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.     

The effect of inappropriate calibration: three case studies in molecular ecology

Time-scales estimated from sequence data play an important role in molecular ecology. They can be used to draw correlations between evolutionary and palaeoclimatic events, to measure the tempo of speciation, and to study the demographic history of an endangered species. In all of these studies, it is paramount to have accurate estimates of time-scales and substitution rates. Molecular ecological studies typically focus on intraspecific data that have evolved on genealogical scales, but often these studies inappropriately employ deep fossil calibrations or canonical substitution rates (e.g., 1% per million years for birds and mammals) for calibrating estimates of divergence times. These approaches can yield misleading estimates of molecular time-scales, with significant impacts on subsequent evolutionary and ecological inferences. We illustrate this calibration problem using three case studies: avian speciation in the late Pleistocene, the demographic history of bowhead whales, and the Pleistocene biogeography of brown bears. For each data set, we compare the date estimates that are obtained using internal and external calibration points. In all three cases, the conclusions are significantly altered by the application of revised, internally-calibrated substitution rates. Collectively, the results emphasise the importance of judicious selection of calibrations for analyses of recent evolutionary events.     

Assessing concordance of fossil calibration points in molecular clock studies: an example using turtles

Although still controversial, estimation of divergence times using molecular data has emerged as a powerful tool to examine the tempo and mode of evolutionary change. Two primary obstacles in improving the accuracy of molecular dating are heterogeneity in DNA substitution rates and accuracy of the fossil record as calibration points. Recent methodological advances have provided powerful methods that estimate relative divergence times in the face of heterogeneity of nucleotide substitution rates among lineages. However, relatively little attention has focused on the accuracy of fossil calibration points that allow one to translate relative divergence times into absolute time. We present a new cross-validation method that identifies inconsistent fossils when multiple fossil calibrations are available for a clade and apply our method to a molecular phylogeny of living turtles with fossil calibration times for 17 of the 22 internal nodes in the tree. Our cross-validation procedure identified seven inconsistent fossils. Using the consistent fossils as calibration points, we found that despite their overall antiquity as a lineage, the most species-rich clades of turtles diversified well within the Cenozoic. Many of the truly ancient lineages of turtles are currently represented by a few, often endangered species that deserve high priority as conservation targets.     

Time dependency of molecular rate estimates and systematic overestimation of recent divergence times

Studies of molecular evolutionary rates have yielded a wide range of rate estimates for various genes and taxa. Recent studies based on population-level and pedigree data have produced remarkably high estimates of mutation rate, which strongly contrast with substitution rates inferred in phylogenetic (species-level) studies. Using Bayesian analysis with a relaxed-clock model, we estimated rates for three groups of mitochondrial data: avian protein-coding genes, primate protein-coding genes, and primate d-loop sequences. In all three cases, we found a measurable transition between the high, short-term (< 1-2 Myr) mutation rate and the low, long-term substitution rate. The relationship between the age of the calibration and the rate of change can be described by a vertically translated exponential decay curve, which may be used for correcting molecular date estimates. The phylogenetic substitution rates in mitochondria are approximately 0.5% per million years for avian protein-coding sequences and 1.5% per million years for primate protein-coding and d-loop sequences. Further analyses showed that purifying selection offers the most convincing explanation for the observed relationship between the estimated rate and the depth of the calibration. We rule out the possibility that it is a spurious result arising from sequence errors, and find it unlikely that the apparent decline in rates over time is caused by mutational saturation. Using a rate curve estimated from the d-loop data, several dates for last common ancestors were calculated: modern humans and Neandertals (354 ka; 222-705 ka), Neandertals (108 ka; 70-156 ka), and modern humans (76 ka; 47-110 ka). If the rate curve for a particular taxonomic group can be accurately estimated, it can be a useful tool for correcting divergence date estimates by taking the rate decay into account. Our results show that it is invalid to extrapolate molecular rates of change across different evolutionary timescales, which has important consequences for studies of populations, domestication, conservation genetics, and human evolution.     

An examination of phylogenetic models of substitution rate variation among lineages

Molecular evolutionary rates can show significant variation among lineages, complicating the task of estimating substitution rates and divergence times using phylogenetic methods. Accordingly, relaxed molecular clock models have been developed to accommodate such rate heterogeneity, but these often make the assumption of rate autocorrelation among lineages. In this paper, I examine the validity of this assumption.     

Can fast early rates reconcile molecular dates with the Cambrian explosion?

