CH. IV] THE HOLLOW CURVE 41 



To this, I have added the facts of the hollow curves, which are 

 universal, not only in the distribution of plants and animals, but 

 in other things, as we have just seen in the case of that of the 

 farmers' surnames in Vaud, which matches to a nicety the distri- 

 bution of plants. It seems to me impossible to reconcile these 

 curves with the theory of natural selection, and there are other 

 very serious objections to this latter theory. To reconcile the 

 theory of differentiation with the hollow curves, I have added to 

 it the supposition that the evolution that goes on, and which is 

 shown in the morphological characters of plants, has little or 

 nothing to do, directly, with adaptation, and certainly not with 

 direct adaptation. The characters do not necessarily indicate 

 adaptation at all. Every now and then a character appears, like, 

 for example, climbing habit, of which natural selection can make 

 use, and which is therefore retained, but natural selection was 

 not the direct cause of its (complete) appearance, nor was its 

 appearance, in all probability, as accidental as that theory would 

 involve. It appeared full-fledged, and was advantageous, or at 

 any rate not harmful. And if it had no necessary adaptational 

 value behind it, there was no particular reason why a species 

 showing it should spread at a different speed from other species 

 of the same or closely allied genera, a supposition which at once 

 made the hollow curves a normal feature of distribution. And 

 there was also no reason why the many new species that have 

 appeared should not appear at a rate that was in any case not 

 determined by the necessities of adaptation, as we have seen in 

 the case of the Podostemaceae. A species that reached a sand 

 dune, for example, if it were reasonably suited to it upon arrival, 

 would gradually adapt itself in more detail to some definite local 

 conditions there, by physiological adaptation controlled by 

 natural selection. 



What the mechanism was by which this evolution was carried 

 on, we do not know. I suggested in 1907 that "a group of allied 

 species represents so many more or less stable positions of equi- 

 librium in cell division". 



The occurrence of the hollow curve for distribution of plants 

 by areas, or for distribution of genera by numbers of species, 

 shows that neither in geographical distribution (strictly so-called) 

 nor in evolution can natural selection be invoked as it once was, 

 as the principal factor. Any influence that it has must either be 

 very small, or else exerted in an indirect way. One cannot, upon 

 such a curve, draw any dividing line, and say that those upon 



