LAUSR

Abstract Estimation of crop nutrient demand, seed nutrient removal, and nutrient use efficiency (yield to nutrient uptake ratio) are crucial for pursuing both balanced nutrition and more sustainable farming systems. However, the estimation of the nutrient requirements as the nutrient uptake per unit of seed yields is impaired in many situations due to the narrow variation of the dataset used to obtain these values or by the overgeneralization of considering a constant value for the nutrient demand at varying yield levels. Past studies focused on other crops and using linear models for estimation of the nutrient requirements, but not yet for soybeans (Glycine max L.). The aims of this research study were to: (i) quantify nitrogen (N), phosphorus (P), potassium (K), and sulfur (S) requirements in soybean and (ii) compare linear and non-linear (spherical) models in their relationship between plant and seed nutrient content all relative to seed yield at varying probabilities utilizing quantile regression. A large dataset from different studies conducted between 2009–2018 period, including data of seed yield, total biomass at physiological maturity, and N, P, K, and S uptake. Soybean seed yield ranged from 955 to 6525 kg ha−1, aboveground biomass from 1990 to 15,814 kg ha−1, and harvest index from 0.16 to 0.57. On average, nutrient uptake was 261 kg N ha−1, 25 kg P ha−1, 133 kg K ha−1, and 16 kg S ha−1 (N:P:K:S ratio = 17:1.6:8.5:1), while nutrient content in seeds averaged 191 kg N ha−1, 17 kg P ha−1, 54 kg K ha−1, and 9 kg S ha−1 (N:P:K:S ratio = 21:1.8:5.8:1). The spherical model described better than the linear model the relationship between plant nutrient uptake or nutrient content in seeds with seed yield in soybean, and thus, nutrient requirements per unit of yield decreased as seed yield increased. A relationship between nutrient internal efficiency and seed yield for the different percentiles as determined by the non-linear quantile regression offered probabilistic values for estimating nutrient uptake in soybean, providing useful information for obtaining more reliable estimates of nutrient balances at the system-level.