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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of molecular evolution 43 (1996), S. 304-311 
    ISSN: 1432-1432
    Keywords: Key words: Maximum likelihood — Phylogeny — Nucleotide substitution — Posterior probability — Empirical Bayes estimation — MAP tree
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract. A new method is presented for inferring evolutionary trees using nucleotide sequence data. The birth–death process is used as a model of speciation and extinction to specify the prior distribution of phylogenies and branching times. Nucleotide substitution is modeled by a continuous-time Markov process. Parameters of the branching model and the substitution model are estimated by maximum likelihood. The posterior probabilities of different phylogenies are calculated and the phylogeny with the highest posterior probability is chosen as the best estimate of the evolutionary relationship among species. We refer to this as the maximum posterior probability (MAP) tree. The posterior probability provides a natural measure of the reliability of the estimated phylogeny. Two example data sets are analyzed to infer the phylogenetic relationship of human, chimpanzee, gorilla, and orangutan. The best trees estimated by the new method are the same as those from the maximum likelihood analysis of separate topologies, but the posterior probabilities are quite different from the bootstrap proportions. The results of the method are found to be insensitive to changes in the rate parameter of the branching process.
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of molecular evolution 48 (1999), S. 274-283 
    ISSN: 1432-1432
    Keywords: Key words: Transition/transversion rate ratio — Maximum likelihood — Species sampling — Saturation — Lemurs — Primates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract. The transition/transversion (ti/tv) rate ratios are estimated by pairwise sequence comparison and joint likelihood analysis using mitochondrial cytochrome b genes of 28 primate species, representing both the Strepsirrhini (lemurs and lories) and the Anthropoidea (monkeys, apes, and humans). Pairwise comparison reveals a strong negative correlation between estimates of the ti/tv ratio and the sequence distance, even when both are corrected for multiple substitutions. The maximum-likelihood estimate of the ti/tv ratio changes with the species included in the analysis. The ti/tv bias within the lemuriform taxa is found to be as strong as in the anthropoids, in contradiction to an earlier study which sampled only one lemuriform. Simulations show the surprising result that both the pairwise correction method and the joint likelihood analysis tend to overcorrect for multiple substitutions and overestimate the ti/tv ratio, especially at low sequence divergence. The bias, however, is not large enough to account for the observed patterns. Nucleotide frequency biases, variation of substitution rates among sites, and different evolutionary dynamics at the three codon positions can be ruled out as possible causes. The likelihood-ratio test suggests that the ti/tv rate ratios may be variable among evolutionary lineages. Without any biological evidence for such a variation, however, we are left with no plausible explanations for the observed patterns other than a possible saturation effect due to the unrealistic nature of the model assumed.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of molecular evolution 51 (2000), S. 423-432 
    ISSN: 1432-1432
    Keywords: Key words: Large phylogenies — Maximum likelihood — Molecular adaptation — Nonsynonymous substitution — Phylogenetics — Positive selection — Synonymous substitution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract. Algorithmic details to obtain maximum likelihood estimates of parameters on a large phylogeny are discussed. On a large tree, an efficient approach is to optimize branch lengths one at a time while updating parameters in the substitution model simultaneously. Codon substitution models that allow for variable nonsynonymous/synonymous rate ratios (ω=d N/d S) among sites are used to analyze a data set of human influenza virus type A hemagglutinin (HA) genes. The data set has 349 sequences. Methods for obtaining approximate estimates of branch lengths for codon models are explored, and the estimates are used to test for positive selection and to identify sites under selection. Compared with results obtained from the exact method estimating all parameters by maximum likelihood, the approximate methods produced reliable results. The analysis identified a number of sites in the viral gene under diversifying Darwinian selection and demonstrated the importance of including many sequences in the data in detecting positive selection at individual sites.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of molecular evolution 42 (1996), S. 294-307 
    ISSN: 1432-1432
