Neo-Darwinism / R.J. Berry.

R. J. Berry

Date:: 1982

Licence: Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)

Credit: Neo-Darwinism / R.J. Berry. Source: Wellcome Collection.

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$THE HARDY-WEINBERG THEOREM 17 2) The gametes will combine to form zygotes, and we can calculate the frequency of the three classes (AA, Aa, ad). 3) Knowing the genotype frequencies in the children, we can calculate the gene (or allele) frequency in them. We begin with a 2 X 2 table (or Punnett square) where the gametes and their frequencies produced by the two parents form the two sides, and the four gametic combinations (which are the children's genotypes) form the body of the table. The frequencies of the filial genotypes can be calculated by the simple product of the gametic frequencies if the two above assumptions hold: FATHER A a P Я Ар MOTHER a q In the filial generation, there will bep^AA,lpqAa, and q^aa. As this includes all zygotes in the sample: p^ + 2pq + q^ = \ One point worth making at this stage, is that we can calculate gene frequencies for a recessive character even where we are unable to 'count' alleles as in our Shetlanders. If we can identify only two phenotypes (dominant homozygotes plus heterozygotes, and recessive homozygotes), the frequency of q is simply the square root of the recessive homozygotes in the sample. Thus in our Shetlanders, the frequency of MM was 104/300 = 0.347; the frequency of Mean be calculated as x/0.347 = 0.588. Our previous estimate is theoretically more accurate, because it was not based on assumptions about population size or random mating. However we are forced to use this method of gene frequency estimation if we cannot identify heterozygotes with confidence. To return to the general case: we know the genotype frequencies in the filial generation, and we can calculate p and q from them by counting. Thus p (in the children) = p^ Л- '/2 {Ipq) = pip+ q) = p (since ^ = 1) This leaves us with an apparently trivial conclusion that allele frequencies remain constant from generation to generation. Furthermore, genotype fre¬ quencies are determined in a random mating population entirely by allele frequencies, so these will also remain constant. This result is in fact extremely important. To restate it: in a large random- mating population, gene and genotype frequencies remain constant in the absence of migration, mutation and selection. This statement is usually dignified by being called the Hardy- Weinberg theorem (or law, or principle). It is really a particular$

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