Model analysis of genotypic difference in the variation of the duration from heading to flower opening based on the flower position on a panicle in high-yielding rice cultivars

There is a large variation in the number of days from heading to flower opening among flowers attached to a single panicle in rice (Oryza sativa L.). However, the details of order and timing of flower opening among flowers and the differences between genotypes in the variation have not been well described. In the present study, we developed a mathematical model to characterize the differences between genotypes in the relationship between the relative position of the flowers on a panicle and the number of days to their openings after heading, using three high-yielding rice cultivars, Tequing, Hokuriku 193, and Momiroman. Our model used the standardized panicle structure: each flower position was scaled based on the number of primary branches, the number of secondary branches on a primary branch, and the number of flowers on a branch. The parameters provided by the model described the variation of the number of days from heading to flower opening for each flower attached to different position on a panicle in each cultivar, so that the parameters could describe the genotypic difference in the variation. Generally, the model analyses showed that the primary branch had a greater effect on the number of days from heading to flower opening than the secondary branch within a primary branch and the position of the flowers within a secondary branch. In term of the genotypic difference among the examined cultivars, Momiroman took more 3–5 days to complete opening of all the flowers on a panicle after heading than the other cultivars. The model analyses showed that the longer duration in Momiroman was caused by the larger difference in days to flower opening among flowers on a single secondary branch and the two-days longer lag until the flowers started opening after heading. Our analyses also suggested that the genotypic difference in the number of branches did not affect the genotypic difference in duration from heading to flower opening among the cultivars examined here. We discussed the application of this model to understand genotypic differences in the relationship between the time required for flower opening and final grain weight.