Fig. 1

Detecting change points in the time series. a Observed results of CAL and change points in the stable and progressing time series based on mean and variance. b Posterior probabilities of a change point at each position. c sPLS-DA (sparse partial least squares discriminant analysis) classification of the whole transcriptome in the host and microbiome. The plots display the first two components from sparse partial least squares discriminant analysis, with explained variance percentages for Component 1 shown for each analysis (human stable: 69%, human progressing: 40%, microbiome stable: 30%, microbiome progressing: 21%). Samples are colored by group and shaped by timepoint (0–12 months), depicting the prediction background as a color-coded probability for each plot region. We used the default method (max.dist) for classification, which assigns classes based on the closest sample from the training set