USE OF THE TABLES. 107 



16. The Use of the Tables. 



The first object of this computation is to show that a partial posi- 

 tive segregation that is ineffectual in preserving a new variety from 

 the swamping effects of crossing becomes very effectual when a mod- 

 erate degree of segregate fecundity cooperates with it. It should be 

 observed that when considering partial segregation cooperating with 

 segregate fecundity I assume that the two varieties that are compet- 

 ing on the same area are equally adapted to the environment, and 

 that the action of other principles is equal in each, in order that I may 

 compute the effects of the two factors under consideration when free 

 from disturbing influences. It has been objected that, according to 

 my Table I,* the eighteenth generation is many thousand times larger 

 than the initial number, which is not the usual result under the condi- 

 tions surrounding natural varieties. In reply I would say that even 

 in natural varieties it is not at all impossible that the number should 

 double with each generation for at least a few generations, especially 

 when a variety has gained the use of resources heretofore unused, 

 and that for the purpose of showing the ratio in which half-breeds and 

 pure-breeds stand to each other it is entirely immaterial whether we 

 assume that the number that arrive at maturity are the same in each 

 generation, or that each successive generation is nearly double that of 

 the preceding generation. 



But does not the assumption that the ratio of cross-breeding re- 

 mains the same in successive generations vitiate the whole computa- 

 tion and render it worthless? I think not. My contention is that 

 when segregate fecundity comes to the aid of such a principle as pre- 

 potential segregation (which is only partial in its action, and therefore 

 by itself unable to prevent swamping), the result is the progressive 

 action of both principles in each successive generation. But before 

 we can show how this cumulative action arises we must have some 

 formula for showing the natural result of any given degree of segre- 

 gation combined with a given degree of segregate fecundity ; and the 

 proper formula for this purpose seems to be the result that would, be 

 reached, if the principles should continue at the given degrees for a 

 considerable number of generations. 



Take for example the case represented in Table I.* What is the 

 ratio between half-breeds and pure-breeds that most truly represents 

 the case? Shall we go to the end of the first generation and say that, 



H Hi 



D = z, or go to the eighteenth generation and find that p= ? 



f I O * 



"- 



* See my paper on Divergent Evolution, Appendix I. 



