Liebig's Law of the Minima: Interpreting Nutrient Response in 2 Dimensions.

The linear-plateau model is well-established for describing plant responses to mineral nutrients. However, visualizing and interpreting such models are a challenge when considering simultaneously varying sources of a nutrient. In these cases, the nutrient saturation point is no longer a point, but rather a frontier across a response surface in multiple dimensions. In this study, we provided a corn crop with N from two organic sources, poultry litter and cover crop residues, for three years at two sites each. The rates of poultry litter ranged from 0-268 kg PAN ha^-1, and the cover crop residues were composed of hairy vetch (Vicia villosa) and cereal rye (Secale cereale) in mixtures and in monocultures (shoot biomass: 1.8-21.1 Mg dm ha^-1, C/N ratio: 9.3-164.4). We then used mixed-effect models to describe the yield response of the following corn crop. We compared the advantages and disadvantages of fitting these types of models in R using non-linear frequentist software (nlme) and using an interface to the Bayesian language Stan (brms).