Statistical models of the overdispersed molecular clock

The most commonly used statistical model to describe the rate constancy of molecular evolution (molecular clock) is a simple Poisson process in which the variance of the number of amino acid or nucleotide substitutions in a particular gene should be equal to the mean and henceforth the dispersion index, the ratio of the variance to the mean, should be equal to one. Recent sequence data, however, have shown that the substitutional process in molecular evolution is often considerably overdispersed and have called into question the generality of using a simple Poisson process. Several efforts have been made to develop more realistic models of molecular evolution. In this paper, I will show that the spatial (site-specific) variation in the rate of molecular evolution is an improbable cause of the overdispersion and then review various statistical models which take the temporal variation into account. Although these models do not immediately specify what the mechanisms of molecular evolution might be, they do make qualitatively different predictions and give some insight into their inference. One way to distinguish them is suggested. In addition, effects of selected substitutions that presumably occur after a major change in a molecule are quasi-quantitatively examined. It is most likely that the overdispersion of molecular clock is due either to a major molecular reconfiguration (fluctuating neutral space) led by a series of subliminal neutral changes or to selected substitutions fine-tuning a molecule after a major molecular change. Although the latter possibility, of course, violates the simplest neutrality assumption, it would not impair the neutral theory as a whole.     

Synonymous and nonsynonymous substitutions in mammalian genes and the nearly neutral theory

The nearly neutral theory of molecular evolution predicts larger generation-time effects for synonymous than for nonsynonymous substitutions. This prediction is tested using the sequences of 49 single-copy genes by calculating the average and variance of synonymous and nonsynonymous substitutions in mammalian star phylogenies (rodentia, artiodactyla, and primates). The average pattern of the 49 genes supports the prediction of the nearly neutral theory, with some notable exceptions.The nearly neutral theory also predicts that the variance of the evolutionary rate is larger than the value predicted by the completely neutral theory. This prediction is tested by examining the dispersion index (ratio of the variance to the mean), which is positively correlated with the average substitution number. After weighting by the lineage effects, this correlation almost disappears for nonsynonymous substitutions, but not quite so for synonymous substitutions. After weighting, the dispersion indices of both synonymous and nonsynonymous substitutions still exceed values expected under the simple Poisson process. The results indicate that both the systematic bias in evolutionary rate among the lineages and the episodic type of rate variation are contributing to the large variance. The former is more significant to synonymous substitutions than to nonsynonymous substitutions. Isochore evolution may be similar to synonymous substitutions. The rate and pattern found here are consistent with the nearly neutral theory, such that the relative contributions of drift and selection differ between the two types of substitutions. The results are also consistent with Gillespie's episodic selection theory.     

Consistent variation in amino-acid substitution rate, despite uniformity of mutation rate: protein evolution in mammals is not neutral

Variation in mutation rate, attributed to differences in both generation time and in metabolic rate, has been invoked under the neutral theory of molecular evolution to account for differences in substitution rate among mammalian lineages. We show that substitution rates at fourfold-degenerate sites and at sites in noncoding regions do not vary between the primate and rodent lineages, implying mutation- rate uniformity. In contrast, the substitution rates at nondegenerate sites vary both within and between lineages. This difference in substitution-rate pattern between the two types of site is incompatible with neutral theory but may result from substitutions occurring by fixation of slightly deleterious mutations. Variation in the rate of protein evolution among mammalian lineages appears to be due more to differences in population fixation rates than to biochemical or physiological differences affecting mutation rates.      

