102 ANALYSIS OF THE TOUR PRINCIPLES. 



pure-breeds, which in my tables is represented by M, is 40; and the 



multiplier for the half-breeds is also 40, i. < ., m 40. And once more, 

 let us assume that of the cross-breeds which have their homes on 

 the ground with the original stock only 1 in 40 reaches maturity; 

 that is, on account of the number of their enemies and the severity of 

 the competition for food, their real multiplier, after all the conditions 

 of survival have had a chance to operate, is 40 4 ' rt -- 1. In other 

 words, the original stock and the half breeds mingled with them are 

 simply able to hold their own, without any continuous increase. On 

 the other hand, the arboreal group are so free from enemies and so 

 well pro\ ided with food that three-fourths of them come to maturity, 

 and their multiplier when corrected is 40 ■ £ = 30. 



Let us assume that the other half of these rats feeding on the trees 

 are of the variation 6, with instincts leading them to spend one third 

 of their time on the ground, and accordingly one-third of them mate 

 with the original stock and have their nests on the ground. As in the 

 ease of variation a, the multiplier for pure arboreal breeds is 30 and 

 for cross-breeds is 1. 



Let us now suppose that there is an arboreal colony of 60 individ- 

 uals occupying a forest on one of these islands, and that 30 of them 

 belong to the variation a, and 30 of them to variation /;. What will 

 be the number of pure-breed arboreal rats in the next generation, and 

 of these how manv will be the offspring of variation a and how many 

 the offspring of variation b ? 



()i variation a one half cross with the original stock and we have — 

 Cross-breeding offspring, 15 x 1 = 15. 

 Pure-breed offspring, 15 x 30 - 450. 



1 m variation b, one-third cross, and we have — 

 Cross-breed offspring, 10 x 1 = io. 

 Pure-breed offspring, 20 x 30 = 600. 



Therefore, in the next generation of the pure-breed colony in the 

 t rees there will be 1 ,050, of which three sevenths are offspring of varia- 

 tion a and four sevenths are offspring of variation b. It follows 

 that through hereditary influences the average instinct for arboreal 

 life will be increased; and we may expect it to continue to increase 

 in the same way in successive generations. 



But there is a psychological influence that will come in to exaggerate 

 the segregative tendency. The 1,050 rats of the generation we have 

 now reached have been reared on the trees of the dense forest or jungle, 

 where they may travel over a considerable area without descending 

 to the ground, and have formed the habit of spending their whole time 

 in the trees, so that not 1 in 100 will mate with the ground rats; and 



