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BACKGROUND: The proportion of nitrogen (N) derived from the atmosphere (Ndfa) is a fundamental component of the plant N demand in legume species. To estimate the N benefit of grain legumes for the subsequent crop in the rotation, a simplified N balance is frequently used. This balance is calculated as the difference between fixed N and removed N by grains. The Ndfa needed to achieve a neutral N balance (hereafter θ ) is usually estimated through a simple linear regression model between Ndfa and N balance. This quantity is routinely estimated without accounting for the uncertainty in the estimate, which is needed to perform formal statistical inference about θ . In this article, we utilized a global database to describe the development of a novel Bayesian framework to quantify the uncertainty of θ . This study aimed to (i) develop a Bayesian framework to quantify the uncertainty of θ , and (ii) contrast the use of this Bayesian framework with the widely used delta and bootstrapping methods under different data availability scenarios. RESULTS: The delta method, bootstrapping, and Bayesian inference provided nearly equivalent numerical values when the range of values for Ndfa was thoroughly explored during data collection (e.g., 6-91%), and the number of observations was relatively high (e.g., ≥ 100 ). When the Ndfa tested was narrow and/or sample size was small, the delta method and bootstrapping provided confidence intervals containing biologically non-meaningful values (i.e. < 0% or > 100%). However, under a narrow Ndfa range and small sample size, the developed Bayesian inference framework obtained biologically meaningful values in the uncertainty estimation. CONCLUSION: In this study, we showed that the developed Bayesian framework was preferable under limited data conditions âby using informative priorsâ and when uncertainty estimation had to be constrained (regularized) to obtain meaningful inference. The presented Bayesian framework lays the foundation not only to conduct formal comparisons or hypothesis testing involving θ , but also to learn about its expected value, variance, and higher moments such as skewness and kurtosis under different agroecological and crop management conditions. This framework can also be transferred to estimate balances for other nutrients and/or field crops to gain knowledge on global crop nutrient balances.
RESUMEN
Continuous potassium (K) removal without replenishment is progressively mining Argentinean soils. Our goals were to evaluate the sensitivity of soil-K to K budgets, quantify soil-K changes over time along the soil profile, and identify soil variables that regulate soil-K depletion. Four on-farm trials under two crop rotations including maize, wheat and soybean were evaluated. Three treatments were compared: (1) control (no fertilizer applied); (2) application of nitrogen, phosphorus, and sulfur fertilizers -NPS-; and (3) pristine condition. After nine years, crops removed from 258 to 556 kg K ha-1. Only two sites showed a decline in the exchangeable-K levels at 0-20 cm but unrelated to K budget. Topsoil exchangeable-K levels under agriculture resulted 48% lower than their pristine conditions, although still above response levels. Both soil exchangeable-K and slowly-exchangeable K vertical distribution patterns (0-100 cm) displayed substantial depletion relative to pristine conditions, mainly concentrated at subsoil (20-100 cm), with 55-83% for exchangeable-K, and 74-95% for slowly-exchangeable-K. Higher pristine levels of exchangeable-K and slowly-exchangeable-K and lower clay and silt contents resulted in higher soil-K depletion. Soil K management guidelines should consider both topsoil and subsoil nutrient status and variables related to soil K buffer capacity.