A new DTAR (diversity–time–area relationship) model demonstrated with the indoor microbiome

Abstract Aim The spatio‐temporal distribution of biodiversity is a core field of biogeography, and the so‐termed species–time–area relationship (STAR), together with its siblings, that is the SAR (species–area relationship) and STR (species–time relationship), has achieved the rare status of classic laws in ecology and biogeography. Traditionally, the STAR or its recent generalization DTAR (diversity–time–area relationship) has been described with the bivariate power law (BPL) model or more recently with Whittaker, Triantis, and Ladle (2008, Journal of Biography ; 35 : 18) general dynamic model (GDM). We propose to extend the classic BPL into a more flexible DTAR model, which offers new quantitative methods for estimating maximal global diversity and charactering the relationship between local and regional diversity. Location Indoor microbiome. Taxon Microbes. Method We revise the BPL model by introducing two taper‐off (cut‐off) parameters or BPLEC (bivariate power law with exponential cutoffs) model, which eventually overwhelms the unsaturated increase of diversity over time and/or space and consequently can offer more realistic modelling of the joint spatio‐temporal distribution of biodiversity. Based on the BPLEC model, we further define three new concepts for DTAR: maximal accrual diversity (MAD) profile, local‐to‐regional diversity (LRD) ratio profile and local‐to‐global diversity (LGD) ratio profile. Results We introduce and demonstrate the new BPLEC model with the indoor microbiome datasets (Lax et al., 2014, Science ; 345 : 1048–1052). The new model fitted to the microbiome datasets equally well or slightly better than existing BPL and GDM models, but it possesses two advantages stated below. Main conclusion First, the new BPLEC model overcomes the unlimited diversity accrual in temporal and/or spatial dimensions and hence offers more realistic modelling to the DTAR. Second, the MAD and LRD/LGD offer useful methods for estimating the “dark” or “potential” diversity, which accounts for the species locally absent but present in a habitat‐specific regional species pool.