Testing Genetic Models of Isozyme Variability Without Breeding Data: Can we Depend on the χ2?

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Abstract
The use of electrophoretic data in fisheries research [with fish] is generally based upon the assumption that isozyme variability reflects genetic variability. This assumption is often based mainly upon nonsignificant .chi.2 [chi-square] values obtained when observed distributions of phenotypes are compared to those predicted by given genetic models with alleles segregating in Hardy-Weinberg equilibrium. The power of such a .chi.2 test of a single-locus, 2 allele genetic model against 3 alternative hypotheses: random phenotypic variation, secondary isozyme formation and the segregation of a 3rd, silent allele was discussed. The power of this test is very low, particularly as it is typically applied with small sample sizes (.mchlt. 200), few phenotypic classes, and a broad acceptance region. The effective power of the test is further reduced by the reluctance of researchers to reject their genetic models even when a significant .chi.2 value is obtained. The dangers of a .beta. error are illustrated with examples, and methods for reducing .beta. to acceptable levels are described.
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