Efficient inference on known phylogenetic trees using Poisson regression

MOTIVATION: We suggest the use of Poisson regression for time inference and hypothesis testing on a bifurcating Phylogenetic tree with known topology. This method is computationally simple and naturally accommodates variable substitution rates across different sites, without requiring the estimation of these rates. We identify the assumptions under which this is a maximum-likelihood inference approach and show that in some realistic situations--in particular, when the probability of repeated mutation within each branch of the tree is small--these assumptions hold with high probability. RESULTS: Our motivating domain is human mitochondrial DNA trees, and we illustrate our method on a problem of estimating the time to most recent common ancestor of all non-African mtDNA, using publicly available data. We test for molecular clock violations using multiple comparisons, and conclude that the global molecular clock hypothesis cannot be rejected based on these data.     

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.     

Testing a molecular clock without an outgroup: derivations of induced priors on branch-length restrictions in a Bayesian framework

We propose a Bayesian method for testing molecular clock hypotheses for use with aligned sequence data from multiple taxa. Our method utilizes a nonreversible nucleotide substitution model to avoid the necessity of specifying either a known tree relating the taxa or an outgroup for rooting the tree. We employ reversible jump Markov chain Monte Carlo to sample from the posterior distribution of the phylogenetic model parameters and conduct hypothesis testing using Bayes factors, the ratio of the posterior to prior odds of competing models. Here, the Bayes factors reflect the relative support of the sequence data for equal rates of evolutionary change between taxa versus unequal rates, averaged over all possible phylogenetic parameters, including the tree and root position. As the molecular clock model is a restriction of the more general unequal rates model, we use the Savage-Dickey ratio to estimate the Bayes factors. The Savage-Dickey ratio provides a convenient approach to calculating Bayes factors in favor of sharp hypotheses. Critical to calculating the Savage-Dickey ratio is a determination of the prior induced on the modeling restrictions. We demonstrate our method on a well-studied mtDNA sequence data set consisting of nine primates. We find strong support against a global molecular clock, but do find support for a local clock among the anthropoids. We provide mathematical derivations of the induced priors on branch length restrictions assuming equally likely trees. These derivations also have more general applicability to the examination of prior assumptions in Bayesian phylogenetics.     

Relaxed clocks and inferences of heterogeneous patterns of nucleotide substitution and divergence time estimates across whales and dolphins (Mammalia: Cetacea)

Various nucleotide substitution models have been developed to accommodate among lineage rate heterogeneity, thereby relaxing the assumptions of the strict molecular clock. Recently developed "uncorrelated relaxed clock" and "random local clock" (RLC) models allow decoupling of nucleotide substitution rates between descendant lineages and are thus predicted to perform better in the presence of lineage-specific rate heterogeneity. However, it is uncertain how these models perform in the presence of punctuated shifts in substitution rate, especially between closely related clades. Using cetaceans (whales and dolphins) as a case study, we test the performance of these two substitution models in estimating both molecular rates and divergence times in the presence of substantial lineage-specific rate heterogeneity. Our RLC analyses of whole mitochondrial genome alignments find evidence for up to ten clade-specific nucleotide substitution rate shifts in cetaceans. We provide evidence that in the uncorrelated relaxed clock framework, a punctuated shift in the rate of molecular evolution within a subclade results in posterior rate estimates that are either misled or intermediate between the disparate rate classes present in baleen and toothed whales. Using simulations, we demonstrate abrupt changes in rate isolated to one or a few lineages in the phylogeny can mislead rate and age estimation, even when the node of interest is calibrated. We further demonstrate how increasing prior age uncertainty can bias rate and age estimates, even while the 95% highest posterior density around age estimates decreases; in other words, increased precision for an inaccurate estimate. We interpret the use of external calibrations in divergence time studies in light of these results, suggesting that rate shifts at deep time scales may mislead inferences of absolute molecular rates and ages.     

