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mutation. Alternatively, aerobic respiration within cells produces free oxygen radicals that cause oxidative damage to DNA. Therefore, high metabolism increases the rate of exposure to mutagenic agents and increases replication-independent rates of mutation. These two mechanisms that couple metabolic rate and mutation rates are not mutually exclusive and both can occur at the same time. Gillooly et al. (2005) proposed a model of the substitution rate that explicitly includes effects of body size and temperature and suggested that the molecular clock may indeed be constant after accounting for rate variation from these causes.

Heterogeneity in the rate of divergence can also be explained by the nearly neutral theory (reviewed by Ohta 1992). To see this, let f0 stand for the proportion of mutations that are selectively neutral because the pressure of negative selection acting on them is weak relative to the effective population size. (All mutations are assumed to be deleterious and advantageous mutations so rare they can be ignored, an assumption of the nearly neutral theory that is problematic (see Gillespie 1995).) The remaining (1 - f0) mutations have a large enough deleterious effect that they are acted on by negative selection and are not neutral. The rate of substitution of neutral mutations under the nearly neutral theory is then k = foM*

analogous to equation 8.3 for neutral theory. This equation says that the rate of divergence will be higher when more mutations are effectively neutral ( f0 is larger) and lower when fewer mutations are effectively neutral ( f0 is smaller).

Because the proportion of mutations that are effectively neutral depends on the effective population size, the rate of divergence also varies with the effective population size under the nearly neutral theory. In nearly neutral theory all substitutions are the result of genetic drift, as in the neutral theory. But a larger effective population size leads to fewer mutations that are effectively neutral and therefore a smaller pool of neutral mutations that can ultimately reach fixation. In contrast, a smaller effective population size leads to more mutations being effectively neutral and therefore a larger pool of neutral mutations that can ultimately experience substitution. Thus, nearly neutral theory predicts that the rate of divergence is negatively correlated with the effective population size because changes in Ne result in changes in f0. Under the nearly neutral theory, rate heterogeneity can then be explained by different effective population sizes among lineages or loci that cause f0 to vary.

Generation time may also influence perceived variation in substitution rates among species under the nearly neutral theory. In the nearly neutral theory, both mutation and substitution rates are expressed in per-generation terms as they are in the neutral theory. This should lead to generation-time effects on the substitution rate just as in the neutral theory. However, generation time effects may be cancelled out under the nearly neutral theory because of a negative correlation between generation time and effective population size. In the nearly neutral theory, the proportion of mutations that are effectively neutral depends on the effective population size. Independently, longer generation times lead to fewer substitutions per year whereas shorter generation times result in more substitutions per year if the mutation rate is constant per generation. The effective population size and the generation time should act independently on substitution rates. However, it turns out that generation time and effective population size are not generally independent (Chao & Carr 1993). For example, mice have short generation times and a large effective population size whereas elephants have long generation times and a small effective population size. Therefore, the impacts of generation time and effective population size tend to cancel each other out, resulting in a nearly neutral theory prediction that substitution rates do not show a generation time effect.

It is possible to test the nearly neutral theory prediction that the impacts of generation time and effective population size on rates of molecular evolution tend to cancel each other out. Ohta (1995) carried out such a test by comparing rates of substitution at synonymous and nonsynonymous sites for 49 genes in primates, artiodactyls, and rodents (recall from earlier in this section that divergence rates for these same animals support the generation time hypothesis). Ohta divided the DNA sequence data into divergence observed at synonymous or nonsynonymous sites within exons. Mutations at non-synonymous sites are exposed to natural selection since they alter the amino acid sequence of a protein and therefore have a phenotypic effect. In contrast, synonymous site mutations are not perceived by natural selection (or selection is much weaker) since they do not alter the amino acid sequence. The nearly neutral theory predicts that nonsynonymous substitution rates should be lower than synonymous substitution rates because of negative selection on the pool of nonsynonymous mutations (nonsynonymous f0 is smaller). In addition, divergence rates at nonsynonymous sites should not exhibit a generation time effect because of the negative correlation between generation time and effective population size for mutations that are nearly neutral. Table 8.4 shows Ohta's divergence data for primates, artiodactyls, and rodents at synonymous and nonsynonymous sites. Synonymous substitution rates are an order of magnitude greater than nonsynonymous rates, as expected if nonsynonymous sites experience frequent negative selection against mutations. The synonymous rate is 2.59 times faster for rodents than for primates. In contrast, the nonsynonymous rate is 1.68 times faster for rodents than for primates. Therefore, divergence at nonsynonymous sites shows less of a generation-time effect, also consistent with nearly neutral theory.

