## Estimating Allelic Frequencies with the Hardy Weinberg

A practical use of the Hardy-Weinberg law is that it allows us to calculate allelic frequencies when dominance is present. For example, cystic fibrosis is an autosomal recessive disorder characterized by respiratory infections, incomplete digestion, and abnormal sweating (see p. 000 in Chapter 6). Among North American Caucasians, the incidence of the disease is approximately 1 person in 2000. The formula for calculating allelic frequency (Equation 23.3) requires that we know the numbers of homozygotes and heterozygotes, but cystic fibrosis is a recessive disease, and so we cannot easily distinguish between homozygous normal persons and heterozygous carriers. Although molecular tests are available for identifying heterozygous carriers of the cystic fibrosis gene, the low frequency of the disease makes widespread screening impractical. In such situations, the Hardy-Weinberg law can be used to estimate the allelic frequencies.

If we assume that a population is in Hardy-Weinberg equilibrium with regard to this locus, then the frequency of the recessive genotype (aa) will be q2, and the allelic frequency is the square root of the genotypic frequency:

The frequency of cystic fibrosis in North American Caucasians is approximately 1 in 2000, or .0005; so q = ^0.0005 = .02. Thus, about 2% of the alleles in the Caucasian population encode cystic fibrosis. We can calculate the frequency of the normal allele by subtracting: p = 1 — q = 1 — .02 = .98. After we have calculated p and q, we can use the Hardy-Weinberg law to determine the frequencies of homozygous normal people and heterozygous carriers of the gene:

f(AA) = p2 = (.98)2 = .960 f(Aa) = 2pq = 2(.02)(.98) = .0392

Thus about 4% (1 of 25) of Caucasians are heterozygous carriers of the allele that causes cystic fibrosis. _ _

Inbreeding is usually measured by the inbreeding coefficient, designated F, which is a measure of the probability that two alleles are "identical by descent." In a diploid organism, homozygous individual has two copies of the same allele. These two copies may be the same in state, which means that the two alleles are alike in structure and function but do not have a common origin. Alternatively, the two alleles in a homozygous individual may be the same because they are identical by descent—the copies are descended from a single allele that was present in an ancestor (< Figure 23.4). If we go back far enough in time, many alleles are likely to be identical by descent but, for calculating the effects of inbreeding, we consider identity by descent by going back only a few generations.

Inbreeding coefficients can range from 0 to 1. A value of 0 indicates that mating in a large population is random; a value of 1 indicates that all alleles are identical by descent. Inbreeding coefficients can be calculated from analyses of pedigrees or they can be determined from the reduction in the heterozygosity of a population. Although we will not go into the details of how F is calculated, it's important to understand how inbreeding affects genotypic frequencies.

When inbreeding occurs, the frequency of the genotypes will be:

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