Rebuilding microbiome diversity theory on the closed simplex
- 1Yale University
Abstract
Ecological diversity theory links diversity within local communities to diversity of higher-level ensembles, but this scale structure is largely absent from microbiome analysis. Alpha diversity is usually treated as a within-sample summary, whereas "beta diversity" often denotes pairwise dissimilarity and gamma diversity is rarely explicit. We restore the local-regional architecture for environmental, host-associated and longitudinal microbiomes and distinguish regional beta diversity from pairwise dissimilarity and predictor-associated compositional variation. To quantify these objects for sparse compositions, we introduce Hellinger-Riemann intrinsic coordinates (HRIC), a one-to-one, bounded normal-coordinate representation of the closed simplex that retains exact zeros. The same coordinates yield Simplex Hellinger alpha and gamma diversity, additive regional beta diversity, taxon contributions, pairwise dissimilarity and model-explained dispersion. Simulations established the correspondence between HRIC dispersion and the between-condition component of PERMANOVA. Across Arctic and North Atlantic communities, local diversity relative to each regional benchmark covaried similarly with vertical environmental gradients despite partly different taxon-level associations. In a randomized autologous faecal microbiota transplantation trial, recipients returned earlier towards their personal pre-transplant compositions, whereas the alpha-diversity difference was smaller and less precise. Explicit local and regional referents therefore connect diversity partitioning with compositional analysis across microbial systems.
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BibTeX
@misc{zhang2026rebuilding,
title = {{Rebuilding microbiome diversity theory on the closed simplex}},
author = {Y. Zhang and Z. Zhu},
howpublished = {bioRxiv},
year = {2026},
month = sep,
doi = {10.64898/2026.09.02.748976},
url = {https://www.biorxiv.org/content/10.64898/2026.09.02.748976v1},
note = {CC BY-NC-ND},
}
RIS
TY - UNPB
TI - Rebuilding microbiome diversity theory on the closed simplex
AU - Y. Zhang
AU - Z. Zhu
PY - 2026
DA - 2026/09/02
PB - bioRxiv
DO - 10.64898/2026.09.02.748976
UR - https://www.biorxiv.org/content/10.64898/2026.09.02.748976v1
AB - Ecological diversity theory links diversity within local communities to diversity of higher-level ensembles, but this scale structure is largely absent from microbiome analysis. Alpha diversity is usually treated as a within-sample summary, whereas "beta diversity" often denotes pairwise dissimilarity and gamma diversity is rarely explicit. We restore the local-regional architecture for environmental, host-associated and longitudinal microbiomes and distinguish regional beta diversity from pairwise dissimilarity and predictor-associated compositional variation. To quantify these objects for sparse compositions, we introduce Hellinger-Riemann intrinsic coordinates (HRIC), a one-to-one, bounded normal-coordinate representation of the closed simplex that retains exact zeros. The same coordinates yield Simplex Hellinger alpha and gamma diversity, additive regional beta diversity, taxon contributions, pairwise dissimilarity and model-explained dispersion. Simulations established the correspondence between HRIC dispersion and the between-condition component of PERMANOVA. Across Arctic and North Atlantic communities, local diversity relative to each regional benchmark covaried similarly with vertical environmental gradients despite partly different taxon-level associations. In a randomized autologous faecal microbiota transplantation trial, recipients returned earlier towards their personal pre-transplant compositions, whereas the alpha-diversity difference was smaller and less precise. Explicit local and regional referents therefore connect diversity partitioning with compositional analysis across microbial systems.
ER -