Standard 7f Preknowledge
7f) ***Students know how to solve the Hardy-Weinberg equation to predict the frequency of genotypes in a population, given the frequency of phenotypes.
CALIFORNIA FRAMEWORKS SUMMARY:
The Hardy-Weinberg equilibrium equation can be used to calculate the frequency of alleles and genotypes in a population’s gene pool. When only two alleles for a trait occur in a population, the letter p is used to represent the frequency of one allele, and the letter q is used to represent the frequency of the other. Students should agree first that the sum of the frequencies of the two alleles is 1, and this equation is written p + q = 1. That is, the combined frequencies of the alleles account for all the genes for a given trait.
Students should then consider the possible combinations of alleles in a diploid organism (the genome of a diploid organism consists of two copies of each chromosome). An individual could be homozygous for one allele (pp) or homozygous for the other (qq) or heterozygous (either pq or qp). These diploid genotypes will appear at frequencies that are the product of the allele frequencies (e.g., the frequency of a diploid pp individual is p2, and the frequency of a diploid qq individual is q2).
The heterozygotes are of two varieties, pq and qp (because the p allele might have been inherited from either parent), but the products of frequency pq and qp are the same. Therefore, the frequency of heterozygotes can simply be expressed as 2pq. The sum of the frequencies of the homozygous and heterozygous individuals must equal 1, since all individuals have been accounted for. These principles are usually expressed as the equation p2 + 2pq + q2 = 1. Both equations represent different statements. The first (p + q = 1) is an accounting of the two types of alleles in the population, and the second (p2 + 2pq + q2 = 1) is an accounting of the three distinguishable genotypes.
If the allele frequencies are known (e.g., if p = 0.1 and q = 0.9) and Hardy-Weinberg equilibrium is assumed, then the frequencies p2, 2pq, and q2 are respectively 0.01, 0.18, and 0.81. That is, 81 percent of individuals would be homozygous qq. If p were a dominant (but nonselective) allele, then p2 + 2pq, or 19 percent of the population, would express the dominant phenotype of the p allele.
The calculation can be used in reverse as well. If Hardy-Weinberg equilibrium conditions exist and 81 percent of the population expresses the qq recessive phenotype, then the allele frequency q is the square root of 0.81, and the rest of the terms can be calculated in a straightforward fashion.
Students can convince themselves of the state of equilibrium by constructing a Punnett Square that assumes random mating. The scenario might be a mass spawning of fish, in which 100,000 eggs and sperm are mixed in a stream and meet with each other randomly to form zygotes. Students can calculate the fraction of p and q type gametes in the stream by thinking through the types of gametes produced by heterozygous and homozygous adult fish. (For this exercise to work, the genotype distribution of adults must agree with Hardy-Weinberg equilibrium.) With the frequencies or numbers of each type of zygote calculated in the cells of a Punnett Square, students will see that equilibrium is preserved. Frequencies of alleles and genotypes, which are the genetic structure of the study population, would remain constant for generations under the premise of Hardy-Weinberg equilibrium.