Distance Methods and the Approximation of Most-Parsimonious Trees

Distance data have posed a number of problems for phylogenetic analysis. Among these are the loss of information about individual character states, and the frequent departures from metric properties of distance matrices derived by molecular techniques. The common degree-of-fit methods for the analysis of such data imply possibly unrealistic assumptions about these distances. As an alternative, a minimum-length criterion is considered. This has the appeal of requiring more conservative assumptions about distance data and represents the equivalent criterion to that for the analysis of character data by numerical cladistic techniques. Based upon its similarity to the character-Wagner algorithm, the distance-Wagner algorithm is suggested as a possible heuristic method for the approximation of most-parsimonious trees from distance data. Both the distance-Wagner algorithm and a recent modification have weaknesses in this role. Computer simulations demonstrate that the new algorithm developed in this study com- pares favorably with not only the distance-Wagner algorithm but also the character-Wagner algorithm in the approximation of most-parsimonious trees. (Metric; molecular distances; Wag- ner algorithm; parsimony; cladistics; immunological distance.) Among current methods for the infer- ence of phylogenetic trees, those relying on the use of character data seem to con- trast increasingly with those methods being developed that depend only upon the analysis of a matrix of pairwise dis- tances among taxa. The contrast is not only in terms of the mathematics of the respec- tive algorithms, but also apparently in terms of the goal of the analysis; what is being optimized may be quite different in the two cases. In the first case, for char- acter data, an approximation to a phylo- genetic tree is usually derived by the ap- plication of some form of a parsimony criterion (for a recent review of parsimony methods see Felsenstein, 1982). For ex- ample, the character-Wagner algorithm of Farris (1970) is used to approximate an overall most-parsimonious tree (Wagner tree) by a sequence of individually most- parsimonious additions of taxa to the tree or network. The best approximation is equivalent to the tree that has minimum length. This length is computed using a Manhattan-metric measure based upon the character data. The second group of methods, using