PAML 4: Phylogenetic Analysis by Maximum Likelihood

This chapter discusses the hypothesis of the molecular clock and its use to date species divergences. It introduces various tests of the molecular clock as well as strategies to relax the clock in divergence time estimation. Bayesian methods of divergence time estimation are discussed in detail, including different prior models of rate drift such as the correlated-rate model based on the geometric Brownian motion process, and specification of the prior on divergence times incorporating uncertainties in fossil calibrations. The chapter describes the infinite-site and finite-site theories, which characterize the uncertainties in posterior divergence time estimates.

The effective population sizes of ancestral as well as modern species are important parameters in models of population genetics and human evolution. The commonly used method for estimating ancestral population sizes, based on counting mismatches between the species tree and the inferred gene trees, is highly biased as it ignores uncertainties in gene tree reconstruction. In this article, we develop a Bayes method for simultaneous estimation of the species divergence times and current and ancestral population sizes. The method uses DNA sequence data from multiple loci and extracts information about conflicts among gene tree topologies and coalescent times to estimate ancestral population sizes. The topology of the species tree is assumed known. A Markov chain Monte Carlo algorithm is implemented to integrate over uncertain gene trees and branch lengths (or coalescence times) at each locus as well as species divergence times. The method can handle any species tree and allows different numbers of sequences at different loci. We apply the method to published noncoding DNA sequences from the human and the great apes. There are strong correlations between posterior estimates of speciation times and ancestral population sizes. With the use of an informative prior for the human-chimpanzee divergence date, the population size of the common ancestor of the two species is estimated to be approximately 20,000, with a 95% credibility interval (8000, 40,000). Our estimates, however, are affected by model assumptions as well as data quality. We suggest that reliable estimates have yet to await more data and more realistic models.

We implement a Bayesian Markov chain Monte Carlo algorithm for estimating species divergence times that uses heterogeneous data from multiple gene loci and accommodates multiple fossil calibration nodes. A birth-death process with species sampling is used to specify a prior for divergence times, which allows easy assessment of the effects of that prior on posterior time estimates. We propose a new approach for specifying calibration points on the phylogeny, which allows the use of arbitrary and flexible statistical distributions to describe uncertainties in fossil dates. In particular, we use soft bounds, so that the probability that the true divergence time is outside the bounds is small but nonzero. A strict molecular clock is assumed in the current implementation, although this assumption may be relaxed. We apply our new algorithm to two data sets concerning divergences of several primate species, to examine the effects of the substitution model and of the prior for divergence times on Bayesian time estimation. We also conduct computer simulation to examine the differences between soft and hard bounds. We demonstrate that divergence time estimation is intrinsically hampered by uncertainties in fossil calibrations, and the error in Bayesian time estimates will not go to zero with increased amounts of sequence data. Our analyses of both real and simulated data demonstrate potentially large differences between divergence time estimates obtained using soft versus hard bounds and a general superiority of soft bounds. Our main findings are as follows. (1) When the fossils are consistent with each other and with the molecular data, and the posterior time estimates are well within the prior bounds, soft and hard bounds produce similar results. (2) When the fossils are in conflict with each other or with the molecules, soft and hard bounds behave very differently; soft bounds allow sequence data to correct poor calibrations, while poor hard bounds are impossible to overcome by any amount of data. (3) Soft bounds eliminate the need for "safe" but unrealistically high upper bounds, which may bias posterior time estimates. (4) Soft bounds allow more reliable assessment of estimation errors, while hard bounds generate misleadingly high precisions when fossils and molecules are in conflict.

