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

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 similar to 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.

Automated summary

By calculating the ratio between plant demand and soil supply, researchers conducted a theoretical analysis of nitrogen and phosphorus fertilization experiments to explore interaction formalisms between nutrients. The study revealed that synergistic co-limitation could occur even using Liebig's law of minimum under certain conditions, emphasizing the sensitivity of nutrient interaction categorization to mathematical formulation.