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Different quantification approaches for nitrogen use efficiency lead to divergent estimates with varying advantages


Nitrogen use efficiency (NUE) is a key indicator with which to study nitrogen cycles and inform nitrogen management. However, different quantification approaches may result in substantially divergent NUE values even for the same production system or for the same experimental plot. Based on our investigation of the differences between and connections among the three principal approaches for NUE quantification, we offer recommendations for choosing the appropriate approach and call for long-term observations to assess the impacts of management practices.

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Fig. 1: Three approaches for quantifying NUE in cropping systems.
Fig. 2: Major NUE quantification approaches and the influence of soil legacy effect.

Data availability

This work used data collected from a variety of publicly available sources. See the references in the main text and Supplementary Information for data specification.

Code availability

The code used for this analysis is available from the corresponding author on request.


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We thank M. Glendining from Rothamsted Research for providing us with the data to indicate the changes of NUE in the long-term Broadbalk Wheat Experiment. Z.Q. is supported by the National Key Research and Development Program of the Ministry of Science and Technology of China (2018YFC0213305), the National Natural Science Foundation of China (41701309) and the Open Research Project of Shouguang Facilities Agriculture Center in the Institute of Applied Ecology (2018SG-B-03). X.Z. is supported by the National Science Foundation (CNS-1739823, CBET-2047165, and CBET-2025826). Y.F. is supported by the National Key Research and Development Program of the Ministry of Science and Technology of China (2016YFA0600802). We also acknowledge support from the Youth Innovation Promotion Association CAS (Z.Q.) and the K.C. Wong Education Foundation (Y.F.).

Author information




Z.Q., X.Z. and Y.F. designed the study. Z.Q. and X.Z. collected data and conducted calculations. Z.Q., X.Z. and Y.F. led the analysis. All authors contributed to writing and revisions.

Corresponding authors

Correspondence to Xin Zhang or Yunting Fang.

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Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Food thanks Tai Maaz and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 The average NUE values estimated by NUEdiff, NUE15N, and NUEbala approaches in the Chinese wheat, rice, and maize cropping system.

Equations in Table 1 (NUEdiff = (HNT - HNC) / FN; NUE15N = (HNT × %Ndff) / FN; NUEbala = HNT / (FN + NFN)) were used to estimate the average NUEdiff, NUE15N, and NUEbala for the three major cereal crops within China’s cereal cropping system. Data sources: the average %Ndff was from Supplementary Table 2; HNC was calculated as the product of HNT and the ratio of HNC to HNT which was estimated based on the observed yield response to fertilizer nitrogen input in Supplementary Fig. 4 and the observed nitrogen concentration response to fertilizer nitrogen input in Supplementary Table 5; the average HNT and FN were from Supplementary Table 3; the average NFN was from Supplementary Table 4 (asymbiotic N fixations were estimated as 30 kg N ha−1 for rice, and 10 kg N ha−1 for wheat or maize). See Fig. 1 caption for definitions of abbreviations.

Extended Data Fig. 2 The potential impact of non-fertilizer nitrogen bioavailability on the NUE for FN use based on the N balance approach (NUEbala_F).

See the legend of Fig. 1 for definitions of abbreviations. According to Fig. 2a, NUEdiff, NUE15N, and NUEbala correspond to the slope of line BD, CD, and OD respectively. Numbers in brackets are from an example developed for the Chinese cereal cropping system. Point A was derived as the cross-point of line OD and the vertical line BC. Strictly speaking, NUEbala measures the efficiency of total N inputs instead of fertilizer inputs only, because the denominator for NUEbala is FN + NFN instead of FN. To derive the NUE for fertilizer based on NUEbala (NUEbala_F, the slope of pD, where p represents a point on the line MN and is not noted in the figure), the non-fertilizer nitrogen input (NFN) and its bioavailability (BANF, or the slope of Op) need to be quantified. When BANF is the same as NUEbala, point p overlaps with point A, and the NUEbala_F is the same as NUEbala (0.52, the red dotted line). If all NFN is harvested as crop products (BANF=1; the maximum value of BANF), then point p moves to point M, and NUEbala_F is the slope of line MD (NUEbala_F=0.38). In contrast, if no NFN is harvested as crop products (BANF=0; the minimum value of BANF), then point p moves to point N, and NUEbala_F is the slope of line ND (NUEbala_F=0.66). Therefore, based on NUEbala for the Chinese cereal cropping system example, the lowest possible value for NUEbala_F is 0.38, and it is still higher than NUE15N (0.30) and NUEdiff (0.32), indicating other important drivers for the differences between NUEbala and the other two approaches.

Extended Data Fig. 3 The yield response curves from short-term and long-term observations, and the relationship between observed NUEdiff and NUEbala.

A typical yield response curve based on field trials shows a “diminishing return” to N inputs. For experimental sites that have been under fertilizer N treatment over a period of time, the yield observed at the control plot tends to decrease over time (the red point on the vertical dashed line of NFN moves downward), mainly due to the gradually reducing legacy effect of N input before the setting of the control plot. See the legend of Fig. 1 for definitions of abbreviations. The slopes of red lines are NUEdiff and NUEbala.

Supplementary information

Supplementary Information

Supplementary notes 1 and 2, discussions 1 and 2, Tables 1–6 and Figs. 1–3.

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Quan, Z., Zhang, X., Fang, Y. et al. Different quantification approaches for nitrogen use efficiency lead to divergent estimates with varying advantages. Nat Food 2, 241–245 (2021).

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