Network analysis to evaluate complexities in relationships among fermentation variables measured within continuous culture experiments

The objective of this study was to leverage a frequentist (ELN) and Bayesian learning (BLN) network analyses to summarize quantitative associations among variables measured in 4 previously published dual-flow continuous culture fermentation experiments. Experiments were originally designed to evaluate effects of nitrate, defaunation, yeast, and/or physiological shifts associated with pH or solids passage rates on rumen conditions. Measurements from these experiments that were used as nodes within the networks included concentrations of individual volatile fatty acids, mM and nitrate, NO3-,%; outflows of non-ammonia nitrogen (NAN, g/d), bacterial N (BN, g/d), residual N (RN, g/d), and ammonia N (NH3-N, mg/dL); degradability of neutral detergent fiber (NDFd, %) and degradability of organic matter (OMd, %); dry matter intake (DMI, kg/d); urea in buffer (%); fluid passage rate (FF, L/d); total protozoa count (PZ, cells/mL); and methane production (CH4, mmol/d). A frequentist network (ELN) derived using a graphical LASSO (least absolute shrinkage and selection operator) technique with tuning parameters selected by Extended Bayesian Information Criteria (EBIC) and a BLN were constructed from these data. The illustrated associations in the ELN were unidirectional yet assisted in identifying prominent relationships within the rumen that were largely consistent with current understanding of fermentation mechanisms. Another advantage of the ELN approach was that it focused on understanding the role of individual nodes within the network. Such understanding may be critical in exploring candidates for biomarkers, indicator variables, model targets, or other measurement-focused explorations. As an example, acetate was highly central in the network suggesting it may be a strong candidate as a rumen biomarker. Alternatively, the major advantage of the BLN was its unique ability to imply causal directionality in relationships. Because the BLN identified directional, cascading relationships, this analytics approach was uniquely suited to exploring the edges within the network as a strategy to direct future work researching mechanisms of fermentation. For example, in the BLN acetate responded to treatment conditions such as the source of N used and the quantity of substrate provided, while acetate drove changes in the protozoal populations, non-NH3-N and residual N flows. In conclusion, the analyses exhibit complementary strengths in supporting inference on the connectedness and directionality of quantitative associations among fermentation variables that may be useful in driving future studies.