THROtiait CUMULATIVE SEGREGATION^. 



249 



small, tlie water will in time find a common level in both tanks, 

 unless there are additions or subtractions of water that prevent 

 such a result. So, in the case under consideration, final fusion 

 will take place, unless difi'erentiation progresses more rapidly than 

 the fusion, or some other influence comes in to counteract the 

 levelling influence o£ occasional crosses. If, under such condi- 

 tions, some branch of the partially Segregated variety becomes 

 more fertile when generating with members of the same variety, 

 and less fertile when generating with other varieties, a principle 

 will be introduced tending to strengthen any form of partial 

 Segregation that already exists between the varieties. This 

 principle when co-operating with partial Segregation will produce 

 pure masses of each variety, when, without the action of this 

 principle, all distinctions would be absorbed by the crossing. 

 We know that a transition from Integrate Fecundity to Segre- 

 gate Fecundity usually takes place at a point in the history of 

 evolution intermediate between the formation of an incipient 

 variety and a strongly-marked species ; and though the causes 

 that produce this transition may be very difficult to trace, I 

 believe the results that must follow can be pointed out with 

 considerable clearness 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 Vigour ; 

 that is, the highest fertility is attained when varieties are crossed, 

 and the vigour of off'spring 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 re- 

 marks 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.' * 



The problems that arise in considering the different results 

 produced by difl'erent degrees of Positive Segregation and Segre- 

 gate Fecundity are of a nature suitable for mathematical treat- 

 ment. Before, however, computing the efl'ects of Segregate 

 Fecundity when co-operating with Positive Segregation, it will be 

 in place to show that it is of itself only a negative form of 



* See 1st edition, p. 238 ; 5tli edition, p. 259 ; 0th edition, p. 258. 



