玉米3个密度试验结果数学模型的构建

Study on Mathematic Model of Three Density Test Results of Maize

比较不同数学模型在3个密度试验结果上适用性,寻求玉米产量-密度的最优模型,为深入挖掘3密度试验信息提供理论依据。数据集包括3个密度89个数据集和4个密度128个数据集,均来自中国1950s至2000s六个年代间的玉米密度试验。通过省略次高或者次低密度的方法从4个密度数据集中导出两组3密度伪数据集。拟合的2参数——模型分别为无常数抛物线(PM2)和无常数指数乘积型(EPM2)。对于真数据集,以模型是否存在极大值、参数的统计显著性、理论适宜密度是否越界进行逐级筛选淘汰。最终按照AIC准则决选最优模型。对于伪数据集,则分别比较PM2和EPM2与真数据集最优模型的相似程度,相似性大者获胜。在3个密度的真数据集中,符合AIC准则的PM2数据集最多有32个,比EPM2多21个。能够获得最优模型的数据集数目远小于数据集总数目的原因是理论最适密度越界。在3个密度的伪数据集中,PM2的试验最适密度、最高产量分别与真数据集最优模型的差异均最小。玉米3个密度处理试验数据集可以拟合数学模型,且最优模型是PM2,其次为EPM2。这些结果对于深入挖掘利用玉米3个密度试验结果的价值具有一定参考价值。

The applicability of different mathematic models on the results of three density experiments was com- pared to find the optimal model of maize yield--density, which provided the theoretical basis for further exca- vation of 3--density test information. The data sets consisted of 89 data sets with 3 densities and 128 datasets with 4 densities, all from the maize density experiments in China from 1950 s to 2000 s. Two sets of 3- density pseudo--data sets were derived from the four density data sets by omitting the second--highest or second-- lowest density method. The fitted two -- parameter model is parabola （PM2） and non -- constant exponential product （EPM2）. For the real data sets, whether the model exists the maximum value, the statistical signifi- cance of the parameters, the theory is suitable for the density of cross--border screening step by step out. Fi- nally, the optimal model is selected according to the AIC criterion. For the pseudo--data set, the similarity be- tween PM2 and EPM2 is compared with that of the true dataset. There are32 PM2 datasets with AIC criteri- on, 21 more than EPM2. The reason that the number of datasets that can obtain the optimal model is far less than the total number of datasets is that the theoretical optimal density is out of bounds. In the pseudo--data set with 3 densities, the difference between the optimum density and the maximum yield of PM2 was the least. Maize 3 density treatment test data set can fit the mathematical model, and the optimal model is PM2, followed by EPM2. These results have a certain reference value for the deep excavation of maize 3 density test results.