Mutation Rate Mu Research Articles

Correcting the Apparent Mutation Rate Acceleration at Shorter Time Scales under a Jukes-Cantor Model

At macroevolutionary time scales, and for a constant mutation rate, there is an expected linear relationship between time and the number of inferred neutral mutations (the "molecular clock"). However, at shorter time scales, a number of recent studies have observed an apparent acceleration in the rate of molecular evolution. We study this apparent acceleration under a Jukes-Cantor model applied to a randomly mating population, and show that, under the model, it arises as a consequence of ignoring short-term effects due to existing diversity within the population. The acceleration can be accounted for by adding the correction term h(0)e(-4μt/3) to the usual Jukes-Cantor formula p(t) = 3/4(1 - e (-(-4μt/3), where h(0) is the expected heterozygosity in the population at time t = 0. The true mutation rate μ may then be recovered, even if h(0) is not known, by estimating μ and h(0) simultaneously using least squares. Rate estimates made without the correction term (i.e., incorrectly assuming the population to be homogeneous) will result in a divergent rate curve of the form μ(div) = μ + C/t, so that the mutation rate appears to approach infinity as the time scale approaches zero. Although our quantitative results apply only to the Jukes-Cantor model, it is reasonable to suppose that the qualitative picture that emerges also applies to more complex models. Our study, therefore, demonstrates the importance of properly accounting for any ancestral diversity, because it may otherwise play a dominant role in rate overestimation.

HALDANE'S RULE IN AN AVIAN SYSTEM: USING CLINE THEORY AND DIVERGENCE POPULATION GENETICS TO TEST FOR DIFFERENTIAL INTROGRESSION OF MITOCHONDRIAL, AUTOSOMAL, AND SEX-LINKED LOCI ACROSS THEPASSERINABUNTING HYBRID ZONE

Using cline fitting and divergence population genetics, we tested a prediction of Haldane's rule: autosomal alleles should introgress more than z-linked alleles or mitochondrial haplotypes across the Passerina amoena/Passerina cyanea (Aves: Cardinalidae) hybrid zone. We screened 222 individuals collected along a transect in the Great Plains of North America that spans the contact zone for mitochondrial (two genes), autosomal (four loci) and z-linked (two loci) markers. Maximum-likelihood cline widths estimated from the mitochondrial (223 km) and z-linked (309 km) datasets were significantly narrower on average than the autosomal cline widths (466 km). We also found that mean coalescent-based estimates of introgression were larger for the autosomal loci (0.63 genes/generation, scaled to the mutation rate mu) than for both the mitochondrial (0.27) and z-linked loci (0.59). These patterns are consistent with Haldane's rule, but the among-locus variation also suggests many independently segregating loci are required to investigate introgression patterns across the genome. These results provide the first comprehensive comparison of mitochondrial, sex-linked, and autosomal loci across an avian hybrid zone and add to the body of evidence suggesting that sex chromosomes play an important role in the formation and maintenance of reproductive isolation between closely related species.

A synthetic theory of molecular evolution.

According to the neo-Darwinian view of evolution evolution rate nu depends solely on the environment variation rate gamma, whereas in the non-Darwinian view evolution rate is determined mainly by the mutation rate mu. We have studied two kinds of population genetics models which exhibit both types of evolution in different parametric regions: one is a dynamical model representing infinite population, and the other is a Markov process model representing a nearly monomorphic finite population. In the infinite population model, after proving general time-derivative and mu-derivative formulas for the population average of quantitative traits, we show that if the mutation rate is adaptively determined, mu must be larger than nu in the stationary state. Loads of evolution are obtained in both regions. A high evolution rate such as nu = 1 per genome per generation is consistent with Haldane's value of tolerable load if and only if the functional constraint is not large and selection is weak, independent of whether the evolution is neo-Darwinian or non-Darwinian. As the selection intensity increases, nu is shown to change discontinuously from nearly mu to gamma at the transition point. In the finite population model, the transition of v is not discontinuous, but is very steep. On the other hand, no steep change of polymorphism takes place at the transition point. The steepness of the transition in our model suggests that real molecular evolution can be divided into either neo-Darwinian or non-Darwinian,and that the intermediate type of evolution is rather rare.

Intensity of natural selection at the major histocompatibility complex loci.

Long persistence of allelic lineages, prevalence of nonsynonymous over synonymous substitutions in the peptide-binding region (PBR), and deviation from neutrality of the expected gene identity parameter F all indicate indirectly that balancing selection is operating at functional major histocompatibility complex (MHC) loci. Direct demonstrations of the existence of balancing selection at MHC loci are, however, either lacking or not fully convincing. To define the conditions under which balancing selection could be demonstrated, we estimated its intensity from the mean number of nonsynonymous substitutions, KB, at the PBR and the mutation rate mu. We compared the five available methods for estimating KB by computer simulation and chose the most reliable ones for estimation of selection intensity. For the human MHC, the selection coefficients of the HLA-A, -B, -C, -DRB1, -DQB1, -DQA1, and -DPB1 loci are 0.015, 0.042, 0.0026, 0.019, 0.0085, 0.0028, and 0.0007, respectively. This low selection intensity places severe restrictions on the possibility of measuring selection directly in vertebrate populations.

Evolutionarily stable mutation rate in a periodically changing environment.

Evolution of mutation rate controlled by a neutral modifier is studied for a locus with two alleles under temporally fluctuating selection pressure. A general formula is derived to calculate the evolutionarily stable mutation rate mu(ess) in an infinitely large haploid population, and following results are obtained. (I) For any fluctuation, periodic or random: (1) if the recombination rate r per generation between the modifier and the main locus is 0, mu(ess) is the same as the optimal mutation rate mu(op) which maximizes the long-term geometric average of population fitness; and (2) for any r, if the strength s of selection per generation is very large, mu(ess) is equal to the reciprocal of the average number T of generations (duration time) during which one allele is persistently favored than the other. (II) For a periodic fluctuation in the limit of small s and r, mu(ess)T is a function of sT and rT with properties: (1) for a given sT, mu(ess)T decreases with increasing rT; (2) for sT </= 1, mu(ess)T is almost independent of sT, and depends on rT as mu(ess)T & 1.6 for rT << 1 and mu(ess)T & 6/rT for rT >> 1; and (3) for sT >/= 1, and for a given rT, mu(ess)T decreases with increasing sT to a certain minimum less than 1, and then increases to 1 asymptotically in the limit of large sT. (III) For a fluctuation consisting of multiple Fourier components (i.e., sine wave components), the component with the longest period is the most effective in determining mu(ess) (low pass filter effect). (IV) When the cost c of preventing mutation is positive, the modifier is nonneutral, and mu(ess) becomes larger than in the case of neutral modifier under the same selection pressure acting at the main locus. The value of c which makes mu(ess) equal to mu(op) of the neutral modifier case is calculated. It is argued that this value gives a critical cost such that, so long as the actual cost exceeds this value, the evolution rate at the main locus must be smaller than its mutation rate mu(ess).