Maximization of fertility transfers from rangeland to cropland: The contribution of control theory.

In traditional mixed farming systems, soil fertility in cropland relies on the transfer of fertility from rangeland through the transfer of manure produced by livestock that grazes in rangeland. In this work, we introduce a simple meta-ecosystem model in which the mixed farming system is represented by a cropland sub-system connected to a rangeland sub-system by nutrient fluxes. The livestock plays the role of nutrient-pump from the rangeland sub-system to the cropland sub-system. We use this model to study how spatial organization and practices of livestock management such as the control of grazing pressure and night corralling can help optimize both nutrient transfers and crop production. We argue that addressing the optimization of crop production requires different methods, depending on whether the agricultural practice in focus is constant or variable over time. We first used classical optimization methods at equilibrium to address optimization when the grazing pressure was assumed to be constant over time. Second, we address optimization for a more realistic configuration of our model, where grazing pressure was assumed to vary over the course of a year. In this case, we used methods developed in the field of the control theory. Classical methods showed the existence of an optimal level of constant grazing pressure that maximizes the transfers from rangeland to cropland, leading to the maximization of crop production. Control methods showed that by varying the grazing pressure adequately an additional gain of production is possible, with higher crop production and lower nutrient transfer from rangeland to cropland. This additional gain arises from the fact that the requirement of nutrient by crops is variable along the year. Consequently, a constant adjustment of the grazing pressure allows a better match between nutrient transfer and nutrient requirement over time, leading to a substantial gain of crop biomass. Our results provide new insights for a "smarter" management of fertility transfers leading to higher crop production with less rangeland surface.