## N

sense, since a new mutation is very rare and is close to loss but very far from fixation. This result also shows that the chance of fixation or loss of a new mutation depends on the effective population size.

Using the diffusion approximation of genetic drift, it is possible to estimate the average number of generations before a new mutation is either fixed or lost (Kimura & Ohta 1969a). Figure 3.14 and equation 3.40 give the average number of generations until fixation or loss for an allele depending on the effective population size and initial allele frequency. Under the assumption that the effective population size is large, those alleles that eventually fix do so in an average of 4Ne generations. Those alleles that are lost go to fixation in many fewer generations, approaching zero generations as the population size gets larger and the initial frequency of-therefore

2Ne gets smaller. However, since genetic drift is a stochastic process we expect that the variance around the average time to fixation or loss will be large. In other words, the allele frequency of each new mutation will take a random walk between zero and one. Although many mutations may be lost quickly others may segregate for several or many generations before being lost or fixed.

The fate of new mutations can be seen readily in a simulation. Figure 5.4 shows the frequency of new mutations introduced every 30 generations into a population of Ne = 10. Of the seven mutations introduced into the population, six go to loss and only one goes to fixation. This is roughly consistent with the prediction that one in 20 new mutations will fix in a population where Ne = 10. Most of the mutations that go to loss do so in fewer than 10 generations, although in one case the mutation segregates for about 25 generations. Equation 3.40 predicts that mutations go to loss in that an average of about six generations, roughly consistent with the simulation. The mutation that goes to fixation does so in 60 generations, taking a zig-zag trajectory of allele frequency. Equation 3.40 predicts that an average of about 39 generations will elapse for those mutations that go to fixation when Ne = 10, suggesting that the simulation result is somewhat greater than the expected average time to fixation.

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