{
  "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.",
  "abstract_shown": true,
  "affiliations": [
    "Yale University"
  ],
  "article_type": "New results",
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "name": "Y. Zhang"
    },
    {
      "affs": [
        0
      ],
      "name": "Z. Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fc73138acca77.bib",
  "cited_by": 0,
  "doi": "10.64898/2026.09.02.748976",
  "fulltext_url": "https://www.biorxiv.org/content/10.64898/2026.09.02.748976v1.full",
  "id": "fc73138acca77",
  "issns": [],
  "landing_url": "https://www.biorxiv.org/content/10.64898/2026.09.02.748976v1",
  "language": null,
  "licence": "CC-BY-NC-ND",
  "licence_label": "CC BY-NC-ND",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "biorxiv",
      "microbiology"
    ],
    [
      "openalex",
      "2303|Microbial Community Ecology and Physiology"
    ]
  ],
  "openalex": "W7208750052",
  "pdf_url": "https://www.biorxiv.org/content/10.64898/2026.09.02.748976v1.full.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fc73138acca77.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:14Z",
      "native_id": "10.64898/2026.09.02.748976",
      "source": "biorxiv",
      "url": "https://www.biorxiv.org/content/10.64898/2026.09.02.748976v1"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "biorxiv:microbiology",
      "subfield": "microbiology"
    }
  ],
  "title": "Rebuilding microbiome diversity theory on the closed simplex",
  "title_text": "Rebuilding microbiome diversity theory on the closed simplex",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:14Z",
  "url": "https://research.draconitic.com/paper/fc73138acca77",
  "venue": "bioRxiv",
  "versions": []
}