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.     

Divergence time and evolutionary rate estimation with multilocus data

Bayesian methods for estimating evolutionary divergence times are extended to multigene data sets, and a technique is described for detecting correlated changes in evolutionary rates among genes. Simulations are employed to explore the effect of multigene data on divergence time estimation, and the methodology is illustrated with a previously published data set representing diverse plant taxa. The fact that evolutionary rates and times are confounded when sequence data are compared is emphasized and the importance of fossil information for disentangling rates and times is stressed.     

Dating the time of viral subtype divergence

Precise dating of viral subtype divergence enables researchers to correlate divergence with geographic and demographic occurrences. When historical data are absent (that is, the overwhelming majority), viral sequence sampling on a time scale commensurate with the rate of substitution permits the inference of the times of subtype divergence. Currently, researchers use two strategies to approach this task, both requiring strong conditions on the molecular clock assumption of substitution rate. As the underlying structure of the substitution rate process at the time of subtype divergence is not understood and likely highly variable, we present a simple method that estimates rates of substitution, and from there, times of divergence, without use of an assumed molecular clock. We accomplish this by blending estimates of the substitution rate for triplets of dated sequences where each sequence draws from a distinct viral subtype, providing a zeroth-order approximation for the rate between subtypes. As an example, we calculate the time of divergence for three genes among influenza subtypes A-H3N2 and B using subtype C as an outgroup. We show a time of divergence approximately 100 years ago, substantially more recent than previous estimates which range from 250 to 3800 years ago.     

Bayesian relaxed clock estimation of divergence times in foraminifera

Accurate and precise estimation of divergence times during the Neo-Proterozoic is necessary to understand the speciation dynamic of early Eukaryotes. However such deep divergences are difficult to date, as the molecular clock is seriously violated. Recent improvements in Bayesian molecular dating techniques allow the relaxation of the molecular clock hypothesis as well as incorporation of multiple and flexible fossil calibrations. Divergence times can then be estimated even when the evolutionary rate varies among lineages and even when the fossil calibrations involve substantial uncertainties. In this paper, we used a Bayesian method to estimate divergence times in Foraminifera, a group of unicellular eukaryotes, known for their excellent fossil record but also for the high evolutionary rates of their genomes. Based on multigene data we reconstructed the phylogeny of Foraminifera and dated their origin and the major radiation events. Our estimates suggest that Foraminifera emerged during the Cryogenian (650-920 Ma, Neo-Proterozoic), with a mean time around 770 Ma, about 220 Myr before the first appearance of reliable foraminiferal fossils in sediments (545 Ma). Most dates are in agreement with the fossil record, but in general our results suggest earlier origins of foraminiferal orders. We found that the posterior time estimates were robust to specifications of the prior. Our results highlight inter-species variations of evolutionary rates in Foraminifera. Their effect was partially overcome by using the partitioned Bayesian analysis to accommodate rate heterogeneity among data partitions and using the relaxed molecular clock to account for changing evolutionary rates. However, more coding genes appear necessary to obtain more precise estimates of divergence times and to resolve the conflicts between fossil and molecular date estimates.     

Molecular evolution of nitrate reductase genes

To understand the evolutionary mechanisms and relationships of nitrate reductases (NRs), the nucleotide sequences encoding 19 nitrate reductase (NR) genes from 16 species of fungi, algae, and higher plants were analyzed. The NR genes examined show substantial sequence similarity, particularly within functional domains, and large variations in GC content at the third codon position and intron number. The intron positions were different between the fungi and plants, but conserved within these groups. The overall and nonsynonymous substitution rates among fungi, algae, and higher plants were estimated to be 4.33 × 10⁻¹⁰ and 3.29 × 10⁻¹⁰ substitutions per site per year. The three functional domains of NR genes evolved at about one-third of the rate of the N-terminal and the two hinge regions connecting the functional domains. Relative rate tests suggested that the nonsynonymous substitution rates were constant among different lineages, while the overall nucleotide substitution rates varied between some lineages. The phylogenetic trees based on NR genes correspond well with the phylogeny of the organisms determined from systematics and other molecular studies. Based on the nonsynonymous substitution rate, the divergence time of monocots and dicots was estimated to be about 340 Myr when the fungi–plant or algae–higher plant divergence times were used as reference points and 191 Myr when the rice–barley divergence time was used as a reference point. These two estimates are consistent with other estimates of divergence times based on these reference points. The lack of consistency between these two values appears to be due to the uncertainty of the reference times. Received: 10 April 1995 / Accepted: 10 September 1995     

