Sufficient statistics and expectation maximization algorithms in phylogenetic tree models
Motivation: Measuring evolutionary conservation is a routine step in the identification of functional elements in genome sequences. Although a number of studies have proposed methods that use the continuous time Markov models (CTMMs) to find evolutionarily constrained elements, their probabilistic s...
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| Veröffentlicht in: | Bioinformatics (Oxford, England) Jg. 27; H. 17; S. 2346 - 2353 |
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01.09.2011
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| Abstract | Motivation: Measuring evolutionary conservation is a routine step in the identification of functional elements in genome sequences. Although a number of studies have proposed methods that use the continuous time Markov models (CTMMs) to find evolutionarily constrained elements, their probabilistic structures have been less frequently investigated.
Results: In this article, we investigate a sufficient statistic for CTMMs. The statistic is composed of the fractional duration of nucleotide characters over evolutionary time, Fd, and the number of substitutions occurring in phylogenetic trees, Ns. We first derive basic properties of the sufficient statistic. Then, we derive an expectation maximization (EM) algorithm for estimating the parameters of a phylogenetic model, which iteratively computes the expectation values of the sufficient statistic. We show that the EM algorithm exhibits much faster convergence than other optimization methods that use numerical gradient descent algorithms. Finally, we investigate the genome-wide distribution of fractional duration time Fd which, unlike the number of substitutions Ns, has rarely been investigated. We show that Fd has evolutionary information that is distinct from that in Ns, which may be useful for detecting novel types of evolutionary constraints existing in the human genome.
Availability: The C++ source code of the ‘Fdur’ software is available at http://www.ncrna.org/software/fdur/
Contact: kiryu-h@k.u-tokyo.ac.jp
Supplementary information: Supplementary data are available at Bioinformatics online. |
|---|---|
| AbstractList | Measuring evolutionary conservation is a routine step in the identification of functional elements in genome sequences. Although a number of studies have proposed methods that use the continuous time Markov models (CTMMs) to find evolutionarily constrained elements, their probabilistic structures have been less frequently investigated.
In this article, we investigate a sufficient statistic for CTMMs. The statistic is composed of the fractional duration of nucleotide characters over evolutionary time, F(d), and the number of substitutions occurring in phylogenetic trees, N(s). We first derive basic properties of the sufficient statistic. Then, we derive an expectation maximization (EM) algorithm for estimating the parameters of a phylogenetic model, which iteratively computes the expectation values of the sufficient statistic. We show that the EM algorithm exhibits much faster convergence than other optimization methods that use numerical gradient descent algorithms. Finally, we investigate the genome-wide distribution of fractional duration time F(d) which, unlike the number of substitutions N(s), has rarely been investigated. We show that F(d) has evolutionary information that is distinct from that in N(s), which may be useful for detecting novel types of evolutionary constraints existing in the human genome.
The C++ source code of the 'Fdur' software is available at http://www.ncrna.org/software/fdur/
kiryu-h@k.u-tokyo.ac.jp
Supplementary data are available at Bioinformatics online. Measuring evolutionary conservation is a routine step in the identification of functional elements in genome sequences. Although a number of studies have proposed methods that use the continuous time Markov models (CTMMs) to find evolutionarily constrained elements, their probabilistic structures have been less frequently investigated.MOTIVATIONMeasuring evolutionary conservation is a routine step in the identification of functional elements in genome sequences. Although a number of studies have proposed methods that use the continuous time Markov models (CTMMs) to find evolutionarily constrained elements, their probabilistic structures have been less frequently investigated.In this article, we investigate a sufficient statistic for CTMMs. The statistic is composed of the fractional duration of nucleotide characters over evolutionary time, F(d), and the number of substitutions occurring in phylogenetic trees, N(s). We first derive basic properties of the sufficient statistic. Then, we