Overdispersion of the molecular clock: temporal variation of gene-specific substitution rates in Drosophila

Simple models of molecular evolution assume that sequences evolve by a Poisson process in which nucleotide or amino acid substitutions occur as rare independent events. In these models, the expected ratio of the variance to the mean of substitution counts equals 1, and substitution processes with a ratio greater than 1 are called overdispersed. Comparing the genomes of 10 closely related species of Drosophila, we extend earlier evidence for overdispersion in amino acid replacements as well as in four-fold synonymous substitutions. The observed deviation from the Poisson expectation can be described as a linear function of the rate at which substitutions occur on a phylogeny, which implies that deviations from the Poisson expectation arise from gene-specific temporal variation in substitution rates. Amino acid sequences show greater temporal variation in substitution rates than do four-fold synonymous sequences. Our findings provide a general phenomenological framework for understanding overdispersion in the molecular clock. Also, the presence of substantial variation in gene-specific substitution rates has broad implications for work in phylogeny reconstruction and evolutionary rate estimation.     

Rates of molecular evolution in bacteria are relatively constant despite spore dormancy

Rates of molecular evolution are known to vary considerably among lineages, partially due to differences in life-history traits such as generation time. The generation-time effect has been well documented in some eukaryotes, but its prevalence in prokaryotes is unknown. "Because many species of Firmicute bacteria spend long periods of time as metabolically dormant spores, which could result in fewer DNA substitutions per unit time, they present an excellent system for testing predictions of the molecular clock hypothesis." To test whether spore-forming bacteria evolve more slowly than their non-spore-forming relatives, I used phylogenetic methods to determine if there were differences in rates of amino acid substitution between spore-forming and non-spore-forming lineages of Firmicute bacteria. Although rates of evolution do vary among lineages, I find no evidence for an effect of spore-formation on evolutionary rate and, furthermore, evolutionary rates are similar to those calculated for enteric bacteria. These results support the notion that variation in generation time does not affect evolutionary rates in bacterial lineages.     

Neutral evolution of the sex-determining gene transformer in Drosophila

The amino acid sequence of the transformer (tra) gene exhibits an extremely rapid rate of evolution among Drosophila species, although the gene performs a critical step in sex determination. These changes in amino acid sequence are the result of either natural selection or neutral evolution. To differentiate between selective and neutral causes of this evolutionary change, analyses of both intraspecific and interspecific patterns of molecular evolution of tra gene sequences are presented. Sequences of 31 tra alleles were obtained from Drosophila americana. Many replacement and silent nucleotide variants are present among the alleles; however, the distribution of this sequence variation is consistent with neutral evolution. Sequence evolution was also examined among six species representative of the genus Drosophila. For most lineages and most regions of the gene, both silent and replacement substitutions have accumulated in a constant, clock-like manner. In exon 3 of D. virilis and D. americana we find evidence for an elevated rate of nonsynonymous substitution, but no statistical support for a greater rate of nonsynonymous relative to synonymous substitutions. Both levels of analysis of the tra sequence suggest that, although the gene is evolving at a rapid pace, these changes are neutral in function.     

Molecular clock mirages

The hypothesis of the molecular clock proposes that molecular evolution occurs at rates that persist through time and across lineages, for a given gene. The neutral theory of molecular evolution predicts that the clock will be a Poisson process, with equal mean and variance. Experimental data have shown that the variance is typically larger than the mean. Hypotheses have been advanced to account for the hypervariance of molecular evolution. Four recent papers show that none of the predictive hypotheses that have been proposed can be generally maintained. The conclusion is that molecular evolution is dependent on the fickle process of natural selection. But it is a time-dependent process, so that accumulation of empirical data often yields an approximate clock, as a consequence of the expected convergence of large numbers.     