ESTIMATING DIVERSIFICATION RATES: HOW USEFUL ARE DIVERGENCE TIMES?

The dynamics of species diversification rates are a key component of macroevolutionary patterns. Although not absolutely necessary, the use of divergence times inferred from sequence data has led to development of more powerful methods for inferring diversification rates. However, it is unclear what impact uncertainty in age estimates have on diversification rate inferences. Here, we quantify these effects using both Bayesian and frequentist methodology. Through simulation, we demonstrate that adding sequence data results in more precise estimates of internal node ages, but a reasonable approximation of these node ages is often sufficient to approach the theoretical minimum variance in speciation rate estimates. We also find that even crude estimates of divergence times increase the power of tests of diversification rate differences between sister clades. Finally, because Bayesian and frequentist methods provided similar assessments of error, novel Bayesian approaches may provide a useful framework for tests of diversification rates in more complex contexts than are addressed here.     

Phylogenetic estimates of diversification rate are affected by molecular rate variation

Molecular phylogenies are increasingly being used to investigate the patterns and mechanisms of macroevolution. In particular, node heights in a phylogeny can be used to detect changes in rates of diversification over time. Such analyses rest on the assumption that node heights in a phylogeny represent the timing of diversification events, which in turn rests on the assumption that evolutionary time can be accurately predicted from DNA sequence divergence. But there are many influences on the rate of molecular evolution, which might also influence node heights in molecular phylogenies, and thus affect estimates of diversification rate. In particular, a growing number of studies have revealed an association between the net diversification rate estimated from phylogenies and the rate of molecular evolution. Such an association might, by influencing the relative position of node heights, systematically bias estimates of diversification time. We simulated the evolution of DNA sequences under several scenarios where rates of diversification and molecular evolution vary through time, including models where diversification and molecular evolutionary rates are linked. We show that commonly used methods, including metric‐based, likelihood and Bayesian approaches, can have a low power to identify changes in diversification rate when molecular substitution rates vary. Furthermore, the association between the rates of speciation and molecular evolution rate can cause the signature of a slowdown or speedup in speciation rates to be lost or misidentified. These results suggest that the multiple sources of variation in molecular evolutionary rates need to be considered when inferring macroevolutionary processes from phylogenies.     

Erratic rates of molecular evolution and incongruence of fossil and molecular divergence time estimates in Ostracoda (Crustacea)

Dating evolutionary origins of taxa is essential for understanding rates and timing of evolutionary events, often inciting intense debate when molecular estimates differ from first fossil appearances. For numerous reasons, ostracods present a challenging case study of rates of evolution and congruence of fossil and molecular divergence time estimates. On the one hand, ostracods have one of the densest fossil records of any metazoan group. However, taxonomy of fossil ostracods is controversial, owing at least in part to homoplasy of carapaces, the most commonly fossilized part. In addition, rates of evolution are variable in ostracods. Here, we report evidence of extreme variation in the rate of molecular evolution in different ostracod groups. This rate is significantly elevated in Halocyprid ostracods, a widespread planktonic group, consistent with previous observations that planktonic groups show elevated rates of molecular evolution. At the same time, the rate of molecular evolution is slow in the lineage leading to Manawa staceyi, a relict species that we estimate diverged approximately 500 million years ago from its closest known living relative. We also report multiple cases of significant incongruence between fossil and molecular estimates of divergence times in Ostracoda. Although relaxed clock methods improve the congruence of fossil and molecular divergence estimates over strict clock models, incongruence is present regardless of method. We hypothesize that this observed incongruence is driven largely by problems with taxonomy of fossil Ostracoda. Our results illustrate the difficulty in consistently estimating lineage divergence times, even in the presence of a voluminous fossil record.     

