrium, model, theorem, or law, states that allele 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, mate choice, assortative mating, natural selection, sexual selection, mutation, gene flow, meiotic drive, genetic hitchhiking, population bottleneck, founder effect, inbreeding and outbreeding depression.
In the simplest case of a single locus with two alleles denoted A and a with frequencies f(A) = p and f(a) = q, respectively, the expected genotype frequencies under random mating are f(AA) = p2 for the AA homozygotes, f(aa) = q2 for the aa homozygotes, and f(Aa) = 2pq for the heterozygotes. 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 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 and other forms of non-random mating.
Consider a population of monoecious 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" population model). A locus in this population has two alleles, A and a, that occur with initial frequencies f0(A) = p and f0(a) = q, respectively. The allele frequencies at each generation are obtained by pooling together the alleles from each genotype 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, 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 p2 + 2pq + q2 = 1, as the genotype frequencies must sum to one.
Note again that as p + q = 1, the binomial expansion of (p + q)2 = p2 + 2pq + q2 = 1 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:
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