AVERAGE RADIUS OF DISTRIBUTION. 221 



the other hand, Apex, which for the most part occupies trees and 

 shrubs on the ridges which are connected with each other through the 

 central ridge of the mountain range, and Amastra and Leptachatina, 

 which are for the most part found on the ground under dead and de- 

 caying leaves, seem to possess better opportunities for migration than 

 either the Achatinella or Bulimella. Corresponding with these facts 

 we find the species of Achatinella and Bulimella especially limited in 

 the areas they occupy, while the species of Apex, Amastra, and Lep- 

 tachatina are less so. For example, the area occupied by Amastra 

 turritella, A. tristis, and A. ventulus includes the areas occupied by 

 many species of Achatinella and Bulimella; and Apex loratus and 

 A . pallidus, occupying the mountain ridges, range from Makiki to 

 Halawa, exceeding the range attained by any arboreal species occupy- 

 ing the valleys of the same region. 



(6) When a group of divergent forms that are fertile with each other is 

 being developed through the influence of local or geographical isolation, 

 other conditions remaining constant, the number of forms that will be pro- 

 duced within a given area will vary inversely as the square of the average 

 radius of distribution for the different forms. As this average radius of 

 distribution may be taken as the measure of the power and opportu- 

 nities for migration, we may say that, other powers and opportunities 

 remaining constant, the number of species developed within a given area 

 will vary inversely as the square of the average power and opportunities for 

 migration. 



Though migration is in one sense a cause of isolation, it is evident 

 that the number of isolated groups of individuals of a given form 

 within a given area does not increase with the increase of migration. 

 Isolation is produced by the great contrast between ordinary and extraor- 

 dinary combinations of opportunities for migration; and this contrast is 

 liable to be as great in the case of species that have limited powers 

 and opportunities as in the case of those that have very great powers 

 and opportunities. The number of isolations thus produced that can 

 exist within the limits of a given area must vary inversely as the square 

 of the power and opportunity for migration. 



The facts of distribution we have been considering seem to corre- 

 spond to this law. 



(7) Forms that are most nearly related, and are, therefore, the least 

 subject to sexual and impregnational isolation, are distributed in such a 

 manner that their divergence is directly porportional to their distance 

 from each other, which is also the measure of the time and degree of their 

 geographical isolation; while those most manifestly held apart by sexual 

 instincts and impregnational incompatibilities do not follow this law. 



