Reply to: Examining microbe–metabolite correlations by linear methods

Abstract

Quinn and Erb propose to apply a centered log-ratio (CLR) transform before performing correlation analysis and make the case that, when used correctly, correlation and proportionality can outperform MMvec in identifying microbe–metabolite interactions. While this may be an appealing strategy, it is important to note that the correlations estimated from CLR-transformed data will have a fundamentally different interpretation than the true correlations in the environment, namely: Cov xi; yj ≠Cov clr(x)i, clr(y)j where xi and yj are the absolute abundances for microbe abundances x and metabolite abundances y in taxon i and metabolite j. Because the absolute abundances are often not available, inferring the true correlations between microbes and metabolites is not tractable (Supplementary Note 1). This phenomenon has been extensively studied in refs. 2–4 , and one of our recent studies provides the intuition behind this in the case of differential abundance . Because of this discrepancy, we proposed to use co-occurrence probabilities instead of correlation.