Identifying site-specific substitution rates

A maximum likelihood framework for estimating site-specific substitution rates is presented that does not require any prior assumptions about the rate distribution. We show that, when the branching pattern of the underlying tree is known, the analysis of pairs of positions is sufficient to estimate site-specific rates. In the abscense of a known topology, we introduce an iterative procedure to estimate simultaneously the branching pattern, the branch lengths, and site-specific substitution rates. Simulations show that the evolutionary rate of fast-evolving sites can be reliably inferred and that the accuracy of rate estimates depends mainly on the number of sequences in the data set. Thus, large sets of aligned sequences are necessary for reliable site-specific rate estimates. The method is applied to the complete mitochondrial DNA sequence of 53 humans, providing a complete picture of the site-specific substitution rates in human mitochondrial DNA.     

Site-Specific Evolutionary Rate Inference: Taking Phylogenetic Uncertainty into Account

The evolutionary rate at an amino acid site is indicative of how conserved this site is and, in turn, allows evaluating the importance of this site in maintaining the structure/function of the protein. When evolutionary rates are estimated, one must reconstruct the phylogenetic tree describing the evolutionary relationship among the sequences under study. However, if the inferred phylogenetic tree is incorrect, it can lead to erroneous site-specific rate estimates. Here we describe a novel Bayesian method that uses Markov chain Monte Carlo methodology to integrate over the space of all possible trees and model parameters. By doing so, the method considers alternative evolutionary scenarios weighted by their posterior probabilities. We show that this comprehensive evolutionary approach is superior over methods that are based on only a single tree. We illustrate the potential of our algorithm by analyzing the conservation pattern of the potassium channel protein family.Itay Mayrose, Amir Mitchell contributed equal. Reviewing Editor : Dr. Nicolas Galtier     

Neutral theory, phylogenies, and the relationship between phenotypic change and evolutionary rates

The neutral theory of molecular evolution predicts that rates of phenotypic change are largely independent from genotypic change. A recent study by Bromham et al. (2002) confirmed this expectation, finding no evidence for correlated phenotypic and molecular evolutionary rates in animals. We reevaluate this hypothesis, sampling at different taxonomic levels in plants and animals, using Bayesian inference to reconstruct phylogenetic trees and estimate rates of molecular evolution. We use independent contrasts in branch lengths to maximize the information extracted from each of the trees and nodal posterior probabilities to assess the influence of phylogenetic error. Our results indicate that in vascular plants between 2% and 11% of the variation in phenotypic rates of change can be explained by the rate of genotypic change. These results may be explained by the idea that processes that affect general evolutionary rates, such as body size, may also be expected to influence rates of morphological change.     

Assessing an unknown evolutionary process: effect of increasing site-specific knowledge through taxon addition

Assessment of the evolutionary process is crucial for understanding the effect of protein structure and function on sequence evolution and for many other analyses in molecular evolution. Here, we used simulations to study how taxon sampling affects accuracy of parameter estimation and topological inference in the absence of branch length asymmetry. With maximum-likelihood analysis, we find that adding taxa dramatically improves both support for the evolutionary model and accurate assessment of its parameters when compared with increasing the sequence length. Using a method we call "doppelg?nger trees," we distinguish the contributions of two sources of improved topological inference: greater knowledge about internal nodes and greater knowledge of site-specific rate parameters. Surprisingly, highly significant support for the correct general model does not lead directly to improved topological inference. Instead, substantial improvement occurs only with accurate assessment of the evolutionary process at individual sites. Although these results are based on a simplified model of the evolutionary process, they indicate that in general, assuming processes are not independent and identically distributed among sites, more extensive sampling of taxonomic biodiversity will greatly improve analytical results in many current sequence data sets with moderate sequence lengths.     

Estimation of effective population size of HIV-1 within a host: a pseudomaximum-likelihood approach

Using pseudomaximum-likelihood approaches to phylogenetic inference and coalescent theory, we develop a computationally tractable method of estimating effective population size from serially sampled viral data. We show that the variance of the maximum-likelihood estimator of effective population size depends on the serial sampling design only because internal node times on a coalescent genealogy can be better estimated with some designs than with others. Given the internal node times and the number of sequences sampled, the variance of the maximum-likelihood estimator is independent of the serial sampling design. We then estimate the effective size of the HIV-1 population within nine hosts. If we assume that the mutation rate is 2.5 x 10(-5) substitutions/generation and is the same in all patients, estimated generation lengths vary from 0.73 to 2.43 days/generation and the mean (1.47) is similar to the generation lengths estimated by other researchers. If we assume that generation length is 1.47 days and is the same in all patients, mutation rate estimates vary from 1.52 x 10(-5) to 5.02 x 10(-5). Our results indicate that effective viral population size and evolutionary rate per year are negatively correlated among HIV-1 patients.     

