Additive partitioning of rarefaction curves and species-area relationships:: unifying α-, β- and γ-diversity with sample size and habitat area

Additive partitioning of species diversity is widely applicable to different kinds of sampling regimes at multiple spatial and temporal scales. In additive partitioning, the diversity within and among samples (alpha and beta) is expressed in the same units of species richness, thus allowing direct comparison of alpha and beta. Despite its broad applicability, there are few demonstrated linkages between additive partitioning and other approaches to analysing diversity. Here, we establish several connections between diversity partitions and patterns of habitat occupancy, rarefaction, and species-area relationships. We show that observed partitions of species richness are equivalent to sample-based rarefaction curves, and expected partitions from randomization tests are approximately equivalent to individual-based rarefaction. Additive partitions can also be applied to species-area relationships to determine the relative contributions of factors influencing the beta-diversity among habitat fragments.