Measuring continuous compositional change using decline and decay in zeta diversity

Incidence, or compositional, matrices are generated for a broad range of research applications in biology. Zeta diversity provides a common currency and conceptual framework that links incidence-based metrics with multiple patterns of interest in biology, ecology, and biodiversity science. It quantifies the variation in species (or OTU) composition of multiple assemblages (or cases) in space or time, to capture the contribution of the full suite of narrow, intermediate, and wide-ranging species to biotic heterogeneity. Here we provide a conceptual framework for the application and interpretation of patterns of continuous change in compositional diversity using zeta diversity. This includes consideration of the survey design context, and the multiple ways in which zeta diversity decline and decay can be used to examine and test turnover in the identity of elements across space and time. We introduce the zeta ratio-based retention rate curve to quantify rates of compositional change. We illustrate these applications using 11 empirical data sets from a broad range of taxa, scales, and levels of biological organization-from DNA molecules and microbes to communities and interaction networks-including one of the original data sets used to express compositional change and distance decay in ecology. We show (1) how different sample selection schemes used during the calculation of compositional change are appropriate for different data types and questions, (2) how higher orders of zeta may in some cases better detect shifts and transitions, and (3) the relative roles of rare vs. common species in driving patterns of compositional change. By exploring the application of zeta diversity decline and decay, including the retention rate, across this broad range of contexts, we demonstrate its application for understanding continuous turnover in biological systems.