A mitogenomic timescale for birds detects variable phylogenetic rates of molecular evolution and refutes the standard molecular clock

Current understanding of the diversification of birds is hindered by their incomplete fossil record and uncertainty in phylogenetic relationships and phylogenetic rates of molecular evolution. Here we performed the first comprehensive analysis of mitogenomic data of 48 vertebrates, including 35 birds, to derive a Bayesian timescale for avian evolution and to estimate rates of DNA evolution. Our approach used multiple fossil time constraints scattered throughout the phylogenetic tree and accounts for uncertainties in time constraints, branch lengths, and heterogeneity of rates of DNA evolution. We estimated that the major vertebrate lineages originated in the Permian; the 95% credible intervals of our estimated ages of the origin of archosaurs (258 MYA), the amniote-amphibian split (356 MYA), and the archosaur-lizard divergence (278 MYA) bracket estimates from the fossil record. The origin of modern orders of birds was estimated to have occurred throughout the Cretaceous beginning about 139 MYA, arguing against a cataclysmic extinction of lineages at the Cretaceous/Tertiary boundary. We identified fossils that are useful as time constraints within vertebrates. Our timescale reveals that rates of molecular evolution vary across genes and among taxa through time, thereby refuting the widely used mitogenomic or cytochrome b molecular clock in birds. Moreover, the 5-Myr divergence time assumed between 2 genera of geese (Branta and Anser) to originally calibrate the standard mitochondrial clock rate of 0.01 substitutions per site per lineage per Myr (s/s/l/Myr) in birds was shown to be underestimated by about 9.5 Myr. Phylogenetic rates in birds vary between 0.0009 and 0.012 s/s/l/Myr, indicating that many phylogenetic splits among avian taxa also have been underestimated and need to be revised. We found no support for the hypothesis that the molecular clock in birds "ticks" according to a constant rate of substitution per unit of mass-specific metabolic energy rather than per unit of time, as recently suggested. Our analysis advances knowledge of rates of DNA evolution across birds and other vertebrates and will, therefore, aid comparative biology studies that seek to infer the origin and timing of major adaptive shifts in vertebrates.     

Body mass‐corrected molecular rate for bird mitochondrial DNA

Mitochondrial DNA remains one of the most widely used molecular markers to reconstruct the phylogeny and phylogeography of closely related birds. It has been proposed that bird mitochondrial genomes evolve at a constant rate of ~0.01 substitution per site per million years, that is that they evolve according to a strict molecular clock. This molecular clock is often used in studies of bird mitochondrial phylogeny and molecular dating. However, rates of mitochondrial genome evolution vary among bird species and correlate with life history traits such as body mass and generation time. These correlations could cause systematic biases in molecular dating studies that assume a strict molecular clock. In this study, we overcome this issue by estimating corrected molecular rates for birds. Using complete or nearly complete mitochondrial genomes of 475 species, we show that there are strong relationships between body mass and substitution rates across birds. We use this information to build models that use bird species’ body mass to estimate their substitution rates across a wide range of common mitochondrial markers. We demonstrate the use of these corrected molecular rates on two recently published data sets. In one case, we obtained molecular dates that are twice as old as the estimates obtained using the strict molecular clock. We hope that this method to estimate molecular rates will increase the accuracy of future molecular dating studies in birds.     

Inconsistencies in estimating the age of HIV-1 subtypes due to heterotachy

Rate heterogeneity among lineages is a common feature of molecular evolution, and it has long impeded our ability to accurately estimate the age of evolutionary divergence events. The development of relaxed molecular clocks, which model variable substitution rates among lineages, was intended to rectify this problem. Major subtypes of pandemic HIV-1 group M are thought to exemplify closely related lineages with different substitution rates. Here, we report that inferring the time of most recent common ancestor of all these subtypes in a single phylogeny under a single (relaxed) molecular clock produces significantly different dates for many of the subtypes than does analysis of each subtype on its own. We explore various methods to ameliorate this problem. We conclude that current molecular dating methods are inadequate for dealing with this type of substitution rate variation in HIV-1. Through simulation, we show that heterotachy causes root ages to be overestimated.     

Estimating absolute rates of molecular evolution and divergence times: a penalized likelihood approach.

