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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Hardy–Weinberg principle ： ウィキペディア英語版 Hardy–Weinberg principle 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 ''mate choice'', ''mutation'', ''selection'', ''genetic drift'', ''gene flow'' and ''meiotic drive''. Because one or more of these influences are typically present in real populations, the Hardy–Weinberg principle describes an ideal condition against which the effects of these influences can be analyzed. In the simplest case of a single locus with two alleles denoted A and a with frequencies and , respectively, the expected genotype frequencies are for the AA homozygotes, for the aa homozygotes, and for the heterozygotes. The genotype proportions ''p''2, 2''pq'', and ''q''2 are called the Hardy–Weinberg proportions. Note that the sum of all genotype frequencies of this case is the binomial expansion of the square of the sum of ''p'' and ''q'', and such a sum, as it represents the total of all possibilities, must be equal to 1. Therefore, . A solution of this equation is . If union of gametes to produce the next generation is random, it can be shown that the new frequency satisfies $\backslash textstyle\; f\text{'}(\backslash text)\; =\; f(\backslash text)$ and $\backslash textstyle\; f\text{'}(\backslash text)\; =\; f(\backslash text)$. That is, allele frequencies are constant between generations. This principle was named after G. H. Hardy and Wilhelm Weinberg, who first demonstrated it mathematically. ==Derivation== 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. 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 and , respectively.〔The term ''frequency'' usually refers to a number or count, but in this context, it is synonymous with ''probability''.〕 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 , 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: :$$ f_1(\text) = f_1(\text) + \frac f_1(\text) = p^2 + p q = p \left(p + q\right) = p = f_0(\text) :$$ f_1(\text) = f_1(\text) + \frac f_1(\text) = q^2 + p q = q \left(p + q\right) = q = f_0(\text) For the more general case of dioecious diploids (are either male or female ) that 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.〔http://www.mun.ca/biology/scarr/2900_HW_for_dioecious.html〕 Equivalently, one considers the six unique diploid-diploid combinations: :$\backslash left((\backslash text,\backslash text),\; (\backslash text,\; \backslash text),\; (\backslash text,\; \backslash text),$ (\text,\text), (\text, \text), (\text, \text) \right ) and constructs a Punnett square for each, so as to calculate its contribution to the next generation's genotypes. These contributions are weighted according to the probability of each diploid-diploid combination, which follows a Multinomial distribution with . For example, the probability of the mating combination is and it can only result in the genotype: . Overall, the resulting genotype frequencies are calculated as: :$$ \begin &\left(f_(\text), f_(\text), f_(\text)\right ) \\ &\quad= f_t(\text) f_t(\text) \left(1, 0, 0 \right ) + 2 f_t(\text) f_t(\text) \left(1/2, 1/2, 0 \right ) + 2 f_t(\text) f_t(\text) \left(0, 1, 0 \right ) \\ &\quad\quad+ f_t(\text) f_t(\text) \left(1/4, 1/2, 1/4 \right ) + 2 f_t(\text) f_t(\text) \left(0, 1/2, 1/2 \right ) + f_t(\text) f_t(\text) \left(0, 0, 1 \right ) \\ &\quad= \left(\left(f_t(\text) + \frac \right)^2, 2 \left(f_t(\text) + \frac \right) \left(f_t(\text) + \frac \right), \left(f_t(\text) + \frac \right)^2 \right )\\ &\quad= \left(f_t(\text)^2, 2 f_t(\text) f_t(\text), f_t(\text)^2 \right ) \end As before, one can show that the allele frequencies at time equal those at time , and so, are constant in time. Similarly, the genotype frequencies depend only on the allele frequencies, and so, after time are also constant in time. If in either monoecious or dioecious organisms, either the allele or genotype proportions are initially unequal in either sex, it can be shown that constant proportions are obtained after one generation of random mating. If dioecious organisms are heterogametic and the gene locus is located on the X chromosome, it can be shown that if the allele frequencies are initially unequal in the two sexes (XX females and XY males, as in humans ), in the heterogametic sex ‘chases’ in the homogametic sex of the previous generation, until an equilibrium is reached at the weighted average of the two initial frequencies. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hardy–Weinberg principle」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.