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

Abstract

The use of electrophoretic data in fisheries research is generally based upon the assumption that isozyme variability reflects genetic variability. This assumption is often based mainly upon nonsignificant χ2 values obtained when observed distributions of phenotypes are compared to those predicted by given genetic models with alleles segregating in Hardy–Weinberg equilibrium. We examine the power of such a χ2 test of a single-locus, two-allele genetic model against three alternative hypotheses: random phenotypic variation, secondary isozyme formation, and the segregation of a third, 'silent' allele. The power of this test is found to be very low, particularly as it is typically applied with small sample sizes [Formula: see text], 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 χ2 value is obtained. The dangers of β error are illustrated with examples, and methods for reducing β to acceptable levels are described.Key words: χ2, power, β, Hardy–Weinberg, isozyme, biochemical genetics, fish