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To test your understanding of these relationships, answer the following questions.
Please explain in your own words what these three formulae tell us about the relationship between allele frequencies in the population and genotype frequencies in the offspring generation when all individuals are equally likely to survive and to reproduce.
In plain English, these three relationships tell us that
1. If we want to know the frequency of the homozygous genotype ( AA or aa ) in the offspring of a population in which all individuals are equally likely to survive and reproduce, then we simply square the frequency with which the appropriate allele ( A or a ) occurs population.
2. If we want to know the frequency of the heterozygous genotype ( Aa ) in the offspring of a population in which all individuals are equally likely to survive and reproduce, then we multiple the frequency with which each allele ( A and a ) occurs in the population and multiply this result by 2.
Return to the scenario described in problem 2. How frequently do you expect to the H1H1, H1H2, and H2H2 genotypes to appear in Europeans if the population is not evolving with respect to this allele?
To solve this problem, review the section above and generate a list of the information you need to generate and describe how you plan to get it.
Check your outline by answering the questions below.
1. How frequently do the H1 and H2 alleles occur in this population? This can be found in solution to problem 2.
2. Calculate the expected frequency of the H1H1, H1H2 and H2H2 genotypes in offspring of this population. To do this, square the frequency with which the H1 allele occurs in the population (p2), multiply the frequency with which the H1 allele occurs with the frequency with which the H2 allele occurs and multiply this result by two (2pq), and finally square the frequency with which the H2 allele occurs in the population (q2).
The formulae generated above - p2, 2pq and q2 - constitute the fundamental components of the Hardy-Weinberg equation. Thus, they describe the genotype frequencies you will see in a population, with respect to a single locus with only two alleles, if the population is not subject to any agent of evolution. That is, all individuals in the population are equally likely to survive and to produce offspring that survive.
Because together these formulae account for 100% of the genotypes this population could produce, they can be summarized and are often written in the following way:
In words, this equation says that the values, p2, 2pq and q2, which describe the frequency with which the AA , Aa and aa genotypes occur respectively, sum to 1.
Importantly, and as you applied it in the previous section, the Hardy-Weinberg equation is not necessarily used in the form in which it is written above. That is, you do not set the equation equal to 1 and solve for an unknown. Rather the individual elements p2, 2pq and q2 along with the relationship p + q = 1 are used as needed to solve problems.
Interestingly, the Hardy-Weinberg equation was actually formulated and published independently by both the British mathematician G. H. Hardy and the German physician cum geneticist W. Weinberg in 1908. Because Weinberg published in native German, however, his contribution was not recognized until 1943 at which point the principle was renamed to recognize both contributions.
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