By Eduardo H. Rapoport
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And the area is A = 6i\r' . Circle b corresponds to the mean value of the radius (r^/n) from the geometric centre to each of the points. Case c, the smallest circle containing all the considered points, seems to be the most convincing method. In d we have the criterion of the smallest convex polygon which, like the other cases, does not accept the existence of "bays" or "peninsulas", making it inapplicable in biogeography. Jennrich and TurnerTs method (1969) based on the covariance matrix of capture points is not practical either because, although it is based on a statistical measurement of distances between points, it is difficult to calculate when the number of points is high, apart from the fact that it produces an image of a relatively bulky area.
6. ~i Three figures with the same area but different perimeters. The elongated rectangle is an abstraction of the perimeter-area relation observed in Central and North American mammal species ranges. The anatomy* and 'Morphology1 of Areas 27 Obviously, Fig. 6 is only a simplification of what is depicted by small-scale maps. The scant available data of large-scale maps suggest that the ratio area/perimeter in nature is characterized by disproportionately large values of the perimeter. The contact between a species and other contiguous species or between a species and the set of surrounding barriers impeding its spreading is extensive and intensive.
With ten points the error is 65%, with twenty points it is 59%, with thirty points it is 40%, and with 100 points it is 13%.
Areography. Geographical Strategies of Species by Eduardo H. Rapoport