The molecular population genetics of HIV-1 group O

HIV-1 group O originated through cross-species transmission of SIV from chimpanzees to humans and has established a relatively low prevalence in Central Africa. Here, we infer the population genetics and epidemic history of HIV-1 group O from viral gene sequence data and evaluate the effect of variable evolutionary rates and recombination on our estimates. First, model selection tools were used to specify suitable evolutionary and coalescent models for HIV group O. Second, divergence times and population genetic parameters were estimated in a Bayesian framework using Markov chain Monte Carlo sampling, under both strict and relaxed molecular clock methods. Our results date the origin of the group O radiation to around 1920 (1890-1940), a time frame similar to that estimated for HIV-1 group M. However, group O infections, which remain almost wholly restricted to Cameroon, show a slower rate of exponential growth during the twentieth century, explaining their lower current prevalence. To explore the effect of recombination, the Bayesian framework is extended to incorporate multiple unlinked loci. Although recombination can bias estimates of the time to the most recent common ancestor, this effect does not appear to be important for HIV-1 group O. In addition, we show that evolutionary rate estimates for different HIV genes accurately reflect differential selective constraints along the HIV genome.     

Perspective: gene divergence, population divergence, and the variance in coalescence time in phylogeographic studies

Molecular methods as applied to the biogeography of single species (phylogeography) or multiple codistributed species (comparative phylogeography) have been productively and extensively used to elucidate common historical features in the diversification of the Earth's biota. However, only recently have methods for estimating population divergence times or their confidence limits while taking into account the critical effects of genetic polymorphism in ancestral species become available, and earlier methods for doing so are underutilized. We review models that address the crucial distinction between the gene divergence, the parameter that is typically recovered in molecular phylogeographic studies, and the population divergence, which is in most cases the parameter of interest and will almost always postdate the gene divergence. Assuming that population sizes of ancestral species are distributed similarly to those of extant species, we show that phylogeographic studies in vertebrates suggest that divergence of alleles in ancestral species can comprise from less than 10% to over 50% of the total divergence between sister species, suggesting that the problem of ancestral polymorphism in dating population divergence can be substantial. The variance in the number of substitutions (among loci for a given species or among species for a given gene) resulting from the stochastic nature of DNA change is generally smaller than the variance due to substitutions along allelic lines whose coalescence times vary due to genetic drift in the ancestral population. Whereas the former variance can be reduced by further DNA sequencing at a single locus, the latter cannot. Contrary to phylogeographic intuition, dating population divergence times when allelic lines have achieved reciprocal monophyly is in some ways more challenging than when allelic lines have not achieved monophyly, because in the former case critical data on ancestral population size provided by residual ancestral polymorphism is lost. In the former case differences in coalescence time between species pairs can in principle be explained entirely by differences in ancestral population size without resorting to explanations involving differences in divergence time. Furthermore, the confidence limits on population divergence times are severely underestimated when those for number of substitutions per site in the DNA sequences examined are used as a proxy. This uncertainty highlights the importance of multilocus data in estimating population divergence times; multilocus data can in principle distinguish differences in coalescence time (T) resulting from differences in population divergence time and differences in T due to differences in ancestral population sizes and will reduce the confidence limits on the estimates. We analyze the contribution of ancestral population size (theta) to T and the effect of uncertainty in theta on estimates of population divergence (tau) for single loci under reciprocal monophyly using a simple Bayesian extension of Takahata and Satta's and Yang's recent coalescent methods. The confidence limits on tau decrease when the range over which ancestral population size theta is assumed to be distributed decreases and when tau increases; they generally exclude zero when tau/(4Ne) > 1. We also apply a maximum-likelihood method to several single and multilocus data sets. With multilocus data, the criterion for excluding tau = 0 is roughly that l tau/(4Ne) > 1, where l is the number of loci. Our analyses corroborate recent suggestions that increasing the number of loci is critical to decreasing the uncertainty in estimates of population divergence time.     

