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This transformation reveals that amino acid models belong to a subset of the codon models and enables us to test whether synonymous substitutions can be ignored by using the likelihood ratio.
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Our theoretical results and analyses of real data indicate that synonymous substitutions are very informative and substantially improve evolutionary inference, even when the sequences are highly divergent. Therefore, we note that amino acid models should be adopted only after carefully investigating and discarding the possibility that synonymous substitutions can reveal important evolutionary information.
Amino acid modelcodon modellikelihood-ratio testmodel comparisonsynonymous saturation The DNA substitutions of protein-coding sequences are categorized into synonymous and nonsynonymous codon substitutions.
Because nonsynonymous substitutions induce amino acid replacement, they may have been subjected to Darwinian selection during the evolutionary process. The relative occurrence of nonsynonymous substitutions with respect to synonymous substitutions is used to represent the strength of selective pressure Yang and Bielawski, Whereas codon models Goldman and Yang, ; Muse and Gaut, consider both synonymous and nonsynonymous DNA substitutions, amino acid models Dayhoff et al.
Although amino acid models lose the information regarding synonymous substitutions, they incorporate the information for amino acid replacement, which is empirically derived from databases.
It has been widely accepted that synonymous substitutions may saturate quickly as sequences diverge e. In this case, the saturation of synonymous substitutions could mask the information provided by nonsynonymous substitutions; thus, amino acid models may be better than codon models.
Unfortunately, there has been no quantitative procedure to verify whether synonymous substitutions can be ignored, and amino acid models have been arbitrarily selected. It is crucial to select an appropriate substitution model for phylogenetic analysis.I Joined a Russian Dating Site - See how it ended [Kult America]
Adopting an inappropriate model may lead to inconsistent branch length estimates, which can result in an incorrect inference of phylogeny Anderson and Swofford, Under the Bayesian framework, incorrect branch length estimates may result in wrong estimations of divergence time Thorne et al. Furthermore, it has been noted that the confidence level of a reconstructed tree may be affected by inappropriate model selection Buckley, The likelihood-ratio test Stuart and Ord, and various model selection criteria such as AIC Akaike, and BIC Schwarz, can be applied to select appropriate substitution models.
Although the problem of model selection has been individually addressed to a great extent for both codon Yang and Nielsen,; Nielsen and Yang, ; Yang et al. In our study, we consider a situation in which protein-coding DNA sequences are provided such that both codon and amino acid models are applicable. The log-likelihood scores for codon and amino acid models cannot be directly compared via conventional model selection criteria Akaike, ; Schwarz, ; Stuart and Ord, This is because the dimensions of their data spaces differ—the dimension of an amino acid space is 20, whereas the standard codon table contains three stop codons and its dimension is Although different codon tables may contain differing numbers of stop codons, we assume that the dimension of the codon space is 61 for the sake of convenience of description.
When an amino acid model is adopted, a dimensional data space is transformed to a dimensional one by translating the codons into amino acids. In the subsequent section, we discuss the procedure to transform an amino acid model in order to make it comparable with the codon one. We propose two types of codon models that can be derived from an amino acid model.
By comparing these two types of codon models, we can verify whether the information provided by synonymous substitutions can be ignored for phylogenetic analysis. We apply our procedure to the analysis of mammalian and yeast sequence data and demonstrate that synonymous substitutions are very informative even when the sequences are highly divergent. Methods Conventional Codon Models For the conventional codon model Goldman and Yang,the instantaneous transition rate from codon i to codon j is represented as follows: Other codon models Muse and Gaut, ; Wong and Nielsen, have been developed in which the instantaneous transition rate is proportional to the frequency of the replaced nucleotide.
Conventional Amino Acid Models For amino acid models, the instantaneous transition rate from amino acid ai to amino acid aj is represented as follows: The values of the parameter saiaj for various amino acid models have been estimated by parsimony-based Dayhoff et al. For the sake of convenience of mathematical notation, we do not consider any normalizing factor for the rate matrix.
Converting Amino Acid Model to Codon Model by Incorporating Synonymous Substitutions We consider a new codon model in which the instantaneous transition rate from codons i to j is given as follows: SK-P1 is designed for the conversion of an amino acid model to a codon model. In an amino acid model, all types of amino acid transitions are allowed in infinitesimal time, even if multiple nucleotide substitutions are involved.
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For the sake of consistency with the amino acid model, we allow instantaneous multiple nucleotide substitution in Equation SK-P1. Multiple-nucleotide substitutions in infinitesimal time is biologically plausible because it can be caused by compensatory mutation, recombination, gene conversion, etc.
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