EXAMINING THE EFFECTS OF EXTINCTION ON DIVERSITY WITH NULL MODELS: BRINGING UP BETA

Diversity may be expressed as alpha (a-within sample), beta (b-among samples), and gamma (g-total samples) diversities.  When studying how extinction affects diversity, only variations in a and g diversity are usually addressed.  Two null models that examine changes in b diversity as a function of percent extinction are presented.

The first model expresses b diversity as the number of shared taxa between two communities using the Jaccard coefficient (J).  Given an initial J (J_i) and an initial total richness for both communities, a random extinction of the same magnitude is carried out on each community, and a post-extinction J (J_p) is calculated. 

For all values of J_i, J_p decreases with increasing extinction magnitude, indicating the number of shared taxa declines with high levels of extinction.  The difference between J_i and J_p is greater for higher values of J_i because of the increased likelihood that shared taxa will be eliminated.

The second model examines diversity in the context of a hierarchical sampling strategy that allows for the additive partitioning of g diversity into mean a and b diversities at varying scales.  For a geographic region, total g diversity is the sum of mean a diversity of the total samples collected and the mean b diversity between samples (b₁), beds (b₂), and facies (b₃), respectively.  The model assumes a regional maximum richness with varying levels of shared and unique taxa between two facies.  All taxa in a facies have the same 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 a and b values are calculated.  A random extinction is imposed at regional level, and the hierarchy is resampled from the remaining taxa.  Post-extinction mean a and b values are calculated.

Extinction has little effect on diversity partitioning except at the highest magnitudes; thus, any observed differences in partitioning from pre- to post-extinction would suggest the extinction was selective.  The relative contribution of a₁ increases with increased probability of taxon occurrence and number of shared taxa between facies, and b values scale accordingly.  b₁ and b₂ contribute equally at low occurrence probabilities, but b₂ is negligible at high probabilities.