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Biogeographers have used biotic resemblances and differences to distinguish discrete biogeographic areas. One of the most useful and commonly applied measures of biotic resemblance is a simple binary similarity coefficient developed by G. G. Simpson (1936). In the present study I apply the Simpson Coefficient of faunal similarity to three distributional data sets (at several taxonomic levels): (1) Recent North American mammals; (2) Recent global mammals; and (3) Early Eocene mammals of North America, Europe, and Asia. These analyses yield the following results.

Faunal realms of large geographic scale can be distinguished both by within-realm faunal similarities/between realm faunal dissimilarity, and by relatively sharp gradients of change of similarity across faunal realm boundaries.

Geographic distribution patterns of Recent North American mammals show several important trends: (1) an inverse relationship between faunal similarity and both longitudinal and latitudinal separation between sites; (2) a latitudinal asymmetry in similarity comparisons; (3) endemism of western North American faunas; and (4) differentiation of lower level faunal provinces is the result of complex interplay between major latitudinal climatic gradients and less influential (frequently longitudinal) regional climatic, tectonic, and geographic factors.

Significant differences in taxonomic diversity between localities makes the Simpson Coefficient a more useful measure of faunal resemblance than other binary similarity coefficients, both for Recent and fossil assemblages.

High similarities for Early Eocene faunal comparisons indicate presence of a single North American-European faunal realm; low resemblances of Asian Early Eocene faunas both to European and North American faunas indicate a distinct Asian faunal realm.

Available, but incomplete, evidence from faunal resemblances indicates that Ellesmere Island was part of a single, continuous European/North American faunal realm.

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