Graph theory, tionary trees and classification

Many methods have been used for analysing information about organisms in order to understand tionary relationships and/or to determine classifications. The reationship between some of these methods is illustrated for the character state matrix, incompatibility and similarity matrices, minimal unrooted and rooted trees, and tionary classifications. Existing methods of determining the shortest possible tree are described. In addition a new method of building a minimal tree is introduced which starts with the largest possible subset (clique) of characters that is compatible for all pairs of characters. The remaining characters are ranked in order of their increasing number of incompatibilities. These characters are added singly, a tree constructed and then tested for minimality by previously described methods for partitioning characters into subsets. The procedure is repeated at least until the tree can no longer be proved minimal. The relationship between trees and tionary and phylogenetic classifications has been neglected but three methods are metioned and a new criterion suggested. It is suggested that graph theory, rather than statistics, is better suited for the primary analysis of comparative data.