    Keywords: Maximum likelihood ; Maximum parsimony ; Molecular evolution ; Molecular systematics ; Phylogeny ; Computer simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract The assumptions underlying the maximum-parsimony (MP) method of phylogenetic tree reconstruction were intuitively examined by studying the way the method works. Computer simulations were performed to corroborate the intuitive examination. Parsimony appears to involve very stringent assumptions concerning the process of sequence evolution, such as constancy of substitution rates between nucleotides, constancy of rates across nucleotide sites, and equal branch lengths in the tree. For practical data analysis, the requirement of equal branch lengths means similar substitution rates among lineages (the existence of an approximate molecular clock), relatively long interior branches, and also few species in the data. However, a small amount of evolution is neither a necessary nor a sufficient requirement of the method. The difficulties involved in the application of current statistical estimation theory to tree reconstruction were discussed, and it was suggested that the approach proposed by Felsenstein (1981,J. Mol. Evol. 17: 368–376) for topology estimation, as well as its many variations and extensions, differs fundamentally from the maximum likelihood estimation of a conventional statistical parameter. Evidence was presented showing that the Felsenstein approach does not share the asymptotic efficiency of the maximum likelihood estimator of a statistical parameter. Computer simulations were performed to study the probability that MP recovers the true tree under a hierarchy of models of nucleotide substitution; its performance relative to the likelihood method was especially noted. The results appeared to support the intuitive examination of the assumptions underlying MP. When a simple model of nucleotide substitution was assumed to generate data, the probability that MP recovers the true topology could be as high as, or even higher than, that for the likelihood method. When the assumed model became more complex and realistic, e.g., when substitution rates were allowed to differ between nucleotides or across sites, the probability that MP recovers the true topology, and especially its performance relative to that of the likelihood method, generally deteriorates. As the complexity of the process of nucleotide substitution in real sequences is well recognized, the likelihood method appears preferable to parsimony. However, the development of a statistical methodology for the efficient estimation of the tree topology remains a difficult open problem.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Journal of molecular evolution 43 (1996), S. 304-311 
    ISSN: 1432-1432
    Keywords: Maximum likelihood ; Phylogeny ; Nucleotide substitution ; Posterior probability ; Empirical Bayes estimation ; MAP tree
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract A new method is presented for inferring evolutionary trees using nucleotide sequence data. The birth-death process is used as a model of speciation and extinction to specify the prior distribution of phylogenies and branching times. Nucleotide substitution is modeled by a continuous-time Markov process. Parameters of the branching model and the substitution model are estimated by maximum likelihood. The posterior probabilities of different phylogenies are calculated and the phylogeny with the highest posterior probability is chosen as the best estimate of the evolutionary relationship among species. We refer to this as the maximum posterior probability (MAP) tree. The posterior probability provides a natural measure of the reliability of the estimated phylogeny. Two example data sets are analyzed to infer the phylogenetic relationship of human, chimpanzee, gorilla, and orangutan. The best trees estimated by the new method are the same as those from the maximum likelihood analysis of separate topologies, but the posterior probabilities are quite different from the bootstrap proportions. The results of the method are found to be insensitive to changes in the rate parameter of the branching process.
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Journal of molecular evolution 46 (1998), S. 409-418 
    ISSN: 1432-1432
    Keywords: Key words: Synonymous rates — Nonsynonymous rates — Mammalian genes — Likelihood — Codon substitution — Transition/transversion rate bias — Neutral theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract. A maximum likelihood approach was used to estimate the synonymous and nonsynonymous substitution rates in 48 nuclear genes from primates, artiodactyls, and rodents. A codon-substitution model was assumed, which accounts for the genetic code structure, transition/transversion bias, and base frequency biases at codon positions. Likelihood ratio tests were applied to test the constancy of nonsynonymous to synonymous rate ratios among branches (evolutionary lineages). It is found that at 22 of the 48 nuclear loci examined, the nonsynonymous/synonymous rate ratio varies significantly across branches of the tree. The result provides strong evidence against a strictly neutral model of molecular evolution. Our likelihood estimates of synonymous and nonsynonymous rates differ considerably from previous results obtained from approximate pairwise sequence comparisons. The differences between the methods are explored by detailed analyses of data from several genes. Transition/transversion rate bias and codon frequency biases are found to have significant effects on the estimation of synonymous and nonsynonymous rates, and approximate methods do not adequately account for those factors. The likelihood approach is preferable, even for pairwise sequence comparison, because more-realistic models about the mutation and substitution processes can be incorporated in the analysis.