Molecular dates consistently place the divergence of major metazoan lineages in the Precambrian, leading to the suggestion that the 'Cambrian explosion' is an artefact of preservation which left earlier forms unrecorded in the fossil record. While criticisms of molecular analyses for failing to deal with variation in the rate of molecular evolution adequately have been countered by analyses which allow both site-to-site and lineage-specific rate variation, no analysis to date has allowed the rates to vary temporally. If the rates of molecular evolution were much higher early in the metazoan radiation, molecular dates could consistently overestimate the divergence times of lineages. Here, we use a new method which uses multiple calibration dates and an empirically determined range of possible substitution rates to place bounds on the basal date of divergence of lineages in order to ask whether faster rates of molecular evolution early in the metazoan radiation could possibly account for the discrepancy between molecular and palaeontological date estimates. We find that allowing basal (interphylum) lineages the fastest observed substitution rate brings the minimum possible divergence date (586 million years ago) to the Vendian period, just before the first multicellular animal fossils, but excludes divergence of the major metazoan lineages in a Cambrian explosion.     

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.     

Estimating divergence times in large phylogenetic trees

A new method, PATHd8, for estimating ultrametric trees from trees with edge (branch) lengths proportional to the number of substitutions is proposed. The method allows for an arbitrary number of reference nodes for time calibration, each defined either as absolute age, minimum age, or maximum age, and the tree need not be fully resolved. The method is based on estimating node ages by mean path lengths from the node to the leaves but correcting for deviations from a molecular clock suggested by reference nodes. As opposed to most existing methods allowing substitution rate variation, the new method smoothes substitution rates locally, rather than simultaneously over the whole tree, thus allowing for analysis of very large trees. The performance of PATHd8 is compared with other frequently used methods for estimating divergence times. In analyses of three separate data sets, PATHd8 gives similar divergence times to other methods, the largest difference being between crown group ages, where unconstrained nodes get younger ages when analyzed with PATHd8. Overall, chronograms obtained from other methods appear smoother, whereas PATHd8 preserves more of the heterogeneity seen in the original edge lengths. Divergence times are most evenly spread over the chronograms obtained from the Bayesian implementation and the clock-based Langley-Fitch method, and these two methods produce very similar ages for most nodes. Evaluations of PATHd8 using simulated data suggest that PATHd8 is slightly less precise compared with penalized likelihood, but it gives more sensible answers for extreme data sets. A clear advantage with PATHd8 is that it is more or less instantaneous even with trees having several thousand leaves, whereas other programs often run into problems when analyzing trees with hundreds of leaves. PATHd8 is implemented in freely available software.     

Molecular evidence on plant divergence times

Estimation of divergence times from sequence data has become increasingly feasible in recent years. Conflicts between fossil evidence and molecular dates have sparked the development of new methods for inferring divergence times, further encouraging these efforts. In this paper, available methods for estimating divergence times are reviewed, especially those geared toward handling the widespread variation in rates of molecular evolution observed among lineages. The assumptions, strengths, and weaknesses of local clock, Bayesian, and rate smoothing methods are described. The rapidly growing literature applying these methods to key divergence times in plant evolutionary history is also reviewed. These include the crown group ages of green plants, land plants, seed plants, angiosperms, and major subclades of angiosperms. Finally, attempts to infer divergence times are described in the context of two very different temporal settings: recent adaptive radiations and much more ancient biogeographic patterns.     

Molecular dating of phylogenetic trees: A brief review of current methods that estimate divergence times

This article reviews the most common methods used today for estimating divergence times and rates of molecular evolution. The methods are grouped into three main classes: (1) methods that use a molecular clock and one global rate of substitution, (2) methods that correct for rate heterogeneity, and (3) methods that try to incorporate rate heterogeneity. Additionally, links to the most important literature on molecular dating are given, including articles comparing the performance of different methods, papers that investigate problems related to taxon, gene and partition sampling, and literature discussing highly debated issues like calibration strategies and uncertainties, dating precision and the calculation of error estimates.     

Expansion dating: calibrating molecular clocks in marine species from expansions onto the Sunda Shelf Following the Last Glacial Maximum

The rate of change in DNA is an important parameter for understanding molecular evolution and hence for inferences drawn from studies of phylogeography and phylogenetics. Most rate calibrations for mitochondrial coding regions in marine species have been made from divergence dating for fossils and vicariant events older than 1-2 My and are typically 0.5-2% per lineage per million years. Recently, calibrations made with ancient DNA (aDNA) from younger dates have yielded faster rates, suggesting that estimates of the molecular rate of change depend on the time of calibration, decaying from the instantaneous mutation rate to the phylogenetic substitution rate. aDNA methods for recent calibrations are not available for most marine taxa so instead we use radiometric dates for sea-level rise onto the Sunda Shelf following the Last Glacial Maximum (starting ～18,000 years ago), which led to massive population expansions for marine species. Instead of divergence dating, we use a two-epoch coalescent model of logistic population growth preceded by a constant population size to infer a time in mutational units for the beginning of these expansion events. This model compares favorably to simpler coalescent models of constant population size, and exponential or logistic growth, and is far more precise than estimates from the mismatch distribution. Mean rates estimated with this method for mitochondrial coding genes in three invertebrate species are elevated in comparison to older calibration points (2.3-6.6% per lineage per million years), lending additional support to the hypothesis of calibration time dependency for molecular rates.     

