Maximum likelihood phylogenetic estimation from DNA sequences with variable rates over sites: Approximate methods
 Ziheng Yang
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Two approximate methods are proposed for maximum likelihood phylogenetic estimation, which allow variable rates of substitution across nucleotide sites. Three data sets with quite different characteristics were analyzed to examine empirically the performance of these methods. The first, called the “discrete gamma model,” uses several categories of rates to approximate the gamma distribution, with equal probability for each category. The mean of each category is used to represent all the rates falling in the category. The performance of this method is found to be quite good, and four such categories appear to be sufficient to produce both an optimum, or nearoptimum fit by the model to the data, and also an acceptable approximation to the continuous distribution. The second method, called “fixedrates model,” classifies sites into several classes according to their rates predicted assuming the star tree. Sites in different classes are then assumed to be evolving at these fixed rates when other tree topologies are evaluated. Analyses of the data sets suggest that this method can produce reasonable results, but it seems to share some properties of a leastsquares pairwise comparison; for example, interior branch lengths in nonbest trees are often found to be zero. The computational requirements of the two methods are comparable to that of Felsenstein's (1981, J Mol Evol 17:368–376) model, which assumes a single rate for all the sites.
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 Title
 Maximum likelihood phylogenetic estimation from DNA sequences with variable rates over sites: Approximate methods
 Journal

Journal of Molecular Evolution
Volume 39, Issue 3 , pp 306314
 Cover Date
 19940901
 DOI
 10.1007/BF00160154
 Print ISSN
 00222844
 Online ISSN
 14321432
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Phylogeny
 Maximum likelihood
 Rate variation over sites
 The gamma distribution
 Approximate methods
 Industry Sectors
 Authors

 Ziheng Yang ^{(1)}
 Author Affiliations

 1. Department of Zoology, The Natural History Museum, SW7 51313, London, United Kingdom