Fig 1.
Granger causality vs Pearson’s correlation coefficient for all four body sites.
Granger causality (GC) is expressed as change in abundance of response variable (in standard deviation) as the abundance of Granger-cause increases by 1 SD. Positive coefficients indicate positive effect of the Granger-cause on response in affecting abundance, and vice versa. For a given taxon-pair, the highest coefficient among all positive coefficients and the lowest one among all negative coefficients are shown in the figure. The relationship between Pearson’s correlation and Granger causality is shown separately for positive GC and negative GC along with separate splines.
Fig 2.
Number of strong coefficients of Granger causality for interspecific (left column) and intraspecific (right column) taxon pairs in the gut, and on the left-hand, right-hand and tongue.
For a given response variable (taxon), the total number of significant coefficients of each predictor taxon was noted. Plots were created by the totality of such coefficients for all response variables. Inset pie-charts show the fraction of taxa with (colored) and without (black) at least one significant predictor.
Fig 3.
Frequency with which strong coefficients appear at different time-lags for interspecific interactions (left column) and for intraspecific interactions (right column).
Coefficients are shown for the gut, left-hand, right-hand and tongue. For each panel, the negative axis reflects time-lags with negative coefficients, while the positive axis reflects time-lags with positive coefficients. Pie-charts adjacent to each panel show the fraction of coefficients that are positive (blue) versus negative (orange).
Fig 4.
Total number of strong interspecific cause and effect interactions that are positive (blue) and negative (orange) in the gut and on the tongue, left-hand and right-hand.
Results are shown for each genus with at least one significant interaction.
Fig 5.
Average time-lag associated with all strong interspecific interactions (purple) and with all strong intraspecific interactions (green) in the gut and on the tongue, left-hand and right-hand.
Results are shown for each genus with at least one significant interaction.
Fig 6.
Fraction of short/long and negative/positive interactions with strong coefficients.
The fractions are shown separately for interspecific and intraspecific interactions within each body site.
Table 1.
Strong qualitative interactions conserved across the left-hand and right-hand.
Taxa pairs that are conserved both for interaction and timescale are shown.
Table 2.
Characteristics of body sites and model.
Each Genus in a body site was predicted by a sum of its own lags as well as that of all other Genus. A separate model was built to predict each Genus by itself (endogeneous variable) and all the other Genus (exogeneous variables). Each Genus in a body site was therefore provided with the same set of predictors but the final model retained different set of predictors (Genus and lags).
Fig 7.
Flow chart of the methods and models we employed.
In one of the first applications of causal models in microbiome interaction network analysis, we used conditional/multivariate model of Granger causality which eliminates spurious causations but retains the true ones (this is in contrast to the traditional more famous pair-wise model of Granger causality which detects spurious causations). LASSO shrinkage and rolling cross validation of the model makes it simpler and more robust. This overall method is novel in microbiome network analysis. The novelty in the findings of our study is that we show conclusively as the first report that correlation does not inform causality at all in human microbiome. For a richer ecological inference, we decomposed the taxa interactions into (1) interspecific vs intraspecific, (2) positive vs negative, (3) cause vs effect, and (4) short vs long timescales.