Detection of convergent and parallel evolution at the amino acid sequence level

Adaptive evolution at the molecular level can be studied by detecting convergent and parallel evolution at the amino acid sequence level. For a set of homologous protein sequences, the ancestral amino acids at all interior nodes of the phylogenetic tree of the proteins can be statistically inferred. The amino acid sites that have experienced convergent or parallel changes on independent evolutionary lineages can then be identified by comparing the amino acids at the beginning and end of each lineage. At present, the efficiency of the methods of ancestral sequence inference in identifying convergent and parallel changes is unknown. More seriously, when we identify convergent or parallel changes, it is unclear whether these changes are attributable to random chance. For these reasons, claims of convergent and parallel evolution at the amino acid sequence level have been disputed. We have conducted computer simulations to assess the efficiencies, of the parsimony and Bayesian methods of ancestral sequence inference in identifying convergent and parallel-change sites. Our results showed that the Bayesian method performs better than the parsimony method in identifying parallel changes, and both methods are inefficient in identifying convergent changes. However, the Bayesian method is recommended for estimating the number of convergent-change sites because it gives a conservative estimate. We have developed statistical tests for examining whether the observed numbers of convergent and parallel changes are due to random chance. As an example, we reanalyzed the stomach lysozyme sequences of foregut fermenters and found that parallel evolution is statistically significant, whereas convergent evolution is not well supported.      

Improved dating of the human/chimpanzee separation in the mitochondrial DNA tree: Heterogeneity among amino acid sites

The internal branch lengths estimated by distance methods such as neighbor joining are shown to be biased to be short when the evolutionary rate differs among sites. The variable-invariable model for site heterogeneity fits the amino acid sequence data encoded by the mitochondrial DNA from Hominoidea remarkably well. By assuming the orangutan separation to be 13 or 16 Myr old, a maximum-likelihood analysis estimates a young date of 3.6 ± 0.6 or 4.4 ± 0.7 Myr (±1 SE) for the human/chimpanzee separation, and these estimates turn out to be robust against differences in the assumed model for amino acid substitutions. Although some uncertainties still exist in our estimates, this analysis suggests that humans separated from chimpanzees some 4–5 Myr ago.Correspondence to: M. Hasewaga     

Maximum-likelihood estimation of site-specific mutation rates in human mitochondrial DNA from partial phylogenetic classification

The mitochondrial DNA hypervariable segment I (HVS-I) is widely used in studies of human evolutionary genetics, and therefore accurate estimates of mutation rates among nucleotide sites in this region are essential. We have developed a novel maximum-likelihood methodology for estimating site-specific mutation rates from partial phylogenetic information, such as haplogroup association. The resulting estimation problem is a generalized linear model, with a nonstandard link function. We develop inference and bias correction tools for our estimates and a hypothesis-testing approach for site independence. We demonstrate our methodology using 16,609 HVS-I samples from the Genographic Project. Our results suggest that mutation rates among nucleotide sites in HVS-I are highly variable. The 16,400–16,500 region exhibits significantly lower rates compared to other regions, suggesting potential functional constraints. Several loci identified in the literature as possible termination-associated sequences (TAS) do not yield statistically slower rates than the rest of HVS-I, casting doubt on their functional importance. Our tests do not reject the null hypothesis of independent mutation rates among nucleotide sites, supporting the use of site-independence assumption for analyzing HVS-I. Potential extensions of our methodology include its application to estimation of mutation rates in other genetic regions, like Y chromosome short tandem repeats.     

A covarion-based method for detecting molecular adaptation: application to the evolution of primate mitochondrial genomes

A new method for detecting site-specific variation of evolutionary rate (the so-called covarion process) from protein sequence data is proposed. It involves comparing the maximum-likelihood estimates of the replacement rate of an amino acid site in distinct subtrees of a large tree. This approach allows detection of covarion at the gene or the amino acid levels. The method is applied to mammalian-mitochondrial-protein sequences. Significant covarion-like evolution is found in the (simian) primate lineage: some amino acid positions are fast-evolving (i.e. unconstrained) in non-primate mammals but slow-evolving (i.e. highly constrained) in primates, and some show the opposite pattern. Our results indicate that the mitochondrial genome of primates reached a new peak of the adaptive landscape through positive selection.     

