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Uncovering the Horseshoe Effect in Microbial Analyses

NCJ Number
Date Published
8 pages
Although the "horseshoe" effect is often considered an artifact of dimensionality reduction, this article demonstrates that this is not true in the case for microbiome data and that, in fact, "horseshoes" can help analysts discover microbial niches across environments.
One phenomenon that commonly occurs in data sets containing ecological gradients is the horseshoe effect or Guttman effect. This phenomenon is typified by a linear gradient that appears as a curve in ordination space. The horseshoe effect, or its relative, the arch effect (where the ends of the gradient do not attract each other along the first principal coordinate as they do in the horseshoe effect), is observed using multiple types of ordinations, including principal-component analysis, principal-coordinate analysis, nonmetric multidimensional scaling, correspondence analysis, and many other methods. 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. The current project provides evidence that horseshoes arise as a consequence of distance metrics that saturatea 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. This article proposes 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. 2 figures and 14 references (publisher abstract modified)

Date Published: January 1, 2017