. Distribution of mammals in Colorado. Mammals. 1972 ARMSTRONG: COLORADAN MAMMALS 339 herein utilized) represents an educated guess. Included in that estimate are the known eco- logical preferences of species and the distri- bution of suitable habitats. The boundary of a species as mapped, then, depends to a greater or lesser degree on the known limits of ecological units. When boundaries drafted on this basis are utilized, in turn, to define natural areas, circularity is complete. None- theless, the fallacy, however obvious, is of minimal biogeographic importance. Round- aries of ranges of sp


. Distribution of mammals in Colorado. Mammals. 1972 ARMSTRONG: COLORADAN MAMMALS 339 herein utilized) represents an educated guess. Included in that estimate are the known eco- logical preferences of species and the distri- bution of suitable habitats. The boundary of a species as mapped, then, depends to a greater or lesser degree on the known limits of ecological units. When boundaries drafted on this basis are utilized, in turn, to define natural areas, circularity is complete. None- theless, the fallacy, however obvious, is of minimal biogeographic importance. Round- aries of ranges of species, where known in detail, do coincide with boundaries of major community-types, biomes, and other such eco- logical units. The coincidence of a number of boundaries in a narrow zone suggests a barrier of considerable strength. Numerical analysis reveals relative strengths of such barriers. Hagmeier and Stults (1964) analyzed oc- currence of limits of mammalian species over North America north of Mexico. Their meth- od was utilized to quantify coincidence of limits in Colorado. A grid of 70 quadrats was superimposed over each of 88 species range maps and a tabulation made of the number of limits per quadrat (for description of the grid, see the preceding discussion of species density). An index of faunal change was cal- culated for each quadrat (IFC = 100 L/n, where L equals the number of species at their limit within a given quadrat, and n equals the total number of species in the quadrat—after Hagmeier and Stults, 1964: 130). The mean of the 70 IFC values is (range, to , standard deviation, ). For a graphic presentation of IFC values over the grid, see figure 123. Rroad agreement is obvious between the qualitative data of figure 122 and its quantification in figure 123. Other quantitative methods are concerned more directly with areas of occurrence than with limits of ranges. Huheey (1965) calcu- lated a faunal divergence factor in analyzing the distr


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