Mathematics and the Genome: Mathematics and Classical Genetics (1900-1953)
3. Mathematics and Classical Genetics (1900-1953)
Another classical contribution of mathematics to genetics is known as the Hardy-Weinberg Equations. G.H. Hardy (1877-1947) was a mathematician at Cambridge and Wilhem Weinberg (1862-1937) was a medical doctor in Stuttgart.They carried out their work independently. The story is that R. C. Punnett raised a genetical question with Hardy at the Cambridge University faculty club in 1908. Reginald Punnett (1875-1967) is known for the Punnett square, which is a diagram that is useful in understanding the results of mating organisms with different possible genotypes. Punnett gave a lecture on Mendelian heredity. In the audience was George Udney Yule (1871-1951), who claimed to Punnett that if a particular allele was dominant that the frequency of this allele would grow until it reached .5; thereafter one would have stability which was consistent with the standard Mendelian observation that phenotypes were seen in the ratio of 3 to 1. Punnett thought this reasoning was not correct and took the problem to Hardy. Yule denies this account. Hardy, using some simple probability theory and the assumption that a trait was governed by the alleles A and a, then derived the result that an equilibrium between the genotypes AA, Aa, and aa would be reached under the assumption that there was random mating of an infinite population, no migration, no mutation, and no natural selection. Under these assumptions one can show that the frequencies of the alleles A and a do not change with time. Furthermore, if p and q represent the frequency of A and a respectively (where p + q = 1), then the frequencies of the genotypes AA, Aa, and aa will be p2, 2pq, and q2, respectively. Thus, genotype frequencies can be predicted from allele frequencies, and though one might think that a trait that one sees rarely in a population would die out after many generations, under the assumptions of the Hardy-Weinberg model this would not be the case.
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