L'Analyse en Composantes Principales: Son Utilisation en Genetique et ses Rapports Avec L'Analyse Discriminatoire

Consider p normally distributed characters measured on individuals divided into genetically determined groups or families. We derive the formulae necessary for the calculation of genetic variances and covariances of the principal components of the phenotypic covariance matrix of the characters, in the case when the individuals are grouped according to a simple parental classification. This calculation, as well as that of the intraclass correlation of a principal component, can be made using estimates of genetic variances and covariances of the characters. Starting from the formula for Mahalanobis' D2, and the general equation |B - kW| = 0, we now indicate how the same method, principal component analysis, can be used to study successfully intra-group and intergroup variability. We show in particular how the canonical variables can be expressed as a function of the principal components of the intra-group covariance matrix.