No. 600] PIEBALD RATS AND MULTIPLE FACTORS 727 



After the third generation there is, in general, a gradual 

 decline in the effectiveness of selection, till in the fifteenth 

 generation the advance is 0.12. In support of this state- 

 ment, which stands in direct disagreement with the quo- 

 tation at the head of this section, Fig. 2 is offered. In 

 this figure the ordinates represent the increases in the 

 differences between the two racial means in successive 

 generations. Since the decline in the second generation, 

 as explained, seems to have no immediate significance, 

 this point has been omitted from the curve. The advance 

 in the third generation has been calculated from the dif- 

 ference between the two races in the first generation, 

 which of course gives a slightly smaller advance than if 

 the difference in the second generation had been used. 

 The greater part of the falling off occurs in the plus race, 

 but both races show the same general tendencies, namely, 

 a sudden advance as the result of the first selection, with 

 much reduced advances following subsequent selections. 

 It may be supposed that there was a greater degree of 

 heterozygosity in the parents selected to start the minus 

 race than in those selected to start the plus race. This 

 might explain the smaller initial advance in the minus 

 race (one unit as compared with two in the plus race) 

 as well as the more prolonged and slower subsequent ad- 

 vances. 



7. Kegression, as Castle uses the term, is the difference 

 between the averages of the selected parents and their 

 offspring. It is due to the imperfect correlation of two 

 variables, intra-germinal and extra-germinal differences, 

 and so, as stated, it forms a gauge of this relationship. 

 Its amount will be reduced by a reduction in the amount 

 of variability of either variable. In the later generations 

 the regression is reduced. We see no reason to suppose 

 that environment as a whole acts any differently in dif- 

 ferent generations. Therefore this reduction in the 

 amount of regression becomes further evidence in sup- 

 port of the supposition that the germ plasm is more uni- 

 form, more homozygous in the later generations. 



