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Proper function of a wastewater treatment plant (WWTP) relies on maintaininga delicate balance between a multitude of competing microorganisms. Gaining adetailed understanding of the complex network of interactions therein isessential to maximising not only current operational efficiencies, but also forthe effective design of new treatment technologies. Metagenomics offers aninsight into these dynamic systems through the analysis of the microbial DNAsequences present. Unique taxa are inferred through sequence clustering to formoperational taxonomic units (OTUs), with per-taxa abundance estimates obtainedfrom corresponding sequence counts. The data in this study comprise weekly OTUcounts from an activated sludge (AS) tank of a WWTP. To model the OTU dynamics,we develop a Bayesian hierarchical vector autoregressive model, which is alinear approximation to the commonly used generalised Lotka-Volterra (gLV)model. To tackle the high dimensionality and sparsity of the data, they arefirst clustered into 12 "bins" using a seasonal phase-based approach. Theautoregressive coefficient matrix is assumed to be sparse, so we exploredifferent shrinkage priors by analysing simulated data sets before selectingthe regularised horseshoe prior for the biological application. We find thatammonia and chemical oxygen demand have a positive relationship with severalbins and pH has a positive relationship with one bin. These results aresupported by findings in the biological literature. We identify severalnegative interactions, which suggests OTUs in different bins may be competingfor resources and that these relationships are complex. We also identify twopositive interactions. Although simpler than a gLV model, our vectorautoregression offers valuable insight into the microbial dynamics of the WWTP.

A sparse Bayesian hierarchical vector autoregressive model for microbial dynamics in a wastewater treatment plant