Effects of branch length uncertainty on Bayesian posterior probabilities for phylogenetic hypotheses

In Bayesian phylogenetics, confidence in evolutionary relationships is expressed as posterior probability--the probability that a tree or clade is true given the data, evolutionary model, and prior assumptions about model parameters. Model parameters, such as branch lengths, are never known in advance; Bayesian methods incorporate this uncertainty by integrating over a range of plausible values given an assumed prior probability distribution for each parameter. Little is known about the effects of integrating over branch length uncertainty on posterior probabilities when different priors are assumed. Here, we show that integrating over uncertainty using a wide range of typical prior assumptions strongly affects posterior probabilities, causing them to deviate from those that would be inferred if branch lengths were known in advance; only when there is no uncertainty to integrate over does the average posterior probability of a group of trees accurately predict the proportion of correct trees in the group. The pattern of branch lengths on the true tree determines whether integrating over uncertainty pushes posterior probabilities upward or downward. The magnitude of the effect depends on the specific prior distributions used and the length of the sequences analyzed. Under realistic conditions, however, even extraordinarily long sequences are not enough to prevent frequent inference of incorrect clades with strong support. We found that across a range of conditions, diffuse priors--either flat or exponential distributions with moderate to large means--provide more reliable inferences than small-mean exponential priors. An empirical Bayes approach that fixes branch lengths at their maximum likelihood estimates yields posterior probabilities that more closely match those that would be inferred if the true branch lengths were known in advance and reduces the rate of strongly supported false inferences compared with fully Bayesian integration.     

Reliabilities of parsimony-based and likelihood-based methods for detecting positive selection at single amino acid sites.

The reliabilities of parsimony-based and likelihood-based methods for inferring positive selection at single amino acid sites were studied using the nucleotide sequences of human leukocyte antigen (HLA) genes, in which positive selection is known to be operating at the antigen recognition site. The results indicate that the inference by parsimony-based methods is robust to the use of different evolutionary models and generally more reliable than that by likelihood-based methods. In contrast, the results obtained by likelihood-based methods depend on the models and on the initial parameter values used. It is sometimes difficult to obtain the maximum likelihood estimates of parameters for a given model, and the results obtained may be false negatives or false positives depending on the initial parameter values. It is therefore preferable to use parsimony-based methods as long as the number of sequences is relatively large and the branch lengths of the phylogenetic tree are relatively small.     

Evaluating the performance of likelihood methods for detecting population structure and migration

A plethora of statistical models have recently been developed to estimate components of population genetic history. Very few of these methods, however, have been adequately evaluated for their performance in accurately estimating population genetic parameters of interest. In this paper, we continue a research program of evaluation of population genetic methods through computer simulation. Specifically, we examine the software MIGRATEE-N 1.6.8 and test the accuracy of this software to estimate genetic diversity (Theta), migration rates, and confidence intervals. We simulated nucleotide sequence data under a neutral coalescent model with lengths of 500 bp and 1000 bp, and with three different per site Theta values of (0.00025, 0.0025, 0.025) crossed with four different migration rates (0.0000025, 0.025, 0.25, 2.5) to construct 1000 evolutionary trees per-combination per-sequence-length. We found that while MIGRATEE-N 1.6.8 performs reasonably well in estimating genetic diversity (Theta), it does poorly at estimating migration rates and the confidence intervals associated with them. We recommend researchers use this software with caution under conditions similar to those used in this evaluation.     

Statistical methods for testing functional divergence after gene duplication

Functional innovations after gene duplication may result in altered functional constraints between member gene clusters of a gene family. This type (type I) of functional divergence is measured by the coefficient of functional divergence (theta lambda), which can be interpreted as the decrease in rate correlation between gene clusters, or the probability that the evolutionary rate at a site is statistically independent between two gene clusters. A simple stochastic model has been developed for estimating theta lambda and testing its statistical significance. The current model includes the model of rate variation among sites as a special case when theta lambda = 0. Moreover, we have developed a site-specific profile based on the hidden Markov model to identify critical amino acid residues that are responsible for these functional differences between two gene clusters, which may have great potential in functional genomics.     

