Analysis and Interpretation of the Variety Cross Diallel and Related Populations

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Abstract
A model has been presented for the estimation of genetic effects from the diallel cross and related populations of a fixed set of random-mating varieties with arbitrary gene frequencies at all loci assuming diploid inheritance, 2 alleles per locus and no epistasis. These parameters are defined as functions of the gene frequencies and additive and dominance effects for individual loci. An analysis of variance and appropriate F-tests are provided for the type of gene effects involved. Deviations from the model provide a test for epistasis and linkage. Data from 6 maize varieties and their crosses were analyzed using a modification of the basic model to illustrate the estimation of constants, the analysis of variance, and the predictive value of the model. Use of the model in choosing parents for a reciprocal recurrent selection breeding program is illustrated. When parents are homozygous lines and only the diallel cross is considered, the model reduces to Hayman''s model, but he does not discuss the problem when the parent must be considered a fixed set and he does not consider the genetics of random-mating parents. He does indicate parameters such as those which shed light on inbreeding depression and heterosis but only with respect to homozygous parents.