Deriving Phylogenetic Trees from Allele Frequencies: A Comparison of Nine Genetic Distances

-An iterative procedure for deriving minimum-length phylogenetic trees from allele frequencies using Rogers' genetic distance as the measure of branch length is extended to include eight additional distances: a modified Rogers' distance; Nei's standard, maximum and minimum distances; Cavalli-Sforza and Edwards' chord and arc distances; and modified forms of the chord and arc distances. The derivation of such trees is defended as a parsimony procedure, and I conclude that any distance used in this procedure must be metric. The nine genetic distances are compared on the criteria of: metricity; ability to produce ancestral allele frequencies with heterozygosity approximating that of the terminal taxa; convergence to a stable solution; and computer time. The modified Cavalli-Sforza and Edwards' chord distance is equal or superior to the other distances on the first three criteria, but requires more computer time than most. Rogers' distance has the properties of metricity and convergence, and ranks below the modified chord distance on ancestral heterozygosity, but generally requires about one-half as much computer time as the modified chord distance. [Minimum-length trees; allele frequencies; parsimony; genetic distances.] In a recent paper (Rogers, 1984), I described a technique for deriving minimumlength phylogenetic trees from allele frequencies by estimating allele frequencies for the ancestral taxa that minimize total tree length as measured by Rogers' (1972) genetic distance. In the present paper, I show how the same procedure can be applied with: a modified Rogers' distance (Wright, 1978); Nei's (1972,1973) standard, minimum and maximum distances; Cavalli-Sforza and Edwards' (1967) arc and chord distances; and modified forms of the arc and chord distances (where the multilocus distances are simple arithmetic averages of the single-locus distances). The derivation of the equations for finding optimal ancestral allele frequencies will be found in the Appendix. I also attempt to justify the construction of minimum-length trees from allele frequencies as a parsimony method and evaluate the suitability of each genetic distance for constructing minimum-length trees using several theoretical and practical criteria. MINIMUM-LENGTH ALLELE-FREQUENCY TREES AND PARSIMONY The goal of the techniques described in this paper and the earlier paper (Rogers, 1984) is to produce from a class of continuous characters (i.e., allele frequencies) minimum-length phylogenetic trees that have the same parsimony property as the minimum-length trees for discrete characters produced by the character-Wagner method described by Kluge and Farris (1969) and Farris (1970). In the latter method, the length of a tree is the total number of independent origins of (discrete) character states required by the topology of the tree and the character states of the ancestral taxa (interior nodes) of the tree. Since, for any one character state, the number of homoplasious (convergent, parallel) origins is always one less than the total number of independent origins (Fig. la, b), minimizing total tree length for all characters minimizes the total number of homoplasious origins for the whole tree. Thus, the character-Wagner method is a parsimony method; it minimizes the number of ad hoc hypotheses of convergent or parallel evolution (Farris, 1983). Farris (1983) has implied that only those minimum-length methods that employ discrete characters qualify as parsimony methods. I believe that this is too restrictive. For example, two of the hypothetical trees (i.e., c and d) in Figure 1 differ only in the choice of allele-frequency character