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A colleague determines that the B1 and B2 alleles of the B locus both occur with a frequency equal 0.45. Surprised, she redoes her work and confirms her results.

a. What could be the cause of your colleague's surprise? Please explain.

b. Because your colleague confirms her results she now needs to explain them. She turns to you for assistance. What do you suggest? Please be sure to explain how your explanation accounts for her observations.

Your colleague was probably surprised because she thought that B1 and B2 were the only two alleles that occurred at this locus in this population. Consequently, the discovery that their frequencies, p and q, summed to 0.9 as opposed to 1 was startling. Your suggestion to look for at least one additional allele to account for the 10% of the alleles unaccounted for in her study is well taken. She realizes that the existence of one or more additional alleles would explain the missing 10% and enable her to bring the summed allele frequencies for the B locus to 1.

Now that we have designated p to represent the freqeuncy of A allele and q, the a allele, we are ready to move forward with our efforts to construct the elements of the Hardy-Weinberg equation. Imagine that every individual in a population, in which both copies of both the A and a allele occur, is equally likely to survive and to reproduce.

What possible genotypes could occur in the offspring of this population?

To answer this question, determine all the possible genotypes that could be formed from a population of individuals whose loci collectively warehouse numerous copies of A and a alleles. Remember that, because these individuals are all equally likely to reproduce, all combinations of these two alleles have the potential to form. Visit this module if you have questions.

There are four possible genotypes:

  • A A
  • a a
  • A a
  • a A

Now that we know what genotypes could form, we can use the rule highlighted at the very beginning of this module to predict how frequently each of these genotypes will appear in the offspring generation.

What are these frequencies? Apply the highlighted (boxed) rule above to complete the phrases below using the symbols p and q.

If all individuals are equally likely to survive and to reproduce, then the

  • frequency of genotype AA will equal ____________________
  • frequency of genotype aa will equal _____________________
  • frequency of genotype Aa will equal ____________________
  • frequency of genotype aA will equal ____________________

Because the Aa and aA genotypes are genetically equivalent, we can summarize the relationships you articulated above as

  • frequency of genotype AA will equal p x p = p2
  • frequency of genotype aa aa will equal q x q = q2
  • frequency of genotype Aa will equal 2 x (p x q) = 2pq

And there you have it, the three fundamental elements of the Hardy-Weinberg equation that describe how frequently the three possible genotypes will appear in the offspring generation of a population that is not subject to an agent of evolution! Remember that only three genotypes are possible because we are only working with a gene for which only two alleles exist in a population.

Questions & Answers

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Source:  OpenStax, Understanding the hardy-weinberg equation. OpenStax CNX. Oct 22, 2007 Download for free at http://cnx.org/content/col10472/1.1
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