Fig. 5: Causal analysis for the selected variables within and across the three module groups.

A The metabolite/energetic group. B The community structure group. C The interaction network group. Panel D illustrates the averaged strength of causality of variables across the three groups, with the self-pointing arrow indicating the averaged causality strength within the group. The summary distribution of CCM skills between pair-wise groups is visualized in Supplementary Fig. 11. The color bar represents the scale of the CCM skill at the maximal library length, ρ(Lmax), indicating the causal strength (See Methods). Only significant (p < 0.05) causal linkages are included in the causal network. Detailed abbreviations can be found in the Methods section. Bu, butyrate; Pr, propionate; Ac, acetate; α-Div, Shannon diversity; PCo1 and PCo2, first and second axis of PCoA; P_IS, average positive interaction strength; N_IS, average negative interaction strength; P %, proportion of the positive interaction; N %, proportion of the negative interaction; centrality, average degree.