Approximate likelihood calculation on a phylogeny for Bayesian estimation of divergence times

The molecular clock provides a powerful way to estimate species divergence times. If information on some species divergence times is available from the fossil or geological record, it can be used to calibrate a phylogeny and estimate divergence times for all nodes in the tree. The Bayesian method provides a natural framework to incorporate different sources of information concerning divergence times, such as information in the fossil and molecular data. Current models of sequence evolution are intractable in a Bayesian setting, and Markov chain Monte Carlo (MCMC) is used to generate the posterior distribution of divergence times and evolutionary rates. This method is computationally expensive, as it involves the repeated calculation of the likelihood function. Here, we explore the use of Taylor expansion to approximate the likelihood during MCMC iteration. The approximation is much faster than conventional likelihood calculation. However, the approximation is expected to be poor when the proposed parameters are far from the likelihood peak. We explore the use of parameter transforms (square root, logarithm, and arcsine) to improve the approximation to the likelihood curve. We found that the new methods, particularly the arcsine-based transform, provided very good approximations under relaxed clock models and also under the global clock model when the global clock is not seriously violated. The approximation is poorer for analysis under the global clock when the global clock is seriously wrong and should thus not be used. The results suggest that the approximate method may be useful for Bayesian dating analysis using large data sets.     

Molecular distance and divergence time in carnivores and primates

Numerous studies have used indices of genetic distance between species to reconstruct evolutionary relationships and to estimate divergence time. However, the empirical relationship between molecular-based indices of genetic divergence and divergence time based on the fossil record is poorly known. To date, the results of empirical studies conflict and are difficult to compare because they differ widely in their choice of taxa, genetic techniques, or methods for calibrating rates of molecular evolution. We use a single methodology to analyze the relationship of molecular distance and divergence time in 86 taxa (72 carnivores and 14 primates). These taxa have divergence times of 0.01-55 Myr and provide a graded series of phylogenetic divergences such that the shape of the curve relating genetic distance and divergence time is often well defined. The techniques used to obtain genetic distance estimates include one- and two-dimensional protein electrophoresis, DNA hybridization, and microcomplement fixation. Our results suggest that estimates of molecular distance and divergence time are highly correlated. However, rates of molecular evolution are not constant; rather, in general they decline with increasing divergence time in a linear fashion. The rate of decline may differ according to technique and taxa. Moreover, in some cases the variability in evolutionary rates changes with increasing divergence time such that the accuracy of nodes in a phylogenetic tree varies predictably with time.     

Playing chicken (Gallus gallus): methodological inconsistencies of molecular divergence date estimates due to secondary calibration points

For any given taxonomic divergence event, one may find in the literature a wide range of time estimates. Many factors contribute to the variation in molecular date estimates for the same evolutionary event. High on the list is the choice of calibration points for converting genetic distances into evolutionary rates and, subsequently, into dates of divergence. In this study, we investigate one critical source of error in estimating divergence times, i.e. the use of secondary calibration points, which are divergence time estimates that have been derived from one molecular dataset on the basis of a primary external calibration point, and which are used again independently of the original external calibration point on a second dataset. Unless particular care is exercised, this practice leads to internal inconsistencies, and the inferred dates of divergence are by necessity unreliable. We present a consistency test for assessing the reliability of divergence time estimates based on secondary calibration points. As a case study, we examine recent estimates of divergence times among phyla and kingdoms based on multiple nuclear protein-coding genes, and show that they fail the consistency test.     

