Fig. 1: Dynamic covariance mapping (DCM) to estimate the community interaction matrix during colonization of the gut microbiota.
a Microbial community is described by abundance time series \([{z}_{i}\left(t\right)]\) of member \(i\) that could include inter- or intra-species composition. b The community matrix \({J}_{{ij}}(\tau )\) estimated over the time interval \(\tau\) reflects the influence of the abundance of a member \(j\) on the rate of increase of another member \(i\). It is quantified by the covariance between \({z}_{j}(t)\) and \({f}_{i}\). When the time-series data includes inter- and intra-species compositions, the covariance matrix describes the community matrix within-community, within-clones, and between community and clones. c The stability and dynamics of the community can be inferred from the eigenvalues of the community matrix \({J}_{{ij}}(\tau )\). Specifically, the abundance timeseries is a linear combination of the periodic functions with frequency defined by \({{\rm{Im}}}({\lambda }_{k})\) and amplitude by \(\exp ({\mathrm{Re}}({\lambda }_{k}))\) (Main text). Consequently, the eigenvalues define stability and oscillatory features of the community. Principal component analysis (PCA) of the time-dependent eigenvalues can reveal distinct temporal domains in community dynamics. In DCM, we look at the first two components PC1 and PC2. d, e Application of DCM to high-resolution community inter-species and intra-species abundance data during gut colonization. A population of ~108 E. coli cells with ~5 × 105 unique chromosomal barcodes is introduced into mice with reduced microbiota by antibiotic pre-treatment (cohort 1, rm) and mice with innate microbiota (cohort 3, im). Community-level and intra-species dynamics were then tracked in fecal samples over a 2-week period. As comparison, samples were also collected in mice with only the colonizing E. coli (germ-free or gf, cohort 2) and in mice with only the resident bacteria and no colonization (cohort 4, nc). Mouse schema is “Created in BioRender. Serohijos, A. (2025) https://BioRender.com/8gmahgd”. e E. coli bacterial load measured as colony-forming units (CFU) per gram of sampled feces for the colonized mice cohorts with innate microbiota (im), reduced microbiota (rm), and germ-free (gf). Dashed line represents the resolution limit.
