Horizontal and vertical aspects of species diversity in the fossil record: Alpha, beta, and the temporal nature of the richness-temperature relation

Species diversity comprises two different and irreducible variables, inventory diversity (the number of species present in some area of a given size) and differential diversity (how diversity scales with space). Existing concepts of (and therefore metrics for) differential diversity either do not really address its spatial nature or are difficult to apply to the fossil record. Here I develop a new metric for differential diversity. When species diversity---corrected for sample size---is measured along the path of minimum length connecting a set of (coeval) localities, it shows an approximately linear relationship to distance in logarithmic space. The slope of this line may be taken as a measure of differential diversity and is viewed as an analog for point-sources of the well-known species-area relation. The metric is tested extensively with modern data-sets in order to validate its meaningfulness in modern biotas (prior to applying it to fossil data).; A diversity time-series for squamates (lizard, snake and amphisbaenian) in the early Eocene is then generated by describing a series of six assemblages from the early Eocene of Wyoming. Eight new genera and 14 new species are named formally. The association of isolated cranial elements permits the reconstruction of portions of the skull of many forms, and so constrains their phylogenetic relationships. Important new records include species on the stems Corytophaninae, Anolis, Lepidophyma, Xantusia and possibly Cordylidae; the earliest certain record of the stem-clade of Gerrhonotinae; several new glyptosaurines; and an enigmatic new anguimorph of uncertain affinities. New material confirms the relationship of Apodosauriscus to Anniella. Provaranosaurus is argued to be a stem-member of Shinisaurus ; the stem-xenosaur Restes is very rare.; The stratigraphic relations of the localities, their documented diversities, and regional temperature profiles for the early Eocene of the Rocky Mountain interior are used finally in a preliminary diachronic test of the relationship between local (inventory) species diversity and temperature. A positive relationship is discovered, but so are two strong departures from expectation. The consideration of additional localities as well as estimation of paleotemperature for the localities using isotopic proxies is needed to determine their significance.