Inferring directional relationships in microbial communities using signed Bayesian networks

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Inferring directional relationships in microbial communities using signed Bayesian networks Musfiqur Sazal1 , Kalai Mathee2,3 , Daniel Ruiz-Perez1 , Trevor Cickovski1 and Giri Narasimhan1,3* From 8th IEEE International Conference on Computational Advances in Bio and medical Sciences (ICCABS 2018) Las Vegas, NV, USA. 18-20 October 2018

Abstract Background: Microbe-microbe and host-microbe interactions in a microbiome play a vital role in both health and disease. However, the structure of the microbial community and the colonization patterns are highly complex to infer even under controlled wet laboratory conditions. In this study, we investigate what information, if any, can be provided by a Bayesian Network (BN) about a microbial community. Unlike the previously proposed Co-occurrence Networks (CoNs), BNs are based on conditional dependencies and can help in revealing complex associations. Results: In this paper, we propose a way of combining a BN and a CoN to construct a signed Bayesian Network (sBN). We report a surprising association between directed edges in signed BNs and known colonization orders. Conclusions: BNs are powerful tools for community analysis and extracting influences and colonization patterns, even though the analysis only uses an abundance matrix with no temporal information. We conclude that directed edges in sBNs when combined with negative correlations are consistent with and strongly suggestive of colonization order. Keywords: Bayesian networks, Conditional dependence, Microbiome, Colonization order, PC-stable

Background Bayesian Networks (BN) (also Belief Networks and Bayes Nets) are graphical models where nodes represent a set of multi-dimensional variables and edges represent conditional dependencies between the nodes. BNs can thus capture implicit and explicit relationships between these nodes [1]. When learning from data, edges in BNs can be directed or undirected. In fact, highly correlated variables very often lead to undirected (or two-way dependencies), *Correspondence: [email protected] Bioinformatics Research Group (BioRG), School of Computing and Information Sciences, Florida International University, Miami 33199, FL, USA 3 Biomolecular Sciences Institute (BSI), Florida International University, Miami 33199, FL, USA Full list of author information is available at the end of the article 1

since knowing one variable provides a lot of information about the other variable. In its simplest form, an edge in a BN expresses the conditional probability of knowing the (multi-dimensional) value of the variable at one node, given the value of the variable at another. BNs were used by Friedman et al. to use gene expression data to infer interactions between genes [2]. Conditional dependencies are often misinterpreted as causation, but are merely mathematical relationships that approximate causation under specific circumstances. A significant feature of BNs is that they can allow us to differentiate between direct and indirect conditional dependence [3]. For example, if t