Identification of complex multidimensional interaction patterns within microbial communities is the key to understand, modulate, and design beneficial microbiomes. Every community has members that fulfill an essential function affecting multiple other community members through secondary metabolism. Since microbial community members are often simultaneously involved in multiple relations, not all interaction patterns for such microorganisms are expected to exhibit a visually uninterrupted pattern. As a result, such relations cannot be detected using traditional correlation, mutual information, principal coordinate analysis, or covariation-based network inference approaches. We present a novel pattern-specific method to quantify the strength and estimate the statistical significance of two-dimensional co-presence, co-exclusion, and one-way relation patterns between abundance profiles of two organisms as well as extend this approach to allow search and visualize three-, four-, and higher dimensional patterns. The proposed approach has been tested using 2380 microbiome samples from the Human Microbiome Project resulting in body site-specific networks of statistically significant 2D patterns as well as revealed the presence of 3D patterns in the Human Microbiome Project data. The presented study suggested that search for Boolean patterns in the microbial abundance data needs to be pattern specific. The reported presence of multidimensional patterns (which cannot be reduced to a combination of two-dimensional patterns) suggests that multidimensional (multi-organism) relations may play important roles in the organization of microbial communities, and their detection (and appropriate visualization) may lead to a deeper understanding of the organization and dynamics of microbial communities.

中文翻译：

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微生物群落中多维布尔模式的识别。

识别微生物群落内复杂的多维相互作用模式是理解、调节和设计有益微生物组的关键。每个社区都有成员履行通过次级代谢影响多个其他社区成员的基本功能。由于微生物群落成员通常同时涉及多种关系，因此并非此类微生物的所有相互作用模式都应表现出视觉上不间断的模式。因此，无法使用传统的相关性、互信息、主坐标分析或基于协变的网络推理方法来检测此类关系。我们提出了一种新颖的特定于模式的方法来量化两种生物体丰度分布之间的二维共存、共排斥和单向关系模式的强度并估计其统计显着性，并扩展该方法以允许搜索并可视化三维、四维和更高维的模式。所提出的方法已经使用人类微生物组项目的 2380 个微生物组样本进行了测试，产生了具有统计显着性 2D 模式的身体部位特定网络，并揭示了人类微生物组项目数据中 3D 模式的存在。本研究表明，在微生物丰度数据中搜索布尔模式需要特定于模式。所报告的多维模式的存在（不能简化为二维模式的组合）表明多维（多有机体）关系可能在微生物群落的组织中发挥重要作用，并且它们的检测（和适当的可视化）可能导致更深入地了解微生物群落的组织和动态。