A model for the effects of a single gene (SG), background genes (BG), an environmental factor (EF) and the effects of their interactions on quantitative traits is developed. It is a mixed model where SG and EF have fixed effects while BG have a random effect. This model is applied to the analysis of the effects of the dwarfing alleles at the Rht1 locus (SG), interfamily variation (representing BG) and the growth régulant CCC (EF) on coleoptile, leaf and culm length of spring wheat. Culm length of F7 families was tested in a field experiment in the absence of lodging. Coleoptile and leaf lengths of F9 seedlings were examined in a growth room at 18°C. Each family was descended from a single F5 plant, heterozygous at the Rht1 locus. Within each family the homozygous tall (Rht1) and the homozygous semi-dwarf (Rht1) genotypes were identified. Thus, comparing nearly isogenic genotypes within random families in advanced generations enabled the estimation of all the main effects and interactions between SG, BG and EF. The restricted maximum likelihood (REML) method was used in the analysis of variance. In all the three organs CCC caused significant shortening which was somewhat greater in the Rht1 than in the Rht1 genotype and the CCC × Rht1 interaction effect on culm length was significant. Considerable and significant interfamily variation was found for all three characters. A significant CCC × family interaction effect on the length of the first leaf was obtained. This interaction effect was of a specific trend indicating a distinct increase in the response to CCC with greater leaf length. No CCC × Rht1 × family or Rht1 × family interaction effects were detected. The use of two graphical/analytical methods proved to be complementary for a complete evaluation of two-way interactions (CCC × families and CCC × Rht1 in the present study).
Bibliographical noteFunding Information:
work of the senior author supported by a grant from Harry and Lillian Freedman.
- Environmental factor
- Quantitative trait
- Single gene
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