Analytical models for β-diversity and the power-law scaling of β-deviation

O_LI{beta}-diversity is a primary biodiversity pattern for inferring community assembly. A randomized null model that generates a standardized {beta}-deviation has been widely used for this purpose. However, the null model has been much debated and its application is limited to abundance data. C_LIO_LIHere we derive analytical models for {beta}-diversity to address the debate, clarify the interpretation, and extend the application to occurrence data. C_LIO_LIThe analytical analyses show unambiguously that the standardized {beta}-deviation is a quantification of the effect size of non-random spatial distribution of species on {beta}-diversity for a given species abundance distribution. It robustly scales with sampling effort following a power law with exponent of 0.5. This scaling relationship offers a simple method for comparing {beta}-diversity of communities of different sizes. C_LIO_LIAssuming logseries distribution for the metacommunity species abundance distribution, our model allows for calculation of the standardized {beta}-deviation using occurrence data plus a datum on the total abundance. C_LIO_LIOur theoretical model justifies and generalizes the use of the {beta} null model for inferring community assembly rules. C_LI