RATIOS BETWEEN CROSS-BREEDS AND PURE-BREEDS. 103 
in afew more generations this ratio will become only 1 in 1,000, 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 codperation 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 codperating 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 of Cross-breeds to Pure-breeds, under 
Given Ratios of Mixed Unions and of 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 
