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Just as the gene frequency is controlled in the genetic laboratory, so is the mating pattern, generation after generation. But outside the laboratory, chance mating is a chance or random affair. Every member of Mendelian population, thus, depends on chance or random matings.
In other words, every male gamete in the gene pool has an equal opportunity of uniting with every female gamete. Zygotic frequencies expected in the next generation from such random gametic unions may be predicted from a knowledge of the gene (allelic) frequencies in the gene pool of the parental population.
For example, the expected zygotic frequencies for allele A and a of a gene pool can be determined by chance mating or panmixis.
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If p stands for percentage of A alleles in the gene pool and q stands for the percentage of a alleles, the checkerboard of both alleles may predict possible chance combinations of A and a gametes as follows:
Thus, p2 is the fraction of the next generation expected to be homozygous (AA), 2pq is the fraction expected to be heterozygous (Aa) and q2 is the fraction expected to be recessive (aa).
The zygotic combinations predicted in a randomly mating population may be represented by p2: 2pq: q2, where p2 represents the AA genotype, 2pq the Aa, and q2 the aa genotype; or, in the form of equation, p2 + 2pq + q2 = When only two alleles are involved, and, therefore, p and q represent the frequencies of all of the alleles concerned p + q = 1. Since p + q = 1, p = 1 – q.
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Now if 1 – q is substituted for p, all relations in the formula can be represented in terms of q as follows:
(1 – q)2 + 2q (1 – q) + q2 = 1.