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Journal of molecular evolution 41 (1995), S. 254-255 
    ISSN: 1432-1432
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Journal of molecular evolution 41 (1995), S. 587-596 
    ISSN: 1432-1432
    Keywords: Nucleotide substitution ; Models ; Maximum likelihood ; Rate heterogeneity at sites ; Phylogeny ; Molecular clock ; Hepatitis B virus
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract The hepatitis B virus (HBV) has a circular DNA genome of about 3,200 base pairs. Economical use of the genome with overlapping reading frames may have led to severe constraints on nucleotide substitutions along the genome and to highly variable rates of substitution among nucleotide sites. Nucleotide sequences from 13 complete HBV genomes were compared to examine such variability of substitution rates among sites and to examine the phylogenetic relationships among the HBV variants. The maximum likelihood method was employed to fit models of DNA sequence evolution that can account for the complexity of the pattern of nucleotide substitution. Comparison of the models suggests that the rates of substitution are different in different genes and codon positions; for example, the third codon position changes at a rate over ten times higher than the second position. Furthermore, substantial variation of substitution rates was detected even after the effects of genes and codon positions were corrected; that is, rates are different at different sites of the same gene or at the same codon position. Such rates after the correction were also found to be positively correlated at adjacent sites, which indicated the existence of conserved and variable domains in the proteins encoded by the viral genome. A multiparameter model validates the earlier finding that the variation in nucleotide conservation is not random around the HBV genome. The test for the existence of a molecular clock suggests that substitution rates are more or less constant among lineages. The phylogenetic relationships among the viral variants were examined. Although the data do not seem to contain sufficient information to resolve the details of the phylogeny, it appears quite certain that the serotypes of the viral variants do not reflect their genetic relatedness.
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Journal of molecular evolution 39 (1994), S. 306-314 
    ISSN: 1432-1432
    Keywords: Phylogeny ; Maximum likelihood ; Rate variation over sites ; The gamma distribution ; Approximate methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Two approximate methods are proposed for maximum likelihood phylogenetic estimation, which allow variable rates of substitution across nucleotide sites. Three data sets with quite different characteristics were analyzed to examine empirically the performance of these methods. The first, called the “discrete gamma model,” uses several categories of rates to approximate the gamma distribution, with equal probability for each category. The mean of each category is used to represent all the rates falling in the category. The performance of this method is found to be quite good, and four such categories appear to be sufficient to produce both an optimum, or near-optimum fit by the model to the data, and also an acceptable approximation to the continuous distribution. The second method, called “fixed-rates model,” classifies sites into several classes according to their rates predicted assuming the star tree. Sites in different classes are then assumed to be evolving at these fixed rates when other tree topologies are evaluated. Analyses of the data sets suggest that this method can produce reasonable results, but it seems to share some properties of a least-squares pairwise comparison; for example, interior branch lengths in nonbest trees are often found to be zero. The computational requirements of the two methods are comparable to that of Felsenstein's (1981, J Mol Evol 17:368–376) model, which assumes a single rate for all the sites.
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Journal of molecular evolution 40 (1995), S. 689-697 
    ISSN: 1432-1432
    Keywords: Phylogeny ; Maximum likelihood ; Least squares ; Consistency ; Sampling error ; Rate variation at sites ; Gamma distribution ; Computer simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Several maximum likelihood and distance matrix methods for estimating phylogenetic trees from homologous DNA sequences were compared when substitution rates at sites were assumed to follow a gamma distribution. Computer simulations were performed to estimate the probabilities that various tree estimation methods recover the true tree topology. The case of four species was considered, and a few combinations of parameters were examined. Attention was applied to discriminating among different sources of error in tree reconstruction, i.e., the inconsistency of the tree estimation method, the sampling error in the estimated tree due to limited sequence length, and the sampling error in the estimated probability due to the number of simulations being limited. Compared to the least squares method based on pairwise distance estimates, the joint likelihood analysis is found to be more robust when rate variation over sites is present but ignored and an assumption is thus violated. With limited data, the likelihood method has a much higher probability of recovering the true tree and is therefore more efficient than the least squares method. The concept of statistical consistency of a tree estimation method and its implications were explored, and it is suggested that, while the efficiency (or sampling error) of a tree estimation method is a very important property, statistical consistency of the method over a wide range of, if not all, parameter values is prerequisite.
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