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Modern Genetic Analysis Chapter 17. Population and Evolutionary Genetics The Effect of Sexual Reproduction on Variation
Genetics In Process 17-2: The Hardy-Weinberg equilibrium

If the frequency of allele A is p in both the sperm and the eggs and the frequency of allele a is q = 1 p, then the consequences of random unions of sperm and eggs are shown in the adjoining figure. The probability that both the sperm and the egg will carry A is p × p = p2, so this will be the frequency of A / A homozygotes in the next generation. In like manner, the chance of heterozygotes A / a will be (p × q) + (q × pq) = 2pq, and the chance of homozygotes a / a will be q × q = q2 The three genotypes, after a generation of random mating, will be in the frequencies p2:2pq:q2. As the figure shows, the allelic frequency of A has not changed and is still p. Therefore, in the second generation, the frequencies of the three genotypes will again be p2:2pq:q2, and so on, forever.

The Hardy-Weinberg equilibrium frequencies that result from random mating. The frequencies of A and a among both eggs and sperm are p and q(= 1 p), respectively. The total frequencies of the zygote genotypes are p2 for A / A, 2pq for A / a, and q2 for a / a. The frequency of the allele A in the zygotes is the frequency of A / A plus half the frequency of A / a, or p2 + pq = p(p + q) = p.

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