Calibrating the Tree of Life: fossils, molecules and evolutionary timescales

Background

Molecular dating has gained ever-increasing interest since the molecular clock hypothesis was proposed in the 1960s. Molecular dating provides detailed temporal frameworks for divergence events in phylogenetic trees, allowing diverse evolutionary questions to be addressed. The key aspect of the molecular clock hypothesis, namely that differences in DNA or protein sequence between two species are proportional to the time elapsed since they diverged, was soon shown to be untenable. Other approaches were proposed to take into account rate heterogeneity among lineages, but the calibration process, by which relative times are transformed into absolute ages, has received little attention until recently. New methods have now been proposed to resolve potential sources of error associated with the calibration of phylogenetic trees, particularly those involving use of the fossil record.

Scope and Conclusions

The use of the fossil record as a source of independent information in the calibration process is the main focus of this paper; other sources of calibration information are also discussed. Particularly error-prone aspects of fossil calibration are identified, such as fossil dating, the phylogenetic placement of the fossil and the incompleteness of the fossil record. Methods proposed to tackle one or more of these potential error sources are discussed (e.g. fossil cross-validation, prior distribution of calibration points and confidence intervals on the fossil record). In conclusion, the fossil record remains the most reliable source of information for the calibration of phylogenetic trees, although associated assumptions and potential bias must be taken into account.     

Estimating divergence dates from molecular sequences

The ability to date the time of divergence between lineages using molecular data provides the opportunity to answer many important questions in evolutionary biology. However, molecular dating techniques have previously been criticized for failing to adequately account for variation in the rate of molecular evolution. We present a maximum- likelihood approach to estimating divergence times that deals explicitly with the problem of rate variation. This method has many advantages over previous approaches including the following: (1) a rate constancy test excludes data for which rate heterogeneity is detected; (2) date estimates are generated with confidence intervals that allow the explicit testing of hypotheses regarding divergence times; and (3) a range of sequences and fossil dates are used, removing the reliance on a single calculated calibration rate. We present tests of the accuracy of our method, which show it to be robust to the effects of some modes of rate variation. In addition, we test the effect of substitution model and length of sequence on the accuracy of the dating technique. We believe that the method presented here offers solutions to many of the problems facing molecular dating and provides a platform for future improvements to such analyses.      

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.     

A Method for Calibrating Molecular Clocks and Its Application to Animal Mitochondrial DNA

A generalized least-squares procedure is introduced for the calibration of molecular clocks and applied to the complete mitochondrial DNA sequences of 13 animal species. The proposed technique accounts for both nonindependence and heteroscedasticity of molecular-distance data, problems that have not been taken into to account in such analyses in the past. When sequence-identity data are transformed to account for multiple substitutions/site, the molecular divergence scales linearly with time, but with substantially more variation in the substitution rate than expected under a Poisson model. Significant levels of divergence are predicted at zero divergence time for most loci, suggesting high levels of site-specific heterozygosity among mtDNA molecules establishing in sister taxa. For nearly all loci, the baseline heterozygosity is lower and the substitution rate is higher in mammals relative to other animals. There is considerable variation in the evolutionary rate among loci but no compelling evidence that the average rate of mtDNA evolution is elevated with respect to that of nuclear DNA. Using the observed patterns of interspecific divergence, empirical estimates are derived for the mean coalescence times of organelles colonizing sister taxa.     

Calibration of a molecular clock in tits (Paridae)--do nucleotide substitution rates of mitochondrial genes deviate from the 2% rule?