Unraveling Selection in the Mitochondrial Genome of Drosophila

We examine mitochondrial DNA variation at the cytochrome b locus within and between three species of Drosophila to determine whether patterns of variation conform to the predictions of neutral molecular evolution. The entire 1137-bp cytochrome b locus was sequenced in 16 lines of Drosophila melanogaster, 18 lines of Drosophila simulans and 13 lines of Drosophila yakuba. Patterns of variation depart from neutrality by several test criteria. Analysis of the evolutionary clock hypothesis shows unequal rates of change along D. simulans lineages. A comparison within and between species of the ratio of amino acid replacement change to synonymous change reveals a relative excess of amino acid replacement polymorphism compared to the neutral prediction, suggestive of slightly deleterious or diversifying selection. There is evidence for excess homozygosity in our world wide sample of D. melanogaster and D. simulans alleles, as well as a reduction in the number of segregating sites in D. simulans, indicative of selective sweeps. Furthermore, a test of neutrality for codon usage shows the direction of mutations at third positions differs among different topological regions of the gene tree. The analyses indicate that molecular variation and evolution of mtDNA are governed by many of the same selective forces that have been shown to govern nuclear genome evolution and suggest caution be taken in the use of mtDNA as a ``neutral' molecular marker.     

Rapid detection of positive selection in genes and genomes through variation clusters

Positive selection in genes and genomes can point to the evolutionary basis for differences among species and among races within a species. The detection of positive selection can also help identify functionally important protein regions and thus guide protein engineering. Many existing tests for positive selection are excessively conservative, vulnerable to artifacts caused by demographic population history, or computationally very intensive. I here propose a simple and rapid test that is complementary to existing tests and that overcomes some of these problems. It relies on the null hypothesis that neutrally evolving DNA regions should show a Poisson distribution of nucleotide substitutions. The test detects significant deviations from this expectation in the form of variation clusters, highly localized groups of amino acid changes in a coding region. In applying this test to several thousand human-chimpanzee gene orthologs, I show that such variation clusters are not generally caused by relaxed selection. They occur in well-defined domains of a protein's tertiary structure and show a large excess of amino acid replacement over silent substitutions. I also identify multiple new human-chimpanzee orthologs subject to positive selection, among them genes that are involved in reproductive functions, immune defense, and the nervous system.     

Mammalian nonsynonymous sites are not overdispersed: comparative genomic analysis of index of dispersion of mammalian proteins

It is often stated that patterns of nonsynonymous rate variation among mammalian lineages are more irregular than expected or overdispersed under the neutral model, whereas synonymous sites conform to the neutral model. Here we reexamined genome-wide patterns of the variance to mean ratio, or index of dispersion (R), of substitutions in proteins from human, mouse, and dog. Contrary to the prevailing notion, we found that the mean index of dispersion for nonsynonymous sites of mammalian proteins is not significantly different from 1. We propose that earlier analyses were biased because the data included disproportionately more protein hormones, which tend to be more dispersed than genes in other functional categories. Synonymous sites exhibit greater degree of dispersion than nonsynonymous sites, although similar to earlier estimates and potentially due to errors associated with correction for multiple hits. Overall, our analysis identifies strong genome-wide generation-time effect and natural selection as important determinants of among-lineage variation of protein evolutionary rates. Furthermore, patterns of lineage-specific selective constraint are consistent with the nearly neutral model of molecular evolution.     

Bottleneck Effect on Evolutionary Rate in the Nearly Neutral Mutation Model

Variances of evolutionary rates among lineages in some proteins are larger than those expected from simple Poisson processes. This phenomenon is called overdispersion of the molecular clock. If population size N is constant, the overdispersion is observed only in a limited range of 2Nσ under the nearly neutral mutation model, where σ represents the standard deviation of selection coefficients of new mutants. In this paper, we investigated effects of changing population size on the evolutionary rate by computer simulations assuming the nearly neutral mutation model. The size was changed cyclically between two numbers, N(1) and N(2) (N(1) > N(2)), in the simulations. The overdispersion is observed if 2N(2)σ is less than two and the state of reduced size (bottleneck state) continues for more than ~0.1/u generations, where u is the mutation rate. The overdispersion results mainly because the average fitnesses of only a portion of populations go down when the population size is reduced and only in these populations subsequent advantageous substitutions occur after the population size becomes large. Since the fitness reduction after the bottleneck is stochastic, acceleration of the evolutionary rate does not necessarily occur uniformly among loci. From these results, we argue that the nearly neutral mutation model is a candidate mechanism to explain the overdispersed molecular clock.     

