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that depends on the effective population size Ne and the mutation rate || (see equation 5.39). In this view of neutral mutations, polymorphism results from either a high rate of input of mutations even if drift is strong, a long dwell time for each mutation due to a large effective population size even if mutations are infrequent, or intermediate levels of mutation and genetic drift.

The neutral theory prediction for polymorphism can be readily compared with polymorphism expected under positive (higher than average genotype fitness) and negative (lower than average genotype fitness) natural selection (Fig. 8.3). New mutations that are deleterious will go to loss faster than neutral mutations since natural selection will deterministically reduce their frequencies and there will be little or no random walk in allele frequency. In contrast, new mutations that are advantageous will increase in frequency to fixation, again deterministically under natural selection without a random walk in frequency. So a locus with new mutations that are influenced by directional natural selection should show less polymorphism than a locus with neutral mutations. The other possibility is that some advantageous mutations are influenced by balancing selection due to overdominance for fitness. In that case two or more alleles will have very long times of segregation since natural selection will maintain several alleles at intermediate frequencies between fixation and loss with the result of increased levels of polymorphism in the population.

As a whimsical metaphor, compare the average times to fixation under directional selection, neutral evolution, and balancing selection with the time it takes a population genetics professor to go from his or her office (initial mutation) to the coffee shop and back (fixation) at different career stages (different processes). A new, over-worked professor goes directly to get a cup of coffee and returns immediately without stopping to talk to anyone, so the trip is short and direct like directional selection. In mid-career, a professor has a bit more free time and will pause more often to greet friends, like a random walk. Late in their career, a professor takes a roundabout path to the shop and stops to talk frequently such that the coffee break takes a very long time, like balancing selection.

Divergence

The neutral theory also predicts the rate of divergence between sequences. Genetic divergence occurs by substitutions that accumulate in two DNA sequences over time. Think of two DNA sequences that are

Figure 8.3 The dwell time for new mutations is different if fixation and loss is due to genetic drift or natural selection. With neutral mutations (b), most mutations go to loss fairly rapidly and a few mutations eventually go to fixation. For eventual fixation or loss of neutral mutations the path to that outcome is a random walk, implying that the time to fixation or loss has a high variance. For mutations that fix because they are advantageous (a), directional selection fixes them rapidly in the population. Therefore under directional selection alleles segregate for a shorter time and there is less polymorphism than with neutrality. For mutations that show overdominance for fitness, natural selection favoring heterozygote genotypes maintains several alleles in the population indefinitely. Therefore balancing selection greatly increases the segregation time of alleles and increases polymorphism compared to neutrality. Both cases of natural selection (a and c) are drawn to show negative selection acting against most new mutations. If new mutations are deleterious then the time to loss is very short and there is very little random walk in allele frequency since selection is nearly deterministic.

Figure 8.3 The dwell time for new mutations is different if fixation and loss is due to genetic drift or natural selection. With neutral mutations (b), most mutations go to loss fairly rapidly and a few mutations eventually go to fixation. For eventual fixation or loss of neutral mutations the path to that outcome is a random walk, implying that the time to fixation or loss has a high variance. For mutations that fix because they are advantageous (a), directional selection fixes them rapidly in the population. Therefore under directional selection alleles segregate for a shorter time and there is less polymorphism than with neutrality. For mutations that show overdominance for fitness, natural selection favoring heterozygote genotypes maintains several alleles in the population indefinitely. Therefore balancing selection greatly increases the segregation time of alleles and increases polymorphism compared to neutrality. Both cases of natural selection (a and c) are drawn to show negative selection acting against most new mutations. If new mutations are deleterious then the time to loss is very short and there is very little random walk in allele frequency since selection is nearly deterministic.

copies of the same ancestral sequence (Fig. 8.4). The two sequences were originally identical before any substitutions occurred. Over time, mutations occurred in each population and some were fixed by chance due to genetic drift (see Fig. 8.2). Each fixed mutation causes a change in the base pairs at random nucleotide positions in the sequence, causing each sequence to diverge slightly from its ancestor as well as from its sibling sequence. A biological example is two species that recently diverged from an ancestral species with no genetic variation. Both of the new species would be founded with identical DNA

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