Biomedical subjects

A Rzhetsky

Publications and source records attributed to A Rzhetsky.

10 recordsLinked to original sources

PubMed1996

When is it safe to use an oversimplified substitution model in tree-making?

The choice of an "optimal" mathematical model for computing evolutionary distances from real sequences is not currently supported by easy-to-use software applicable to large data sets, and an investigator frequently selects one of the simplest models available. Here we study properties of the observed proportion of differences (p-distance) between sequences as an estimator of evolutionary distance for tree-making. We show that p-distances allow for consistent tree-making with any of the popular methods working with evolutionary distances if evolution of sequences obeys a "molecular clock" (more precisely, if it follows a stationary time-reversible Markov model of nucleotide substitution). Next, we show that p-distances seem to be efficient in recovering the correct tree topology under a "molecular clock," but produce "statistically supported" wrong trees when substitutions rates vary among evolutionary lineages. Finally, we outline a practical approach for selecting an "optimal" model of nucleotide substitution in a real data analysis, and obtain a crude estimate of a "prior" distribution of the expected tree branch lengths under the Jukes-Cantor model. We conclude that the use of a model that is obviously oversimplified is inadvisable unless it is justified by a preliminary analysis of the real sequences.

Base Sequence↗

PubMed1995

Estimating substitution rates in ribosomal RNA genes.

A model is introduced describing nucleotide substitution in ribosomal RNA (rRNA) genes. In this model, substitution in the stem and loop regions of rRNA is modeled with 16- and four-state continuous time Markov chains, respectively. The mean substitution rates at nucleotide sites are assumed to follow gamma distributions that are different for the two types of regions. The simplest formulation of the model allows for explicit expressions for transition probabilities of the Markov processes to be found. These expressions were used to analyze several 16S-like rRNA genes from higher eukaryotes with the maximum likelihood method. Although the observed proportion of invariable sites was only slightly higher in the stem regions, the estimated average substitution rates in the stem regions were almost two times as high as in the loop regions. Therefore, the degree of site heterogeneity of substitution rates in the stem regions seems to be higher than in the loop regions of animal 16S-like rRNAs due to presence of a few rapidly evolving sites. The model appears to be helpful in understanding the regularities of nucleotide substitution in rRNAs and probably minimizing errors in recovering phylogeny for distantly related taxa from these genes.

Animals↗

PubMed1995

Tests of applicability of several substitution models for DNA sequence data.

Using linear invariants for various models of nucleotide substitution, we developed test statistics for examining the applicability of a specific model to a given dataset in phylogenetic inference. The models examined are those developed by Jukes and Cantor (1969), Kimura (1980), Tajima and Nei (1984), Hasegawa et al. (1985), Tamura (1992), Tamura and Nei (1993), and a new model called the eight-parameter model. The first six models are special cases of the last model. The test statistics developed are independent of evolutionary time and phylogeny, although the variances of the statistics contain phylogenetic information. Therefore, these statistics can be used before a phylogenetic tree is estimated. Our objective is to find the simplest model that is applicable to a given dataset, keeping in mind that a simple model usually gives an estimate of evolutionary distance (number of nucleotide substitutions per site) with a smaller variance than a complicated model when the simple model is correct. We have also developed a statistical test of the homogeneity of nucleotide frequencies of a sample of several sequences that takes into account possible phylogenetic correlations. This test is used to examine the stationarity in time of the base frequencies in the sample. For Hasegawa et al.'s and the eight-parameter models, analytical formulas for estimating evolutionary distances are presented. Application of the above tests to several sets of real data has shown that the assumption of stationarity of base composition is usually acceptable when the sequences studied are closely related but otherwise it is rejected. Similarly, the simple models of nucleotide substitution are almost always rejected when actual genes are distantly related and/or the total number of nucleotides examined is large.

Base Sequence↗

PubMed1995

Four-cluster analysis: a simple method to test phylogenetic hypotheses.

A simple statistical test for comparing three alternative phylogenetic hypotheses for four monophyletic groups is presented. This test is based on the minimum-evolution principle, and it does not require any information regarding the branching order within each monophyletic group. It is computationally efficient and can be easily extended to five or more monophyletic groups.

Animals↗

PubMed1995

Interior-branch and bootstrap tests of phylogenetic trees.

