Obtaining common pruned trees

Abstract

Given two or more dendrograms (rooted tree diagrams) based on the same set of objects, ways are presented of defining and obtaining common pruned trees. Bounds on the size of a largest common pruned tree are introduced, as is a categorization of objects according to whether they belong to all, some, or no largest common pruned trees. Also described is a procedure for regrafting pruned branches, yielding trees for which one can assess the reliability of the depicted relationships. The tree obtained by regrafting branches on to a largest common pruned tree is shown to contain all the classes present in the strict consensus tree. The theory is illustrated by application to two classifications of a set of forty-nine stratigraphical pollen spectra. © 1985 Springer-Verlag New York Inc.