Probabilities of negative estimates of genetic variances

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Abstract
The probability of negative analysis of variance estimates of genetic variance components due to sampling error (Ps) was investigated. The objectives were to evaluate the magnitude of Ps, to compare Ps for estimates of σ A 2 and σ D 2 , and to compare Ps for genetic variance component estimates from the nested and factorial mating designs. Ps was defined in terms of ratios of mean squares and the F distribution was used to calculate probabilities of the negative estimates. The results indicated that Ps is often greater than 0.20 for σ D 2 . It is generally lower for σ A 2 than for σ D 2 , and lower for the factorial mating design than the nested mating design.