Use of the Beta function to quantify effects of photoperiod on flowering and leaf number in rice

The time of flowering in rice (Oryza sativa L.) is affected by photoperiod, A nonlinear response has been reported with an optimum photoperiod, either below or above which flowering can be delayed. Three equations which account for both short- and long-day nonlinear effects were compared to describe the response of rice to photoperiod. The Beta model is unique in that it can describe an asymmetric shape of the relation between days to flowering (f) or rate of development to flowering (1/f) and photoperiod (P). The other two models were the quadratic relation between f and P (QFP) and the quadratic relation between the rate, 1/f, and P (QRP). The Beta model accurately described the flowering response to a wide range of photoperiods, and was superior to QFP and QRP in predicting the photoperiod effect on the flowering time as observed in several published data sets involving diverse rice cultivars. To provide the basis for predicting final main-stem leaf number in rice, the relationship between leaf number and photoperiod was studied experimentally for eight cultivars with different photoperiod sensitivities. A new equation for describing this relationship was derived based on the Beta model and a power-law model for rice leaf appearance, The equation adequately described the response of final leaf number to photoperiod in the eight cultivars.