二元非结构肥效模型构建及其田间试验验证

Binary Non-structural Fertilizer Response Model and Its Validaiton via Field Experiment

二次多项式肥效模型假设单位养分增产量与施肥量之间为线性模型,结果导致最高施肥量之前和最高施肥量之后的施肥效应是对称关系。这种模型设定偏误以及模型存在的强烈多重共线性和异方差是建模成功率明显偏低的重要原因。本研究研发二元非结构肥效模型,旨在提高二元肥效模型的适用性。在一元非结构肥效模型基础上,根据植物营养元素功能不可相互替代原理,构建二元非结构肥效模型,并通过氮、磷、钾二元组合的田间肥效试验结果检验新模型的拟合效果和推荐施肥量的可靠性。结果表明,在水稻、花生、马铃薯、毛豆、冬小麦和夏玉米的17个氮磷、氮钾、磷钾二因素肥效田间试验结果中,二元二次多项式肥效模型均能通过统计显著性检验,但典型肥效模型仅占试验点总数的58.8%,模型一次项系数或二次项系数代数符号不合理以及推荐施肥量属于外推的非典型式占41.2%。基于二元非结构肥效模型拟合上述试验结果,同样均能通过统计显著性检验,典型肥效模型的比例占试验点总数的88.2%,非典型式模型(均属于推荐施肥量外推)比例仅占11.8%,建模成功率较二元二次多项式肥效模型提高了29.4个百分点。两种模型的最高产量施肥量之间、经济产量施肥量之间存在显著的线性正相关,但线性回归方程的一次项系数分别仅有0.9153和0.9161,表明当二元二次多项式模型推荐的最高施肥量或经济施肥量每增加1 kg时,二元非结构肥效模型的相应推荐施肥分别仅增加0.915 3 kg和0.916 1 kg,较好地克服了二次多项式模型推荐施肥量偏高的问题。分析表明,二元二次多项式肥效模型是二元非结构肥效模型的简化式和特例,新模型具有更广的适用范围。

【Objective】The binary quadratic polynomial fertilizer response model is set up on the assumption that crop yield increment per unit of nutrient is linearly related to fertilizer application rate,thus leading to a symmetric relationship in crop response to fertilization between before the maximum application rate and after the maximum application rate of fertilizer is applied.This model obviously tends to be low in modeling success ratio mainly because of its set biased error and existence of multicollinearity and heteroscedasticity.This study has developed a binary non-structural fertilizer response model,which is designed to have better applicability.【Method】On the basis of the unary non-structured fertilizer response model and the principle that the functions of plant nutrient elements cannot be replaced by each other,a binary non-structural fertilizer response model is constructed.Its fitting effect and its reliability in recommendation of fertilization rates is verified via NPK binary combination field experiments on crop response.【Result】The model is OKed through all the statistical significance tests in all the 17 field experiments on crop response of rice,peanut,potato,edamame,winter wheat and summer maize,but only 58.8%of the total test sites showed typical crop responses,and 41.2%did non-typical ones with irrational algebetic symbols of monomial or quadratic term coefficient in model and extrapolated fertilizer recommendation.Fitting tests of the model demonstrate that it has been OKed through all the statistical significance tests,with 88.2%of the test sites showing typical crop responses,and only 11.8%non-typical ones,all of the type of extrapolated recommendation,which demonstrates that the new model has improved in modeling success rate by 29.4%as compared with the binary quadratic polynomial fertilizer response model.Both models show significant linear positive relationships between maximum fertilization rate for highest crop yield and economic fertilization rate for highest crop yield,but the first term coefficient of the linear regression equation is 0.915 3 and 0.916 1,only,which means that for the increment of each kg of fertilizer recommended by the binary quadratic polynomial fertilizer response model only 0.915 3 kg and 0.916 1 kg is recommended by the new model.The new model has fairly well overcome the problem of the quadratic polynomial model’s recommendation tending to be higher.【Conclusion】All the analyses indicate that the binary quadratic polynomial fertilizer response model is a simple and specific one of the binary non-structural fertilizer response model.The new model has a wider range of applications.