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.     

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.     

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.     

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.     

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.     

A compound poisson process for relaxing the molecular clock

The molecular clock hypothesis remains an important conceptual and analytical tool in evolutionary biology despite the repeated observation that the clock hypothesis does not perfectly explain observed DNA sequence variation. We introduce a parametric model that relaxes the molecular clock by allowing rates to vary across lineages according to a compound Poisson process. Events of substitution rate change are placed onto a phylogenetic tree according to a Poisson process. When an event of substitution rate change occurs, the current rate of substitution is modified by a gamma-distributed random variable. Parameters of the model can be estimated using Bayesian inference. We use Markov chain Monte Carlo integration to evaluate the posterior probability distribution because the posterior probability involves high dimensional integrals and summations. Specifically, we use the Metropolis-Hastings-Green algorithm with 11 different move types to evaluate the posterior distribution. We demonstrate the method by analyzing a complete mtDNA sequence data set from 23 mammals. The model presented here has several potential advantages over other models that have been proposed to relax the clock because it is parametric and does not assume that rates change only at speciation events. This model should prove useful for estimating divergence times when substitution rates vary across lineages.     

Explosive radiations and the reliability of molecular clocks: island endemic radiations as a test case

The reliability of molecular clocks has been questioned for several key evolutionary radiations on the basis that the clock might run fast in explosive radiations. Molecular date estimates for the radiations of metazoan phyla (the Cambrian explosion) and modern orders of mammals and birds are in many cases twice as old as the palaeontological evidence would suggest. Could some aspect of explosive radiations speed the molecular clock, making molecular date estimates too old? Here we use 19 independent instances of recent explosive radiations of island endemic taxa as a model system for testing the proposed influence of rapid adaptive radiation on the rate of molecular evolution. These radiations are often characterized by many of the potential mechanisms for fast rates in explosive radiations--such as small population size, elevated speciation rate, rapid rate of morphological change, release from previous ecological constraints, and adaptation to new niches--and represent a wide variety of species, islands, and genes. However, we find no evidence of a consistent increase in rates in island taxa compared to their mainland relatives, and therefore find no support for the hypothesis that the molecular clock runs fast in explosive radiations.     

Adaptive evolution of relish, a Drosophila NF-kappaB/IkappaB protein

NF-kappaB and IkappaB proteins have central roles in regulation of inflammation and innate immunity in mammals. Homologues of these proteins also play an important role in regulation of the Drosophila immune response. Here we present a molecular population genetic analysis of Relish, a Drosophila NF-kappaB/IkappaB protein, in Drosophila simulans and D. melanogaster. We find strong evidence for adaptive protein evolution in D. simulans, but not in D. melanogaster. The adaptive evolution appears to be restricted to the IkappaB domain. A possible explanation for these results is that Relish is a site of evolutionary conflict between flies and their microbial pathogens.     

Intercontinental and intracontinental biogeography patterns and methods

The study of biogeography has benefited from the exponential increase of DNA sequence data from recent molecular systematic studies, the development of analytical methods in the last decade concerning divergence time estimation and geographic area analyses, and the availability of large-scale distributiofi data of species in many groups of organisms. The underlying principle of divergence time estimation from DNA and protein data is that sequence divergence depends on the product of evolutionary rate and time. With their molecular clock hypothesis, Zuckerkandl and Pauling （1965） separated rates of molecular evolution from time by incorporating fossil evidence. Originally,     

Correlated evolutionary divergence of egg size and a mitochondrial protein across the Isthmus of Panama

An explicit assumption of studies that employ a mitochondrial DNA (mtDNA) molecular clock is that mtDNA evolves independently of morphology. Here we report a very strong correlation between egg size divergence and cytochrome c oxidase-1 (CO1) amino acid sequence divergence among sister species of bivalve molluscs separated by the Central American Isthmus (i.e., "geminate" species). Analyses of the molecular data reveal that CO1 sequences likely did not diverge as a function of time or evolve in response to positive natural selection. Given that an excess of CO1 amino acid polymorphism exists within species (as expected if most mutations are only slightly deleterious), a third hypothesis is that reductions in effective population size could simultaneously increase the fixation rate of nearly neutral mtDNA polymorphisms and in some way also facilitate egg size evolution. The remarkable strength of the relationship between egg size and CO1 amino acid sequence demonstrates that, even in the absence of an obvious functional relationship or clock-like evolution, the amounts of molecular and morphological change can be tightly correlated, and therefore may reflect common processes. Accordingly, the assumption that the evolutionary divergence of molecules and morphology are independent must always be carefully examined.     

Molecular clocks in reptiles: life history influences rate of molecular evolution

Life history has been implicated as a determinant of variation in rate of molecular evolution amongst vertebrate species because of a negative correlation between body size and substitution rate for many molecular data sets. Both the generality and the cause of the negative body size trend have been debated, and the validity of key studies has been questioned (particularly concerning the failure to account for phylogenetic bias). In this study, a comparative method has been used to test for an association between a range of life-history variables-such as body size, age at maturity, and clutch size-and DNA substitution rate for three genes (NADH4, cytochrome b, and c-mos). A negative relationship between body size and rate of molecular evolution was found for phylogenetically independent pairs of reptile species spanning turtles, lizards, snakes, crocodile, and tuatara. Although this study was limited by the number of comparisons for which both sequence and life-history data were available, the results suggest that a negative body size trend in rate of molecular evolution may be a general feature of reptile molecular evolution, consistent with similar studies of mammals and birds. This observation has important implications for uncovering the mechanisms of molecular evolution and warns against assuming that related lineages will share the same substitution rate (a local molecular clock) in order to date evolutionary divergences from DNA sequences.     

