Molecular Clock of Neutral Mutations in a Fitness-Increasing Evolutionary Process

The molecular clock of neutral mutations, which represents linear mutation fixation over generations, is theoretically explained by genetic drift in fitness-steady evolution or hitchhiking in adaptive evolution. The present study is the first experimental demonstration for the molecular clock of neutral mutations in a fitness-increasing evolutionary process. The dynamics of genome mutation fixation in the thermal adaptive evolution of Escherichia coli were evaluated in a prolonged evolution experiment in duplicated lineages. The cells from the continuously fitness-increasing evolutionary process were subjected to genome sequencing and analyzed at both the population and single-colony levels. Although the dynamics of genome mutation fixation were complicated by the combination of the stochastic appearance of adaptive mutations and clonal interference, the mutation fixation in the population was simply linear over generations. Each genome in the population accumulated 1.6 synonymous and 3.1 non-synonymous neutral mutations, on average, by the spontaneous mutation accumulation rate, while only a single genome in the population occasionally acquired an adaptive mutation. The neutral mutations that preexisted on the single genome hitchhiked on the domination of the adaptive mutation. The successive fixation processes of the 128 mutations demonstrated that hitchhiking and not genetic drift were responsible for the coincidence of the spontaneous mutation accumulation rate in the genome with the fixation rate of neutral mutations in the population. The molecular clock of neutral mutations to the fitness-increasing evolution suggests that the numerous neutral mutations observed in molecular phylogenetic trees may not always have been fixed in fitness-steady evolution but in adaptive evolution.     

Divergence times in Caenorhabditis and Drosophila inferred from direct estimates of the neutral mutation rate

Accurate inference of the dates of common ancestry among species forms a central problem in understanding the evolutionary history of organisms. Molecular estimates of divergence time rely on the molecular evolutionary prediction that neutral mutations and substitutions occur at the same constant rate in genomes of related species. This underlies the notion of a molecular clock. Most implementations of this idea depend on paleontological calibration to infer dates of common ancestry, but taxa with poor fossil records must rely on external, potentially inappropriate, calibration with distantly related species. The classic biological models Caenorhabditis and Drosophila are examples of such problem taxa. Here, I illustrate internal calibration in these groups with direct estimates of the mutation rate from contemporary populations that are corrected for interfering effects of selection on the assumption of neutrality of substitutions. Divergence times are inferred among 6 species each of Caenorhabditis and Drosophila, based on thousands of orthologous groups of genes. I propose that the 2 closest known species of Caenorhabditis shared a common ancestor <24 MYA (Caenorhabditis briggsae and Caenorhabditis sp. 5) and that Caenorhabditis elegans diverged from its closest known relatives <30 MYA, assuming that these species pass through at least 6 generations per year; these estimates are much more recent than reported previously with molecular clock calibrations from non-nematode phyla. Dates inferred for the common ancestor of Drosophila melanogaster and Drosophila simulans are roughly concordant with previous studies. These revised dates have important implications for rates of genome evolution and the origin of self-fertilization in Caenorhabditis.     

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.     

On the virtues and pitfalls of the molecular evolutionary clock

"Informational" macromolecules--i.e., proteins and nucleic acids--have in their sequences a register of evolutionary history. Zuckerkandl and Pauling suggested in 1965 that these molecules might provide a "molecular clock" of evolution. The molecular clock would time evolutionary events and make it possible to reconstruct phylogenetic history--the branching relationships among lineages leading to modern species. Kimura's neutrality theory postulates that rates of molecular evolution are stochastically constant and, hence, that there is a molecular clock. A variety of tests have shown that molecular evolution does not behave like a stochastic clock. The variance in evolutionary rates is much too large and thus inconsistent with the neutrality theory. This, however, does not invalidate the clock, but rather leaves it without a theoretical foundation to anticipate its properties. Sequence comparisons show that molecular evolution is sufficiently regular to serve in many situations as a clock, but uncertainty concerning the properties of the clock (for example, about the circumstances that may yield large oscillations in substitution rates from time to time or from lineage to lineage) demands that it be used with caution. Few DNA or protein sequences are known from organisms that range from closely related, e.g., different mammals, to very remote, e.g., mammals and fungi. One example is cytochrome c, which has an acceptable clockwise behavior over the whole span, in spite of some irregularities. Another example is the copper-zinc superoxide dismutase (SOD), which behaves like a very erratic clock. The SOD average rate of amino acid substitution per 100 residues per 100 million years (MY) is 5.5 when fungi and animals are compared, 9.1 when comparisons are made between insects and mammals, and 27.8 when mammals are compared with each other. The question is which mode is more common over broad evolutionary spans: the regularity of cytochrome c or the capriciousness of SOD? Additional data sets will be required in order to obtain the answer and to develop expectations about the accuracy of the clock in particular instances. Until such data exist, conclusions solely based on the molecular clock are potentially fraught with error.     

