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EVOLUTIONARY TREES FROM GENE FREQUENCIES AND QUANTITATIVE CHARACTERS: FINDING MAXIMUM LIKELIHOOD ESTIMATES
Author(s) -
Felsenstein Joseph
Publication year - 1981
Publication title -
evolution
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.84
H-Index - 199
eISSN - 1558-5646
pISSN - 0014-3820
DOI - 10.1111/j.1558-5646.1981.tb04991.x
Subject(s) - citation , maximum likelihood , biology , genealogy , library science , statistics , computer science , history , mathematics
A small but complex literature on the estimation of evolutionary trees from quantitative characters (including gene frequencies) has existed for over 15 years (Edwards and Cavalli-Sforza, 1964; Cavalli-Sforza and Edwards, 1967, 1970; Edwards, 1970; Kidd and Sgaramella-Zonta, 1971; Thompson, 1973; Felsenstein, 1973a; Thompson, 1975; Cavalli-Sforza and Piazza, 1975; Astolfi et al., 1978). In general its methods are little-known and even less used by those in possession of relevant gene frequencies or quantitative character data. Though this results in part from the complexity of the mathematics in these papers and in part from their concentration in human genetics journals, a major block to the use of these statistical methods has been the difficulty of the computations. Thompson (1975) has produced an iterative computer program which is probably the most efficient method of finding maximum likelihood evolutionary trees. Thompson's method is the strict application of maximum likelihood estimation in a situation in which each character added to the data brings with it one new parameter to be estimated. It is easily demonstrated that in this case, these "nuisance parameters" cause the estimation procedure to fail to be consistent: that is, the estimate will not converge to the true tree as more and more characters are added. My own procedure (Felsenstein, 1973a) makes a restricted maximum likelihood (REML) estimate, but eliminates the presence of the nuisance parameters and thereby makes a consistent estimate of the evolutionary tree. Some of the differences between these approaches will be briefly dealt with later in this paper. This paper introduces an iterative REML method which makes rapid computation of the REML estimate of the evolutionary tree feasible. It may also serve as a review of the basic logic of these estimates and tests for those readers unfamiliar with the existing human geneticsoriented literature.