Insights on nitrogen and phosphorus co-limitation in global croplands from theoretical and modelling fertilization experiments

Crossed fertilization additions are a common tool to assess nutrient interaction in a given ecosystem. Such fertilization experiments lead to the definition of nutrient interaction categories: e.g. simultaneous co-limitation, single resource response, etc. (Harpole et al., 2011). However, the implications of such categories in terms of nutrient interaction modeling are not clear. 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. The theoretical analysis is developed following two mathematical formalisms of interaction: Liebig's law of minimum and multiple limitation hypothesis. As results of the theoretical framework, we defined the corresponding between most Harpole categories and the values of the limitation by each nutrient when considered alone in the control experiment (i.e. without additional nutrient supply). We showed that synergistic co-limitation could occur even using Liebig's formalism under certain conditions as a function of the amount of N and P added in fertilization experiments. We then applied our framework with global maps of soil supply and plant demand for croplands to achieve their potential yield. This allowed us to estimate the global occurrence of each limitation category, for each of the possible interaction formalism. We found that a true co-limitation could affect a large proportion of the global crop area (e.g. ~ 42 % for maize) if multiple limitation hypothesis is assumed. Our work clarifies the conditions required to achieve N and P co-limitation as function of the interaction formalism. Combined with compilation of field trials in cropland, our study would improve our understanding of nutrient limitation in cropland at the global scale.