A Simple Method for Estimating and Testing Minimum-Evolution Trees

A simple method for estimating and testing phylogenetic trees under the principle of minimum evolution (ME) is presented. The basic procedure of this method is first to obtain the neighbor-joining (NJ) tree by Saitou and Nei’s method and then to search for a tree with the minimum value of the sum (S) of branch lengths by examining all trees that are closely related to the NJ tree. Once the ME tree is identified, a statistical test is conducted for the difference in S between this tree and other closely related trees. The mathematical method required for conducting this test is developed by using the least-squares approach. Computer simulation has shown that this method identifies the correct tree with a high probability, as long as the number of nucleotides examined is sufficiently large. It has also been shown that the topology of the NJ tree is almost always identical with that of the ME tree. A method for obtaining least-squares estimates (and their standard errors) of branch lengths for a given topology is also presented. This method can be used for testing the reliability of the branching pattern of the ME tree. However, the statistical test of S values is more powerful in rejecting incorrect trees than is the branch-length test or bootstrapping. Furthermore, both a mathematical method for computing the number of trees with a given value of topological difference from the NJ tree and a computer algorithm for identifying all the topologies are developed.

[1]  R. Fisher.  The Advanced Theory of Statistics , 1943, Nature.

[2]  Maurice G. Kendall.  The advanced theory of statistics , 1958 .

[3]  W. Fitch,et al.  Construction of phylogenetic trees. , 1967, Science.

[4]  L. Cavalli-Sforza,et al.  PHYLOGENETIC ANALYSIS: MODELS AND ESTIMATION PROCEDURES , 1967, Evolution; international journal of organic evolution.

[5]  T. Jukes.  CHAPTER 24 – Evolution of Protein Molecules , 1969 .

[6]  D. Penny.  Towards a basis for classification: the incompleteness of distance measures, incompatibility analysis and phenetic classification. , 1982, Journal of theoretical biology.

[7]  B. Efron,et al.  The Jackknife: The Bootstrap and Other Resampling Plans. , 1983 .

[8]  M. Nei,et al.  Estimation of evolutionary distance between nucleotide sequences. , 1984, Molecular biology and evolution.

[9]  D. Penny,et al.  The Use of Tree Comparison Metrics , 1985 .

[10]  J. Felsenstein.  CONFIDENCE LIMITS ON PHYLOGENIES: AN APPROACH USING THE BOOTSTRAP , 1985, Evolution; international journal of organic evolution.

[11]  J. Stephens,et al.  Methods for computing the standard errors of branching points in an evolutionary tree and their application to molecular data from humans and apes. , 1985, Molecular biology and evolution.

[12]  M. Nei.  Molecular Evolutionary Genetics , 1987 .

[13]  N. Saitou,et al.  The neighbor-joining method: a new method for reconstructing phylogenetic trees. , 1987, Molecular biology and evolution.

[14]  B. Efron.  The jackknife, the bootstrap, and other resampling plans , 1987 .

[15]  M. Nei,et al.  Relative efficiencies of the maximum parsimony and distance-matrix methods in obtaining the correct phylogenetic tree. , 1988, Molecular biology and evolution.

[16]  N. Saitou,et al.  Relative Efficiencies of the Fitch-Margoliash, Maximum-Parsimony, Maximum-Likelihood, Minimum-Evolution, and Neighbor-joining Methods of Phylogenetic Tree Construction in Obtaining the Correct Tree , 1989 .

[17]  L. Jin,et al.  Variances of the average numbers of nucleotide substitutions within and between populations. , 1989, Molecular biology and evolution.

[18]  W. Li,et al.  A statistical test of phylogenies estimated from sequence data. , 1989, Molecular biology and evolution.

[19]  M. Bulmer,et al.  Estimating the variability of substitution rates. , 1989, Genetics.

[20]  L. Jin,et al.  Limitations of the evolutionary parsimony method of phylogenetic analysis. , 1990, Molecular biology and evolution.

[21]  S. Hedges,et al.  Tetrapod phylogeny inferred from 18S and 28S ribosomal RNA sequences and a review of the evidence for amniote relationships. , 1990, Molecular biology and evolution.

[22]  M. Bulmer.  Use of the Method of Generalized Least Squares in Reconstructing Phylogenies from Sequence Data , 1991 .