Temporal scaling of molecular evolution in primates and other mammals

Molecular clocks are routinely tested for linearity using a relative rate test and routinely calibrated against the geological time scale using a single or average paleontologically determined time of divergence between living taxa. The relative rate test is a test of parallel rate equality, not a test of rate constancy. Temporal scaling provides a test of rates, where scaling coefficients of 1.0 (isochrony) represent stochastic rate constancy. The fossil record of primates and other mammals is now known in sufficient detail to provide several independent divergence times for major taxonomic groups. Molecular difference should scale negatively or isochronically (scaling coefficients less than 1.0) with divergence time: where two or more divergence times are available, molecular difference appears to scale positively (scaling coefficient greater than 1.0). A minimum of four divergence times are required for adequate statistical power in testing the linear model: scaling is significantly nonlinear and positive in six of 11 published investigations meeting this criterion. All groups studied show some slowdown in rates of molecular change over Cenozoic time. The break from constant or increasing rates during the Mesozoic to decreasing rates during the Cenozoic appears to coincide with extraordinary diversification of placental mammals at the beginning of this era. High rates of selectively neutral molecular change may be concentrated in such discrete events of evolutionary diversification.      

New dates and new rates for divergence across the Isthmus of Panama

Sister species separated by the Isthmus of Panama have been widely used to estimate rates of molecular evolution. These estimates are based on the assumption that geographic isolation occurred nearly simultaneously for most taxa, when connections between the Caribbean and eastern Pacific closed approximately three million years ago. Here we show that this assumption is invalid for the only genus for which many taxa and multiple genetic markers have been analysed. Patterns of divergence exhibited by allozymes and the mitochondrial COI gene are highly concordant for 15 pairs of snapping shrimp in the genus Alpheus, indicating that they provide a reasonable basis for estimating time since cessation of gene flow. The extent of genetic divergence between pairs of sister species varied over fourfold. Sister species from mangrove environments showed the least divergence, as would be expected if these were among the last habitats to be divided. Using this pair yields a rate of sequence divergence of 1.4% per one million years, with implied times of separation for the 15 pairs of 3 to 18 million years ago. Many past studies may have overestimated rates of molecular evolution because they sampled pairs that were separated well before final closure of the Isthmus.     

Data partitioning and correction for ascertainment bias reduce the uncertainty of placental mammal divergence times inferred from the morphological clock

Bayesian estimates of divergence times based on the molecular clock yield uncertainty of parameter estimates measured by the width of posterior distributions of node ages. For the relaxed molecular clock, previous works have reported that some of the uncertainty inherent to the variation of rates among lineages may be reduced by partitioning data. Here we test this effect for the purely morphological clock, using placental mammals as a case study. We applied the uncorrelated lognormal relaxed clock to morphological data of 40 extant mammalian taxa and 4,533 characters, taken from the largest published matrix of discrete phenotypic characters. The morphologically derived timescale was compared to divergence times inferred from molecular and combined data. We show that partitioning data into anatomical units significantly reduced the uncertainty of divergence time estimates for morphological data. For the first time, we demonstrate that ascertainment bias has an impact on the precision of morphological clock estimates. While analyses including molecular data suggested most divergences between placental orders occurred near the K‐Pg boundary, the partitioned morphological clock recovered older interordinal splits and some younger intraordinal ones, including significantly later dates for the radiation of bats and rodents, which accord to the short‐fuse hypothesis.     

Comparison of likelihood and Bayesian methods for estimating divergence times using multiple gene Loci and calibration points, with application to a radiation of cute-looking mouse lemur species

