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and are inherently unable to detect mutations with very small effects or that do not affect the pheno-type within the laboratory environment where the phenotype is measured. There is also the possibility that the distribution of mutation fitnesses varies among taxa. For example, a mutation-accumulation experiment in the plant Arabidopsis thaliana showed that deleterious and beneficial mutations were about equally frequent (Shaw et al. 2000).

Inherent in the mutation fitness spectrum in Fig. 5.1 is that beneficial mutations are rarer than deleterious mutations. This makes estimating of the frequency distribution of beneficial mutations even more difficult than it is for deleterious mutations. Nonetheless, a number of studies have directly measured the effects of advantageous mutations. Bacterial populations have been used to study mutations due to their short generation times and the ease of constructing and maintaining replicate populations. Using E. coli, several studies have shown that beneficial mutations with small effects on fitness are much more common than mutations with larger effects (Imhof & Schlotterer 2001; Rozen et al. 2002). Using an RNA virus, Sanjuan et al. (2004) used site-directed mutagenesis to make numerous single-nucleotide mutations. Beneficial mutations were much rarer than deleterious mutations, but the eight beneficial mutations had an average of a 7% improvement in fitness and small mutation effects were more common. An important caveat to these studies is that the beneficial mutations detected are biased toward those of larger effects because: very small mutation effects cannot be measured; beneficial mutations with larger effects increase in frequency more rapidly under natural selection making them more likely to reach a high enough frequency to be detected; and there is the possibility of competition among lineages with different beneficial mutations in asexual organisms (a phenomenon called clonal interference).

5.2 The fate of a new mutation

• The chance a neutral or beneficial mutation is lost due to Mendelian segregation.

• Mutations fixed by natural selection.

• Frequency of a mutant allele in a finite population.

• Accumulation of deleterious mutations by Muller's Ratchet without recombination.

This simple question is central to understanding the chance of fixation and loss for new mutations and therefore their ultimate fate in a population. The mutation rate dictates how often a new mutation will appear in a population. But once a mutation has occurred, population genetic processes acting on it will determine whether it increases or decreases in frequency. This section will consider four distinct perspectives on the frequency of a new mutation based on the processes of genetic drift and natural selection. Each of the four perspectives makes different assumptions about the population context in which a new mutation is found, considering different effective population sizes, levels of recombination, and whether mutations are neutral, advantageous, or deleterious. Naturally, these four perspectives do not cover all possible situations but are meant to explore a range of possibilities and communicate several distinct approaches to determining the fate of a new mutation. Although this section will consider the action of natural selection on mutations, the simple forms of selection assumed should be accessible to most readers. Natural selection and fitness are defined and developed rigorously in Chapter 6.

Chance a mutation is lost due to Mendelian segregation

The fate of a new mutation can be tracked by considering its pattern of Mendelian inheritance, as shown by R.A. Fisher in 1930 (see Fisher 1999). Call all the existing alleles at a locus Ax where x is an integer 1, 2, 3 . . . , x to index the different alleles, and a new selectively neutral mutation Am. Any new mutation appears initially as a single-allele copy and it therefore must be found in a heterozygous genotype (AxAm). To form the next generation, this AxAm heterozygote experiences random mating with the other AxAx genotypes in the population. For each progeny produced by the AxAm genotype, there is a 1/2 chance that the mutant allele is inherited and a 1/2 chance that the mutant allele is not inherited (the Ax allele is transmitted instead). The total chance that an AxAm heterozygote passes the mutant allele on to the next generation depends on the number of progeny produced. If k is the number of progeny parented by the AxAm heterozygote and there is independent assortment of alleles, then

How does the frequency of a new mutation change over time after it is introduced into a population?

Table 5.3 The expected frequency of each family size per pair of parents (k) under the Poisson distribution with a mean family size of 2 (Y = 2). Also given is the expected probability that a mutant allele Am would not be transmitted to any progeny for a given family size. Note that 0! equals one.

Family size per pair of parents (k) .. .

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