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. 2023 Apr 11;24:72. doi: 10.1186/s13059-023-02902-3

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© The Author(s) 2023

Open AccessThis 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/. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data.

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Fig. 4 — Analysis of mouse cecal microbiome data. a Phylogenetic tree with the size of the circle at each internal node proportional to $- log 10$ (PhyloMed local mediation test p-value). The identified internal node with the minimum subcomposition mediation test p-value and the subtree under the node are highlighted in a blue rectangle. b Quantile-quantile plots of different subcomposition mediation test p-values across internal nodes. PhyloMed: proposed mixture-distribution-based test; JS: joint significance test; Sobel: Sobel’s test. c Associations of the subcomposition (in log-ratio) at the highlighted node in a with the treatment and the body fat percentage after adjusting for the treatment effect. d The highlighted subtree in a. Pair the OTU under the left child node to each of the five OTUs under the right child node. For the subcomposition of each pair, examine the treatment-subcomposition and subcomposition-outcome associations and report the maximum p-value of the two associations