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0.5 1 1.5 2 2.5 3 Phenotypic effect of mutation (arbitrary units)

Figure 5.6 The probability that a mutation is fixed by natural selection depends on the magnitude of its effect on fitness. Using the geometric model of mutation and assuming that fitness is determined by many phenotypes, Fisher showed the probability that a mutation improves fitness approaches V2 as the effect of a mutation approaches 0 (top panel). This result comes about because smaller mutations have a better chance of moving the phenotype toward the optimum than do larger mutations (see Fig. 5.5). Kimura pointed out that mutations with small effects on fitness are also the most likely to be fixed or lost due to genetic drift rather than by natural selection. Combining the chance that a mutation moves the phenotype toward higher fitness and the chance that a mutation has a large-enough fitness difference to escape genetic drift suggests that mutations with intermediate effects are most likely to be fixed by natural selection (bottom panel). Both models assume that mutations of any effect on fitness are equally likely to occur.

a version of equation 5.12 which assumes that fitness is determined by many independent phenotypes. This shows the distribution of the probability that a mutation improves fitness as the multi-dimensional phenotypic effect of a mutation increases.

The conclusion from the geometric model of mutation is evident in the top panel of Fig. 5.6. Mutations with small effects are most likely to bring an organism closer to its fitness optimum and are therefore most likely to be fixed by natural selection. Mutations of larger effect have a lower probability of improving fitness and are therefore less likely to be fixed by natural selection. Fisher compared the situation to the focus adjustment on a microscope. If a microscope is close to being in focus, then large random changes to the adjustment are likely to make things worse while small random changes are more likely to make the focus better. A logical consequence of Fisher's model is that the mutation fitness spectrum approaches 50% deleterious and 50% beneficial mutations as mutation effects approach zero. This prediction is not consistent with the general picture of the mutation fitness spectrum in Fig. 5.1.

Many years later, Kimura (1983a) reevaluated the predictions of the geometric model of mutation by relaxing Fisher's implicit assumption of an infinite effective population size. This change allows genetic drift to operate on the frequency of mutations along with natural selection. In a finite population, allele frequency is determined by a combination of sampling error and the effect of natural selection to fix alleles with higher average fitness. Natural selection will only determine the fate of an allele if it is stronger than the randomizing effect of genetic drift. The pressure of natural selection also depends on the phenotypic effect of a mutation - mutations with a larger effect experience a stronger push toward fixation. Thus, the push toward fixation by natural selection is strongest for those new mutations that have the largest effects. In other words, new mutations with small effects are likely to experience random fixation or loss by genetic drift. The bottom panel of Fig. 5.6 shows the probability that a new mutation is fixed by natural selection in a finite population. The mutations with the smallest phenotypic effects are still most likely to move the phenotype toward higher fitness. However, this is now balanced by the effect of genetic drift, which has the greatest impact on new mutations with small effects on fitness. The modified result is that new mutations with an intermediate effect on fitness are the most likely to fix under natural selection in a finite population.

Orr (1998) provides an analysis of the effect sizes of mutations that are fixed by natural selection in a finite population that compensates for the fact that the effect of mutations must shrink as a population gets closer to the maximum fitness over time. The net balance of natural selection and genetic drift is considered in detail in later chapters and the pheno-typic effects of loci and alleles are treated in detail in Chapter 9 on quantitative genetics.

Muller's Ratchet and the fixation of deleterious mutations

The fourth and final perspective on the fate of a new mutation focuses on deleterious mutations that

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