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.     

Effective population size is positively correlated with levels of adaptive divergence among annual sunflowers

The role of adaptation in the divergence of lineages has long been a central question in evolutionary biology, and as multilocus sequence data sets have become available for a wide range of taxa, empirical estimates of levels of adaptive molecular evolution are increasingly common. Estimates vary widely among taxa, with high levels of adaptive evolution in Drosophila, bacteria, and viruses but very little evidence of widespread adaptive evolution in hominids. Although estimates in plants are more limited, some recent work has suggested that rates of adaptive evolution in a range of plant taxa are surprisingly low and that there is little association between adaptive evolution and effective population size in contrast to patterns seen in other taxa. Here, we analyze data from 35 loci for six sunflower species that vary dramatically in effective population size. We find that rates of adaptive evolution are positively correlated with effective population size in these species, with a significant fraction of amino acid substitutions driven by positive selection in the species with the largest effective population sizes but little or no evidence of adaptive evolution in species with smaller effective population sizes. Although other factors likely contribute as well, in sunflowers effective population size appears to be an important determinant of rates of adaptive evolution.     

Evidence of adaptive evolution of accessory gland proteins in closely related species of the Drosophila repleta group

Accessory gland proteins (Acps) are part of the seminal fluid of Drosophila species. These proteins have important reproductive functions, being responsible for the proper functioning of several steps of the fertilization process. Acps also contribute indirectly for the reproductive success of males by modulating female behavior. Evidence that Acps participate in sperm competition and sexual conflict includes findings that, on average, Acps have fast evolutionary rates, suggestive of adaptive evolution. This is especially true in species of the Drosophila repleta group. Nevertheless, only in a few occasions have robust statistical tests been used to determine whether observed evolutionary rates are in fact due to positive selection on amino acid substitutions between related species. Here we apply maximum likelihood tests for positive selection on 14 Acps of the D. repleta group. To increase statistical robustness, we use at least 8 sequences, all belonging to species of the Drosophila mulleri complex, for each gene analyzed. We found significant evidence of adaptive evolution for 10 of the tested genes. Among these, the ones with a conserved protein domain had positively selected sites within the functional region of the sequence. We also detected one instance of lineage-specific adaptive evolution in a clade formed by 2 sister species.     

The rate of the molecular clock and the cost of gratuitous protein synthesis

Background  

The nature of the protein molecular clock, the protein-specific rate of amino acid substitutions, is among the central questions of molecular evolution. Protein expression level is the dominant determinant of the clock rate in a number of organisms. It has been suggested that highly expressed proteins evolve slowly in all species mainly to maintain robustness to translation errors that generate toxic misfolded proteins. Here we investigate this hypothesis experimentally by comparing the growth rate of Escherichia coli expressing wild type and misfolding-prone variants of the LacZ protein.     

Neutral evolution of robustness in Drosophila microRNA precursors

Mutational robustness describes the extent to which a phenotype remains unchanged in the face of mutations. Theory predicts that the strength of direct selection for mutational robustness is at most the magnitude of the rate of deleterious mutation. As far as nucleic acid sequences are concerned, only long sequences in organisms with high deleterious mutation rates and large population sizes are expected to evolve mutational robustness. Surprisingly, recent studies have concluded that molecules that meet none of these conditions--the microRNA precursors (pre-miRNAs) of multicellular eukaryotes--show signs of selection for mutational and/or environmental robustness. To resolve the apparent disagreement between theory and these studies, we have reconstructed the evolutionary history of Drosophila pre-miRNAs and compared the robustness of each sequence to that of its reconstructed ancestor. In addition, we "replayed the tape" of pre-miRNA evolution via simulation under different evolutionary assumptions and compared these alternative histories with the actual one. We found that Drosophila pre-miRNAs have evolved under strong purifying selection against changes in secondary structure. Contrary to earlier claims, there is no evidence that these RNAs have been shaped by either direct or congruent selection for any kind of robustness. Instead, the high robustness of Drosophila pre-miRNAs appears to be mostly intrinsic and likely a consequence of selection for functional structures.     

Diversity-enhancing selection acts on a female reproductive protease family in four subspecies of Drosophila mojavensis

Protein components of the Drosophila male ejaculate are critical modulators of reproductive success, several of which are known to evolve rapidly. Recent evidence of adaptive evolution in female reproductive tract proteins suggests this pattern may reflect sexual selection at the molecular level. Here we explore the evolutionary dynamics of a five-paralog gene family of female reproductive proteases within geographically isolated subspecies of Drosophila mojavensis. Remarkably, four of five paralogs show exceptionally low differentiation between subspecies and unusually structured haplotypes that suggest the retention of old polymorphisms. These gene genealogies are accompanied by deviations from neutrality consistent with diversifying selection. While diversifying selection has been observed among the reproductive molecules of mammals and marine invertebrates, our study provides the first evidence of this selective regime in any Drosophila reproductive protein, male or female.     

Gene duplication and complex circadian clocks in mammals

The circadian clock arose early in the evolution of life to enable organisms to adapt to the cycle of day and night. Recently, the extent and importance of circadian regulation of behaviour and physiology has come to be more fully realized. Core molecular cogs of circadian oscillators appear to have been largely conserved between such diverse organisms as Drosophila melanogaster and mammals. However, gene duplication events have produced multiple copies of many clock genes in mammals. Recent studies suggest that genome duplication has lead to increased circadian complexity and local tissue regulation. This has important implications for temporal regulation of behaviour via multiple clocks in the central nervous system, and also extends to the local physiology of major body organs and tissues.     

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.