CHAPTER IV 



THE HOLLOW CURVE 



J. H E chief result of the work upon Age and Area, perhaps, was 

 the discovery of the " hollow curve of distribution " (cf. chap, xviii 

 of Age and Area, p. 195), a curve which shows in all cases of dis- 

 tribution that I have yet examined, whether of animate or even 

 of inanimate things. My opponents have gone to great trouble to 

 show that it holds, for example, with the names in a telephone 

 book, or even with the distribution by size and shape of a pile of 

 gravel, in other words that distribution is in general what one 

 may call very largely accidental, and not determined by adapta- 

 tion in so far as concerns general distribution about the world, 

 which is exactly what I wished to prove. 



The curve was first noticed in 1912 in regard to the flora of 

 Ceylon, which consisted of 573/1 (573 genera each with one species 

 in Ceylon), 176/2, 85/3, 49/4, 36/5, 20/6 and so on. If one take the 

 first few numbers, one finds that the numbers to right and left 

 of any single number (e.g. of 176/2) add up to more than twice as 

 many (573/1 -f- 85/3 = 658) as itself, so that the curve must be 

 hollow as shown in the figures below. It turns the corner between 

 3 and 5, and as the numbers get small it becomes more or less 

 irregular. 



The curve was also found to show, but not in such detail, with 

 the areas covered by species. If one divide the species of a genus 

 or family into those of large, small, and medium areas, one finds 

 that if one add together the numbers in the large and the small, 

 they make more than twice as many as those in the medium, or 

 in other words they make a hollow curve, like those shown in the 

 illustrations. 



Now not only does this hollow curve show with the distribution 

 of species by areas, but it also shows with the distribution of 

 genera in a family by the number of species that they contain. 

 We must always remember that statistics must only be applied 

 to numbers and to related forms, which as a general rule will 

 behave in much the same way. Take, for example, the family 

 Monimiaceae, of 33 genera and 337 species. The two largest 

 genera, Siparuna with 107, and Mollinedia with 75 species, range 



WED ^ 



