No. 590] FECUNDITY IN THE DOMESTIC FOWL 



101 



From a methodological standpoint, however, it is neces- 

 sary to have a very different sort of evidence from that 

 afforded by changing general population means, such as 

 Castle gives for his rats, and I for fecundity, to prove 

 that the process of selection has been the cause of a change 

 in the absolute somatic equivalent of a particular gene or 

 hereditary determinant. 



3. It is just in connection with this last point that there 

 seems to me to be a good deal of unclear thinking and ar- 

 guing at cross-purposes about the selection problem. Let 

 us examine the logic of the matter symbolically. 



Let there be a character A, whose somatic variation in 

 the general population is given by a frequency distribu- 

 tion of area Z% A A " A, where Z is the frequency of occur- 

 rence of the somatic state or condition A t , and so on to Z n 

 and An. Now suppose that selection is practised for the 

 somatic condition A 40 , but that in the original population 

 A 38 is the most extreme variation in that direction found 

 to exist. Then for A 40 , Z 40 = 0, and for A 3S , Z 3S is very 

 small. Let it be further supposed that the somatic differ- 

 ence between the A 3S and A 39 condition may be of any de- 

 terminate magnitude R. It makes no difference to the 

 logic of the case whether R is large or is extremely minute. 

 Now suppose, as a limiting case, that we assume a gamete- 

 soma correlation of 1, i. e., perfect. Then in the gonads 

 of an individual somatically A 3S , all the germ cells will 

 bear the factor a 3S . If two such individuals are bred to- 

 gether the progeny will be somatically A 3S } 1 Suppose 

 that for m generations the matings are of A 3S X A 3S . This 

 is continued selection. Then suppose in the m + 1th 

 generation, ex A 38 X A 3S parents, appears an A 30 indi- 

 vidual. 



Concretely this represents a step in advance in the di- 

 rection of selection. Let us analyze the possible ways in 

 which this may have happened. 



11 This is precisely the condition which prevails in a pure line of oats, 

 except for purely phsenotypic variation, superimposed by environmental 



