Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-26T15:11:02.041Z Has data issue: false hasContentIssue false
  • English
  • Français

Mixed model approaches for diallel analysis based on a bio-model

Published online by Cambridge University Press:  14 April 2009

Jun Zhu  and
Bruce S. Weir
Jun Zhu
Affiliation:
Department of Agronomy, Zhejiang Agricultural University, Hangzhou, Zhejiang, China
Bruce S. Weir*
Affiliation:
Program in Statistical Genetics, Department of Statistics, North Carolina State University, Raleigh, NC 27695-8203, USA
*
* Corresponding author.
Rights & Permissions [Opens in a new window]

Summary

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A MINQUE(l) procedure, which is minimum norm quadratic unbiased estimation (MINQUE) method with 1 for all the prior values, is suggested for estimating variance and covariance components in a bio-model for diallel crosses. Unbiasedness and efficiency of estimation were compared for MINQUE(l), restricted maximum likelihood (REML) and MINQUE(θ) which has parameter values for the prior values. MINQUE(l) is almost as efficient as MINQUE(θ) for unbiased estimation of genetic variance and covariance components. The bio-model is efficient and robust for estimating variance and covariance components for maternal and paternal effects as well as for nuclear effects. A procedure of adjusted unbiased prediction (AUP) is proposed for predicting random genetic effects in the bio-model. The jack-knife procedure is suggested for estimation of sampling variances of estimated variance and covariance components and of predicted genetic effects. Worked examples are given for estimation of variance and covariance components and for prediction of genetic merits.

Type
Research Article
Information
Genetics Research , Volume 68 , Issue 3 , December 1996 , pp. 233 - 240
Copyright
Copyright © Cambridge University Press 1996

References

Cockerham, C. C., (1963). Estimation of genetic variances. In Statistical Genetics and Plant Breeding (ed. Hanson, W. D. & Robinson, H. F.), publication 982, pp. 53–94. Washington, DC: National Academy of Sciences/National Research Council.Google Scholar
Cockerham, C. C., & Weir, B. S., (1977). Quadratic analyses of reciprocal crosses. Biometrics 33, 187–203.CrossRefGoogle ScholarPubMed
Cockerham, C. C., & Weir, B. S., (1984). Covariances of relatives stemming from a population undergoing mixed self and random mating. Biometrics 40, 157–164.CrossRefGoogle ScholarPubMed
Comstock, R. E., & Robinson, H. F., (1952). Estimation of average dominance of genes. In Heterosis (ed. Gowan, J. W.), pp. 494–516. Ames, Iowa: Iowa State University Press.Google Scholar
Corbeil, R. R., & Searle, S. R., (1976). Restricted maximum likelihood (REML) estimation of variance components in the mixed model. Technometrics 18, 31–38.CrossRefGoogle Scholar
Efron, B., (1982). The Jackknife, the Bootstrap and Other Resampling Plans. Philadelphia: Society for Industrial and Applied Mathematics.CrossRefGoogle Scholar
Gardner, C. O. & Eberhart, S.A. (1966). Analysis and interpretation of the variety cross diallel and related populations. Biometrics 22, 439–452.CrossRefGoogle ScholarPubMed
Giesbrecht, F. G., (1985). MIXMOD: a SAS procedure for analyzing mixed models. Mimeo series no. 1659. Raleigh, NC: Institute of Statistics, North Carolina State University.Google Scholar
Griffing, B., (1956). Concept of general and specific combining ability in relation to diallel crossing systems. Australian Journal of Biological Sciences 9, 463–493.CrossRefGoogle Scholar
Hallauer, A. R., & Miranda, J. B., (1981). Quantitative Genetics in Maize Breeding. Ames, Iowa: Iowa State University Press.Google Scholar
Hayman, B. I., (1954). The theory and analysis of diallel crosses. Genetics 39, 789–809.CrossRefGoogle ScholarPubMed
Henderson, C. R., (1963). Selection index and expected genetic advance. In Statistical Genetics and Plant Breeding (ed. Hanson, W. D. & Robinson, H. F.), publication 982, pp. 141–163. Washington, DC: National Academy of Sciences/National Research Council.Google Scholar
Henderson, C. R., (1979). Using estimates in predictions of breeding values under a selection model. In Variance Components and Animal Breeding (ed. Van, L. D. Vleck & Searle, S. R.), pp. 217–227. Ithaca, NY: Cornell University.Google Scholar
Kackar, R. N., & Harville, D. A., (1984). Approximations for standard errors of estimators of fixed and random effects in mixed linear models. Journal of the American Statistical Association 79, 853–862.Google Scholar
Kinderman, A. J., & Monahan, J. F., (1977). Computer generation of random variables using the ratio of normal deviates. Association for Computing Machinery Transactions on Mathematical Software 3, 257–260.CrossRefGoogle Scholar
Matzinger, D. F., & Kempthorne, O., (1956). The modified diallel table with partial inbreeding and interactions with environment. Genetics 41, 822–833.CrossRefGoogle ScholarPubMed
Miller, R. G., (1974). The jackknife: a review. Biometrika, 61, 1–15.Google Scholar
Patterson, H. D., & Thompson, R., (1971). Recovery of inter-block information when block sizes are unequal. Biometrika 58, 545–554.CrossRefGoogle Scholar
Rao, C. R., (1970). Estimation of heteroscedastic variances in linear models. Journal of the American Statistical Association 65, 161–172.CrossRefGoogle Scholar
Rao, C. R., (1971). Estimation of variance and covariance components: MINQUE theory. Journal of Multivariate Analysis 1, 257–275.CrossRefGoogle Scholar
Rao, C. R., (1972). Estimation of variance and covariance components in linear models. Journal of the American Statistical Association 67, 112–115.CrossRefGoogle Scholar
Rao, C. R., & Kleffe, J., (1980). Estimation of variance components. In Handbook of Statistics, Vol. 1 (ed. Krishnaiah, P. R.), pp. 1–40. New York: North-Holland.Google Scholar
Searle, S. R., Casella, G., & McCulloch, C. E., (1992). Variance Components. New York: Wiley.CrossRefGoogle Scholar
Yates, F., (1947). Analysis of data from all possible reciprocal crosses between a set of parental lines. Heredity 1, 287–301.CrossRefGoogle Scholar
Zhu, J., (1989). Estimation of genetic variance components in the general mixed model. PhD dissertation, North Carolina State University, Raleigh, NC.Google Scholar