Extended Data Fig. 1: Statistical validations of association between Veillonella abundance and marathon running.

a, Histogram of P values (Wald Z-tests) for time coefficient from LOOCV models predicting 16S Veillonella abundance. The red line represents the P value for the model trained without any hold outs. b, Histogram of P values for time coefficients from 1,000 label permutations in GLMM models predicting Veillonella relative abundance. The red line represents the P value for the model trained without any label permutation.