The application of zeta diversity as a continuous measure of compositional change in ecology
Zeta diversity provides the average number of shared species across n sites (or shared operational taxonomic units (OTUs) across n cases). It quantifies the variation in species composition of multiple assemblages in space and time to capture the contribution of the full suite of narrow, intermediate and wide-ranging species to biotic heterogeneity. Zeta diversity was proposed for measuring compositional turnover in plant and animal assemblages, but is equally relevant for application to any biological system that can be characterised by a row by column incidence matrix. Here we illustrate the application of zeta diversity to explore compositional change in empirical data, and how observed patterns may be interpreted. We use 10 datasets from a broad range of scales and levels of biological organisation - from DNA molecules to microbes, plants and birds - including one of the original data sets used by R.H. Whittaker in the 1960s to express compositional change and distance decay using beta diversity. The applications show (i) how different sampling schemes used during the calculation of zeta diversity may be appropriate for different data types and ecological questions, (ii) how higher orders of zeta may in some cases better detect shifts, transitions or periodicity, and importantly (iii) the relative roles of rare versus common species in driving patterns of compositional change. By exploring the application of zeta diversity across this broad range of contexts, our goal is to demonstrate its value as a tool for understanding continuous biodiversity turnover and as a metric for filling the empirical gap that exists on spatial or temporal change in compositional diversity.