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Application of size-free canonical discriminant analysis to studies of geographic differentiation

Sérgio F. dos Reis^I; Leila M. Pessôa^II; Richard E. Straus^III

^IDepartamento de Parasitologia, Instituto de Biologia, Universidade Estadual de Campinas, Caixa Postal 6109, 13081 Campinas, SP, Brasil. Send correspondence to S.F.R.
^IIDepartamento de Zoologia, Centro de Ciências da Saúde, Universidade Federal do Rio de Janeiro, 21941 Rio de Janeiro, RJ, Brasil
^IIIDepartament of Ecology and Evolutionary Biology, University of Arizona, Tucson, Arizona 85721, USA

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 variation within groups is removed by regressing each character separately 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.

Keywords: Size-free canonical discriminant; Geographic differentiation.

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