Disentangling nonrandom structure from random placement when estimating β-diversity through space or time

There is considerable interest in understanding patterns of β-diversity that measure the amount of change in species composition through space or time. Most hypotheses for β-diversity evoke nonrandom processes that generate spatial and temporal within-species aggregation; however, β-diversity can also be driven by random sampling processes. Here, we describe a framework based on rarefaction curves that quantifies the nonrandom contribution of species compositional differences across samples to β-diversity. We isolate the effect of within-species spatial or temporal aggregation on beta-diversity using a coverage standardized metric of β-diversity (β_C). We demonstrate the utility of our framework using simulations and an empirical case study examining variation in avian species composition through space and time in engineered versus natural riparian areas. The primary strengths of our approach are that it provides an intuitive visual null model for expected patterns of biodiversity under random sampling that allows integrating analyses across α-, γ-, and β-scales. Importantly, the method can accommodate comparisons between communities with different species pool sizes, and it can be used to examine species turnover both within and between meta-communities.