RATIOS BETWEEN CROSS-BREEDS AND PURE-BREEDS. 103 



in a few more generations this ratio will become only i in i ,000, or 

 i in many thousands. Under such conditions the arboreal variety 

 will soon develop a manner and movement by which they recognize 

 each other; and their social instincts will lead them to band together 

 in driving away the rare intruders from the ground who venture to 

 invade their sphere of influence. Their isolation from the original 

 stock may thus become complete in the course of a few generations, 

 and that, too, without any action of the principles of segregate fecun- 

 dity and segregate vigor; that is, without the cooperation of any form 

 of what Romanes has called " physiological segregation." 



Segregate freedom from competition and segregate escape from ene- 

 mies favor segregation in the earlier stages of newly adopted methods 

 of life, and so tend to exaggerate the importance of slight changes 

 attained by the first stages of divergent forms of environal selection. 

 When the new colony has so multiplied as to appropriate nearly all the 

 newly opened resources, competition will again become an important 

 factor, and by that time the gradual appearance of segregate fecun- 

 dity and segregate vigor may fortify the new type against being 

 swamped by crossing. Segregate adaptation is also an important 

 factor cooperating in the whole process. So the five principles of 

 segregate survival are found to sustain and supplement each other in 

 producing divergent evolution. 



15. Computation of the Ratio oj Cross-breeds to Pure-breeds, under 

 Given Ratios of Mixed Unions and 0} Fertility. 



It will simplify the problem if individuals of different degrees of 

 crossed descent are classed together and compared with those of pure 

 descent. It will also be a convenience to make M the multiplier 

 that represents the influence of all the conditions of survival for those 

 of pure descent, and m = the multiplier that represents the influence 

 of all the conditions of survival for those of mixed descent. A the 

 initial number of the new variety ; c the fraction that represents 

 the proportion of the pure-breed individuals that form cross-unions ; 

 and P the whole number of individuals of pure descent. C - the 

 whole number of individuals of cross descent. 



It may be observed that a problem of completely parallel terms will 

 be obtained if we make A = an initial number of dollars left as an 

 endowment to draw compound interest for many years ; c = a rate 

 of taxation corresponding in its periods with the periods for estimat- 

 ing interest, the avails of this taxation being kept for another institu- 

 tion. M -= the multiplier by which we obtain the principal plus the 

 interest remaining in the endowment ; m == the multiplier by which 