Rates of molecular evolution vary widely between lineages, but quantification of how rates change has proven difficult. Recently proposed estimation procedures have mainly adopted highly parametric approaches that model rate evolution explicitly. In this study, a semiparametric smoothing method is developed using penalized likelihood. A saturated model in which every lineage has a separate rate is combined with a roughness penalty that discourages rates from varying too much across a phylogeny. A data-driven cross-validation criterion is then used to determine an optimal level of smoothing. This criterion is based on an estimate of the average prediction error associated with pruning lineages from the tree. The methods are applied to three data sets of six genes across a sample of land plants. Optimally smoothed estimates of absolute rates entailed 2- to 10-fold variation across lineages.     

On the Overdispersed Molecular Clock

Rates of molecular evolution at some loci are more irregular than described by simple Poisson processes. Three situations under which molecular evolution would not follow simple Poisson processes are reevaluated from the viewpoint of the neutrality hypothesis: concomitant or multiple substitutions in a gene, fluctuating substitution rates in time caused by coupled effects of deleterious mutations and bottlenecks, and changes in the degree of selective constraints against a gene (neutral space) caused by successive substitutions. The common underlying assumption that these causes are lineage nonspecific excludes the case where mutation rates themselves change systematically among lineages or taxonomic groups, and severely limits the extent of variation in the number of substitutions among lineages. Even under this stringent condition, however, the third hypothesis, the fluctuating neutral space model, can generate fairly large variation. This is described by a time-dependent renewal process, which does not exhibit any episodic nature of molecular evolution. It is argued that the observed elevated variances in the number of nucleotide or amino acid substitutions do not immediately call for positive Darwinian selection in molecular evolution.     

Effects of models of rate evolution on estimation of divergence dates with special reference to the metazoan 18S ribosomal RNA phylogeny

The molecular clock, i.e., constancy of the rate of evolution over time, is commonly assumed in estimating divergence dates. However, this assumption is often violated and has drastic effects on date estimation. Recently, a number of attempts have been made to relax the clock assumption. One approach is to use maximum likelihood, which assigns rates to branches and allows the estimation of both rates and times. An alternative is the Bayes approach, which models the change of the rate over time. A number of models of rate change have been proposed. We have extended and evaluated models of rate evolution, i.e., the lognormal and its recent variant, along with the gamma, the exponential, and the Ornstein-Uhlenbeck processes. These models were first applied to a small hominoid data set, where an empirical Bayes approach was used to estimate the hyperparameters that measure the amount of rate variation. Estimation of divergence times was sensitive to these hyperparameters, especially when the assumed model is close to the clock assumption. The rate and date estimates varied little from model to model, although the posterior Bayes factor indicated the Ornstein-Uhlenbeck process outperformed the other models. To demonstrate the importance of allowing for rate change across lineages, this general approach was used to analyze a larger data set consisting of the 18S ribosomal RNA gene of 39 metazoan species. We obtained date estimates consistent with paleontological records, the deepest split within the group being about 560 million years ago. Estimates of the rates were in accordance with the Cambrian explosion hypothesis and suggested some more recent lineage-specific bursts of evolution.     

A survey of nuclear ribosomal internal transcribed spacer substitution rates across angiosperms: an approximate molecular clock with life history effects

Background  

A full understanding of the patterns and processes of biological diversification requires the dating of evolutionary events, yet the fossil record is inadequate for most lineages under study. Alternatively, a molecular clock approach, in which DNA or amino acid substitution rates are calibrated with fossils or geological/climatic events, can provide indirect estimates of clade ages and diversification rates. The utility of this approach depends on the rate constancy of molecular evolution at a genetic locus across time and across lineages. Although the nuclear ribosomal internal transcribed spacer region (nrITS) is increasingly being used to infer clade ages in plants, little is known about the sources or magnitude of variation in its substitution rate. Here, we systematically review the literature to assess substitution rate variation in nrITS among angiosperms, and we evaluate possible correlates of the variation.     

