三种数学模型模拟不同播期小麦籽粒灌浆过程的比较分析

为比较分析Logistic、Richards和三次多项式（Cubic）3种小麦籽粒灌浆模型的特点，用其分别对4个小麦品种（济麦44、品育8012、周麦36和晋麦84）在4个播期下的籽粒灌浆过程进行拟合。结果表明，不同播期小麦籽粒灌浆过程用三种模型均可拟合，各模型方程的决定系数均在0.98以上，且达极显著水平，Cubic和Richards模型拟合效果优于Logistic模型；通过Cubic模型模拟的灌浆起始期较观测值晚0.58~6.65 d，10月12日播期起始灌浆日期模拟值与观测值最接近；在本试验条件下，Logistic模型可以假定粒重达理论最大粒重的2.76%左右时为灌浆起始期（开花期）；Richard模型中，播期对起始粒重比例（灌浆起始期粒重/理论最大粒重）有显著影响，第一、第二播期（10月12日、10月20日）的超始粒重比例显著低于第三、第四播期（10月28日、11月5日）；三种模型理论最大粒重在品种和播期间的规律与灌浆终止粒重一致；Cubic模型模拟的理论最大粒重与灌浆终止粒重最接近，终止粒重比例（灌浆终止粒重/理论最大粒重）平均值达 97.84%；Logistic与Richards模型中，终止粒重比例随播期的推迟呈增加趋势，Richards模型终止粒重比例在播期间的变异系数大于Logistic和Cubic模型。小麦快增期灌浆参数T₂（快增期持续时间）、T_max（最大灌浆速率出现时间）、V₂（快增期平均灌浆速率）、V_max（最大灌浆速率）在三种模型间存在差异，Richards模型在播期间差异最大（T₂、T_max、V₂、V_max变异系数分别为35.25%、20.43%、11.94%、10.8%），Logistic模型在播期间差异最小（T₂、T_max、V₂、V_max变异系数分别为8.79%、7.59%、3.30%、3.30%）。

Comparison of Three Mathematical Equation for Simulating the Wheat Grain Filling Process with Different Sowing Dates

In order to compare and analyze the characteristics of three wheat grain filling models of Logistic,Richards and Cubic polynomial,the grain filling process of four wheat varieties (Jimai 44,Pinyu 8012,Zhoumai 36 and Jinmai 84) with four sowing dates was simulated. The results showed that the wheat grain filling process can be described by the three equations and the determination coefficients were all greater than 0.98. The fitting effect of Cubic and Richards equation was better than that of Logistic equation. The starting date of filling simulated by the Cubic model was 0.58-6.65 days later than the observed value,and the simulated value of sowing date on October 12 was the closest to the observed value. Under the conditions of this experiment,Logistic model can specify that initial grain filling when the proportion of grain weight reaches about 2.76% of the theoretical maximum grain weight. Sowing date had significant effects on initial grain weight proportion in Richards model,where the first and second sowing dates were significantly lower than the third and fourth sowing dates. The theoretical maximum grain weight of the three models was consistent with the measured value relative to variety and sowing date. The theoretical maximum grain weight of Cubic model was the closest to the measured value,and the final grain weight proportion was 97.84%. In Logistic and Richards models,the final grain weight proportion increased with the delay of sowing date. The coefficient of variation of the final grain weight proportion in Richards model was greater than that of Logistic and Cubic models. There are differences among the three models in wheat filling parameters T₂ (duration of rapid growth period),T_max (occurrence time of maximum filling rate),V₂ (average filling rate of the rapid growth period),and V_max (maximum filling rate). Differences were highest between different sowing dates in Ricgards model and lowest in Logistic model.