Lark Richard M, Gillingham Vincent, Langton David, Marchant Ben P
School of Biosciences University of Nottingham Nottingham UK.
AgSpace Agriculture Ltd. Dorcan Business Village Swindon UK.
Eur J Soil Sci. 2020 May;71(3):334-351. doi: 10.1111/ejss.12891. Epub 2019 Nov 15.
In boundary line analysis a biological response (e.g., crop yield) is assumed to be a function of a variable (e.g., soil nutrient concentration), which limits the response in only some subset of observations because other limiting factors also apply. The response function is therefore expressed by an upper boundary of the plot of the response against the variable. This model has been used in various branches of soil science. In this paper we apply it to the analysis of some large datasets, originating from commercial farms in England and Wales, on the recorded yield of wheat and measured concentrations of soil nutrients in within-field soil management zones. We considered boundary line models for the effects of potassium (K), phosphorus (P) and magnesium (Mg) on yield, comparing the model with a simple bivariate normal distribution or a bivariate normal censored at a constant maximum yield. We were able to show, using likelihood-based methods, that the boundary line model was preferable in most cases. The boundary line model suggested that the standard RB209 soil nutrient index values (Agriculture and Horticulture Development Board, nutrient management guide (RB209), 2017) are robust and apply at the within-field scale. However, there was evidence that wheat yield could respond to additional Mg at concentrations above index 0, contrary to RB209 guidelines. Furthermore, there was evidence that the boundary line model for yield and P differs between soils at different pH and depth intervals, suggesting that shallow soils with larger pH require a larger target P index than others.
Boundary line analysis is one way to examine how soil variables influence crop yield in large datasets.We showed that boundary line models could be applied to large datasets on soil nutrients and crop yield.The resulting models are consistent with current practice for P and K, but not for Mg.Models suggest that more refined recommendations for P requirement could be based on soil pH and depth.
在边界线分析中，生物响应（如作物产量）被假定为一个变量（如土壤养分浓度）的函数，由于还存在其他限制因素，该变量仅在部分观测值中限制响应。因此，响应函数由响应相对于该变量的绘图的上边界表示。该模型已应用于土壤科学的各个分支。在本文中，我们将其应用于对一些大型数据集的分析，这些数据集来自英格兰和威尔士的商业农场，涉及田间土壤管理区内小麦的记录产量和测量的土壤养分浓度。我们考虑了钾（K）、磷（P）和镁（Mg）对产量影响的边界线模型，并将该模型与简单的二元正态分布或在恒定最大产量处进行删失的二元正态分布进行比较。我们能够使用基于似然的方法表明，在大多数情况下边界线模型更可取。边界线模型表明，标准的RB209土壤养分指数值（农业和园艺发展委员会，养分管理指南（RB209），2017年）是稳健的，并且适用于田间尺度。然而，有证据表明，与RB209指南相反，当镁浓度高于指数0时，小麦产量可能会对额外的镁作出响应。此外，有证据表明，不同pH值和深度区间的土壤中，产量与磷的边界线模型存在差异，这表明pH值较大的浅层土壤比其他土壤需要更高的目标磷指数。
边界线分析是检验土壤变量如何影响大型数据集中作物产量的一种方法。我们表明，边界线模型可应用于关于土壤养分和作物产量的大型数据集。所得模型与当前关于磷和钾的实践一致，但与镁的实践不一致。模型表明，可以根据土壤pH值和深度对磷需求提出更精确的建议。