Synonymous rates at the RpII215 gene of Drosophila: variation among species and across the coding region

The region encompassing the RpII215 gene that encodes the largest component of the RNA polymerase II complex (1889 amino acids) has been sequenced in Drosophila subobscura, D. madeirensis, D. guanche, and D. pseudoobscura. Nonsynonymous divergence estimates (Ka) indicate that this gene has a very low rate of amino acid replacements. Given its low Ka and constitutive expression, synonymous substitution rates are, however, unexpectedly high. Sequence comparisons have allowed the molecular clock hypothesis to be tested. D. guanche is an insular species and it is therefore expected to have a reduced effective size relative to D. subobscura. The significantly higher rate of synonymous substitutions detected in the D. guanche lineage could be explained if synonymous mutations behave as nearly neutral. Significant departure from the molecular clock hypothesis for synonymous and nonsynonymous substitutions was detected when comparing the D. subobscura, D. pseudoobscura, and D. melanogaster lineages. Codon bias and synonymous divergence between D. subobscura and D. melanogaster were negatively correlated across the RpII215 coding region, which indicates that selection coefficients for synonymous mutations vary across the gene. The C-terminal domain (CTD) of the RpII215 protein is structurally and functionally differentiated from the rest of the protein. Synonymous substitution rates were significantly different in both regions, which strongly indicates that synonymous mutations in the CTD and in the non-CTD regions are under detectably different selection coefficients.     

Correlated rates of synonymous site evolution across plant genomes

Synonymous substitution rates have been shown to vary among evolutionary lineages of both nuclear and organellar genes across a broad range of taxonomic groups. In animals, rate heterogeneity does not appear to be correlated across nuclear and mitochondrial genes. In this paper, we contrast substitution rates in two plant groups and show that grasses evolve more rapidly than palms at synonymous sites in a mitochondrial, a nuclear, and a plastid gene. Furthermore, we show that the relative rates of synonymous substitution between grasses and palms are similar at the three loci. The correlation in synonymous substitution rates across genes is particularly striking because the three genes evolve at very different absolute rates. In contrast, relative rates of nonsynonymous substitution are not conserved among the three genes.      

Molecular Evolution of the Plant Virus Family Bromoviridae Based on RNA3-Encoded Proteins

We have carried out an evolutionary study of the two proteins encoded by the RNA 3 from members of the plant virus family Bromoviridae. Using maximum likelihood methods, we have inferred the patterns of amino acid substitution that better explain the diversification of this viral family. The results indicate that the molecular evolution of this family was rather complex, with each protein evolving at different rates and according to different patterns of amino acid substitution. These differences include different amino acid equilibrium frequencies, heterogeneity in substitution rates among sites, and covariation among sites. Despite these differences, the model of protein evolution that better fits both proteins is one specifically proposed for the evolution of globular proteins. We also found evidence for coevolution between domains of these two proteins. Finally, our analyses suggest that the molecular clock hypothesis does not hold, since different lineages evolved at different rates. The implications of these results for the taxonomy of this important family of plant viruses are discussed. [Reviewing Editor: Dr. Martin Kreitman and Dr. James Bull]     

Simulating and detecting autocorrelation of molecular evolutionary rates among lineages

Evolutionary timescales can be estimated from genetic data using phylogenetic methods based on the molecular clock. To account for molecular rate variation among lineages, a number of relaxed‐clock models have been developed. Some of these models assume that rates vary among lineages in an autocorrelated manner, so that closely related species share similar rates. In contrast, uncorrelated relaxed clocks allow all of the branch‐specific rates to be drawn from a single distribution, without assuming any correlation between rates along neighbouring branches. There is uncertainty about which of these two classes of relaxed‐clock models are more appropriate for biological data. We present an R package, NELSI, that allows the evolution of DNA sequences to be simulated according to a range of clock models. Using data generated by this package, we assessed the ability of two Bayesian phylogenetic methods to distinguish among different relaxed‐clock models and to quantify rate variation among lineages. The results of our analyses show that rate autocorrelation is typically difficult to detect, even when there is complete taxon sampling. This provides a potential explanation for past failures to detect rate autocorrelation in a range of data sets.     

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.     