Although the effects of the coalescent process on sequence divergence and genealogies are well understood, the virtual majority of studies that use molecular sequences to estimate times of divergence among species have failed to account for the coalescent process. Here we study the impact of ancestral population size and incomplete lineage sorting on Bayesian estimates of species divergence times under the molecular clock when the inference model ignores the coalescent process. Using a combination of mathematical analysis, computer simulations and analysis of real data, we find that the errors on estimates of times and the molecular rate can be substantial when ancestral populations are large and when there is substantial incomplete lineage sorting. For example, in a simple three-species case, we find that if the most precise fossil calibration is placed on the root of the phylogeny, the age of the internal node is overestimated, while if the most precise calibration is placed on the internal node, then the age of the root is underestimated. In both cases, the molecular rate is overestimated. Using simulations on a phylogeny of nine species, we show that substantial errors in time and rate estimates can be obtained even when dating ancient divergence events. We analyse the hominoid phylogeny and show that estimates of the neutral mutation rate obtained while ignoring the coalescent are too high. Using a coalescent-based technique to obtain geological times of divergence, we obtain estimates of the mutation rate that are within experimental estimates and we also obtain substantially older divergence times within the phylogeny.

Discrete morphological data have been widely used to study species evolution, but the use of quantitative (or continuous) morphological characters is less common. Here, we implement a Bayesian method to estimate species divergence times using quantitative characters. Quantitative character evolution is modeled using Brownian diffusion with character correlation and character variation within populations. Through simulations, we demonstrate that ignoring the population variation (or population "noise") and the correlation among characters leads to biased estimates of divergence times and rate, especially if the correlation and population noise are high. We apply our new method to the analysis of quantitative characters (cranium landmarks) and molecular data from carnivoran mammals. Our results show that time estimates are affected by whether the correlations and population noise are accounted for or ignored in the analysis. The estimates are also affected by the type of data analyzed, with analyses of morphological characters only, molecular data only, or a combination of both; showing noticeable differences among the time estimates. Rate variation of morphological characters among the carnivoran species appears to be very high, with Bayesian model selection indicating that the independent-rates model fits the morphological data better than the autocorrelated-rates model. We suggest that using morphological continuous characters, together with molecular data, can bring a new perspective to the study of species evolution. Our new model is implemented in the MCMCtree computer program for Bayesian inference of divergence times.

PAML, currently in version 1.2, is a package of programs for phylogenetic analyses of DNA and protein sequences using the method of maximum likelihood (ML). The programs can be used for (i) maximum likelihood estimation of evolutionary parameters such as branch lengths in a phylogenetic tree, the transition/transversion rate ratio, the shape parameter of the gamma distribution for variable evolutionary rates at sites, and rate parameters for different genes; (ii) likelihood ratio test of hypotheses concerning sequence evolution, such as rate constancy and independence among sites and rate constancy among lineages (the molecular clock); (iii) calculation of substitution rates at sites and reconstruction of ancestral nucleotide or amino acid sequences; and (iv) phylogenetic tree reconstruction by maximum likelihood and Bayesian methods. The strength of PAML, in comparison with other phylogenetic packages currently available, is its implementation of a variety of evolutionary models. These include several models of variable evolutionary rates among sites, models for combined analyses of multiple gene sequence data and models for amino acid sequences. Multifurcating trees are supported, as well as trees in which some sequences are ancestral to some others. A heuristic tree search algorithm (star decomposition) is used in the package, but tree making is not a strong point of the current version, although work is under way to implement efficient search algorithms. Major programs in the package, as well as the types of analyses they perform, are listed in Table 1. More details are available in the documentation included in the package, written using Microsoft Word. PAML is distributed free of charge for academic use only. The package, including ANSI C source codes, documentation, example data sets, and control files, can be obtained by anonymous ftp at mw511.biol.berkeley.edu/pub, or from the Indiana molecular biology ftp site at ftp.bio.indiana.edu under the directory Incoming or molbio/evolve . MAC and PowerMac executables are also available, although DOS executables are not prepared yet. Further information about the package is available from the World Wide Web at

The primary structures of proteins can be determined by two distinct methods: directly by sequence analysis of the protein or indirectly by DNA sequence analysis of the corresponding gene or c-DNA. The direct protein sequence analysis methods are strongly influenced by the nature of the protein. They have been largely developed to accommodate water-soluble globular proteins, and methods for isolation and sequence analysis of hydrophobic proteins are relatively deficient and underdeveloped. The indirect sequence analysis by DNA sequence analysis is not influenced by the nature of the protein.

