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Figure 5.9 Expected change in allele frequency due to irreversible or one-way mutation for a diallelic locus for five initial allele frequencies. Here the chance that an A allele mutates into an a allele (or the per locus rate of mutation) is 0.00001. This rate of mutation is high compared with estimates of the per-locus mutation rate (see Table 5.1). The expected equilibrium allele frequency is p = 0 since there is no process acting to replace A alleles in the population. The population has not reached equilibrium even after 100,000 generations have elapsed. Changes in allele frequency due to mutation alone occur over very long time scales.

10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000 100,000 Generation

10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000 100,000 Generation

Figure 5.9 Expected change in allele frequency due to irreversible or one-way mutation for a diallelic locus for five initial allele frequencies. Here the chance that an A allele mutates into an a allele (or the per locus rate of mutation) is 0.00001. This rate of mutation is high compared with estimates of the per-locus mutation rate (see Table 5.1). The expected equilibrium allele frequency is p = 0 since there is no process acting to replace A alleles in the population. The population has not reached equilibrium even after 100,000 generations have elapsed. Changes in allele frequency due to mutation alone occur over very long time scales.

even using a mutation rate at the high end of the observed range (Table 5.1). To generalize from the irreversible mutation model, we can expect that the process of mutation does influence allele frequencies but that substantial changes to allele frequency caused by mutation alone will take thousands or tens of thousands of generations depending on the mutation rate.

The assumption of irreversible mutation is not biologically realistic. Mutation can usually change the state of all alleles, resulting in both forward (A ^ a) and reverse (a ^ A) mutation for a diallelic locus. The bi-directional or reversible mutation model takes this possibility into account using independent rates of forward mutation (|) and reverse mutation (v, pronounced "nu"). With mutation pressure in both directions we can again ask how mutation will change allele frequencies in a population over time. Each generation, || of the A alleles mutate to a alleles while at the same time v of the a alleles mutate to A alleles. The allele frequency after one generation is therefore

because the frequency of A alleles will decline due to the proportion of alleles that experience forward mutation ( pt(1 -||)) but increase due to the proportion of the alleles in the population that experience reverse mutation ((1 - pt)v). The general result is that the equilibrium value of the frequency of A is determined by the net balance of the two rates of mutation:

equilibrium

as derived in Math box 5.1. So whatever the starting frequency of the A allele, the population will converge to pequinf,rium that is closer to one for the allele produced by the higher of the two mutation rates. Figure 5.10 shows the frequency of the A allele over time with bi-directional mutation for five different initial allele frequencies. Because the forward and backward mutation rates used for the figure are not equal but are within a factor of five, both alleles have intermediate frequencies at equilibrium. The number of generations required to reach the equilibrium allele frequency is again very long, just as it is with the irreversible mutation model.

It turns out that the process of mutation within a population is exactly analogous to the process of gene flow among several subpopulations. Compare allele frequency in Fig. 5.9 with irreversible mutation and Fig. 4.13 which shows allele frequency under oneway gene flow in the continent-island model. Both processes cause allele frequencies to change toward a state of fixation and loss and the shape of both curves is identical. Then compare allele frequency in Fig. 5.10 with the process of bi-directional mutation and the process of bi-directional gene flow in the two-island model shown in Fig. 4.14. Here too the shape of both curves is identical and both processes result in intermediate frequencies of both alleles at equilibrium. The major differences in the mutation and gene-flow graphs are the time scales. In the absence of other processes, gene flow causes allele frequencies to approach equilibrium values in tens or hundreds of generations whereas mutation requires tens to hundreds of thousands of generations to approach equilibrium allele frequencies. It is

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