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.     

Weak selection and protein evolution

The "nearly neutral" theory of molecular evolution proposes that many features of genomes arise from the interaction of three weak evolutionary forces: mutation, genetic drift, and natural selection acting at its limit of efficacy. Such forces generally have little impact on allele frequencies within populations from generation to generation but can have substantial effects on long-term evolution. The evolutionary dynamics of weakly selected mutations are highly sensitive to population size, and near neutrality was initially proposed as an adjustment to the neutral theory to account for general patterns in available protein and DNA variation data. Here, we review the motivation for the nearly neutral theory, discuss the structure of the model and its predictions, and evaluate current empirical support for interactions among weak evolutionary forces in protein evolution. Near neutrality may be a prevalent mode of evolution across a range of functional categories of mutations and taxa. However, multiple evolutionary mechanisms (including adaptive evolution, linked selection, changes in fitness-effect distributions, and weak selection) can often explain the same patterns of genome variation. Strong parameter sensitivity remains a limitation of the nearly neutral model, and we discuss concave fitness functions as a plausible underlying basis for weak selection.     

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.      

Directional mutation pressure,mutator mutations,and dynamics of molecular evolution

Using a general form of the directional mutation theory, this paper analyzes the effect of mutations in mutator genes on the G + C content of DNA, the frequency of substitution mutations, and evolutionary changes (cumulative mutations) under various degrees of selective constraints. Directional mutation theory predicts that when the mutational bias between A/T and G/C nucleotide pairs is equilibrated with the base composition of a neutral set of DNA nucleotides, the mutation frequency per gene will be much lower than the frequency immediately after the mutator mutation takes place. This prediction explains the wide variation of the DNA G + C content among unicellular organisms and possibly also the wide intragenomic heterogeneity of third codon positions for the genes of multicellular eukaryotes. The present analyses lead to several predictions that are not consistent with a number of the frequently held assumptions in the field of molecular evolution, including belief in a constant rate of evolution, symmetric branching of phylogenetic trees, the generality of higher mutation frequency for neutral sets of nucleotides, the notion that mutator mutations are generally deleterious because of their high mutation rates, and teleological explanations of DNA base composition. Presented at the NATO Advanced Research Workshop onGenome Organization and Evolution, Spetsai, Greece, 16–22 September 1992     

Understanding Neutral Genomic Molecular Clocks

The molecular clock hypothesis is a central concept in molecular evolution and has inspired much research into why evolutionary rates vary between and within genomes. In the age of modern comparative genomics, understanding the neutral genomic molecular clock occupies a critical place. It has been demonstrated that molecular clocks run differently between closely related species, and generation time is an important determinant of lineage specific molecular clocks. Moreover, it has been repeatedly shown that regional molecular clocks vary even within a genome, which should be taken into account when measuring evolutionary constraint of specific genomic regions. With the availability of a large amount of genomic sequence data, new insights into the patterns and causes of variation in molecular clocks are emerging. In particular, factors such as nucleotide composition, molecular origins of mutations, weak selection and recombination rates are important determinants of neutral genomic molecular clocks.     

