BRINGING UP BETA: EXAMINING THE EFFECTS OF EXTINCTION ON DIVERSITY WITH AN ADDITIVE PARTITIONING MODEL

Diversity may be expressed as alpha (within sample), beta (among samples), and gamma (total samples) diversities. When studying how extinction affects diversity, only variations in alpha and gamma diversity are typically addressed. A null model that examines changes in beta diversity as a function of percent extinction is presented.

The model presents 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. For a geographic region, total gamma diversity is the sum of mean alpha diversity of the total samples collected and the mean beta diversity between samples (beta one), beds (beta two), and facies (beta three), respectively. The model assumes a regional maximum richness with varying levels of shared and unique taxa between two facies. All taxa within a facies are assigned a probability of occurrence in a sample and are randomly assigned to samples. Taxa in each sample have lognormally distributed abundances. For each facies, a given number of beds and samples are generated, and initial mean alpha and beta values are calculated. Two conditions of extinction are tested, including random extinction and selective extinction that preferentially targets rare taxa. The extinction is imposed at the regional level, and the hierarchy is resampled from the remaining taxa. Post-extinction mean alpha and beta values are then calculated.

Both random and selective extinction have little effect on diversity partitioning except at the highest magnitudes, where alpha one increases and beta three decreases. Beta one and beta two vary little with increasing extinction magnitude. The relative contribution of alpha one increases with increased probability of taxon occurrence and number of shared taxa between facies, and beta values scale accordingly. Beta one and beta two contribute equally at low occurrence probabilities, but beta two is negligible at high probabilities. Field data collected across a regional extinction boundary using a similar sampling hierarchy to that of the model are in accordance with the model results, showing little change in diversity partitioning from pre- to post-extinction intervals.