Rev. BrasiL Genet. 13,3,509-520 (1990) (Brazil. J. Genetics) APPLICATION OF SIZE-FREE CANONICAL DISCRIMINANT ANALYSIS TO STUDIES OF GEOGRAPHIC DIFFERENTIATION Sergio F. dos Reis 1 , Leila M. Pessoa 2 and Richard E. Strauss 3 ABSTRACT Canonical discriminant analysis (CDA) is a multivariate procedure employed in the study of geographic variation, species differentiation, and macroevolution. However, the application of CDA to study organisms where character size-frequency distribution varies within samples due to sampling bias, may result in artifactual discrimination due to shifts in mean character values. In such cases it would be desirable to discriminate among samples that have been corrected for within-group size differences. In this note we illustrate the application of size-free canonical discriminant analysis. In this procedure the effect of size variationwithin groups is removed byregressing each characterseparately on the first pooled within-group principal component, which is an estimate of general size. The application of this procedure is illustrated by a study of geographic differentiation in the echimyid rodent Proechimys dimidiatus. A command file of SAS-PC procedures necessary for the implementation of size-free CDA is also provided. INTRODUcnON Canonical discriminant analysis (CDA) is a multivariate statistical proce- dure employed in evolutionary biology and systematics (Campbell and Atchley, 1981; Neff and Marcus, 1980). CDA is used in studies of geographic differentiation and in the analysis of species differentiation and macroevolution (Thorpe, 1983; Lessa and Patton, 1989; Patton and Smith, 1989). The usefulness of CDA resides in the mathe- 1 Departamento de Parasitologia, Instituto de Biologia, Universidade Estadual de Campinas, Caixa Pos- tal 6109, 13081 Campinas, SP, Brasil. Send correspondence to S.P.R. 2 Departamento de Zoologia, Centro de Ciencias da Saude, Universidade Federal do Rio de Janeiro, 21941 Rio de Janeiro, RJ, Brasil. 3 Departament of Ecology and Evolutionary Biology, University of Arizona, Tucson, Arizona 85721, USA.