Summary Weeds tend to aggregate in patches within fields, and there is evidence that this is partly owing to variation in soil properties. Because the processes driving soil heterogeneity operate at various scales, the strength of the relations between soil properties and weed density would also be expected to be scale‐dependent. Quantifying these effects of scale on weed patch dynamics is essential to guide the design of discrete sampling protocols for mapping weed distribution. We developed a general method that uses novel within‐field nested sampling and residual maximum‐likelihood (reml) estimation to explore scale‐dependent relations between weeds and soil properties. We validated the method using a case study of Alopecurus myosuroides in winter wheat. Using reml, we partitioned the variance and covariance into scale‐specific components and estimated the correlations between the weed counts and soil properties at each scale. We used variograms to quantify the spatial structure in the data and to map variables by kriging. Our methodology successfully captured the effect of scale on a number of edaphic drivers of weed patchiness. The overall Pearson correlations between A. myosuroides and soil organic matter and clay content were weak and masked the stronger correlations at >50 m. Knowing how the variance was partitioned across the spatial scales, we optimised the sampling design to focus sampling effort at those scales that contributed most to the total variance. The methods have the potential to guide patch spraying of weeds by identifying areas of the field that are vulnerable to weed establishment.

中文翻译：

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设计采样方案以揭示多空间尺度上杂草与土壤特性之间的相关性

总结杂草倾向于在田间聚集成块状，有证据表明这部分是由于土壤性质的变化。由于驱动土壤异质性的过程在不同的尺度上运行，因此土壤性质与杂草密度之间的关系强度也预计与尺度有关。量化这些规模对杂草斑块动态的影响对于指导用于绘制杂草分布图的离散采样协议的设计至关重要。我们开发了一种通用方法，该方法使用新颖的田间嵌套采样和残余最大似然 (reml) 估计来探索杂草与土壤特性之间的尺度相关关系。我们使用冬小麦中的 Alopecurus myosuroides 的案例研究验证了该方法。使用 reml，我们将方差和协方差划分为特定于尺度的分量，并估计了每个尺度上杂草数量和土壤特性之间的相关性。我们使用变异函数来量化数据中的空间结构并通过克里金法来映射变量。我们的方法成功地捕捉到了规模对许多杂草斑驳的土壤驱动因素的影响。A. myosuroides 与土壤有机质和粘土含量之间的整体 Pearson 相关性较弱，掩盖了 >50 m 处的较强相关性。了解方差是如何在空间尺度上划分的，我们优化了抽样设计，将抽样工作集中在对总方差贡献最大的那些尺度上。这些方法有可能通过识别易受杂草滋生的田地区域来指导杂草喷洒。