8.5 Testing the neutral theory null model of DNA sequence evolution

• The Hudson-Kreitman-Aguade (HKA) test.

• Mismatch distributions.

This section provides the opportunity to apply the conceptual results of the neutral theory developed earlier in the chapter to test the neutral null model for the causes of molecular evolution. Some tests take advantage of the neutral theory predictions for levels of polymorphism and divergence while others rely on coalescent model results that were developed in earlier chapters. These tests have been widely employed in empirical studies of DNA sequences sampled from a wide array of loci, genomes, and species (see review by Ford 2002). The tests described in this section have contributed much to our knowledge of how natural selection has acted on DNA sequences as well as our understanding of how multiple population genetic processes (mating, gene flow, genetic drift, mutation, changes in Ne, and natural selection) interact in natural populations.

HKA test of neutral theory expectations for DNA sequence evolution

The HKA test, so named after its authors Hudson, Kreitman, and Aguade (Hudson et al. 1987), is a test that compares neutral theory predictions for

DNA sequence evolution with empirically estimated polymorphism and divergence. The test utilizes the expectation that under neutrality both polymorphism within species and divergence between species are a product of the mutation rate. In fact, under neutral evolution levels of polymorphism and divergence at a locus should be correlated because they are both products of the very same mutations. If a locus has a high mutation rate, for example, then the population should be highly polymorphic (see equation 8.1). At the same time, divergence at that locus when compared with another species should also be substantial since the rate of substitutions that contribute to divergence is also equal to the mutation rate (see equations 8.2 and 8.3). Alternatively, a combination of both low polymorphism and low levels of divergence should be apparent if a neutral locus has a low mutation rate. In this way, expected levels of polymorphism and divergence are not independent under neutrality. Evidence that divergence and polymorphism are not correlated would be at odds with neutral expectations and therefore evidence to reject the neutral null model for the locus under study.

The HKA test requires DNA sequence data from two loci. One locus is chosen because it is selectively neutral and serves as a reference or control locus. Examples of a neutral reference locus include non-coding regions of the genome or duplicate copies of genes that are not functional (pseudo-genes), both of which are expected to be relatively free of functional constraints on nucleotide substitutions. The other locus used is the focus of the test and the locus for which the neutral null model of evolution is being tested.

The HKA test also requires that DNA sequence data for two loci be collected in a particular manner. First, DNA sequences for two loci must be obtained from two species to estimate divergence between the species for both the neutral reference and the test loci. In addition, DNA sequences from multiple individuals within one of the species need to be obtained to estimate levels of polymorphism present at both loci. Polymorphism is measured by nucleotide diversity (n) for each locus. Divergence is estimated by comparing the DNA sequences for both loci between an individual of each species, employing a nucleotide substitution model to correct for homoplasy.

Once the estimates of polymorphism and divergence are made from DNA sequence data, they can be compared in a format like that shown in Table 8.5. Panel a in Table 8.5 shows the neutral theory expectations for polymorphism and divergence at the two loci.

Table 8.5 Estimates of polymorphism and divergence for two loci sampled from two species that form the basis of the HKA test. (a) The correlation of polymorphism and divergence under neutrality results in a constant ratio of divergence and polymorphism between loci independent of their mutation rate as well as a constant ratio of polymorphism or divergence between loci. (b) An illustration of ideal polymorphism and divergence estimates that would be consistent with the neutral null model. (c) Data for the Adh gene and flanking region (Hudson et al. 1987) is not consistent with the neutral model of sequence evolution because there is more Adh polymorphism within Drosophila melanogaster than expected relative to flanking region divergence between D. melanogaster and D. sechellia.

(a) Neutral case expectations

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