116 SIZE AND SPACE [pt. ii 



means greater variety of forms, and as to obtain that greater 

 variety of conditions means in general larger areas, size of a 

 genus and space occupied go largely together. 



A good proof for the general correctness of Size and Space is 

 that, as we shall see in more detail below, the further out we go 

 among the islands, the larger on the average do the genera 

 become (in the number of species they contain in the world). 

 Whilst the world average for a genus is 12-13 species, the non- 

 endemic genera found in India contain on the average about 

 50 species in the world, in New Zealand about 75, and in the 

 Hawaiian Islands about 100. 



Prof. Small (see beloAv, Chapter xiii) has worked out the hypo- 

 thesis of Size and Space with reference to the Compositae, and 

 his results form a remarkable verification of its correctness in 

 broad outline, and consequently a further proof that however 

 much the distribution of an individual form may be subject to 

 the many and various factors already mentioned, on the average 

 of large numbers the results go very largely in accordance with 

 the laws of probability, so that the distribution, under the steady 

 pull of age, is, on the large scale, much more mechanical than 

 we had previously been inclined to suppose. 



If one take again such a group as the order Helobieae (7 

 families) which are chiefly water or marsh plants, and closely 

 related, one finds: 



-1 cosmopolitan genera, witli ... ... 138 species; average 34 



12 genera occupying large areas in the tropics, 



with .". 83 „ „ r 



2 genera, temperate and subtropical regions 7 ,, ,, 3-5 



26 genera of small area ... ... ... 5.5 ,, ,, 2 



showing very clearly how size goes with space. And yet it is 

 quite possible here as usual to pick out genera that go in the 

 reverse direction; e.g. Zannichellia with one species is cosmo- 

 politan, while Philotria with five is confined to North America. 



On the whole, therefore, the principle we have laid down may 

 be seen to be justified by the facts when large numbers are dealt 

 with. But this is a recognised necessity of all statistical work^ 

 as, for instance, in working out results under Mendel's Law. 



Now, taking this principle together with Age and Area, it 

 is clear that Age and Size, or Antiquity and Amplitude, if an 

 alliterative title be preferred, go together, and on the whole the 

 larger a genus, the older will it be, within its ozvn circle of affinity. 

 No one would suggest that a herbaceous genus of 100 species was- 



