HIERARCHICAL SAMPLING AND ADDITIVE DIVERSITY PARTITIONING ACROSS MULTIPLE SPATIAL AND TEMPORAL SCALES: AN EXAMPLE WITH UPPER MISSISSIPPIAN (CHESTERIAN) BRACHIOPODS FROM THE SOUTHERN OZARK UPLIFT, NORTH AMERICA

Documenting changes in biodiversity at multiple spatial and temporal levels has become a major focus of paleoecological research. The most familiar and commonly used levels of diversity are alpha, beta and gamma, usually calculated multiplicatively such that beta is the ratio of gamma to alpha, or some other multiplicative metric such as the Jaccard Coefficient. Multiplicative computations of beta provide valuable information on similarity or turnover between alpha and gamma. However, multiplicative calculations are not directly comparable to either alpha or gamma because of unit incongruence. Recently, modern ecologists have begun using additive diversity partitioning (beta is the difference between gamma and alpha) where all three measures have the same units and are directly comparable. Additionally, additive partitioning allows simultaneous comparison of multiple levels. Additive diversity partitioning provides a flexible framework for analyzing spatial and temporal biodiversity patterns and should be applied more widely to paleoecological data.

To illustrate additive diversity partitioning, quantitative samples of upper Mississippian brachiopods were collected from the southern Ozark uplift in Arkansas and Oklahoma using a spatio-temporal hierarchy. The sampling hierarchy has four levels: collection, bed, facies and depositional sequence. Additive partitioning of three diversity metrics (simple richness, Shannon information, Gini coefficient) are compared. The richness partition shows that most diversity is gained between beds and faces. The Shannon information and the Gini coefficient, taken as measures of abundance structure, have similar partitions and show that most of the diversity is at the collection level. These results are interpreted to mean that taxonomic heterogeneity of beds within facies is more important for generating richness than within bed patchiness or differences between facies, and there is little change in the abundance structure above the collection level. These results are specific to this study, but the methods of hierarchical sampling and additive partitioning can be applied to any paleoecological study with any number of spatial and temporal scales.