LEVELS OF INTEGRATION IN MAMMALIAN DENTITIONS: AN ANALYSIS OF CORRELATIONS IN NESOPHONTES MICRUS (INSECTIVORA) AND ORYZOMYS COUESI (RODENTIA).

Prominent among the early casualties of 20th century science was the simplistic myth that linked gene to body character by ties of direct and complete causation. This consummation, so devoutly wished by many early Mendelians, yielded to an acknowledgment that the efficient cause of form involved an array of influences both environmental and genetic. Among the methods devised for sorting out such influences, those based on correlation coefficients gained much favor. Early students, including Pearl (1905) and Pearson (1907), compared the raw coefficients directly; later workers devised techniques for manipulating matrices of coefficients to yield simpler patterns (viz. the "path coefficients" of Sewall Wright, 1932). Other techniques, more promising in design but far more laborious in application, required an assist from the computer, our midwife of modern technology, to make the transition from theory to practice. This paper uses two such methods, morphological integration (Olson and Miller, 1958) and factor analysis (Harman, 19,60) to study causal hierarchies implied by the correlation among parts of a particularly favorable system, the mammalian molar dentition. The mammalian dentition is favored for what it does not measure. The erupted molar has no ontogeny, except in so far as the tooth is worn down with use. As an organism grows, most of its parts increase in size. As a consequence of this unenlightening observation, a common size factor so strongly governs the correlation of growing parts that other influences are swampedviz. the exhaustion by a single "growth" or "size" axis of nearly all information in factor analytic studies of ontogenetic development (review in Ouellette and Qadri, 19,66 and Gould, 1966, p. 627). On the other hand, the disposition of teeth as several spatially separate units, increases information by permitting types of independent and correlated variation not found in all systems. In jaws of the same length, the teeth can vary independently or all can increase in area by filling in the spaces between them. This is not possible in jigsaw puzzle systems like the turtle carapace (Mosimann, 1956) and the echinoid test (Raup, 1968). Here correlations are imposed by the mechanics of complete contiguity in restricted spaces. We can arrange the expected influences upon tooth form into the somewhat artificial hierarchy of Sewall Wright (1932). 1) General factors producing correlated variation in all major systems of the body. We speak here of adult variability, not of ontogeny. Larger jaws in larger bodies might tend to bear larger teeth. Olson and Miller (1958, p. 202) write: "It is evident that the sizes of dentitions in general are not unrelated to the size of the organism in which they develop and more specifically to the dimensions of adjacent bones." Tooth and skull measures are significantly correlated in the fox Vulpes vulpes, but not in the bear Ursus arctos (Kurten, 1953, p. 29). Garn et al. (1967) related the degree of tooth size dimorphism in brothersister pairs with the extent of body size differences in Ohio teenagers. 2) Group factors affecting teeth independently of other body systems and affecting several teeth in similar ways. The notion of "morphogenetic fields" belongs to this category. The molarization of pos-