![]() In contrast, when one of the alleles is rare (i.e. The highest frequency of heterozygotes, H, is then reached when p = q and H = 2pq = 0.50. The figure shows the correspondence between the allele frequency q of a and the genotype frequencies in the case of two alleles in a panmictic system. a very large population), which is panmictic (mariages occur randomly), and in the absence of mutation and selection, the frequency of the genotypes will be the development of (p+q) 2, p and q being the allele frequencies. ![]() In a population consisting of an infinite number of individuals (i.e. Or drawing A1A2: H x 1/2 then drawing A1 amongst A1A2Ĭalculate the following frequencies: F(P: phenotypes), F(G: genotypes), F(A: alleles), F (gametes) :į(A) = F(gam), because there is 1 allele (of each gene) per gamete In addition, here F(p) = F(G), because these are co-dominant alleles Proba of drawing A1 =drawing A1A1: : D x 1 then drawing A1 into A1A1 Second demonstration, by calculating the probabilities: Q = nb A2 / nb total = (2RN + HN) / 2N = R + H/2 (note the symmetry between p and q) P = nb A1 / nb total = (2DN + HN) / 2N = D + H/2 similarly for A2 P = nb A1 / nb total = (2DN + HN) / 2N = D + H/2 The frequencies of genotypes F(G) be called D, H, and R with 0 = number of alleles = 2N Under these circumstances, the genetic diversity of the population is maintained and must tend towards a stable equilibrium of the distribution of the genotype.Ģ.1 For an autosomal, diallele, co-dominant gene Successive generations are discrete (no crosses between different generations). There must be no selection, mutation, migration (no allele loss /gain). The population is "infinite" (very large: to minimize differences due to sampling). The population is panmictic (couples form randomly (panmixia), and their gametes encounter each other randomly (pangamy)). The concept of equilibrium in the Hardy-Weinberg model is subject to the following hypotheses/conditions: The Hardy-Weinberg equilibrium is the central theoretical model in population genetics. The Hardy-Weinberg equilibium, which is also known as the panmictic equilibrium, was discovered at the beginning of the 20th century by several researchers, notably by Hardy, a mathematician and Weinberg, and physician. We use these equations implicitly, in formal genetics and in the genetics of pooled populations, usually without considering whether, and under what conditions, they are applicable. Note that there are a lot of heterozygotes: 1/50, two hundred times more than there are individuals suffering from the condition.įor a rare disease, p is very little different from 1, and the frequency of the heterozygotes = 2q. The frequency of this disease is q 2 = 1/10 000,Īnd the frequency of heterozygotes is 2pq = 2 x 99/100 x 1/100 = 2/100 P is the frequency of allele A1 0 = q = 1/100 Let A1 and A2 be two alleles at the same locus, The Hardy-Weinberg law can be used under some circumstances to calculate genotype frequencies from allele frequences.
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