Fig. 6: Analytical stability analysis of microbiomes demonstrates significantly more stable dynamics than expected by chance and reveals cycle feedback motifs.
From: Learning ecosystem-scale dynamics from microbiome data with MDSINE2
a, Two- and three-cycle motifs and their corresponding eigenvalue asymptotes for increased interaction strength. The cycle interaction strength is denoted by k. Axes are labelled with I and R to denote the imaginary and real axes, respectively. Only the two-cycle with negative feedback can remain stable for all feedback gains (top motif). b, As a measure of stability, we computed the number of right half plane eigenvalues for each posterior sample of our model trained on the healthy cohort (n = 100,000), and for the null model (n = 100,000 ‘permuted’ samples, one for each posterior sample). Our model had an 80% probability of having no unstable eigenvalues. c, Distribution of cycle motifs over posterior samples and permuted networks from b; all pairwise comparisons are based on BH-corrected two-sided Wilcoxon signed-rank test, ****P < 0.0001. In the violin plots, filled boxes denote interquartile region with a dot for the median; whiskers denote 1.5× the interquartile region. P values are provided in Supplementary Data. d, Analyses showing networks derived with three different levels of confidence for including edges (i), descriptive statistics for the networks (ii), and statistical test for significance of mutualism to competition ratio (MCR: (+,+)/(−,−)) (iii), which was significant for the network constructed from edges with ‘strong’ evidence P = 0.01. Significance was determined by permutation test comparing the topology in d(i) to 10,000 permutated networks. See Methods section ‘Network null model’ for network permutation details.