The ongoing debate on the reliability of avian molecular clocks is actually based on only a small number of calibrations carried out under different assumptions with respect to the choice and constraints of calibration points or to the use of substitution models. In this study, we provide substitution rate estimates for two mitochondrial genes, cytochrome b and the control region, and age estimates for lineage splits within four subgenera of tits (Paridae: Parus, Cyanistes, Poecile and Periparus). Overall sequence divergence between cytochrome b lineages covers a range of 0.4-1.8% per million years and is thus consistent with the frequently adopted approximation for a sequence divergence between avian lineages of 1.6-2% per my. Overall rate variation is high and encompasses the 2% value in a 95% CI for model corrected data. Mean rate estimates for cytochrome b range between 1.9 and 8.9 x 10(-3) substitutions per site per lineage. Local rates differ significantly between taxonomic levels with lowest estimates for haplotype lineages. At the population/subspecies level mean sequence divergence between lineages matches the 2% rule best for most cytochrome b datasets (1.5-1.9% per my) with maximum estimates for small isolated populations like those of the Canarian P. teneriffae complex (up to 3.9% per my). Overall rate estimates for the control region range at similar values like those for cytochrome b (2.7-8.8 x 10(-3), 0.5-1.8% per my), however, within some subgenera mean rates are higher than those for cytochrome b for uncorrected sequence data. The lowest rates for both genes were calculated for coal tits of subgenus Periparus (0.04-0.6% per my). Model-corrected sequence data tend to result in higher rate estimates than uncorrected data. Increase of the gamma shape parameter goes along with a significant decrease of rate and partly age estimates, too. Divergence times for earliest deep splits within tit subgenera Periparus and Parus were dated to the mid Miocene at 10-14my bp. Most recent splits between east and west Palearctic taxa of blue, willow and great tits were dated to the Pliocene/Pleistocene boundary with the earliest estimates based on model-corrected trees. Relaxation of the Messinian calibration point leads to more recent divergence times for North African coal and blue tit populations during the mid Pliocene. Despite a relatively broad age constraint for the split between Nearctic and Palearctic Poecile due to the Pliocene re-opening of the Bering Strait, the split between chickadees and willow tits is dated considerably earlier than in former studies to the upper bound of the age constraint at 7.4 my BP.     

Accuracy of rate estimation using relaxed-clock models with a critical focus on the early metazoan radiation

In recent years, a number of phylogenetic methods have been developed for estimating molecular rates and divergence dates under models that relax the molecular clock constraint by allowing rate change throughout the tree. These methods are being used with increasing frequency, but there have been few studies into their accuracy. We tested the accuracy of several relaxed-clock methods (penalized likelihood and Bayesian inference using various models of rate change) using nucleotide sequences simulated on a nine-taxon tree. When the sequences evolved with a constant rate, the methods were able to infer rates accurately, but estimates were more precise when a molecular clock was assumed. When the sequences evolved under a model of auto-correlated rate change, rates were accurately estimated using penalized likelihood and by Bayesian inference using lognormal and exponential models of rate change, while other models did not perform as well. When the sequences evolved under a model of uncorrelated rate change, only Bayesian inference using an exponential rate model performed well. Collectively, the results provide a strong recommendation for using the exponential model of rate change if a conservative approach to divergence time estimation is required. A case study is presented in which we use a simulation-based approach to examine the hypothesis of elevated rates in the Cambrian period, and it is found that these high rate estimates might be an artifact of the rate estimation method. If this bias is present, then the ages of metazoan divergences would be systematically underestimated. The results of this study have implications for studies of molecular rates and divergence dates.     

Birth-death prior on phylogeny and speed dating

Background  

In recent years there has been a trend of leaving the strict molecular clock in order to infer dating of speciations and other evolutionary events. Explicit modeling of substitution rates and divergence times makes formulation of informative prior distributions for branch lengths possible. Models with birth-death priors on tree branching and auto-correlated or iid substitution rates among lineages have been proposed, enabling simultaneous inference of substitution rates and divergence times. This problem has, however, mainly been analysed in the Markov chain Monte Carlo (MCMC) framework, an approach requiring computation times of hours or days when applied to large phylogenies.     

A molecular phylogeny of African kestrels with reference to divergence across the Indian Ocean

In this paper we examine the evolutionary relationships of kestrels from mainland Africa, Indian Ocean islands and related areas. We construct a molecular phylogeny of African kestrels, using approximately 1.0 kb of mitochondrial cytochrome b sequence. Our molecular results support an Old World origin for typical kestrels and an ancient divergence of kestrels into the New World, and indicate a more recent radiation of kestrels from Africa via Madagascar towards Mauritius and the Seychelles. Phylogenetic placement of the Australian kestrel suggests a recent origin from African kestrel stock. We compare evolutionary relationships based on kestrel plumage pattern and morphology to our molecular results for the African and Indian Ocean kestrels, and reveal some consistency with the different island forms. We apply a range of published avian cytochrome b substitution rates to our data, as an alternative to internal calibration of a molecular clock arising from incomplete paleontological information. We align these divergence estimates to the geological history of Indian Ocean island formation inferred from potassium-argon dating methods. The arrival of kestrels on Mauritius appears consistent with the cessation of volcanic activity on Mauritius. The estimated time and route of divergence of the Seychelles kestrel from Madagascar may be compatible with the emergence of smaller islands during Pleistocene sea level fluctuations.     

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.