476 SCIENCE PROGRESS 



highly controversial mathematical problems in the book. The author appears 

 to be insufficiently critical of his own hypothesis. Nothing is more im- 

 portant than the New Zealand case, but there are fundamental aspects 

 of the problem involved in this case which Dr. Willis ignores. 



It is necessary to recall in imagination what happens when a small frag- 

 ment is severed from a large island. In the large island there will no doubt 

 be species with varying ranges ; some species will be almost or quite universal ; 

 others will be very local ; others again will have intermediate ranges. It is 

 here that the ordinary law of probability comes into play. The severed 

 fragment of the island will have, at the moment of separation, a higher 

 percentage of the species with large ranges than of the species with small 

 ranges. Of the species that are universal it will have loo per cent. Of the 

 very local species, it will have few or even none. Hence, from the very 

 moment of separation, and before any new species have come into existence 

 on the main island, the average range on the main island of those species that 

 are also on the little island will be greater than the average range of all the 

 species on the main island, and, a fortiori, greater than the average range 

 of those species which do not extend to the little island. This of course is a 

 law of chance that is not applicable to individual species, but only to groups 

 of species. But it is this, and nothing more, that we find in New Zealand ; 

 and the phenomenon is explicable by the ordinary law of probability without 

 any need for the age and area hypothesis. Taking large numbers of species, 

 the chances of those species being represented on the Kermadecs, Chathams, 

 or Aucklands, will have varied with their ranges in ancient greater New 

 Zealand. A homely example will perhaps make this point even more clear. 

 Take a group of five mammals that are widespread in Great Britain, such 

 as the rabbit, the brown rat, the wood mouse, the weasel, and the stoat. 

 Then take another group of five mammals that are rare and local in Great 

 Britain, such as the wild-cat, the pine-marten, the polecat, the red deer, and the 

 yellow-necked mouse. Now let it be supposed that fragments are struck off 

 Great Britain. A moment's consideration will convince anybody that most 

 of the animals of the first group will occur on all the fragments, and that on 

 many fragments all five species would occur. On the other hand, it is equally 

 obvious that a single fragment could hardly include all five species of the 

 second group, and that many fragments would miss all five of them. Hence 

 the average range in Great Britain of the species on any such fragment would 

 be greater than the average range of all the ten species, and it is to be noted 

 that such a result will be reached, whatever be the cause of varying ranges 

 on the mainland. 



The law of probability is also applicable, though in a different manner, 

 to the question of " size and space." Dr. Willis finds that the most widely 

 dispersed species of a large genus is (again taking averages of a number of 

 genera) more widely dispersed than that of a small genus. But this fact is 

 merely in accordance with ordinary biometrical expectation. Whatever 

 may be the real causes of varying ranges among species, if one selects the 

 widest range of a group of, say, twenty (a large genus), it is likely to be wider 

 than the widest of a group of, say, three (a smaU genus). The fact that, on 

 the average, the range of a genus, as such, varies with its size is merely another 

 aspect of the same phenomenon. The error consists in supposing that a small 

 group of species is comparable to a large group of species merely because 

 each is classed as a single genus. A genus of one species is a homogeneous 

 assemblage of individuals. A genus of three species is a more heterogeneous 

 assemblage. A genus of twenty species is a much more heterogeneous 

 assemblage again. The real meaning of the " size and space " principle is 

 therefore that, as we study more and more heterogeneous assemblages of 

 organisms, we find that their geographical ranges become larger and larger. 

 And since, on the average, a large stretch of country will possess greater 



