Evaluating Undirected Positional Congruence of Individual Taxa Between Two Estimates of the Phylogenetic Tree for a Group of Taxa

?The method of Estabrook, McMorris, and Meacham (1985, Syst. Zool. 34:193-200) to measure the similarity of two phylogenetic trees for the same collection of evolutionary units (EUs) has been generalized to include an evaluation of the similarity of the placement of in? dividual EUs. These measures do not vary when the direction of evolutionary change along the individual branches is changed in either of the two trees being compared. Thus, these measures depend only on the convexity of various groups of EUs on the two trees. These measures are also applicable to phylogenetic trees that are only partially resolved. These concepts are illus? trated with previously published pairs of estimates of the phylogenetic tree for genera of rodents and for genera of ducks. [Congruence; undirected; phylogenetic tree; consensus index.] For the past two decades, there has been great interest in comparing two or more estimates of the phylogenetic tree for a group, S, of evolutionary units (EUs). One approach has been to determine a single "consensus" tree that somehow summariz? es the trees being compared (Adams, 1972; Margush and McMorris, 1981; Neumann, 1983; Stinebrickner, 1984). Other workers have attempted to mea? sure the similarity of two trees for the same study collection of EUs. This approach pro? duces a consensus index, not a consensus tree. Early consideration of the measure? ment of tree similarity was made by Sneath (1966), who used the cophenetic correla? tion coefficient (Sokal and Rohlf, 1962) to compare pairs of random trees. Robinson and Foulds (1981) proposed a partition metric to compare trees. Williams and Clif? ford (1971) and Rohlf (1982) applied con? sensus index concepts to classifications. Shao and Sokal (1986) and Lapointe and Legendre (1990) proposed statistical tests of consensus indices. For each of several groups of taxa for which a pair of estimates of their phylo? genetic tree has been published, Bledsoe and Raikow (1990) used a variety of meth? ods to compare the two members of each of these pairs with each other. One of the methods they used was that of Estabrook et al. (1985), which eliminates any differences due solely to direction of evolution? ary change along the branches of the es? timated trees. Although this and the other methods compare whole trees, discussion by these authors usually addressed the placement of individual EUs in the two trees being compared. They pointed out that the topological relationships with the other EUs were more different between the two trees for some EUs than for others. Quantification of how different the topo? logical relations of a given EU with the other EUs in one tree are compared with those relations in the other tree would be useful. Some EUs could be quantitatively recognized as placed in a similar evolu? ionary context by different data sets or by different inferential methods, whereas the placement of other EUs would be more de? pendent on data or methods used to esti? mate the trees. Here I describe and illus? trate a quantitative measure of positional congruence of individual EUs when two estimates of the phylogenetic tree of a group of taxa have been made. In the fol? lowing discussion, a tree will mean an es? timate of the branching pattern and direc? tion of evolutionary change along the branches of the phylogenetic tree for the study group, S, and an undirected tree will mean an estimate of the branching pattern only. These estimates need not be fully re? solved, i.e., there may be more than three