Grain legumes are key components of sustainable production systems in sub-Saharan Africa, but wide-spread nutrient deficiencies severely restrict yields. Whereas legumes can meet a large part of their nitrogen (N) requirement through symbiosis with N₂-fixing bacteria, elements such as phosphorus (P), potassium (K) and secondary and micronutrients may still be limiting and require supplementation. Responses to P are generally strong but variable, while evidence for other nutrients tends to show weak or highly localised effects. Here we present the results of a joint statistical analysis of a series of on-farm nutrient addition trials, implemented across four legumes in four countries over two years. Linear mixed models were used to quantify both mean nutrient responses and their variability, followed by a random forest analysis to determine the extent to which such variability can be explained or predicted by geographic, environmental or farm survey data. Legume response to P was indeed variable, but consistently positive and we predicted application to be profitable for 67% of farms in any given year, based on prevailing input costs and grain prices. Other nutrients did not show significant mean effects, but considerable response variation was found. This response heterogeneity was mostly associated with local or temporary factors and could not be explained or predicted by spatial, biophysical or management factors. An exception was K response, which displayed appreciable spatial variation that could be partly accounted for by spatial and environmental covariables. While of apparent relevance for targeted recommendations, the minor amplitude of expected response, the large proportion of unexplained variation and the unreliability of the predicted spatial patterns suggests that such data-driven targeting is unlikely to be effective with current data.

豆类是撒哈拉以南非洲可持续生产系统的关键组成部分，但广泛的营养缺乏严重限制了产量。_{虽然豆类可以通过与固氮}细菌共生来满足大部分氮 (N) 需求，但磷 (P)、钾 (K) 以及次生和微量营养素等元素可能仍然受到限制，需要补充。对磷的反应通常很强但又存在差异，而其他营养素的反应往往表现出较弱或高度局部化的影响。在这里，我们展示了两年来在四个国家的四种豆类中实施的一系列农场营养添加试验的联合统计分析结果。使用线性混合模型来量化平均养分反应及其变异性，然后进行随机森林分析，以确定地理、环境或农场调查数据可以在多大程度上解释或预测这种变异性。豆科植物对磷的反应确实是可变的，但始终是积极的，根据当前的投入成本和谷物价格，我们预测在任何给定年份，应用磷可以为 67% 的农场带来利润。其他营养素没有表现出显着的平均效果，但发现了相当大的反应变化。这种反应异质性主要与局部或暂时因素有关，无法通过空间、生物物理或管理因素来解释或预测。K 响应是一个例外，它显示出明显的空间变化，部分原因可能是空间和环境协变量造成的。虽然与有针对性的建议具有明显的相关性，但预期响应的较小幅度、大量无法解释的变化以及预测空间模式的不可靠性表明，这种数据驱动的目标对于当前数据不太可能有效。