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. 2021 Apr 27;11:9012. doi: 10.1038/s41598-021-88588-8

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© The Author(s) 2021

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Grains biomass, grain-specific nitrogen (N) efficiency (E_N,g) and grain N concentration (C_N,g) or grain protein concentration (C_prot,g) as functions of the scaling exponent for macroelements (A to C) and Mg:P ratio (D to F) for nine wheat varieties field-grown in Sweden during two years (2018, 2019). *Indicates that scaling exponents were based on data from tillering (BBCH29) and flowering (BBCH65)³⁵. Regressions: y = 2.069x − 2.008, N = 18, R² = 0.73, P < 0.001 (A); y = 209.9x − 229.34, N = 18, R² = 0.63, P < 0.001 (B); y = − 0.166x² + 0.422x − 0.236, N = 18, R² = 0.68, P < 0.001 (C); y = − 6.434E − 5x² + 0.019x − 0.269, N = 18, R² = 0.70, P < 0.001 (D); y = − 0.008x² + 2.419x − 80.15, N = 18, R² = 0.88, P < 0.001 (E); y = − 0.000184x + 0.044, N = 18, R² = 0.77, P < 0.001 (F); the y₂ axes applied for (C) and (F) were adjusted according to the linear regression C_prot,g = 5288.5 * C_N,g + 23.5, R² = 0.97, P < 0.001, N = 36. Dots represent means from 4 replicates.