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

¹ Karen M. Layou. Department of Geology, University of Georgia, Athens, Georgia 30602. klayou{at}uga.edu

Paleobiological diversity is often expressed as (within-sample), ß (among-sample), and (total) diversities. However, when studying the effects of extinction on diversity patterns, only variations in and diversities are typically addressed. A null model that examines changes in ß 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 diversity into mean and ß diversities at varying scales. Here, the sampling hierarchy has four levels: samples, beds, facies, and region; thus, there are four levels of diversity (₁, ₂, ₃, ₄) and three levels of ß diversity (ß₁, ß₂, and ß₃). Taxa are randomly assigned to samples within the hierarchy according to probability of occurrence, and initial mean and ß values are calculated. A regional extinction is imposed, and the hierarchy is resampled from the remaining extant taxa. Post-extinction mean and ß values are then calculated.

Both non-selective and selective extinctions with respect to taxon abundance yield decreases in , ß, and 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 ₁ to total increases at the expense of ß₃, with ß₁ and ß₂ varying little with increasing extinction magnitude. The pre-extinction contribution of ₁ to total diversity increases with increased probabilities of taxon occurrence and the number of shared taxa between facies. Both ß₁ and ß₂ contribute equally to total diversity at low occurrence probabilities, but ß₂ 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 ₁ and constant decrease in ß₃ with increasing extinction magnitudes, whereas selective extinction with respect to abundant taxa yields the opposite pattern of an initial decrease in ₁ and increase in ß₃. Both ß₁ and ß₂ 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 , ß, and diversities, and a decrease in ₁ and increase in ß₃, which suggests this extinction may have targeted abundant taxa.

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