Alpha diversity (α-diversity) is the biodiversity within a particular area, community or ecosystem, and is measured by counting the number of taxa within the ecosystem (usually species).
The field of ecology includes researchers who study current biodiversity. Biodiversity of the past is the realm of Paleoecology. Past biodiversity is usually viewed by plotting the taxonomic richness of a geographic area over a temporal scale. For example, Sepkoski produced a diagram showing the diversification of skeletonized marine invertebrate taxa. This famous diagram shows a distinct three distinct logistic curves representing the diversification of three distinct faunas.
Richard K. Bambach is Professor Emeritus of Paleontology at Harvard University. His research is focused on community paleoecology emphasizing the nature of fossil assemblages, analysis of gradients in the distribution of fossil assemblages reflecting environmental patterns, analysis of ecologic structure of fossil assemblages and changes in apparent community organization through time. http://www.geol.vt.edu/profs/rkb/rkb-r.html
Jonathan M. Adrain is an associate professor at the University of Iowa, studying Silurian trilobite alpha diversity and the end-Ordovician mass extinction. http://www.uiowa.edu/~geology/people/faculty/adrain
Sarda Sahney is a researcher at the University of Bristol in England who is conducting a large-scale macroevolutionary study on tetrapod alpha diversity through the Phanerozoic. http://seis.bris.ac.uk/~glxss/
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