Bayesian inference of species divergence times is an unusual statistical problem, because the divergence time parameters are not identifiable unless both fossil calibrations and sequence data are available. Commonly used marginal priors on divergence times derived from fossil calibrations may conflict with node order on the phylogenetic tree causing a change in the prior on divergence times for a particular topology. Care should be taken to avoid confusing this effect with changes due to informative sequence data. This effect is illustrated with examples. A topology-consistent prior that preserves the marginal priors is defined and examples are constructed. Conflicts between fossil calibrations and relative branch lengths (based on sequence data) can cause estimates of divergence times that are grossly incorrect, yet have a narrow posterior distribution. An example of this effect is given; it is recommended that overly narrow posterior distributions of divergence times should be carefully scrutinized.This article is part of the themed issue 'Dating species divergences using rocks and clocks'.

Fossil calibrations are the utmost source of information for resolving the distances between molecular sequences into estimates of absolute times and absolute rates in molecular clock dating analysis. The quality of calibrations is thus expected to have a major impact on divergence time estimates even if a huge amount of molecular data is available. In Bayesian molecular clock dating, fossil calibration information is incorporated in the analysis through the prior on divergence times (the time prior). Here, we evaluate three strategies for converting fossil calibrations (in the form of minimum- and maximum-age bounds) into the prior on times, which differ according to whether they borrow information from the maximum age of ancestral nodes and minimum age of descendent nodes to form constraints for any given node on the phylogeny. We study a simple example that is analytically tractable, and analyze two real datasets (one of 10 primate species and another of 48 seed plant species) using three Bayesian dating programs: MCMCTree, MrBayes and BEAST2. We examine how different calibration strategies, the birth-death process, and automatic truncation (to enforce the constraint that ancestral nodes are older than descendent nodes) interact to determine the time prior. In general, truncation has a great impact on calibrations so that the effective priors on the calibration node ages after the truncation can be very different from the user-specified calibration densities. The different strategies for generating the effective prior also had considerable impact, leading to very different marginal effective priors. Arbitrary parameters used to implement minimum-bound calibrations were found to have a strong impact upon the prior and posterior of the divergence times. Our results highlight the importance of inspecting the joint time prior used by the dating program before any Bayesian dating analysis.

We have previously described programs for a variety of types of sequence analysis (1-4). These programs have now been integrated into a single package. They are written in the standard C programming language and run on virtually any computer system with a C compiler, such as the IBM/PC and other computers running under the MS/DOS and UNIX operating systems. The programs are widely distributed and may be obtained from the authors as described below.

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.

The first empirically supported phylogenetic hypothesis of relationships for the southern African endemic butterfly tribe Dirini is presented. Data derived from the morphology and ecology of the adults and immature stages (33 characters), and portions of the mitochondrial gene cytochrome oxidase I ( COI ) and the nuclear genes elongation factor 1α ( EF1α ) and wingless ( WG ) (totalling 1734 bp) were used to infer the relationships of the in‐group genera. An expanded molecular dataset using four genera from the Nymphalini and Satyrini to root the tree, and three genera from the Melanitini to test the monophyly of the tribe, was analysed using parsimony and Bayesian methods. Estimates of divergence times were calculated using two fossil calibrations under a relaxed molecular clock model. The monophyly of the tribe and each in‐group genus were strongly supported. Key findings are the sister‐taxon relationship of Aeropetes and Tarsocera , the apparent simultaneous or nearly simultaneous radiation of four lineages, the polyphyly of the species within Torynesis , and the apparent trans‐Atlantic dispersal of the ancestors of Manataria about 40 Ma. Estimates of divergence times indicate that the tribe has undergone two major radiations since its origin: the first when they left forest habitats in the mid–late Oligocene, shortly after the radiation of the grasses (Poaceae), and the second in the early‐middle Pliocene, coinciding with the aridification of southern Africa and the spread of conditions that favoured C 4 grasses over the C 3 grasses that dirine larvae prefer to eat. The high species diversity within the tribe appears to be partly a taxonomic artefact that may have resulted from the misinterpretation of climate‐related phenotypic variation within extant species. Relocation and breeding experiments should test this hypothesis.