derive an expectation maximization (EM) algorithm for estimating the parameters of a phylogenetic model, which iteratively computes the expectation values of the sufficient statistic. We show that the EM algorithm exhibits much faster convergence than other optimization methods that use numerical gradient descent algorithms. Finally, we investigate the genome-wide distribution of fractional duration time F(d) which, unlike the number of substitutions N(s), has rarely been investigated. We show that F(d) has evolutionary information that is distinct from that in N(s), which may be useful for detecting novel types of evolutionary constraints existing in the human genome.RESULTSIn this article, we investigate a sufficient statistic for CTMMs. The statistic is composed of the fractional duration of nucleotide characters over evolutionary time, F(d), and the number of substitutions occurring in phylogenetic trees, N(s). We first derive basic properties of the sufficient statistic. Then, we derive an expectation maximization (EM) algorithm for estimating the parameters of a phylogenetic model, which iteratively computes the expectation values of the sufficient statistic. We show that the EM algorithm exhibits much faster convergence than other optimization methods that use numerical gradient descent algorithms. Finally, we investigate the genome-wide distribution of fractional duration time F(d) which, unlike the number of substitutions N(s), has rarely been investigated. We show that F(d) has evolutionary information that is distinct from that in N(s), which may be useful for detecting novel types of evolutionary constraints existing in the human genome.The C++ source code of the 'Fdur' software is available at http://www.ncrna.org/software/fdur/AVAILABILITYThe C++ source code of the 'Fdur' software is available at http://www.ncrna.org/software/fdur/kiryu-h@k.u-tokyo.ac.jpCONTACTkiryu-h@k.u-tokyo.ac.jpSupplementary data are available at Bioinformatics online.SUPPLEMENTARY INFORMATIONSupplementary data are available at Bioinformatics online. Motivation: Measuring evolutionary conservation is a routine step in the identification of functional elements in genome sequences. Although a number of studies have proposed methods that use the continuous time Markov models (CTMMs) to find evolutionarily constrained elements, their probabilistic structures have been less frequently investigated. Results: In this article, we investigate a sufficient statistic for CTMMs. The statistic is composed of the fractional duration of nucleotide characters over evolutionary time, Fd, and the number of substitutions occurring in phylogenetic trees, Ns. We first derive basic properties of the sufficient statistic. Then, we derive an expectation maximization (EM) algorithm for estimating the parameters of a phylogenetic model, which iteratively computes the expectation values of the sufficient statistic. We show that the EM algorithm exhibits much faster convergence than other optimization methods that use numerical gradient descent algorithms. Finally, we investigate the genome-wide distribution of fractional duration time Fd which, unlike the number of substitutions Ns, has rarely been investigated. We show that Fd has evolutionary information that is distinct from that in Ns, which may be useful for detecting novel types of evolutionary constraints existing in the human genome. Availability: The C++ source code of the ‘Fdur’ software is available at http://www.ncrna.org/software/fdur/ Contact: kiryu-h@k.u-tokyo.ac.jp Supplementary information: Supplementary data are available at Bioinformatics online. |
| Author | Kiryu, Hisanori |
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| Cites_doi | 10.1186/gb-2007-8-6-r124 10.1101/gr.3715005 10.1038/nmeth.1267 10.1145/279232.279236 10.1371/journal.pcbi.0030254 10.1101/gr.097857.109 10.1186/1471-2105-7-428 10.1007/11732990_17 10.1101/gr.229102 10.1007/BF01734359 10.1093/bioinformatics/btm165 10.1093/acprof:oso/9780198567028.001.0001 10.1126/science.1081331 10.1093/gbe/evp056 10.1006/jmbi.2002.5405 10.1093/bioinformatics/btp190 10.1007/BF00160154 10.1093/nar/gkn579 10.1101/gr.3577405 10.1098/rsta.1922.0009 10.1093/oso/9780198522195.001.0001 10.1093/molbev/msh039 10.1090/S0025-5718-1980-0572855-7 10.2202/1544-6115.1127 10.1101/gr.1933104 10.1126/science.1130738 10.1111/j.2517-6161.1977.tb01600.x |
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| Keywords | Tree algorithm Maximization Phylogenetic tree Models Phylogeny EM algorithm Statistics |
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| Title | Sufficient statistics and expectation maximization algorithms in phylogenetic tree models |
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