Jaccard dissimilarity in stochastic community models based on the species-independence assumption
A fundamental problem in ecology is understanding the causes of change in species composition among sites (i.e. beta diversity). At present it is unclear how spatial heterogeneity in species occupancy across sites shapes these patterns. To address this question, we develop probabilistic models that consider two spatial or temporal sites, where presence probabilities vary both among species and between the sites. We derive analytical and approximate formulae for the expectation of pairwise beta-diversity. Using a novel graphical tool, Stochastic Incidence Plots (SIPs), which depict the presence probabilities in two sites across species labels, we develop a means to conceptualize the heterogeneity in presence probabilities: the steepness or unevenness of SIPs reflects species-level heterogeneity, while the degree of overlap between SIPs indicates site-level heterogeneity. Utilizing SIPs and a combinatorial approach in a two-species scenario, we demonstrate that beta-diversity is lower when SIPs are parallel compared to when they are anti-parallel. We also find that this prediction is testable with the well-known checkerboard pattern in incidence matrices. Finally, we applied the method to the species distribution models for five woodpecker species in Switzerland, showing that their spatial distributions will change significantly in the future. Overall, this work improves our understanding of how pairwise beta-diversity responds to occupancy heterogeneity.