The spatial structure of Phanerozoic marine animal diversity

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Abstract

The global fossil record of marine animals has fueled long-standing debates about diversity change through time and the drivers of this change. However, the fossil record is not truly global. It varies considerably in geographic scope and in the sampling of environments among intervals of geological time. We account for this variability using a spatially explicit approach to quantify regional-scale diversity through the Phanerozoic. Among-region variation in diversity is comparable to variation through time, and much of this is explained by environmental factors, particularly the extent of reefs. By contrast, influential hypotheses of diversity change through time, including sustained long-term increases, have little explanatory power. Modeling the spatial structure of the fossil record transforms interpretations of Phanerozoic diversity patterns and their macroevolutionary explanations. This necessitates a refocus of deep-time diversification studies.

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Mass extinctions in the marine fossil record.

D Raup, J Sepkoski (1982)

A new compilation of fossil data on invertebrate and vertebrate families indicates that four mass extinctions in the marine realm are statistically distinct from background extinction levels. These four occurred late in the Ordovician, Permian, Triassic, and Cretaceous periods. A fifth extinction event in the Devonian stands out from the background but is not statistically significant in these data. Background extinction rates appear to have declined since Cambrian time, which is consistent with the prediction that optimization of fitness should increase through evolutionary time.

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Scaling regression inputs by dividing by two standard deviations.

Andrew Gelman (2008)

Interpretation of regression coefficients is sensitive to the scale of the inputs. One method often used to place input variables on a common scale is to divide each numeric variable by its standard deviation. Here we propose dividing each numeric variable by two times its standard deviation, so that the generic comparison is with inputs equal to the mean +/-1 standard deviation. The resulting coefficients are then directly comparable for untransformed binary predictors. We have implemented the procedure as a function in R. We illustrate the method with two simple analyses that are typical of applied modeling: a linear regression of data from the National Election Study and a multilevel logistic regression of data on the prevalence of rodents in New York City apartments. We recommend our rescaling as a default option--an improvement upon the usual approach of including variables in whatever way they are coded in the data file--so that the magnitudes of coefficients can be directly compared as a matter of routine statistical practice. (c) 2007 John Wiley & Sons, Ltd.