Ontogenic and interspecific skeletal allometry in nonhuman primates: bivariate versus multivariate analysis

The critical problem confronting all allometric studies is the choice of an appropriate size variable, especially when body mass or some other measure of total size is unavailable. A method proposed by Jolicoeur (1963a,b) claims to generate an internal size variable by a principal components analysis of the covariance matrix of logarithmically transformed data, from which allometric coefficients can be computed. Despite the current popularity of this method, the precise relationship and degree of campatibility between such multivariate coefficients and the exponent of the bivariate power function (Y = βX(α)) is unknown. This study evaluates the comparability and interpretability of allometric values computed by Jolicoeur's procedure and by standard bivariate regressions (least squares and major axis). Two primate data sets with known measures of size were utilized for these purposes: Longitudinal growth data from radiographs of two species of capuchin monkeys, Cebus apella and Cebus albifrons; and interspecific osteometric data from a series of adult lemurs, species of prosimians from Madagascar. Consistent differences exist between multivariate and bivariate allometric coefficients for both ontogenetic and static data sets. Multivariate analysis underestimated the coefficients in the formed and overestimated them in the latter. The internal size variable generated by principal components analysis is clearly not equivalent to, and hence not a suitable substitute for, known measures of size. Moreover, multivariate coefficients are very sensitive to the composition of variables in a given data set; α values of a variable changed appreciably depending on the other variables included in the analysis. The multivariate coefficients are also sample-specific, and provide misleading biological information when compared between samples (e.g., between species of capuchin monkey). For allometric investigations designed to evaluate scalling paremeters relative to total size, alternative analytical solutions to the Jolicoeur method should be considered.