Euphytica

, Volume 26, Issue 3, pp 537–551

A general method for the analysis of genetic variation in complete and incomplete diallels and North Carolina II designs. Part I: Procedures and general formulas for the random model

  • M. Keuls
  • Frida Garretsen
Article

Summary

In two papers formulas are given which can be used in analysing genetic variation in all types of connected diallel cross designs: complete and incomplete, balanced and unbalanced as well as North Carolina II designs.

This first paper gives explicit expressions for the coefficients of variance components in the random model analysis for the general diallel cross.

Computations are illustrated with simple balanced examples. For the same examples a fixed model analysis, introducing reduced parameters has been worked out for the sake of completeness. The details of the fixed model analysis will be presented in the second paper.

Index words

Diallel cross incomplete diallel cross 

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References

  1. England F., 1974. A general approximate method for fitting additive and specific combining abilities to the diallel cross with unequal numbers of observations in the cells. Theoretical and Applied Genetics 44: 378–380.CrossRefGoogle Scholar
  2. Garretsen. F. & M. Keuls, 1973. Analysis of genetic variation in an incomplete diallel cross. Proc. of the first meeting of the section Biometrics in Plant Breeding of Eucarpia. Hanover 1973. 24–35.Google Scholar
  3. Griffing B., 1956. Concept of general and specific combining ability in relation to diallel crossing systems. Australian Journal of Biological Sciences 9: 463–493.Google Scholar
  4. Rao J. K. N., 1968. On expectations, variances and covariances of Anova mean squares by ‘synthesis’. Biometrics 24: 963–978.Google Scholar
  5. Schaffer H. E. & R. A. Usanis, 1969. General least squares analysis of diallel experiments. A computer program-DIALL. Genetics Department Research Report Number 1 North Carolina State University Raleigh, North Carolina 27607, May 1969.Google Scholar
  6. Searle S. R., 1971. Topics in variance component estimation. Biometrics 27: 1–76.Google Scholar

Copyright information

© H. Veenman en Zonen B.V. 1977

Authors and Affiliations

  • M. Keuls
    • 1
  • Frida Garretsen
    • 2
  1. 1.Department of MathematicsAgricultural UniversityWageningenthe Netherlands
  2. 2.Institute for Horticultural Plant Breeding (IVT)Wageningenthe Netherlands

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