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 Section 4.3). Among North American Caucasians, the incidence of the disease is approximately 1 person in 2000. The formula for calculating allelic frequency (see Equation 18.3) requires that we know the numbers of homozygotes and heterozygotes, but cystic fibrosis is a recessive disease, so we cannot easily distinguish between homozygous unaffected 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) is q², and the allelic frequency is the square root of the genotypic frequency:

If the frequency of cystic fibrosis in North American Caucasians is approximately 1 in 2000, or 0.0005, then . 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 − 0.02 = 0.98. After we have calculated p and q, we can use the Hardy–Weinberg law to determine the frequencies of homozygous unaffected people and heterozygous carriers of the cystic fibrosis allele:

f(AA) = p² = (0.98)² = 0.960

f(Aa) = 2pq = 2(0.02)(0.98) = 0.0392

Thus, about 4% (1 of 25) of Caucasians are heterozygous carriers of the allele that causes cystic fibrosis. TRY PROBLEM 29