Rebuilding microbiome diversity theory on the closed simplex
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…
Diversity within local communities intertwines with the variety of higher-level groups, yet this hierarchical structure often eludes microbiome studies. Alpha diversity typically serves as an internal measurement, while beta diversity usually signifies pairwise dissimilarity; gamma diversity remains less defined. Our work reinstates the local-regional framework for environmental, host-associated, and longitudinal microbiomes, distinguishing regional beta diversity from pairwise dissimilarity and compositional variation influenced by predictors.
To measure these entities, especially in cases of sparse compositions, we propose Hellinger-Riemann intrinsic coordinates (HRIC), a one-to-one, bounded coordinate system applied to the closed simplex that preserves exact zeros. These coordinates facilitate the calculation of Simplex Hellinger alpha and gamma diversity, regional beta diversity, taxon contributions, pairwise dissimilarity, and dispersion attributable to models.
Simulations confirmed the alignment between HRIC dispersion and the component of PERMANOVA accounting for differences between conditions. Across Arctic and North Atlantic communities, the local diversity relative to each regional benchmark showed a similar correlation with vertical environmental gradients, even when taxon-level associations diverged.
In a randomized trial involving the transfer of an individual's fecal microbiota, recipients gradually returned to their original microbial compositions, albeit with a smaller and less precise difference in alpha diversity. Hence, explicit local and regional references establish a connection between diversity partitioning and compositional analysis across diverse microbial systems.
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