Summary
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 2A and σ 2D , 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 2D . It is generally lower for σ 2A than for σ 2D , and lower for the factorial mating design than the nested mating design.
Similar content being viewed by others
References
Comstock RE, Robinson HF (1948) The components of genetic variance in populations of biparental progenies and their use in estimating the average degree of dominance. Biometrics 4:254–266
Comstock RE, Robinson HF (1952) Estimation of average degree of dominance of genes. In: Gowen JW (ed) Heterosis. Iowa State University Press, Ames, Iowa, pp 494–516
ElRouby MM, Penny LH (1967) Variation and covariation in a high oil population of corn (Zea mays L.) and their implications in selection. Crop Sci 7:216–219
Gill JL, Jensen EL (1968) Probability of obtaining negative estimates of heritability. Biometrics 24:517–526
Hallauer AR, Miranda JB (1981) Quantitative genetics in maize breeding. Iowa State University Press, Ames, Iowa
Hayman BI (1960) Maximum likelihood estimation of genetic components of variation. Biometrics 16:369–381
Leone FC, Nelson LS, Johnson NL, Eisenhart S (1968) Sampling distributions of variance components. 2. Empirical studies of unbalanced nested designs. Technometrics 10:719–738
Lindsey MD, Lonnquist JH, Gardner CO (1962) Estimates of genetic variance in open-pollinated varieties of corn-belt corn. Crop Sci 2:105–108
Robinson HF, Comstock RE, and Harvey PH (1955) Genetic variances in open pollinated varieties of corn. Genetcis 40:45–60
Satterthwaite FE (1946) An approximate distribution of estimates of variance components. Biom Bull 2:110–114
Searle SR (1971) Linear models. Wiley and Sons, New York
Sentz JC (1971) Genetic variances in a synthetic variety of maize estimated by two mating designs. Crop Sci 11:234–238
Williams JC, Penny LH, Sprague GF (1965) Full-sib and halfsib estimates of genetic variance in an open-pollinated variety of corn, Zea mays L. Crop Sci 5:125–129
Author information
Authors and Affiliations
Additional information
Communicated by A. R. Hallauer
Technical Contribution No. 2589 from the South Carolina Agricultural Experiment Station, Clemson University
Rights and permissions
About this article
Cite this article
Bridges, W.C., Knapp, S.J. Probabilities of negative estimates of genetic variances. Theoret. Appl. Genetics 74, 269–274 (1987). https://doi.org/10.1007/BF00289979
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00289979