Fig. 1

Different approaches to microbiome-metabolites relations. A The linear approach assumes each microbe produces some metabolites, and the metabolite concentration is a positive linear combination of the microbe concentration. The environmental/host effect if any is only through the microbiome (gray). B The dominant microbes approach assumes that given the dominance of a small number of microbe species composing the vast majority of microbes in the gut, the concentration of each metabolite is determined by the most frequent microbes (gray). C Multiview assumes the environment directly affects the metabolites and microbiome separately (gray). D The latent variables approach assumes that the microbiome and metabolome represent the steady state of a bi-directional interaction. In such a case, the equilibrium can differ between hosts. However, it may be represented by some combined latent representation (blue). In all plots, microbiome taxa are symbolized by bacteria icons of various sizes, reflecting their frequencies. “Mic.” denotes the microbiome, and “Met.” stands for metabolites. The arrows denote interactions, with arrow thickness indicating the strength of the interaction and the arrow direction indicating the direction of the interaction