Evolutionary trees from gene frequencies and quantitative characters: finding maximum likelihood estimates and testing hypotheses

Technical Report · Tue Jul 01 04:00:00 EDT 1980

OSTI ID:7099873

Felsenstein, J

The assumptions involved in maximum likelihood estimation of evolutionary trees from quantitative character data are described. A strict maximum likelihood method applied to the case of two populations encounters singularities in the likelihood surface, and even when restrictions are placed on the parameters to avoid this the resulting estimate is converged to the wrong value as more characters are considered. These problems arise because new nuisance parameters are introduced every time a new character is added. If the data are assumed to consist only of the differences between population phenotypes, and a maximum likelihood solution based on this transformed data is found, this restricted maximum likelihood (REML) method behaves well. Two computational techniques, the pruning algorithm and the pulley principle, are described which allow rapid computation of the restricted likelihood. They allow construction of an iterative procedure for finding the maximum of the restricted likelihood within a given tree topology. Combined with an algorithm for searching among similar tree topologies, this allows construction of a computer program to find the REML estimate of the tree. The fact that the REML estimate is a maximum likelihood estimate obtained from transformed data allows use of likelihood-ratio testing of evolutionary hypotheses. Constancy of evolutionary rate per unit time can be tested, but it appears that discrimination between gradualist and punctuated-equilibrium hypotheses will require fossil data.

• Research Organization: Washington Univ., Seattle (USA)
• OSTI ID: 7099873
• Report Number(s): RLO-2225-5-53
• Country of Publication: United States
• Language: English

Related Subjects

550100* -- Behavioral Biology
550400 -- Genetics
59 BASIC BIOLOGICAL SCIENCES
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ALGORITHMS
BIOLOGICAL EVOLUTION
BIOLOGY
DATA ANALYSIS
GENES
GENETICS
HYPOTHESIS
ITERATIVE METHODS
MATHEMATICAL LOGIC
MATHEMATICS
MUTATION FREQUENCY
PHENOTYPE
POPULATIONS
TESTING
TOPOLOGY