Construction and application of dynamic tillering model for rice population

Here a dynamic model was developed on the tiller number of the rice population. The double Logistic model was also used to quantitatively analyze the dynamic process of the tiller occurrence and the extinction. A set of indicators was defined to describe the tillering dynamics, including the total number of growing tillers(N_g), the total number of dead tillers(N_d), the number of retained tillers(N_r), the start time of tillering(T_st), the peak time of tillering(T_pt), the end time of tillering(T_et), the start time of tillers death(T_sd), the peak time of tillers death(T_pd), the end time of tillers death(T_ed), the duration of tillering(D_t), the duration of tillers death(D_d), the inherent rate of tillering(R_it), the inherent rate of tillers death(R_id), the maximum tillering rate(R_mt), the maximum tillers death rate(R_md). According to the temporal characteristics of the rice tillering, the formula was derived to calculate the indicators of the tillering dynamics. The goodness and adaptability of the model were tested with the dynamic datasets of the rice tillers under different genotypes, transplanting, sowing time, and transplanting density. The model and the indicators were used to explore the dynamic tillering response to the cultivation density. The results were as follows. (1) The model shared the better fitting for the dynamic dataset of rice tillers under different genotypes, transplanting, planting time, and transplanting density. The standard root mean square error (S_RMSE) was followed by the Gamma distribution with the mean was less than 5% and 99% S_RMSE less than 10%. (2) The dynamic indicators and model parameters of tillers after calculation showed a better response to the cultivation density. Taking the planting density test of Huiliangyou 898 as an example, the number of tillers per unit area was accelerated and then slowed down after transplanting at 15 to 33.75 hills/m^2. The number of tillers per unit area reached the peak at 45-50 d after transplanting. After the peak, the number of tillers per unit area decreased rapidly and then slowed down slowly. There was no change in the number of tillers per unit area about 70 d after transplanting. T_pt and T_pd were about (26±3) d and (54±3) d after transplantation, respectively. An outstanding trend was achieved in the response of the tillering characteristic index to planting density. Except for T_pt and T_sd, the tillering characteristic index followed the power function. N_g, R_it, N_r, T_ed, D_d, R_mt, and R_md showed a power function increase with the increase of planting density, and the exponent of the power function was less than 1, indicating the slow-down trend. T_pt, R_id, T_st, T_et, and D_t also decreased as a power function with the increase of planting density. The exponent of the power function was greater than -1, that is, the decreasing rate gradually decreased with the increase in planting density. N_d increased as a power function with the increase of planting density, where the exponent of the power function was greater than 1, indicating the accelerated increase. T_pd and T_sd decreased with the increase of planting density and then increased gradually after reaching the minimum. (3) A better prediction was achieved, where the R² between the observed and simulated values were 0.96. Therefore, the model can accurately describe the evolution in the number of rice tillers, indicating the better goodness of fitting, adaptability, and interpretability. The model can be applied to the dynamic regularity of the tiller number under the genotypic varieties and the agronomic measures. The tillering dynamic indicators can be expected to serve as the important phenotype in the interaction between genes and environments.