A quantitative null model of additive diversity partitioning: examining the response of beta diversity to extinction

Paleobiological diversity is often expressed as alpha (within-sample), beta (among-sample), and gamma (total) diversities. However, when studying the effects of extinction on diversity patterns, only variations in alpha and gamma diversities are typically addressed. A null model that examines changes in beta diversity as a function of percent extinction is presented here. The model examines diversity in the context of a hierarchical sampling strategy that allows for the additive partitioning of gamma diversity into mean alpha and beta diversities at varying scales. Here, the sampling hierarchy has four levels: samples, beds, facies, and region; thus, there are four levels of a diversity (alpha(1), alpha(2), alpha(3), alpha(4)) and three levels of beta diversity (beta(1), beta(2), and beta(3)). Taxa are randomly assigned to samples within the hierarchy according to probability of occurrence, and initial mean alpha and beta values are calculated. A regional extinction is imposed, and the hierarchy is resampled from the remaining extant taxa. Post-extinction mean alpha and beta values are then calculated. Both non-selective and selective extinctions with respect to taxon abundance yield decreases in alpha, beta, and gamma diversities. Non-selective extinction with respect to taxon abundance shows little effect on diversity partitioning except at the highest extinction magnitudes (above 75% extinction), where the contribution of alpha(1) to total gamma increases at the expense of beta(3), with beta(1) and beta(2) varying little with increasing extinction magnitude. The pre-extinction contribution of alpha(1) to total diversity increases with increased probabilities of taxon occurrence and the number of shared taxa between facies. Both, and, contribute equally to total diversity at low occurrence probabilities, but beta(2) is negligible at high probabilities, because individual samples preserve all the taxonomic variation present within a facies. Selective extinction with respect to rare taxa indicates a constant increase in alpha(1) and constant decrease in beta(3) with increasing extinction magnitudes, whereas selective extinction with respect to abundant taxa yields the opposite pattern of an initial decrease in a, and increase in beta(3). Both beta(1) and beta(2) remain constant with increasing extinction for both cases of selectivity. By comparing diversity partitioning before and after an extinction event, it may be possible to determine whether the extinction was selective with respect to taxon abundances, and if so, whether that selectivity was against rare or abundant taxa. Field data were collected across a Late Ordovician regional extinction in the Nashville Dome of Tennessee, with sampling hierarchy similar to that of the model. These data agree with the abundant-selective model, showing declines in alpha, beta, and gamma diversities, and a decrease in alpha(1) and increase in P3, which suggests this extinction may have targeted abundant taxa.