Using null models to disentangle variation in community dissimilarity from variation in α-diversity

β-diversity represents the compositional variation among communities from site-to-site, linking local (α-diversity) and regional (γ-diversity). Researchers often desire to compare values of β-diversity across localities or experimental treatments, and to use this comparison to infer possible mechanisms of community assembly. However, the majority of metrics used to estimate β-diversity, including most dissimilarity metrics (e.g., Jaccard's and Sørenson's dissimilarity index), can vary simply because of changes in the other two diversity components (α or γ-diversity). Here, we overview the utility of taking a null model approach that allows one to discern whether variation in the measured dissimilarity among communities results more from changes in the underlying structure by which communities vary, or instead simply due to difference in α-diversity among localities or experimental treatments. We illustrate one particular approach, originally developed by Raup and Crick (1979) in the paleontological literature, which creates a re-scaled probability metric ranging from −1 to 1, indicating whether local communities are more dissimilar (approaching 1), as dissimilar (approaching 0), or less dissimilar (approaching −1), than expected by random chance. The value of this metric provides some indication of the possible underlying mechanisms of community assembly, in particular the degree to which deterministic processes create communities that deviate from those based on stochastic (null) expectations. We demonstrate the utility of this metric when compared to analyses of Jaccard's dissimilarity index with case studies from disparate empirical systems (coral reefs and freshwater ponds) that differ in the degree to which disturbance altered α-diversity, as well as the selectivity by which disturbance acted on members of the community.