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Inbreeding coefficient (F)

23.6 Inbreeding often has deleterious effects on crops. As inbreeding increases, the average yield of corn, for example, decreases.

lation of 25 diploid individuals. Each individual possesses two alleles at the locus under consideration; so the gene pool of the population consists of 50 allelic copies. Let us assume that there are two different alleles, designated G1 and G2 with frequencies p and q, respectively. If there are 45 copies of G1 and 5 copies of G2 in the population, p = .90 and q = .10. Now suppose that a mutation changes a G1 allele into a G2 allele. After this mutation, there are 44 copies of G1 and 6 copies of G2, and the frequency of G2 has increased from .10 to .12. Mutation has changed the allelic frequency.

If copies of G1 continue to mutate to G2, the frequency of G2 will increase and the frequency of G1 will decrease (Figure 23.8). The amount that G2 will change (Aq) as a result of mutation depends on: (1) the rate of G1-to-G2 mutation and (2) p, the frequency of G1 in the population When p is large, there are many copies of G1 available to mutate to G2, and the amount of change will be relatively large. As more mutations occur and p decreases, there will be fewer copies of G1 available to mutate to G2. The change in G2 as a result of mutation equals the mutation rate times the allelic frequency:

23.7 Although inbreeding is generally harmful, a number inbreeding organisms are successful.

Because most alleles are G1, there are more forward mutations than reverse mutations.

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Forward mutations increase the frequency of G2.

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Forward mutations increase the frequency of G2.

Eventually, an equilibrium is reached, where the number of forward mutations equals the number of reverse mutations.

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Equilibrium

Conclusion: At equilibrium, the allelic frequencies do not change even though mutation in both directions continues.

initially available to mutate to G2, and the increase in G2 due to forward mutation will be relatively large. However, as the frequency of G2 increases as a result of forward mutations, fewer copies of G1 are available to mutate; so the number of forward mutations decreases. On the other hand, few copies of G2 are initially available to undergo a reverse mutation to G1 but, as the frequency of G2 increases, the number of copies of G2 available to undergo reverse mutation to G1 increases; so the number of genes undergoing reverse mutation will increase. Eventually, the number of genes undergoing forward mutation will be counterbalanced by the number of genes undergoing reverse mutation. At this point, the increase in q due to forward mutation will be equal to the decrease in q due to reverse mutation, and there will be no net change in allelic frequency (q _ 0), in spite of the fact that forward and reserve mutations continue to occur. The point at which there is no change in the allelic frequency of a population is referred to as equilibrium (see Figure 23.8).

Factors determining allelic frequencies at equilibrium We can determine the allelic frequencies at equilibrium by manipulating Equation 23.13. Recall that p _ 1 — q. Substituting 1 — q for p in Equation 23.13, we get:

At equilibrium, Aq will be 0; so:

23.8 Recurrent mutation changes allelic frequencies. Forward and reserve mutations eventually lead to a stable equilibrium.

As the frequency of p decreases as a result of mutation, the change in frequency due to mutation will be less and less

So far we have considered only the effects of G1 : G2 forward mutations. Reverse G2 : G1 mutations also occur at rate v, which will probably be different from the forward mutation rate, Whenever a reverse mutation occurs, the frequency of G2 decreases and the frequency of G1 increases (see Figure 23.8). The rate of change due to reverse mutations equals the reverse mutation rate times the allelic frequency of G2 (Aq _ vq). The overall change in allelic frequency is a balance between the opposing forces of forward mutation and reverse mutation:

Reaching equilibrium of allelic frequencies Consider an allele that begins with a high frequency of G1 and a low frequency of G2. In this population, many copies of G1 are

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