On Comparing the Shapes of Taxonomic Trees

Farris, J. S. (Dept. of Ecology and Evolution, State University of New York, Stony Brook, New York 11790) 1973. On comparing the shapes of taxonomic trees. Syst. Zool. 22:50–54.—A hierarchic clustering, or tree, of several objects can be described by an object × object matrix, whose elements are the number of nodes of the tree lying on the path connecting a pair of objects. It has been suggested that two trees for the same objects might be compared by calculating a coefficient of similarity or difference between the corresponding matrices. This approach has the drawbacks that heterogeneities in the degree of disagreement of the trees with respect to individual clusters cannot be taken into account and that the bounds of the similarity/difference coefficient are difficult to calculate. To avoid these difficulties, a new method, the cluster distortion method, is introduced. This method operates by counting the number of fragments into which the clusters of one tree are broken on another tree, and permits the user considerable flexibility in summarizing the extent and nature of the disagreement between two trees.