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. 2018 Sep 18;8:14015. doi: 10.1038/s41598-018-30248-5

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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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Relative fit of a linear versus sigmoidal model based on the r² value of the model fit. Here a window of size x is used to calculate the variant frequencies, where x is related to the number of previous observations from the population. As x increased, the fit of a linear model (solid line) decreases. However, a linear model remains a better fit than a sigmoid model until a very large window size.