The index of dispersion of molecular evolution: slow fluctuations

The most simple neutral model of molecular evolution predicts that the number of substitutions within a lineage in T generations ought to be Poisson distributed. Therefore, the variance in the number of substitutions ought to equal the mean number. The ratio of the variance to the mean number of substitutions is called the index of dispersion, R(T). Assuming infinite sites, no recombination model of the gene, and a haploid, Moran population structure, R(T) is derived for a general stationary model of molecular evolution. R(T) is shown to be affected by fluctuations in parameters only when they occur on a very slow time scale. In order for parameter fluctuations to cause R(T) to deviate significantly from one, the time between parameter changes must be roughly as large, or larger, than the time between substitutions.     

Rates of nucleotide substitution in Cornaceae (Cornales)-Pattern of variation and underlying causal factors

Identifying causes of genetic divergence is a central goal in evolutionary biology. Although rates of nucleotide substitution vary among taxa and among genes, the causes of this variation tend to be poorly understood. In the present study, we examined the rate and pattern of molecular evolution for five DNA regions over a phylogeny of Cornus, the single genus of Cornaceae. To identify evolutionary mechanisms underlying the molecular variation, we employed Bayesian methods to estimate divergence times and to infer how absolute rates of synonymous and nonsynonymous substitutions and their ratios change over time. We found that the rates vary among genes, lineages, and through time, and differences in mutation rates, selection type and intensity, and possibly genetic drift all contributed to the variation of substitution rates observed among the major lineages of Cornus. We applied independent contrast analysis to explore whether speciation rates are linked to rates of molecular evolution. The results showed no relationships for individual genes, but suggested a possible localized link between species richness and rate of nonsynonymous nucleotide substitution for the combined cpDNA regions. Furthermore, we detected a positive correlation between rates of molecular evolution and morphological change in Cornus. This was particularly pronounced in the dwarf dogwood lineage, in which genome-wide acceleration in both molecular and morphological evolution has likely occurred.     

A neutral model of transcriptome evolution

Microarray technologies allow the identification of large numbers of expression differences within and between species. Although environmental and physiological stimuli are clearly responsible for changes in the expression levels of many genes, it is not known whether the majority of changes of gene expression fixed during evolution between species and between various tissues within a species are caused by Darwinian selection or by stochastic processes. We find the following: (1) expression differences between species accumulate approximately linearly with time; (2) gene expression variation among individuals within a species correlates positively with expression divergence between species; (3) rates of expression divergence between species do not differ significantly between intact genes and expressed pseudogenes; (4) expression differences between brain regions within a species have accumulated approximately linearly with time since these regions emerged during evolution. These results suggest that the majority of expression differences observed between species are selectively neutral or nearly neutral and likely to be of little or no functional significance. Therefore, the identification of gene expression differences between species fixed by selection should be based on null hypotheses assuming functional neutrality. Furthermore, it may be possible to apply a molecular clock based on expression differences to infer the evolutionary history of tissues.     

Exploring the correlations between sequence evolution rate and phenotypic divergence across the Mammalian tree provides insights into adaptive evolution

Sequence evolution behaves in a relatively consistent manner, leading to one of the fundamental paradigms in biology, the existence of a ??molecular clock??. The molecular clock can be distilled to the concept of accumulation of substitutions, through time yielding a stable rate from which we can estimate lineage divergence. Over the last 50?years, evolutionary biologists have obtained an in-depth understanding of this clock??s nuances. It has been fine-tuned by taking into account the vast heterogeneity in rates across lineages and genes, leading to ??relaxed?? molecular clock methods for timetree reconstruction. Sequence rate varies with life history traits including body size, generation time and metabolic rate, and we review recent studies on this topic. However, few studies have explicitly examined correlates between molecular evolution and morphological evolution. The patterns observed across diverse lineages suggest that rates of molecular and morphological evolution are largely decoupled. We discuss how identifying the molecular mechanisms behind rapid functional radiations are central to understanding evolution. The vast functional divergence within mammalian lineages that have relatively ??slow?? sequence evolution refutes the hypotheses that pulses in diversification yielding major phenotypic change are the result of steady accumulation of substitutions. Patterns rather suggest phenotypic divergence is likely caused by regulatory alterations mediated through mechanisms such as insertions/deletions in functional regions. These can rapidly arise and sweep to fixation faster than predicted from a lineage??s sequence neutral substitution rate, enabling species to leapfrog between phenotypic ??islands??. We suggest research directions that could illuminate mechanisms behind the functional diversity we see today.     

