Modal Blocks in Dentition of West Coast Mammals

The dentitions of West Coast North American mammals, from Ingles (1965), are given in Table 1. A casual survey reveals distinctive patterns characterizing the various groups. For example, the Rodentia are characterized by reduced numbers of incisors, canines and premolars; the carnivores with some exceptions by increased numbers of premolars and reduced number of molars. The data will be considered in data matrix form with the rows corresponding to species and the columns to types of teeth. A block (or cluster) is a submatrix of the data in which all values within each column of the submatrix are equal, except for values lying within a subblock of the block. Many submatrices conform to this definition, for example the set of mammals with 3 top molars, or the set with 1 top canine. Selection of just a few blocks to accurately represent the data is performed by finding in succession the patterns of teeth which occur most frequently, ignoring those patterns, found in previous steps. This technique is called the modal block method. The modal block method is designed for categorical data; a different technique for continuous data was proposed in Hartigan (1972) and a number of block clustering algorithms are proposed in Hartigan (1975). For the dentition data, seven clusters of species are generated, with their characteristic patterns of dentition. The first of these clusters is a distinct one, consisting of RODENTIA and LAGOMORPHA characterized by reduced counts in other than molar teeth. There are two clusters of CARNIVORA and three clusters of CHIROPTERA, and a small cluster of ARTIODACTYLA. Some overlapping