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- 
tinctton.—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 
codperating 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 te 
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 
ei; that.1 species will be is 37; that 2 species, 4; that 3 species, 
2”; that 4 species, 45; that 5 species, ;;,; that 7 species, 4,. These 

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