Maximum Likelihood Trees from DNA Sequences: A Peculiar Statistical Estimation Problem

Yang, Ziheng; Goldman, Nick; Friday, Adrian

doi:10.2307/2413599

Cited by 132 publications

(149 citation statements)

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“…Estimates of under the gamma-rates model are also larger than those obtained under the constantrate model, especially for the third codon positions and sites in the tRNA region, where the transition/transversion rate bias is large. These results agree with previous findings that ignoring the rate variation among sites causes underestimation of branch lengths and the transition/transversion rate ratio (e.g., Wakeley 1994; Yang et al 1994Yang et al , 1995.…”

Section: Separate Analyses Of Data From Different Codon Positionssupporting

confidence: 93%

“…Use of rate parameters for codon positions alleviated this problem to some extent ‫ס(‬ 16.232 by model 1 of Table 4a), and the estimate became even greater when nucleotide frequency differences at codon positions were also taken into account ‫ס(‬ 22.877 by model 2). These results parallel the previous observation that ignoring the nucleotide frequency bias led to underestimation of the transition/transversion rate bias (Yang et al 1995). In model 3 (Table 4a), different rate parameters, nucleotide frequencies, and transition/transversion rate ratios were used for different codon positions, and the only constraint was the proportionality of branch lengths at codon positions (see Table 2).…”

Section: Estimation Of Parameterssupporting

confidence: 85%

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Maximum-likelihood models for combined analyses of multiple sequence data

1996

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Abstract. Models of nucleotide substitution were constructed for combined analyses of heterogeneous sequence data (such as those of multiple genes) from the same set of species. The models account for different aspects of the heterogeneity in the evolutionary process of different genes, such as differences in nucleotide frequencies, in substitution rate bias (for example, the transition/transversion rate bias), and in the extent of rate variation across sites. Model parameters were estimated by maximum likelihood and the likelihood ratio test was used to test hypotheses concerning sequence evolution, such as rate constancy among lineages (the assumption of a molecular clock) and proportionality of branch lengths for different genes. The example data from a segment of the mitochondrial genome of six hominoid species (human, common and pygmy chimpanzees, gorilla, orangutan, and siamang) were analyzed. Nucleotides at the three codon positions in the protein-coding regions and from the tRNA-coding regions were considered heterogeneous data sets. Statistical tests showed that the amount of evolution in the sequence data reflected in the estimated branch lengths can be explained by the codon-position effect and lineage effect of substitution rates. The assumption of a molecular clock could not be rejected when the data were analyzed separately or when the rate variation among sites was ignored. However, significant differences in substitution rate among lineages were found when the data sets were combined and when the rate variation among sites was accounted for in the models. Under the assumption that the orangutan and African apes diverged 13 million years ago, the combined analysis of the sequence data estimated the times for the human-chimpanzee separation and for the separation of the gorilla as 4.3 and 6.8 million years ago, respectively.

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Section: Separate Analyses Of Data From Different Codon Positionssupporting

confidence: 93%

Section: Estimation Of Parameterssupporting

confidence: 85%

Maximum-likelihood models for combined analyses of multiple sequence data

1996

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“…It, however, does not fit in the framework of statistical parameter estimation as the aforementioned working hypothesis is invalid in the context of topology estimation. Different topologies involve different sets of branch-length parameters; and the functional form of f(X; ) changes with tree topology, so that the distribution of the data is not fully specified without knowledge of the true topology (Yang 1994b;Yang et al 1995;see also Nei 1987:325). The problem of phylogeny reconstruction concerns more the question of what the (branch length) parameters are than the question of what numerical values the parameters take.…”

Section: The Problem Of Phylogenetic Tree Estimation: Complexitiesmentioning

confidence: 99%

“…The likelihood method recovers the true tree if and only if the likelihood value for the true tree is greater than those for the wrong trees. When a wrong model is used, the likelihood values of all tree topologies are decreased (normally by a great margin; see, e.g., Yang et al 1994Yang et al , 1995, but it is possible for the aforementioned condition (i.e., the likelihood of the true tree being the greatest) to be satisfied more often if a wrong model is assumed than if the true model is assumed. The fact that using a wrong model can recover the true tree with a higher probability has been observed in computer simulations where distance-matrix methods were used (e.g., Saitou and Nei 1987;Sourdis and Krimbas 1987;Tateno et al 1994).…”

Section: The Problem Of Phylogenetic Tree Estimation: Complexitiesmentioning

confidence: 99%

“…Perhaps it is not that using the true model sometimes fails to give the best performance but rather that we have not found the right way of using the true model. Yang et al (1995) noted that different tree topologies have similarities to different statistical distributions. One possibility that might be worth exploring is construction of a ''super model'' that has all tree topologies as its special cases, in the same way that a family of distributions can encompass many different distributions.…”

Section: The Problem Of Phylogenetic Tree Estimation: Complexitiesmentioning

confidence: 99%

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Phylogenetic analysis using parsimony and likelihood methods

1996

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Abstract. The assumptions underlying the maximumparsimony (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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Effects of sequence alignment procedures on estimates of phylogeny

Goldman¹

1998

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Maximum Likelihood Trees from DNA Sequences: A Peculiar Statistical Estimation Problem

Cited by 132 publications

References 0 publications

Maximum-likelihood models for combined analyses of multiple sequence data

Maximum-likelihood models for combined analyses of multiple sequence data

Phylogenetic analysis using parsimony and likelihood methods

Effects of sequence alignment procedures on estimates of phylogeny

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