Insights on Nitrogen and Phosphorus Co‐Limitation in Global Croplands From Theoretical and Modeling Fertilization Experiments

Abstract 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.