CH. XVIII] THE HOLLOW CURVE OF DISTRIBUTION 199 



sway of the theory of natural selection, which demands origin 

 of species upon large areas, as well as the occurrence of many 

 species that are "going under" in the struggle for existence. 

 The result has been, consequently, that the species of small areas 

 have been regarded as the failures, and this has derived support 

 from the fact that fossil botany shows that there are vast num- 

 bers of extinct forms. Most botanical work has been done in 

 the regions that were affected by the last glacial period, which 

 has left very many survivals in them (cf. p. 86, footnote). It is 

 not fully realised that though there may be perhaps a thousand 

 of such survivals, they are completely lost in the crowd when one 

 deals with the forms of limited area, or with the monotypic 

 genera as a w^hole. It would be absurd to apply the explanation 

 of relicdom in face of such facts as those given in Chapters xv 

 to XVII. Few people would now be found to express themselves 

 in support of natural selection as a cause for origin of species, but 

 though the premises of the argument are damaged or abandoned, 

 they hold strongly to the deductions that were made from them, 

 chief among which, in the present connection, is that species 

 have reached their limits of possible dispersal, and that those of 

 small area are the defeated in the struggle for existence. 



So long as such a view was taken of distribution, so long would 

 it have seemed absurd to expect to get any result from statistical 

 investigations. But the figures that have actually been obtained, 

 and of which many instances are given above, show that what we 

 have called the hollow curve obtains throughout. It obtains, for 

 example, in the grand total of genera in the world, and for the 

 totals of genera in every single family : for the distribution of 

 endemics, and of local floras, whether for areas occupied by the 

 species, or for the sizes of the genera; for animals as well as for 

 plants. The hollow curve is apparently a universal principle of 

 distribution, Avhether it be distribution in space— geographical 

 distribution— or distribution in time— evolution. A species as 

 it increases in age, expands its area, while a genus increases its 

 number of species, the younger occupying smaller and smaller 

 areas, usually within the area of the first species, until that 

 becomes very large (and sometimes even then). 



The very "important bearings of this work upon the general 

 theory of evolution must be left for later publications. It will 

 suffice to have called attention to the facts. 