Divergence time and substitution rate are seriously confounded in phylogenetic analysis, making it difficult to estimate divergence times when the molecular clock (rate constancy among lineages) is violated. This problem can be alleviated to some extent by analyzing multiple gene loci simultaneously and by using multiple calibration points. While different genes may have different patterns of evolutionary rate change, they share the same divergence times. Indeed, the fact that each gene may violate the molecular clock differently leads to the advantage of simultaneous analysis of multiple loci. Multiple calibration points provide the means for characterizing the local evolutionary rates on the phylogeny. In this paper, we extend previous likelihood models of local molecular clock for estimating species divergence times to accommodate multiple calibration points and multiple genes. Heterogeneity among different genes in evolutionary rate and in substitution process is accounted for by the models. We apply the likelihood models to analyze two mitochondrial protein-coding genes, cytochrome oxidase II and cytochrome b, to estimate divergence times of Malagasy mouse lemurs and related outgroups. The likelihood method is compared with the Bayes method of Thorne et al. (1998, Mol. Biol. Evol. 15:1647-1657), which uses a probabilistic model to describe the change in evolutionary rate over time and uses the Markov chain Monte Carlo procedure to derive the posterior distribution of rates and times. Our likelihood implementation has the drawbacks of failing to accommodate uncertainties in fossil calibrations and of requiring the researcher to classify branches on the tree into different rate groups. Both problems are avoided in the Bayes method. Despite the differences in the two methods, however, data partitions and model assumptions had the greatest impact on date estimation. The three codon positions have very different substitution rates and evolutionary dynamics, and assumptions in the substitution model affect date estimation in both likelihood and Bayes analyses. The results demonstrate that the separate analysis is unreliable, with dates variable among codon positions and between methods, and that the combined analysis is much more reliable. When the three codon positions were analyzed simultaneously under the most realistic models using all available calibration information, the two methods produced similar results. The divergence of the mouse lemurs is dated to be around 7-10 million years ago, indicating a surprisingly early species radiation for such a morphologically uniform group of primates.     

Historical connectivity,contemporary isolation and local adaptation in a widespread but discontinuously distributed species endemic to Taiwan,Rhododendron oldhamii (Ericaceae)

Elucidation of the evolutionary processes that constrain or facilitate adaptive divergence is a central goal in evolutionary biology, especially in non-model organisms. We tested whether changes in dynamics of gene flow (historical vs contemporary) caused population isolation and examined local adaptation in response to environmental selective forces in fragmented Rhododendron oldhamii populations. Variation in 26 expressed sequence tag-simple sequence repeat loci from 18 populations in Taiwan was investigated by examining patterns of genetic diversity, inbreeding, geographic structure, recent bottlenecks, and historical and contemporary gene flow. Selection associated with environmental variables was also examined. Bayesian clustering analysis revealed four regional population groups of north, central, south and southeast with significant genetic differentiation. Historical bottlenecks beginning 9168–13,092 years ago and ending 1584–3504 years ago were revealed by estimates using approximate Bayesian computation for all four regional samples analyzed. Recent migration within and across geographic regions was limited. However, major dispersal sources were found within geographic regions. Altitudinal clines of allelic frequencies of environmentally associated positively selected outliers were found, indicating adaptive divergence. Our results point to a transition from historical population connectivity toward contemporary population isolation and divergence on a regional scale. Spatial and temporal dispersal differences may have resulted in regional population divergence and local adaptation associated with environmental variables, which may have played roles as selective forces at a regional scale.     

Likelihood analysis of ongoing gene flow and historical association

Abstract.— We develop a Monte Carlo-based likelihood method for estimating migration rates and population divergence times from data at unlinked loci at which mutation rates are sufficiently low that, in the recent past, the effects of mutation can be ignored. The method is applicable to restriction fragment length polymorphisms (RFLPs) and single nucleotide polymorphisms (SNPs) sampled from a subdivided population. The method produces joint maximum-likelihood estimates of the migration rate and the time of population divergence, both scaled by population size, and provides a framework in which to test either for no ongoing gene flow or for population divergence in the distant past. We show the method performs well and provides reasonably accurate estimates of parameters even when the assumptions under which those estimates are obtained are not completely satisfied. Furthermore, we show that, provided that the number of polymorphic loci is sufficiently large, there is some power to distinguish between ongoing gene flow and historical association as causes of genetic similarity between pairs of populations.     

Site stripping based on likelihood ratio reduction is a useful tool to evaluate the impact of non-clock-like behavior on viral phylogenetic reconstructions

The site stripping for clock detection procedure was implemented in the recently developed maximum likelihood framework for estimating evolutionary rates and divergence times in measurably evolving populations. The method was used to investigate the effect of rate variability on estimating divergence times in non-clock-like trees for human immunodeficiency viruses and hepatitis C viruses. We validate our approach by comparing dated coalescent nodes in molecular phylogenies with known dates of transmission. Our method was able to rapidly recover clock-like behavior and to indicate the presence and direction of a bias when estimates of divergence times using the unstripped data were flawed.