Null models reveal three-way interactions are significant predictors of ecological interactions in microbiome abundance data
Information about interactions between taxa is vital to understanding microbial ecosystems and their functionality, as well as how communities change over time. A common approach to classifying these interactions is to construct a network of pairwise correlations above some threshold. These networks are derived from abundance matrices of operational taxonomic units (OTUs) across a set of similar environments. The structure of microbial networks is important for predicting species interactions, as well as for inferring resistance of the network to perturbation.
Null models are key tools in understanding when a statistical pattern in the abundance matrices is indicating some non-random structure. In this study, we demonstrate the efficacy of these models using data from the soil microbiome collected in North and South America. We describe appropriate numerical null models for correctly estimating statistically significant structure at each of the stages of the analysis pipeline. In our analysis, we infer the network at different correlation thresholds, examine the degree sequence by rewiring edges in the true correlation network, and test the distribution of network metrics such as triangle density over many randomized permutations of the abundance matrix.
We find that many of the reported network metrics in the literature result from basic network properties such as average degree and the degree distribution. However, within the soil data, we find a statistically significant clustering coefficient. This finding agrees with observations of high clustering coefficients in other biological networks, such as protein-protein interactions and food webs. The apparent triadic enrichment of these microbial interaction networks may indicate the presence of interesting ecological interactions, which provides specific targets for future work to address.
The interpretation of abundance-location matrices can be improved by using appropriate null models. Anticipated applications of this robust statistical approach include understanding how bacterial networks will react to climate change and using soil engineering in order to increase agricultural yield.