Null model analyses in presence-absence data have enjoyed much success in pursuit of measuring biodiversity, typically by assessing statistically significant deviations of observed species distributions in space, from randomly expected (null) patterns. However, the null model approach has faced technical and conceptual limitations in (i) large species-pool sizes or large landscape sizes, (ii) species equivalence in colonization-extinction parameters, (iii) spatial homogeneity, and/or (iv) statics (rather than dynamics) of biodiversity.

In this talk, I demonstrate a theoretical framework resolving those restrictions, on the basis of MacArthur and Wilson's (1967) island biogeography theory. We carry out two types of analyses: (1) two species inhabiting a variable number of sites using Jaccard dissimilarity index, and (2) two sites inhabited by a variable number of species using segregation and co-occurrence indices. By means of probabilistic methods, we derive the analytical formulae of those indices which are in general dynamical (time-dependent). I also introduce Fast Fourier Transform to achieve better computational speed, and conclude with some applications and further generalization of the framework beyond pairwise analyses.

Take home message: Our method offers a powerful, user-friendly platform to assess dynamic biodiversity.