COOPERATION OF POSITIVE AND NEGATIVE SEGREGATION. 99 



this transition may be very difficult to trace, I believe that the 

 results that must follow can be pointed out with considerable clear- 

 ness and certainty. 



Darwin's investigations have shown that in many cases, if not in the 

 majority, the relation of varieties to each other is that which I have 

 called "integrate fecundity" and "integrate vigor"; that is, the 

 highest fertility is attained when varieties are crossed and the vigor 

 of offspring thus produced is greater than when the intergeneration is 

 within the limits of one variety. He, however, gives in Variation 

 under Domestication, chapter xvi, some special cases, in which 

 " varieties of the same species behave when crossed like closely allied 

 but distinct species," and remarks that similar cases "may not be of 

 very rare occurrence ; for the subject has not been attended to. ' ' The 

 same cases are also mentioned in all the editions of the Origin of 

 Species.* 



(5) Negative segregation unaided by positive segregation tends to ex- 

 tinction. The problems that arise in considering the different results 

 produced by different degrees of positive segregation and segregate 

 fecundity are of a nature suitable for mathematical treatment. Be- 

 fore, however, computing the, effects of segregate fecundity when 

 cooperating with positive segregation, it will be in place to show that 

 it is of itself only a negative form of segregation, having no power to 

 insure the propagation of varieties thus characterized, though they are 

 fully adapted to the environment. This is most easily brought to 

 light by considering the effect of a high degree of this quality when 

 positive segregation is entirely wanting, or when it is sufficient to give 

 simply a chance of segregate breeding by bringing each individual near 

 to its natural mate. For example, let us suppose, first, that a male 

 and a female each of several allied but mutually sterile species are 

 brought together on one small island, all tendencies to positive segre- 

 gation being removed, while mutual sterility still remains; second, 

 that a male and female when once mated remain together for the 

 breeding season; and, third, that all find mates. Now, if we have 

 seven species each represented by one individual of each sex, what 

 is the probability that all the species will be propagated? And what 

 the probability for the propagation of none, or of but one, or of but 

 two, or of but three of the species? The answers, as I have computed 

 them, are as follows : The probability that none will be propagated is 

 =|jj5 ; that i species will be is ~ ; that 2 species, |^, ; that 3 species, 

 ~ ; that 4 species, ~ ; that 5 species, ^ ; that 7 species, ^. These 



* See first edition, p. 238; fifth edition, p. 259; sixth edition, p. 258. 