The alpha replicons of the multi-replicon plasmids pGSH500 and pLV1402 have been characterized by DNA sequence analysis. Analysis of the DNA sequence of a 3672 bp HIN:dIII fragment from pFDT100, which contains the pGSH500 alpha replicon, revealed similarity to a number of replicons belonging to, or related to, those of the IncFII family. The replicon region contains copA, tapA, repA and oriR, and replication initiation and termination sites are related to those from the IncFII replicon of R1. A copB gene was found to lie upstream of the HIN:dIII site in the parental plasmid pGSH500. Downstream of oriR, a 707 bp region shows 72.6% identity to a region of the Escherichia coli chromosome at 43.3', suggesting this region of pGSH500 may have been incorporated into the plasmid during a past chromosomal recombination event. Oligonucleotide primers homologous to consensus regions in the copB and repA genes, and the oriR regions from a number of IncFII-related replicons were used to amplify replication regions from pLV1402. Analysis of the amplified regions has shown the presence of copB, copA, tapA and repA genes. Phylogenetic analysis of Rep protein sequences from the RepFIIA family of antisense-control-regulated replicons revealed the presence of three distinct subgroups of Rep proteins. Comparative analysis of DNA and protein sequences from members of the RepFIIA family provides evidence supporting the roles of both non-selective divergence in co-integrate (multi-replicon) plasmids and Chi-mediated-recombination in replicon evolution, and in particular, that such processes may have been widespread in the evolution of the RepFIIA family.

A phylogenetic analysis of woodpeckers and their allies using 12S, Cyt b, and COI nucleotide sequences (class Aves; order Piciformes)

The explosive growth of molecular sequence data has made it possible to estimate species divergence times under relaxed-clock models using genome-scale data sets with many gene loci. In order to improve both model realism and to best extract information about relative divergence times in the sequence data, it is important to account for the heterogeneity in the evolutionary process across genes or genomic regions. Partitioning is a commonly used approach to achieve those goals. We group sites that have similar evolutionary characteristics into the same partition and those with different characteristics into different partitions, and then use different models or different values of model parameters for different partitions to account for the among-partition heterogeneity. However, how to partition data in practical phylogenetic analysis, and in particular in relaxed-clock dating analysis, is more art than science. Here, we use computer simulation and real data analysis to study the impact of the partition scheme on divergence time estimation. The partition schemes had relatively minor effects on the accuracy of posterior time estimates when the prior assumptions were correct and the clock was not seriously violated, but showed large differences when the clock was seriously violated, when the fossil calibrations were in conflict or incorrect, or when the rate prior was mis-specified. Concatenation produced the widest posterior intervals with the least precision. Use of many partitions increased the precision, as predicted by the infinite-sites theory, but the posterior intervals might fail to include the true ages because of the conflicting fossil calibrations or mis-specified rate priors. We analyzed a data set of 78 plastid genes from 15 plant species with serious clock violation and showed that time estimates differed significantly among partition schemes, irrespective of the rate drift model used. Multiple and precise fossil calibrations reduced the differences among partition schemes and were important to improving the precision of divergence time estimates. While the use of many partitions is an important approach to reducing the uncertainty in posterior time estimates, we do not recommend its general use for the present, given the limitations of current models of rate drift for partitioned data and the challenges of interpreting the fossil evidence to construct accurate and informative calibrations.