Abstract
An analysis based on Elston's model of mixed major locus and polygenic inheritance is extended to include populations of progeny testing such as F3, B1s and B2s families derived from F2 and backcrosses in a cross between two inbred lines. Genetic hypotheses that can be validly tested by the likelihood ratio method in the analysis of a breeding experiment include homogeneity of variances due to environment and/or polygenes with transformable scale effect by Box-Cox power function, random and independent segregation of major genes, invariance of the effects of major genes with population types and additive and dominant models for polygenes. Testing hypotheses in the order suggested here can lead to a gradual simplification of the models and increases the feasibility of the subsequent analysis, but caution must be paid to the possible bias in parameter estimation and hypotheses tests. The procedure is applied to a set of data on plant height of rice with the effects of dwarf genes in crosses among three varieties. Two recessive dwarf genes are shown to be nonallelic and unlinked. One dwarf gene is shown to reduce plant height about 36-56 cm, and another 52-61 cm. The effect of polygenes, estimated as the standard deviation among possible inbred lines derived from these crosses, is about 11.7 cm. Interactions between the dwarf genes and the polygenic background are found, especially for one of the two genes. Both the polygenic effects and the interactions are much smaller than the effects of the major dwarf genes.