422 DISCUSSION. 



tion X^ to arise suddenly at an internal point a(fig. 1), and to 

 propagate itself in the vicinity of a(6g.2). This may finally 

 establish itself as a definite species X^ in a smaller region (dark 

 area in fig. 3), completely surrounded by the region of the original 

 species. This would be an example of an Inlying Pair. 



(B). Let the large lightly-shaded area, represent, as before, 

 the region of a species, X. Suppose a mutation X^, to arise 

 suddenly at a point 6(fig.4), near the border of the region; and 

 to propagate itself, partly within, and partly without that region 

 (fig. 5). This may finally establish itself as a definite species, 

 X^, in a smaller region partly overlapping the other region(fig.6). 

 This would be an example of an Overlapping Pair. 



(C). Taking the large area, as before, for the region of X, 

 let a geological change raise a barrier across the region at ab 

 (fig.7). Let this gradually increase the isolation of one portion 

 of X from the other(fig.8). The two portions of X may be 

 expeeted finally to evolve in slightly different directions, yielding 

 two closely allied species, Xj and Xg, separated by a definite 

 barrier(fig.9). This would be an example of an Isolated Pair. 



(D). If, at a later period of time, the geographical barrier 

 raised in C be removed, the two species Xj^ and Xj may extend 

 their bounds, and remain as a distinct Overlapping Pair, pro- 

 vided they are sufficiently diflferentiated to preserve their par- 

 ticular characters*(fig.lO). 



Assuming that, in taking a very large number of cases, all 

 four possibilities are equally likely, a result may be expected, 

 approximating to : — 



o 



Inlying Pairs(Case A) 25% 



Overlapping Pairs(Cases B and D) 50% 



Isolated Pairs(Case C) 25% 



* Mr. C. Hedley has suggested the term " area of cohabitation " for the 

 region common to both species in this case. The same term would apply 

 to the similar region in case B. 