Molecular bases of evolution

The general notions of the theory of evolution are listed. The unity of the "engineering principles" of the living nature is emphasized. The generalists and specialists species are discussed. The estimation of their evolution rates must be different if it is expressed by the number of species or by the morphological changes. The principles of "protein engineering" of the organisms and the role of metals in protein evolution are discussed. It is suggested that in the presence of ions of transition metals and zinc the Fox's proteinoids can possess more specific forms of enzymatic activity. In the evolution of language the horizontal transfer plays a much more important role than in the biological evolution. However in this case also the initial basis of the language remains. The random drift is considered and it is shown that in concordance with the neutralist theory there are no grounds to replace the calculation of the rates of mutational changes per time unity by the calculation per generation. The molecular drive is the main source of the evolutionary novelties. The drive is connected with drift. The synonymic mutations and the mutations in non-functional DNA are evolutionary important. The future mathematical theory of evolution must be based on the theory of Markov's chains with the stochastic matrix changing along the chain and containing the set of the non-diagonal members equal to zero. The results obtained in the theory of ontogeny are presented. The evolution of species is the evolution of ontogenies, the formation of the molecular theory of evolution can be possible only on the basis of the molecular theory of ontogeny. The internal causes of extinction of species reduce the accumulation of neutral and pseudo-neutral mutations.     

A generation‐time effect on the rate of molecular evolution in bacteria

Molecular evolutionary rate varies significantly among species and a strict global molecular clock has been rejected across the tree of life. Generation time is one primary life‐history trait that influences the molecular evolutionary rate. Theory predicts that organisms with shorter generation times evolve faster because of the accumulation of more DNA replication errors per unit time. Although the generation‐time effect has been demonstrated consistently in plants and animals, the evidence of its existence in bacteria is lacking. The bacterial phylum Firmicutes offers an excellent system for testing generation‐time effect because some of its members can enter a dormant, nonreproductive endospore state in response to harsh environmental conditions. It follows that spore‐forming bacteria would—with their longer generation times—evolve more slowly than their nonspore‐forming relatives. It is therefore surprising that a previous study found no generation‐time effect in Firmicutes. Using a phylogenetic comparative approach and leveraging on a large number of Firmicutes genomes, we found sporulation significantly reduces the genome‐wide spontaneous DNA mutation rate and protein evolutionary rate. Contrary to the previous study, our results provide strong evidence that the evolutionary rates of bacteria, like those of plants and animals, are influenced by generation time.     

The nearly neutral and selection theories of molecular evolution under the fisher geometrical framework: substitution rate, population size, and complexity

The general theories of molecular evolution depend on relatively arbitrary assumptions about the relative distribution and rate of advantageous, deleterious, neutral, and nearly neutral mutations. The Fisher geometrical model (FGM) has been used to make distributions of mutations biologically interpretable. We explored an FGM-based molecular model to represent molecular evolutionary processes typically studied by nearly neutral and selection models, but in which distributions and relative rates of mutations with different selection coefficients are a consequence of biologically interpretable parameters, such as the average size of the phenotypic effect of mutations and the number of traits (complexity) of organisms. A variant of the FGM-based model that we called the static regime (SR) represents evolution as a nearly neutral process in which substitution rates are determined by a dynamic substitution process in which the population's phenotype remains around a suboptimum equilibrium fitness produced by a balance between slightly deleterious and slightly advantageous compensatory substitutions. As in previous nearly neutral models, the SR predicts a negative relationship between molecular evolutionary rate and population size; however, SR does not have the unrealistic properties of previous nearly neutral models such as the narrow window of selection strengths in which they work. In addition, the SR suggests that compensatory mutations cannot explain the high rate of fixations driven by positive selection currently found in DNA sequences, contrary to what has been previously suggested. We also developed a generalization of SR in which the optimum phenotype can change stochastically due to environmental or physiological shifts, which we called the variable regime (VR). VR models evolution as an interplay between adaptive processes and nearly neutral steady-state processes. When strong environmental fluctuations are incorporated, the process becomes a selection model in which evolutionary rate does not depend on population size, but is critically dependent on the complexity of organisms and mutation size. For SR as well as VR we found that key parameters of molecular evolution are linked by biological factors, and we showed that they cannot be fixed independently by arbitrary criteria, as has usually been assumed in previous molecular evolutionary models.     

