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. 2019 Feb 28;9:3176. doi: 10.1038/s41598-019-39512-8

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© The Author(s) 2019

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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Bimodal distribution analysis. (a) After the initial unimodal distribution analysis, it is assessed how well the observed distribution is explained. (b) If a significant portion is not explained, the next bimodal distribution analysis is performed, where weights of the two distributions are optimized. (c) After bimodal distribution analysis, it is assessed how much the error is improved and whether both distributions are all fairly abundant. Only if all criteria are satisfied, two deuterium numbers are reported.