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I extend the traditional SAR, which has achieved status of ecological law andplays a critical role in global biodiversity assessment, to the general (alpha-or beta-diversity in Hill numbers) diversity area relationship (DAR). Theextension was motivated to remedy the limitation of traditional SAR that onlyaddress one aspect of biodiversity scaling, i.e., species richness scaling overspace. The extension was made possible by the fact that all Hill numbers are inunits of species (referred to as the effective number of species or as speciesequivalents), and I postulated that Hill numbers should follow the same orsimilar pattern of SAR. I selected three DAR models, the traditional power law(PL), PLEC (PL with exponential cutoff) and PLIEC (PL with inverse exponentialcutoff). I defined three new concepts and derived their quantifications: (i)DARprofile: z-q series where z is the PL scaling parameter at different diversityorder (q); (ii)PDO (pair-wise diversity overlap) profile: g-q series where g isthe PDO corresponding to q; (iii) MAD (maximal accrual diversity) profile:Dmax-q series where Dmax is the MAD corresponding to q. Furthermore, the PDO-gis quantified based on the self-similarity property of the PL model, and Dmaxcan be estimated from the PLEC parameters. The three profiles constitute anovel DAR approach to biodiversity scaling. I verified the postulation with theAmerican gut microbiome project (AGP) dataset of 1473 healthy North Americanindividuals (the largest human dataset from a single project to date). The PLmodel was preferred due to its simplicity and established ecological propertiessuch as self-similarity (necessary for establishing PDO profile), and PLEC hasan advantage in establishing the MAD profile. All three profiles for the AGPdataset were successfully quantified and compared with existing SAR parametersin the literature whenever possible.

Extending species-area relationships (SAR) to diversity-area relationships (DAR)