## 2 Materials and Methods
### Statistical Analyses  
Our primary analyses were conducted among all participants (\(N\) = 441). Non-normally distributed variables were transformed using natural logarithm for continuous variables and arcsine-square-root for proportions. For appropriate logarithmic transformation, it was necessary to add constants to some variables to avoid infinite values (1 to physical activity; 0.5 to adiponectin; 0.1 to total SCFAs and acetate; 0.05 to propionate; 0.01 to butyrate; and 0.001 to isobutyrate). To understand how the participant characteristics varied across levels of the dependent variables in our study, we calculated and presented unadjusted means, or percentages when appropriate, of demographic, lifestyle and clinical factors across tertiles of fecal butyrate concentrations and gut microbiota diversity. Tertile 1 corresponds to the lowest level, tertile 2 the intermediate level, and tertile 3 the highest level. We tested for significant trends across tertiles using ANOVA (for continuous variables) or chi-squared tests (for categorical variables), and adjusted \(p\)-values for multiple comparisons [26]. Similar comparisons were performed across tertiles of acetate, propionate, isobutyrate, and total SCFAs. To address potential confounding associations, we next performed various regression models adjusted for pertinent covariates. Our main multivariable models included participant age (years; continuous), city of residence (Bogota, Medellin, Cali, Barranquilla and Bucaramanga), physical activity (MET/min/week; continuous), fiber intake (g/day; continuous), and total caloric intake (kcal/day; continuous). We adjusted for dietary fiber intake because it is the main substrate for SCFA production, and it is associated with obesity and cardiometabolic risk factors. Similarly, adjustment for caloric intake was justified because individuals might have higher SCFA levels because they eat more overall, which can contribute to obesity. The other covariates included in multivariable models also constitute potential confounders because of their association with cardiometabolic health, microbiota diversity, and SCFA production [27; 28; 29]. After evaluating non-linear associations with restricted cubic splines, we proceeded to use multivariable-adjusted models to examine differences in microbiota diversity and cardiometabolic parameters by tertiles of SCFAs. Procrustes analysis [30] was implemented with 10,000 permutations to explore associations of microbial community beta diversity with multivariable-adjusted SCFA concentrations (total SCFAs, acetate, propionate, butyrate, and isobutyrate), BMI, waist circumference, and blood pressure. Multivariable-adjusted Pearson correlation coefficients were calculated between pairs of variables (SCFAs, adiposity, blood chemistry, blood pressure, and microbiota OTU richness), and adjusted \(p\)-values were obtained using the Benjamini and Hochberg correction (FDR). To determine associations between specific microbial taxa and SCFAs, we first extracted OTUs with median abundances \(\geq\)0.001% and then fitted the quasi-Poisson generalized linear models on rarefied sequence counts. Multivariable-adjusted Spearman correlation coefficients between OTU abundances and individual SCFAs were next calculated, and FDR-adjusted \(p\)-values were obtained [26]. Finally, we used log-binomial multivariable regression models with robust variance to examine tertiles of butyrate (and the other SCFAs) and microbiota diversity in relation to the prevalence of obesity (defined as BMI \(\geq\) 30 kg/m\({}^{2}\)), central obesity (defined as waist circumference \(\geq\)102 cm in men, or \(\geq\)88 cm in women), and hypertension (defined as SBP \(\geq\) 130 mm Hg, or DBP \(\geq\) 80 mm Hg, or previous diagnosis of hypertension or use of antihypertensive medications). Log-binomial multivariable regression models were restricted to individuals with no missing values (\(N\) = 431).