Uncovering the Horseshoe Effect in Microbial Analyses.

The horseshoe effect is a phenomenon that has long intrigued ecologists. The effect was commonly thought to be an artifact of dimensionality reduction, and multiple techniques were developed to unravel this phenomenon and simplify interpretation. Here, we provide evidence that horseshoes arise as a consequence of distance metrics that saturate-a familiar concept in other fields but new to microbial ecology. This saturation property loses information about community dissimilarity, simply because it cannot discriminate between samples that do not share any common features. The phenomenon illuminates niche differentiation in microbial communities and indicates species turnover along environmental gradients. Here we propose a rationale for the observed horseshoe effect from multiple dimensionality reduction techniques applied to simulations, soil samples, and samples from postmortem mice. An in-depth understanding of this phenomenon allows targeting of niche differentiation patterns from high-level ordination plots, which can guide conventional statistical tools to pinpoint microbial niches along environmental gradients. The horseshoe effect is often considered an artifact of dimensionality reduction. We show that this is not true in the case for microbiome data and that, in fact, horseshoes can help analysts discover microbial niches across environments.