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Abstract Background 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. Results 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. Conclusions 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. Video Abstract

Aim: Assembly of protist communities is known to be driven mainly by environmental filtering, but the imprint of phylogenetic relatedness is unknown. In this study, we aimed to test the degree to which co‐occurrences and co‐exclusions of protists in different phylogenetic relatedness classes deviate from random expectation in two ecosystems, in order to link them to ecological processes. Location: Global open oceans and Neotropical rain‐forest soils. Major taxa: Protists. Time period: 2009–2013. Methods: Protist metabarcoding data originated from two large‐scale studies. Co‐occurrence and co‐exclusion networks were constructed using a recent method combining a null distribution model with Spearman's rank correlation coefficients among pairs of operational taxonomic units. Phylogenetic relatedness was estimated using either global pairwise sequence distance or phylogenetic distance inferred from best maximum‐likelihood trees derived from multiple alignments of operational taxonomic unit representative sequences. The significance of observed patterns relating networks and phylogenies was evaluated by distance classes against two null models, in which either the tips of the phylogenetic trees or the network edges were randomized. Results: Closely related protists co‐occurred more often than expected by chance in all datasets, but also co‐excluded less often than expected by chance in the marine dataset only. Concurrent excesses of co‐occurrences and co‐exclusions were observed at intermediate phylogenetic distances in the marine dataset. Main conclusions: This suggests that environmental filtering and dispersal limitation are the dominant forces driving protist co‐occurrences in both environments, whereas a signal of competitive exclusion is detected only in the marine environment. Differences in co‐exclusion are potentially linked to the individual environments, in that marine waters are more homogeneous, whereas rain‐forest soils contain a myriad of nutrient‐rich microenvironments, reducing the strength of mutual exclusion. [ABSTRACT FROM AUTHOR]

Virtually every biological system is governed by complex relations among its components. Identifying such relations requires a rigorous or heuristics-based search for patterns among variables/features of a system. Various algorithms have been developed to identify two-dimensional (involving two variables) patterns employing correlation, covariation, mutual information, etc. It seems obvious, however, that comprehensive descriptions of complex biological systems need also to include more complicated multivariable relations, which can only be described using patterns that simultaneously embrace 3, 4, and more variables. The goal of this manuscript is to (a) introduce a novel type of associations (multivariable Boolean patterns) that can be manifested between features of complex systems but cannot be identified (described) by traditional pair-vise metrics; (b) propose patterns classification method, and (c) provide a novel definition of the pattern's strength (pattern's score) able to accommodate heterogeneous multi-omics data. To demonstrate the presence of such patterns, we performed a search for all possible 2-, 3-, and 4-dimensional patterns in historical data from the Human Microbiome Project (15 body sites) and collection of H. pylori genomes associated with gastric ulcers, gastritis, and duodenal ulcers. In all datasets under consideration, we were able to identify hundreds of statistically significant multivariable patterns. These results suggest that such patterns can be common in microbial genomics/microbiomics systems. [ABSTRACT FROM AUTHOR]