Single and combined fertilization additions are a common tool to assess the interactions between nutrients in a given ecosystem. While such experiments can allow systems to be defined into categories of nutrient interactions, for example, simultaneous co-limitation or single resource response, this categorization may itself be sensitive to way nutrient interactions are mathematically formulated. To this end, we developed a theoretical analysis of nitrogen (N) and phosphorus (P) fertilization experiments based on the computation of ratios between plant demand and soil supply for each nutrient to explore two mathematical interaction formalisms: Liebig's law of minimum (LM) and the multiple limitation hypothesis (MH). We defined, for each interaction formalism, what conditions (in terms of supply and demand in N and P) are required to make the ecosystem in each category of nutrient interaction. Notably, we showed that synergistic co-limitation could occur even using LM formalism under certain conditions. We then applied our framework to global maps of soil nutrient supply and of crop nutrient demand to achieve the potential yield. This was done to examine how the choice of interaction formalism influenced the occurrence of nutrient interaction categories. MH predicts true co-limitation for ∼40% of the global maize area where LM predicts other categories of nutrient interaction, particularly single resource P limitation (whose the exact occurrence is, however, sensitive to the amount of P applied in the fertilization experiments). Our study identified areas where real fertilization experiments are required to choose between LM or MH to best represent nutrient interaction in croplands.

中文翻译：

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从理论和模拟施肥实验中洞察全球农田中氮和磷的共同限制

单一和组合施肥添加是评估给定生态系统中养分之间相互作用的常用工具。虽然这样的实验可以允许系统被定义为营养相互作用的类别，例如，同时共同限制或单一资源响应，但这种分类本身可能对营养相互作用的数学公式很敏感。为此，我们开发了氮 (N) 和磷 (P) 施肥实验的理论分析，基于对每种养分的植物需求和土壤供应之间的比率的计算，以探索两种数学相互作用形式：李比希最小值定律 (LM)和多重限制假设（MH）。我们为每个交互形式定义了，需要什么样的条件（就氮和磷的供需而言）才能使生态系统处于每类养分相互作用中。值得注意的是，我们表明，即使在某些条件下使用 LM 形式主义，也可能发生协同限制。然后，我们将我们的框架应用于土壤养分供应和作物养分需求的全球地图，以实现潜在产量。这样做是为了检查相互作用形式主义的选择如何影响营养相互作用类别的发生。MH 预测全球约 40% 的玉米面积的真正共同限制，其中 LM 预测其他类别的养分相互作用，特别是单一资源 P 限制（然而，其确切发生对施肥实验中应用的 P 量敏感） .