Capturing temporal heterogeneity of communities: A temporal β-diversity based on Hill numbers and time series analysis

Beta-diversity is a term used to refer to the heterogeneity in the composition of species through space or time. Despite a consensus on the advantages of measuring β-diversity using data on species abundances through Hill numbers, we still lack a measure of temporal β-diversity based on this framework. In this paper, we present the mathematical basis for a temporal β-diversity measure, based on both signal processing and Hill numbers theory through the partition of temporal ƴ-diversity. The proposed measure was tested in four hypothetical simulated communities with species varying in temporal concurrence and abundance and two empirical data sets. The values of each simulation reflected community heterogeneity and changes in abundance over time. In terms of ƴ-diversity, q-values are closely related to total richness (S) and show a negative exponential pattern when they increase. For α-diversity, q-value profiles were more variable than ƴ-diversity, and different decaying patterns in α-diversity can be observed among simulations. Temporal β-diversity shows different patterns, which are principally related to the rate of change between ƴ- and α-diversity. Our framework provides a direct and objective approach for comparing the heterogeneity of temporal community patterns; this measure can be interpreted as the effective number of completely different unique communities over the sampling period indicating either a larger variety of community structures or higher species heterogeneity through time. This method can be applied to any ecological community that has been monitored over time.