ABRUPT DECELERATION OF MOLECULAR EVOLUTION LINKED TO THE ORIGIN OF ARBORESCENCE IN FERNS

Molecular rate heterogeneity, whereby rates of molecular evolution vary among groups of organisms, is a well‐documented phenomenon. Nonetheless, its causes are poorly understood. For animals, generation time is frequently cited because longer‐lived species tend to have slower rates of molecular evolution than their shorter‐lived counterparts. Although a similar pattern has been uncovered in flowering plants, using proxies such as growth form, the underlying process has remained elusive. Here, we find a deceleration of molecular evolutionary rate to be coupled with the origin of arborescence in ferns. Phylogenetic branch lengths within the “tree fern” clade are considerably shorter than those of closely related lineages, and our analyses demonstrate that this is due to a significant difference in molecular evolutionary rate. Reconstructions reveal that an abrupt rate deceleration coincided with the evolution of the long‐lived tree‐like habit at the base of the tree fern clade. This suggests that a generation time effect may well be ubiquitous across the green tree of life, and that the search for a responsible mechanism must focus on characteristics shared by all vascular plants. Discriminating among the possibilities will require contributions from various biological disciplines, but will be necessary for a full appreciation of molecular evolution.     

Time scale of eutherian evolution estimated without assuming a constant rate of molecular evolution

Controversies over the molecular clock hypothesis were reviewed. Since it is evident that the molecular clock does not hold in an exact sense, accounting for evolution of the rate of molecular evolution is a prerequisite when estimating divergence times with molecular sequences. Recently proposed statistical methods that account for this rate variation are overviewed and one of these procedures is applied to the mitochondrial protein sequences and to the nuclear gene sequences from many mammalian species in order to estimate the time scale of eutherian evolution. This Bayesian method not only takes account of the variation of molecular evolutionary rate among lineages and among genes, but it also incorporates fossil evidence via constraints on node times. With denser taxonomic sampling and a more realistic model of molecular evolution, this Bayesian approach is expected to increase the accuracy of divergence time estimates.     

DNA Barcoding Works in Practice but Not in (Neutral) Theory

Background

DNA barcode differences within animal species are usually much less than differences among species, making it generally straightforward to match unknowns to a reference library. Here we aim to better understand the evolutionary mechanisms underlying this usual “barcode gap” pattern. We employ avian barcode libraries to test a central prediction of neutral theory, namely, intraspecific variation equals 2 Nµ, where N is population size and µ is mutations per site per generation. Birds are uniquely suited for this task: they have the best-known species limits, are well represented in barcode libraries, and, most critically, are the only large group with documented census population sizes. In addition, we ask if mitochondrial molecular clock measurements conform to neutral theory prediction of clock rate equals µ.

Results

Intraspecific COI barcode variation was uniformly low regardless of census population size (n = 142 species in 15 families). Apparent outliers reflected lumping of reproductively isolated populations or hybrid lineages. Re-analysis of a published survey of cytochrome b variation in diverse birds (n = 93 species in 39 families) further confirmed uniformly low intraspecific variation. Hybridization/gene flow among species/populations was the main limitation to DNA barcode identification.

Conclusions/Significance

To our knowledge, this is the first large study of animal mitochondrial diversity using actual census population sizes and the first to test outliers for population structure. Our finding of universally low intraspecific variation contradicts a central prediction of neutral theory and is not readily accounted for by commonly proposed ad hoc modifications. We argue that the weight of evidence–low intraspecific variation and the molecular clock–indicates neutral evolution plays a minor role in mitochondrial sequence evolution. As an alternate paradigm consistent with empirical data, we propose extreme purifying selection, including at synonymous sites, limits variation within species and continuous adaptive selection drives the molecular clock.     

