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INTRODUCMIONACCEPTANCE OF the theory of evolution as the means of explaining observed similarities and differences among organisms invites the construction of trees of descent purporting to show evolutionary relationships.Whether such trees are based on fossil or living specimens, they may often be criticized for having a subjective element.The purpose of this paper is to show how suitable evolutionary models can be constructed and applied objectively.In it we amplify and extend the methods we have given in previous communications (Edwards and Cavalli-Sforza, 1963a, b, 1964, 1965; Cavalli-Sforza and Edwards, 1964, 1966; Cavalli-Sforza et al., 1964; Cavalli-Sforza, 1966).Considering the great variety of information provided by living organisms, it is clear that the type of data will affect both the method of treatment and the validity of the results: the higher the correlation of data and genotype, the greater the validity is likely to be.Information on nucleic acid and pro- tein structure comes first in the scale of relevance and that on phenotype mea- surements last; discrete and continuous variation demand different treatments, and evolutionary models appropriate to both cases will therefore be required for estimation purposes.Differences which are the result of mutation are formally discrete, and evolution at the molecular level thus needs discontinu- ous treatment; but even in this case the limit of observation may turn the data into the continuous type, as happens, for instance, when the similarity in nucleotide sequences in the nucleic acids of two organisms is measured by hybridization techniques or when differences between closely related orga- nisms are examined.In the latter case, the differences may be sufficiently small to suggest that the analysis be carried out at the level of gene frequenciessemicontinuous variables which may be treated as continuous.