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. 2018 Mar 12;8:4387. doi: 10.1038/s41598-018-22616-y

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© The Author(s) 2018

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 license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license 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 license, visit http://creativecommons.org/licenses/by/4.0/.

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The just noticeable difference Δv increases with the magnitude of random fluctuations. (left) the Weber fraction increases with decreasing system size S (i.e., for increasing random fluctuations), see Supplementary Table S1. (right) Just noticeable difference as a function of S for base quality $\bar{v}$ . The data points are fitted with the red curve (z + aS^−b), with a ≈ 12.13, b ≈ 0.626, z ≈ 0.013, and quality of fit R² > 0.999 (see Sec. 5.4). The inset shows examples of commitment change for v₁ = 10, v₂ = 11 and varying number of bees S; the largest fluctuations are displayed for S = 10. Plots show results for signalling ratio r = 3.