Evaluating the robustness of phylogenetic methods to among-site variability in substitution processes

Computer simulations provide a flexible method for assessing the power and robustness of phylogenetic inference methods. Unfortunately, simulated data are often obviously atypical of data encountered in studies of molecular evolution. Unrealistic simulations can lead to conclusions that are irrelevant to real-data analyses or can provide a biased view of which methods perform well. Here, we present a software tool designed to generate data under a complex codon model that allows each residue in the protein sequence to have a different set of equilibrium amino acid frequencies. The software can obtain maximum-likelihood estimates of the parameters of the Halpern and Bruno model from empirical data and a fixed tree; given an arbitrary tree and a fixed set of parameters, the software can then simulate artificial datasets.We present the results of a simulation experiment using randomly generated tree shapes and substitution parameters estimated from 1610 mammalian cytochrome b sequences.We tested tree inference at the amino acid, nucleotide and codon levels and under parsimony, maximum-likelihood, Bayesian and distance criteria (for a total of more than 650 analyses on each dataset). Based on these simulations, nucleotide-level analyses seem to be more accurate than amino acid and codon analyses. The performance of distance-based phylogenetic methods appears to be quite sensitive to the choice of model and the form of rate heterogeneity used. Further studies are needed to assess the generality of these conclusions. For example, fitting parameters of the Halpern Bruno model to sequences from other genes will reveal the extent to which our conclusions were influenced by the choice of cytochrome b. Incorporating codon bias and more sources heterogeneity into the simulator will be crucial to determining whether the current results are caused by a bias in the current simulation study in favour of nucleotide analyses.     

The relative performance of Bayesian and parsimony approaches when sampling characters evolving under homogeneous and heterogeneous sets of parameters

We tested whether it is beneficial for the accuracy of phylogenetic inference to sample characters that are evolving under different sets of parameters, using both Bayesian MCMC (Markov chain Monte Carlo) and parsimony approaches. We examined differential rates of evolution among characters, differential character-state frequencies and character-state space, and differential relative branch lengths among characters. We also compared the relative performance of parsimony and Bayesian analyses by progressively incorporating more of these heterogeneous parameters and progressively increasing the severity of this heterogeneity. Bayesian analyses performed better than parsimony when heterogeneous simulation parameters were incorporated into the substitution model. However, parsimony outperformed Bayesian MCMC when heterogeneous simulation parameters were not incorporated into the Bayesian substitution model. The higher the rate of evolution simulated, the better parsimony performed relative to Bayesian analyses. Bayesian and parsimony analyses converged in their performance as the number of simulated heterogeneous model parameters increased. Up to a point, rate heterogeneity among sites was generally advantageous for phylogenetic inference using both approaches. In contrast, branch-length heterogeneity was generally disadvantageous for phylogenetic inference using both parsimony and Bayesian approaches. Parsimony was found to be more conservative than Bayesian analyses, in that it resolved fewer incorrect clades.
© The Willi Hennig Society 2006.     

Accounting for uncertainty in the tree topology has little effect on the decision-theoretic approach to model selection in phylogeny estimation

Currently available methods for model selection used in phylogenetic analysis are based on an initial fixed-tree topology. Once a model is picked based on this topology, a rigorous search of the tree space is run under that model to find the maximum-likelihood estimate of the tree (topology and branch lengths) and the maximum-likelihood estimates of the model parameters. In this paper, we propose two extensions to the decision-theoretic (DT) approach that relax the fixed-topology restriction. We also relax the fixed-topology restriction for the Bayesian information criterion (BIC) and the Akaike information criterion (AIC) methods. We compare the performance of the different methods (the relaxed, restricted, and the likelihood-ratio test [LRT]) using simulated data. This comparison is done by evaluating the relative complexity of the models resulting from each method and by comparing the performance of the chosen models in estimating the true tree. We also compare the methods relative to one another by measuring the closeness of the estimated trees corresponding to the different chosen models under these methods. We show that varying the topology does not have a major impact on model choice. We also show that the outcome of the two proposed extensions is identical and is comparable to that of the BIC, Extended-BIC, and DT. Hence, using the simpler methods in choosing a model for analyzing the data is more computationally feasible, with results comparable to the more computationally intensive methods. Another outcome of this study is that earlier conclusions about the DT approach are reinforced. That is, LRT, Extended-AIC, and AIC result in more complicated models that do not contribute to the performance of the phylogenetic inference, yet cause a significant increase in the time required for data analysis.     

