The gene pool of a population can also be described in terms of allelic frequencies. There are always fewer alleles than genotypes, so the gene pool of a population can be described in fewer terms when allelic frequencies are used. In a sexually reproducing population, the genotypes are only temporary assemblages of the alleles. As described by Mendel’s principle of segregation, the genotypes break down each generation, and individual alleles are passed to the next generation through the gametes. Thus, the types and numbers of alleles, rather than genotypes, have real continuity from one generation to the next.

Allelic frequencies can be calculated from (1) the numbers or (2) the frequencies of the genotypes. To calculate the allelic frequency from the numbers of genotypes, we count the number of copies of a particular allele present among the genotypes and divide by the total number of all alleles in the sample:

For a locus with only two alleles (A and a), the frequencies of the alleles are usually represented by the symbols p and q. The frequencies can be calculated as follows:

where n_AA, n_Aa, and n_aa represent the numbers of AA, Aa, and aa individuals, and N represents the total number of individuals in the sample. To obtain the number of copies of the allele in the numerator of the equation, we add twice the number of homozygotes (because each has two copies of the allele for which the frequency is being calculated) to the number of heterozygotes (because each has a single copy of the allele). We divide by 2N because each diploid individual has two alleles at a locus. The sum of the allelic frequencies always equals 1 (p + q = 1); so, after p has been obtained, q can be determined by subtraction: q = 1 − p.

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Alternatively, allelic frequencies can be calculated from the genotypic frequencies. This calculation is useful if the genotypic frequencies have already been calculated and the numbers of the different genotypes are not available. To calculate allelic frequencies from genotypic frequencies, we add the frequency of the homozygote for each allele to half the frequency of the heterozygote (because half of the heterozygote’s alleles are of each type):

We obtain the same values of p and q whether we calculate the allelic frequencies from the numbers of genotypes (­Equation 18.3) or from the genotypic frequencies (Equation 18.4). A sample calculation of allelic frequencies is provided in the next Worked Problem. TRY PROBLEM 23

LOCI WITH MULTIPLE ALLELES We can use the same principles to determine the frequencies of alleles for loci with more than two alleles. To calculate the allelic frequencies from the numbers of genotypes, we count up the number of copies of an allele by adding twice the number of homozygotes to the number of heterozygotes that possess the allele and divide this sum by twice the number of individuals in the sample. For a locus with three alleles (A¹, A², and A³) and six genotypes (A¹A¹, A¹A², A²A², A¹A³, A²A³, and A³A³), the frequencies (p, q, and r) of the alleles are

Alternatively, we can calculate the frequencies of multiple alleles from the genotypic frequencies by extending Equation 18.4. Once again, we add the frequency of the homozygote to half the frequency of each heterozygous genotype that possesses the allele: