Multivariate Analysis of Hybrid Fishes

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Abstract
Principal components analysis and linear discriminant function analysis were applied to 2 data sets comprised of a sample of laboratory-reared hybrid fish and wild-caught parental samples. For each method, the assumptions required for making statistical inferences and the biological assumptions employed in hybrid studies were reviewed. The degree to which biological data sets can be expected to conform to both types of assumptions is assessed by examination of the 2 data sets discussed. The usefulness of each method for hybrid identification, quantification of hybrid variability and general determination of morphological distance from the suspected parents is evaluated by considering the results of the methods when applied to known hybrids. Evidence is presented for decreased developmental integration in the hybrids. Principal components analysis indicates the difference in the branchial baskets of the very similar Notropis spilopterus and N. whipplei, suggesting an ecological separation related to this morphology. The hybrids of both the Notropis and Lepomis cyanellus .times. L. macrochirus crosses had generally intermediate scores in both analyses, but were not uniformly intermediate, instead graded into the parental phenotypes. In the results of principal components analysis, F1 variability precludes the confident identification of all hybrid individuals and any specific identification of F2 and backcross individuals; the majority of hybrids should be identifiable as being of mixed genetic origin. Principal components analysis is used in the examination of variation in hybrid fishes. Linear discriminant function analysis as it is presently employed does not appear useful for hybrid analysis, for both practical and theoretical reasons. Discriminant function analysis of samples of known hybrid origin may permit subsequent analysis of suspected hybrids.

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