Despite substantial advances in plate tectonic modeling in the last three decades, the postulated position of terranes in the Paleozoic has seldom been validated by faunal data. Fewer studies still have attempted a quantitative approach to distance based on explicit data sets. As a test case, we examine the position of Avalonia in the Ordovician (Arenig, Llanvirn, early Caradoc, and Ashgill) to mid-Silurian (Wenlock) with respect to Laurentia, Baltica, and West Gondwana. Using synoptic lists of 623 trilobite genera and 622 brachiopod genera for these four plates, summarized as Venn diagrams, we have devised proportional indices of mean endemism (ME, normalized by individual plate faunas to eliminate area biogeographic effects) and complementarity (C) for objective paleobiogeographic comparisons. These can discriminate the relative position of Avalonia by assessing the optimal arrangement of inter-centroid distances (measured as great circles) between relevant pairs of continental masses. The proportional indices are used to estimate the “goodness-of-fit” of the faunal data to two widely used dynamic plate tectonic models for these time slices, those of Smith and Rush (1998) and Ross and Scotese (1997). Our faunal data are more consistent with the latter model, which we use to suggest relationships between faunal indices for the five time slices and new rescaled inter-centroid distances between all six plate pairs. We have examined linear and exponential models in relation to continental separation for these indices. For our generic data, the linear model fits distinctly better overall. The fits of indices generated by using independent trilobite and brachiopod lists are mostly similar to each other at each time slice and for a given plate, reflecting a common biogeographic signal; however, the indices vary across the time slices. Combining groups into the same matrix in a “total evidence” analysis performs better still as a measure of distance for mean endemism in the “Scotese” plate model. Four-plate mean endemism performs much better than complementarity as an indicator of pairwise distance for either plate model in the test case.
An Universal, Simple, Circular Statistics-Based Estimator of α for Symmetric Stable Family