Simulation studies on the evolution of amino acid sequences

Summary A model of molecular evolution in which the parameter (intrinsic rate of amino acid substitution) fluctuates from time to time was investigated by simulating the process. It was found that the usual method of estimation such as Poisson fitting underestimates this variation of the parameter when remote comparisons are made. At the same time, four distance measures (minimum base difference, Poisson fitting, random nucleotide substitutions and negative binomial fitting) were tested for their accuracy. When the substitution rate is not uniform among the amino acid sites, the negative binomial fitting gives most satisfactory results, however, one needs to know the parameter beforehand in order to use this method. It was pointed out that the fluctuation of the evolutionary rate is expected if the nearly neutral but very slightly deleterious mutations play an important role on molecular evolution.Contribution No. 1087 from the National Institute of Genetics, Mishima, Shizuoka-ken, 411 Japan.     

Rates of molecular evolution and the fraction of nucleotide positions free to vary

Summary Selective constraints on DNA sequence change were incorporated into a model of DNA divergence by restricting substitutions to a subset of nucleotide positions. A simple model showed that both mutation rate and the fraction of nucleotide positions free to vary are strong determinants of DNA divergence over time.When divergence between two species approaches the fraction of positions free to vary, standard methods that correct for multiple mutations yield severe underestimates of the number of substitutions per site. A modified method appropriate for use with DNA sequence, restriction site, or thermal renaturation data is derived taking this fraction into account. The model also showed that the ratio of divergence in two gene classes (e.g., nuclear and mitochondrial) may vary widely over time even if the ratio of mutation rates remains constant.DNA sequence divergence data are used increasingly to detect differences in rates of molecular evolution. Often, variation in divergence rate is assumed to represent variation in mutation rate. The present model suggests that differing divergence rates among comparisons (either among gene classes or taxa) should be interpreted cautiously. Differences in the fraction of nucleotide positions free to vary can serve as an important alternative hypothesis to explain differences in DNA divergence rates.     

Parallel evolution of site‐specific changes in divergent caribou lineages

The parallel evolution of phenotypes or traits within or between species provides important insight into the basic mechanisms of evolution. Genetic and genomic advances have allowed investigations into the genetic underpinnings of parallel evolution and the independent evolution of similar traits in sympatric species. Parallel evolution may best be exemplified among species where multiple genetic lineages, descended from a common ancestor, colonized analogous environmental niches, and converged on a genotypic or phenotypic trait. Modern North American caribou (Rangifer tarandus) originated from three ancestral sources separated during the Last Glacial Maximum (LGM): the Beringian–Eurasian lineage (BEL), the North American lineage (NAL), and the High Arctic lineage (HAL). Historical introgression between the NAL and the BEL has been found throughout Ontario and eastern Manitoba. In this study, we first characterized the functional differentiation in the cytochrome‐b (cytB) gene by identifying nonsynonymous changes. Second, the caribou lineages were used as a direct means to assess site‐specific parallel changes among lineages. There was greater functional diversity within the NAL despite the BEL having greater neutral diversity. The patterns of amino acid substitutions occurring within different lineages supported the parallel evolution of cytB amino acid substitutions suggesting different selective pressures among lineages. This study highlights the independent evolution of identical amino acid substitutions within a wide‐ranging mammal species that have diversified from different ancestral haplogroups and where ecological niches can invoke parallel evolution.