Bayesian models of episodic evolution support a late precambrian explosive diversification of the Metazoa

Multicellular animals, or Metazoa, appear in the fossil records between 575 and 509 million years ago (MYA). At odds with paleontological evidence, molecular estimates of basal metazoan divergences have been consistently older than 700 MYA. However, those date estimates were based on the molecular clock hypothesis, which is almost always violated. To relax this hypothesis, we have implemented a Bayesian approach to describe the change of evolutionary rate over time. Analysis of 22 genes from the nuclear and the mitochondrial genomes under the molecular clock assumption produced old date estimates, similar to those from previous studies. However, by allowing rates to vary in time and by taking small species-sampling fractions into account, we obtained much younger estimates, broadly consistent with the fossil records. In particular, the date of protostome-deuterostome divergence was on average 582 +/- 112 MYA. These results were found to be robust to specification of the model of rate change. The clock assumption thus had a dramatic effect on date estimation. However, our results appeared sensitive to the prior model of cladogenesis, although the oldest estimates (791 +/- 246 MYA) were obtained under a suboptimal model. Bayes posterior estimates of evolutionary rates indicated at least one major burst of molecular evolution at the end of the Precambrian when protostomes and deuterostomes diverged. We stress the importance of assumptions about rates on date estimation and suggest that the large discrepancies between the molecular and fossil dates of metazoan divergences might partly be due to biases in molecular date estimation.     

Molecular phylogenetics and biogeography of transisthmian and amphi-Atlantic needlefishes (Belonidae: Strongylura and Tylosurus): perspectives on New World marine speciation

Phylogenetic relationships among New World and eastern Atlantic species in the belonid genera Strongylura and Tylosurus were hypothesized using 3689bp of nucleotide sequence; including the entire mitochondrial (mtDNA) ATP synthase 6 and 8 genes; partial cytochrome b; 12S and 16S ribosomal genes; and introns and exons, 2 and 3 of the nuclear-encoded creatine kinase B gene. Concordant mtDNA and nuclear genealogies permitted well-supported inference of species relationships within Strongylura and Tylosurus, and of the chronology of diversification in the two genera. Our phylogenetic hypothesis permitted an assessment of Rosen's [Syst. Zool. 24 (1975) 431] model of species diversification across the eastern Atlantic to eastern Pacific marine biogeographic track. The spatial predictions of the Rosen model were generally supported, but not the temporal predictions. Furthermore, long branches leading to terminal Belonidae indicated that many species have persisted for millions of years or that nucleotide substitution rates were elevated for some clades. Though heterogeneity of nucleotide substitution rate was indicated across some belonid lineages, molecular clock estimates were used to hypothesize biogeographic scenarios for Strongylura across the eastern Pacific and Atlantic region. Furthermore, use of a molecular clock indicated; that early diversification among contemporary Strongylura may have been initiated by changes in Atlantic Ocean circulation precipitated by closure of the Tethys Sea; and provided approximate dates for the isolation of the freshwater species on the American continents.     

Inferring speciation times under an episodic molecular clock

We extend our recently developed Markov chain Monte Carlo algorithm for Bayesian estimation of species divergence times to allow variable evolutionary rates among lineages. The method can use heterogeneous data from multiple gene loci and accommodate multiple fossil calibrations. Uncertainties in fossil calibrations are described using flexible statistical distributions. The prior for divergence times for nodes lacking fossil calibrations is specified by use of a birth-death process with species sampling. The prior for lineage-specific substitution rates is specified using either a model with autocorrelated rates among adjacent lineages (based on a geometric Brownian motion model of rate drift) or a model with independent rates among lineages specified by a log-normal probability distribution. We develop an infinite-sites theory, which predicts that when the amount of sequence data approaches infinity, the width of the posterior credibility interval and the posterior mean of divergence times form a perfect linear relationship, with the slope indicating uncertainties in time estimates that cannot be reduced by sequence data alone. Simulations are used to study the influence of among-lineage rate variation and the number of loci sampled on the uncertainty of divergence time estimates. The analysis suggests that posterior time estimates typically involve considerable uncertainties even with an infinite amount of sequence data, and that the reliability and precision of fossil calibrations are critically important to divergence time estimation. We apply our new algorithms to two empirical data sets and compare the results with those obtained in previous Bayesian and likelihood analyses. The results demonstrate the utility of our new algorithms.     

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.