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

Paleobiological diversity is often expressed as α (within-sample), β (among-sample), and γ (total) diversities. However, when studying the effects of extinction on diversity patterns, only variations in α and γ diversities are typically addressed. A null model that examines changes in β 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 γ diversity into mean α and β diversities at varying scales. Here, the sampling hierarchy has four levels: samples, beds, facies, and region; thus, there are four levels of α diversity (α1, α2, α3, α4) and three levels of β diversity (β1, β2, and β3). Taxa are randomly assigned to samples within the hierarchy according to probability of occurrence, and initial mean α and β values are calculated. A regional extinction is imposed, and the hierarchy is resampled from the remaining extant taxa. Post-extinction mean α and β values are then calculated.Both non-selective and selective extinctions with respect to taxon abundance yield decreases in α, β, and γ 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 α1 to total γ increases at the expense of β3, with β1 and β2 varying little with increasing extinction magnitude. The pre-extinction contribution of α1 to total diversity increases with increased probabilities of taxon occurrence and the number of shared taxa between facies. Both β1 and β2 contribute equally to total diversity at low occurrence probabilities, but β2 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 α1 and constant decrease in β3 with increasing extinction magnitudes, whereas selective extinction with respect to abundant taxa yields the opposite pattern of an initial decrease in α1 and increase in β3. Both β1 and β2 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 α, β, and γ diversities, and a decrease in α1 and increase in β3, which suggests this extinction may have targeted abundant taxa.