Thermodynamics of neutral protein evolution

Naturally evolving proteins gradually accumulate mutations while continuing to fold to stable structures. This process of neutral evolution is an important mode of genetic change and forms the basis for the molecular clock. We present a mathematical theory that predicts the number of accumulated mutations, the index of dispersion, and the distribution of stabilities in an evolving protein population from knowledge of the stability effects (delta deltaG values) for single mutations. Our theory quantitatively describes how neutral evolution leads to marginally stable proteins and provides formulas for calculating how fluctuations in stability can overdisperse the molecular clock. It also shows that the structural influences on the rate of sequence evolution observed in earlier simulations can be calculated using just the single-mutation delta deltaG values. We consider both the case when the product of the population size and mutation rate is small and the case when this product is large, and show that in the latter case the proteins evolve excess mutational robustness that is manifested by extra stability and an increase in the rate of sequence evolution. All our theoretical predictions are confirmed by simulations with lattice proteins. Our work provides a mathematical foundation for understanding how protein biophysics shapes the process of evolution.     

The neutral theory of molecular evolution and the world view of the neutralists

The main tenet of the neutral theory is that the great majority of evolutionary changes at the molecular level are caused not by Darwinian selection but by random fixation of selectively neutral (or very nearly neutral) alleles through random sampling drift under continued mutation pressure. The theory also asserts that the majority of protein and DNA polymorphisms are selectively neutral, and that they are maintained in the species by mutational input balanced by random extinction rather than by "balancing selection." The neutral theory is based on simple assumptions. This enabled us to develop mathematical theories (using the diffusion equation method) that can treat these phenomena in quantitative terms and that permit theory to be tested against actual observations. Although the neutral theory has been severely criticized by the neo-Darwinian establishment, supporting evidence has accumulated over the last 20 years. In particular, the recent burst of DNA sequence data helped to strengthen the theory a great deal. I believe that the neutral theory triggered reexamination of the traditional "synthetic theory of evolution." In this paper, I review the present status of the neutral theory, including discussions of such topics as "molecular evolutionary clock," very high evolutionary rates observed in RNA viruses, a deviant coding system found in Mycoplasm together with the concept of mutation-driven neutral evolution, and the origin of life. I also present a worldview based on the conception of what I call "survival of the luckiest."     

Making a robust biomolecular time scale for phylogenetic studies

The further evolution of informational molecular sequences should depend on the number of viable alternatives possible for the sequences as set by selection, the unrepaired mutation rate, and time. Most biomolecular clocks are based on Kimura's nearly neutral mutation random-drift hypothesis. This clock assumes that informational sequences are in equilibrium, i.e., the nucleotides mutate at a uniform rate and the number of nucleotides unconstrained by selection remains constant. Correcting for deviations from these assumptions should produce a more accurate clock. Informational molecules probably formed from polynucleotides having some other function such as nitrogen or nucleotide storage, thus being initially functionally unselected. At any time the rate of development of functionality in a protein may be expected to be proportional to the number of viable alternatives of sequence in its potentially interacting regions. Assuming the rate of unrepaired mutations is constant, these clocks should exponentially slow as they evolve, each with a different rate toward individual equilibria. Also if the degree of selection changes, its clock rate should change. For a more precise clock two approaches are suggested to estimate these time dependent changes in evolutionary rate. An improved clock could improve estimation of phylogeny and put a time scale on that phylogeny.     

Overdispersion of the molecular clock varies between yeast, Drosophila and mammals

Although protein evolution can be approximated as a "molecular evolutionary clock," it is well known that sequence change departs from a clock-like Poisson expectation. Through studying the deviations from a molecular clock, insight can be gained into the forces shaping evolution at the level of proteins. Generally, substitution patterns that show greater variance than the Poisson expectation are said to be "overdispersed." Overdispersion of sequence change may result from temporal variation in the rate at which amino acid substitutions occur on a phylogeny. By comparing the genomes of four species of yeast, five species of Drosophila, and five species of mammals, we show that the extent of overdispersion shows a strong negative correlation with the effective population size of these organisms. Yeast proteins show very little overdispersion, while mammalian proteins show substantial overdispersion. Additionally, X-linked genes, which have reduced effective population size, have gene products that show increased overdispersion in both Drosophila and mammals. Our research suggests that mutational robustness is more pervasive in organisms with large population sizes and that robustness acts to stabilize the molecular evolutionary clock of sequence change.     

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.