AN INITIAL APPROACH TO THE ESTIMATION OF UNCERTAINTY IN BIODIVERSITY ESTIMATES OBTAINED FROM COMPOSITE SECTIONS, WITH AN EXAMPLE FROM THE HIRNANTIAN MASS EXTINCTION

Comparisons of patterns of biodiversity change require an understanding of the uncertainty in estimates of standing diversity, and in the rates extinction and origination. Diversity data depend heavily on the preservation potential of the species under study, the completeness of the rock record itself, and the sampling effort expended. The effects of binning and stratigraphic range determination are all key issues in developing an understanding of the nature and sources of the uncertainty appearing in diversity patterns. We present here the initial results of a long term project to develop a framework for assessing variation in diversity patterns. An analytic framework has been developed to form a composite listing of the presence and absence of taxa based on occurrence data from individual sections, using the constrained optimization approach to stratigraphic section matching. This composite pattern of observations of taxa over time is then analyzed using maximum likelihood methods to estimate the rates of recovery, extinction, origination and diversity. Jackknifing methods may then be applied to the original section data to estimate the variability of both composite section formation and subsequent rate estimations. We here apply these methods to patterns of graptolite diversity during the Hirnantian Mass Extinction based on collections from the Yangtze Platform region of SE China. Initial results are similar to our prior bootstrap estimates of this history and its standard errors, but suggest a substantially lower (and geologically more reasonable) recovery rate than previous analyses. We present a discussion of how the current analytic procedure will be expanded to accommodate additional geological data and/or statistical approaches to variance estimation.