Epistasis Creates Invariant Sites and Modulates the Rate of Molecular Evolution

Invariant sites are a common feature of amino acid sequence evolution. The presence of invariant sites is frequently attributed to the need to preserve function through site-specific conservation of amino acid residues. Amino acid substitution models without a provision for invariant sites often fit the data significantly worse than those that allow for an excess of invariant sites beyond those predicted by models that only incorporate rate variation among sites (e.g., a Gamma distribution). An alternative is epistasis between sites to preserve residue interactions that can create invariant sites. Through computer-simulated sequence evolution, we evaluated the relative effects of site-specific preferences and site-site couplings in the generation of invariant sites and the modulation of the rate of molecular evolution. In an analysis of ten major families of protein domains with diverse sequence and functional properties, we find that the negative selection imposed by epistasis creates many more invariant sites than site-specific residue preferences alone. Further, epistasis plays an increasingly larger role in creating invariant sites over longer evolutionary periods. Epistasis also dictates rates of domain evolution over time by exerting significant additional purifying selection to preserve site couplings. These patterns illuminate the mechanistic role of epistasis in the processes underlying observed site invariance and evolutionary rates.     

Transition rates between specialization and generalization in phytophagous insects

Although most species of animals exhibit specialized patterns of resource use, it is unclear whether specialization evolves at a faster rate than generalization. To test this hypothesis, transition rates toward specialization and toward generalization were estimated using phylogenies from 15 groups of phytophagous insects. Among the groups studied, maximum-likelihood analyses showed that the forward transition rate from generalization to specialization was significantly higher than the reverse transition rate from specialization to generalization (mean ratio of forward to reverse transition rate = 1.47 using uniform branch lengths and 1.76 using Grafen branch lengths). Although phylogenetic conservatism of host-plant use is common, the results suggest that the evolution of specialization is a highly dynamic process. For example, higher transitions rates both toward and away from specialization as well as equal transition rates were inferred. Collectively, the results reveal a tendency for directional evolution toward increased specialization but also indicate that specialization does not always represent an evolutionary dead-end that strongly limits further evolution.     

Mitochondrial genes and mammalian phylogenies: increasing the reliability of branch length estimation

Since branch lengths provide important information about the timing and the extent of evolutionary divergence among taxa, accurate resolution of evolutionary history depends as much on branch length estimates as on recovery of the correct topology. However, the empirical relationship between the choice of genes to sequence and the quality of branch length estimation remains ill defined. To address this issue, we evaluated the accuracy of branch lengths estimated from subsets of the mitochondrial genome for a mammalian phylogeny with known subordinal relationships. Using maximum-likelihood methods, we estimated branch lengths from an 11-kb sequence of all 13 protein-coding genes and compared them with estimates from single genes (0.2-1.8 kb) and from 7 different combinations of genes (2-3.5 kb). For each sequence, we separated the component of the log-likelihood deviation due to branch length differences associated with alternative topologies from that due to those that are independent of the topology. Even among the sequences that recovered the same tree topology, some produced significantly better branch length estimates than others did. The combination of correct topology and significantly better branch length estimation suggests that these gene combinations may prove useful in estimating phylogenetic relationships for mammalian divergences below the ordinal level. Thus, the proper choice of genes to sequence is a critical factor for reliable estimation of evolutionary history from molecular data.     

A simple statistical method for estimating type-II (cluster-specific) functional divergence of protein sequences

Predicting functional amino acid residues in silico is important for comparative genomics. In this paper, we focus on the issue of how to statistically identify cluster-specific amino acid residues that are related to the functional divergence after gene duplication. We approach this problem using a framework based on site-specific shift of amino acid property (type-II functional divergence), as opposed to site-specific shift of evolutionary rate (type-I functional divergence). An efficient statistical procedure is implemented to facilitate the development of phylogenomic database for cluster-specific residues of large-scale protein families. Our method has the following features: 1) statistical testing of the type-II functional divergence and 2) the site-specific Bayesian profile to measure how amino acid residues contribute to type-II (cluster-specific) functional divergence. Consequently, one may obtain the posterior probability for "functional" cluster-specific residues. Case studies are presented and indicate that radical cluster-specific residues are responsible for most of inferred type-II functional divergence, whereas conserved cluster-specific residues appear less than even those imperfect radical cluster-specific residues to this type of functional divergence.