By Eduardo H. Rapoport
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270% with respect to the area taken as the "true" one. 8. Taking three points, the different calculations give an area 234% larger than the "true" one, this being a little more realistic. The curve in Fig. 3 shows that a sample of fifteen to thirty points or localities gives a reasonable approximation to the "real" area of a species (149% and 127% respectively)·. 1) we would need to have data from at least forty-five localities. But the problem is not so simple. Suppose we take a square area, 100 x 100 mm (= 10,000 m m 2 ) , outlined on a millimetre graph paper, and we choose points at random, each point 1 mm 2 in size, we shall see what happens as the number of points increases.
A = the most equitable division of lands, according to the expression y = 100/tf; B = random model, obtained through iterative simulations of random meshs like the one illustrated in Fig. 15. Dots represent values taken from 449 mammal species. If the longer portions of the sticks broken at random into two pieces tend to represent three-quarters of the original length, we can suppose that each piece, broken again, will show the same three-quarters and one-quarter tendencies. e. 7, etc. , that is y = r n-\ a which is represented by a hatched line in Fig.
The proportion of external and internal subspecies is schematically represented in Fig. 9. If the statement "the subspecies have an innate tendency to retain a portion of the species' external frontier" were valid, we could then ask a related question: what happens when there are internal frontiers, that is, empty territories like deserts, lakes, or some other uninhabited surfaces? If these empty lands had the same properties as a real frontier, it would be fore seeable to find a higher-than-predicted number of subspecies around them.