# P q2 p2 2pq q2

Figure 19.3 A cross-multiplication (Punnett) square showing Hardy—Weinberg frequencies resulting from combining two alleles A and a with frequencies p and q, respectively. Note that p + q = 1 and that the Hardy—Weinberg genotype proportions are simply a binomial expansion of (p + q)2, or p2 + 2pq + q2.

cross between alleles A and a from both parents is referred to as a Punnett square. Godfrey Hardy (1877-1947) and Wilhelm Weinberg (1862-1937) both independently discovered the mathematics for independent assortment that is now associated with their names as the Hardy-Weinberg principle (Crow 1999). HWE proportions of genotype frequencies can be reached in a single generation of random mating. HWE is simply a way to relate allele frequencies to genotype frequencies.

Checking for HWE is performed by taking the observed allele frequencies and calculating the expected genotype frequencies based on the allele frequencies. If the observed genotype frequencies are close to the expected genotype frequencies calculated from the observed allele frequencies, then the population is in Hardy-Weinberg equilibrium and allele combinations are assumed to be independent of one another.

One of the principal implications of HWE is that the allele and genotype frequencies remain constant from generation to generation (Hartl and Clark 1997). Another implication is that when an allele is rare, the population contains more heterozygotes for the allele than it contains homozygotes for the same allele (e.g., allele 15 in Table 20.2).

Genes (or genetic markers like STR loci) that are in random association are said to be in a state of linkage equilibrium while those genes that are not in random association are said to be in linkage disequilibrium (Hartl and Clark 1997). Computer programs and tests for checking linkage equilibrium will be discussed in more detail in Chapter 20.