We have compared statistical properties of the interior-branch and bootstrap tests of phylogenetic trees when the neighbor-joining tree-building method is used. For each interior branch of a predetermined topology, the interior-branch and bootstrap tests provide the confidence values, PC and PB, respectively, that indicate the extent of statistical support of the sequence cluster generated by the branch. In phylogenetic analysis these two values are often interpreted in the same way, and if PC and PB are high (say, > or = 0.95), the sequence cluster is regarded as reliable. We have shown that PC is in fact the complement of the P-value used in the standard statistical test, but PB is not. Actually, the bootstrap test usually underestimates the extent of statistical support of species clusters. The relationship between the confidence values obtained by the two tests varies with both the topology and expected branch lengths of the true (model) tree. The most conspicuous difference between PC and PB is observed when the true tree is starlike, and there is a tendency for the difference to increase as the number of sequences in the tree increases. The reason for this is that the bootstrap test tends to become progressively more conservative as the number of sequences in the tree increases. Unlike the bootstrap, the interior-branch test has the same statistical properties irrespective of the number of sequences used when a predetermined tree is considered. Therefore, the interior-branch test appears to be preferable to the bootstrap test as long as unbiased estimators of evolutionary distances are used. However, when the interior-branch is applied to a tree estimated from a given data set, PC may give an overestimate of statistical confidence. For this case, we developed a method for computing a modified version (P'C) of the PC value and showed that this P'C tends to give a conservative estimate of statistical confidence, though it is not as conservative as PB. In this paper we have introduced a model in which evolutionary distances between sequences follow a multivariate normal distribution. This model allowed us to study the relationships between the two tests analytically.

Computer Simulation↗

PubMed1995

Phylogenetic test of the molecular clock and linearized trees.

To estimate approximate divergence times of species or species groups with molecular data, we have developed a method of constructing a linearized tree under the assumption of a molecular clock. We present two tests of the molecular clock for a given topology: two-cluster test and branch-length test. The two-cluster test examines the hypothesis of the molecular clock for the two lineages created by an interior node of the tree, whereas the branch-length test examines the deviation of the branch length between the tree root and a tip from the average length. Sequences evolving excessively fast or slow at a high significance level may be eliminated. A linearized tree will then be constructed for a given topology for the remaining sequences under the assumption of rate constancy. We have used these methods to analyze hominoid mitochondrial DNA and drosophilid Adh gene sequences.

Alcohol Dehydrogenase↗

PubMed1994

Unbiased estimates of the number of nucleotide substitutions when substitution rate varies among different sites.

When the number of nucleotides examined is relatively small, the estimators of nucleotide substitutions between DNA sequences often introduce systematic error even if the data used fit the mathematical model underlying the estimation formula. The systematic error of this kind is especially large for models that allow variation in substitution rate among different sites. In the present paper we present a number of formulas that produce virtually bias-free estimates of evolutionary distances for these models.

Amino Acid Sequence↗

PubMed1994

METREE: a program package for inferring and testing minimum-evolution trees.

The METREE program package for estimating phylogenetic trees with the minimum evolution method is written in Turbo C 2.0 and is intended to be used on any IBM-compatible personal computers that have a mathematical coprocessor. The package is simple to use and is menu driven. A program for visualizing and printing out the final tree is also included.

Animals↗

PubMed1993

Theoretical foundation of the minimum-evolution method of phylogenetic inference.

The minimum-evolution (ME) method of phylogenetic inference is based on the assumption that the tree with the smallest sum of branch length estimates is most likely to be the true one. In the past this assumption has been used without mathematical proof. Here we present the theoretical basis of this method by showing that the expectation of the sum of branch length estimates for the true tree is smallest among all possible trees, provided that the evolutionary distances used are statistically unbiased and that the branch lengths are estimated by the ordinary least-squares method. We also present simple mathematical formulas for computing branch length estimates and their standard errors for any unrooted bifurcating tree, with the least-squares approach. As a numerical example, we have analyzed mtDNA sequence data obtained by Vigilant et al. and have found the ME tree for 95 human and 1 chimpanzee (outgroup) sequences. The tree was somewhat different from the neighbor-joining tree constructed by Tamura and Nei, but there was no statistically significant difference between them.

Algorithms↗

PubMed1992

Statistical properties of the ordinary least-squares, generalized least-squares, and minimum-evolution methods of phylogenetic inference.

Statistical properties of the ordinary least-squares (OLS), generalized least-squares (GLS), and minimum-evolution (ME) methods of phylogenetic inference were studied by considering the case of four DNA sequences. Analytical study has shown that all three methods are statistically consistent in the sense that as the number of nucleotides examined (m) increases they tend to choose the true tree as long as the evolutionary distances used are unbiased. When evolutionary distances (dij's) are large and sequences under study are not very long, however, the OLS criterion is often biased and may choose an incorrect tree more often than expected under random choice. It is also shown that the variance-covariance matrix of dij's becomes singular as dij's approach zero and thus the GLS may not be applicable when dij's are small. The ME method suffers from neither of these problems, and the ME criterion is statistically unbiased. Computer simulation has shown that the ME method is more efficient in obtaining the true tree than the OLS and GLS methods and that the OLS is more efficient than the GLS when dij's are small, but otherwise the GLS is more efficient.

Biological Evolution↗