12 PIEBALD RATS AND SELECTION. 



actually produce offspring of higher grade than themselves, viz, 3.83. 

 It will thus be seen that the regression is uniformly toward the mean of the 

 race and changes its direction ivhen that mean changes its position with 

 reference to a particular grade of parents. This conclusion is supported 

 by other columns of Table 15, but is best illustrated by this particular 

 case because here the selection has extended over a greater number of 

 generations than elsewhere in the series. 



If one examines the horizontal rows of Table 15, he finds in general 

 that numbers increase toward the right. Exceptions are coimiionest 

 toward the ends of the rows Vv^iere fewest individuals are represented. 

 This increase means that, within any generation, as the grade of the 

 parents rises, that of their offspring rises also. Since in general the 

 selected parents are above the general average of the race for the time 

 being, regression is naturally downward in nearly all cases. 



From what precedes we may conclude (1) that in this series of rats 

 the somatic character (appearance) of an individual is in general a true 

 indication of its germinal character, since the higher the grade of the 

 parents the higher the grade of the offspring, and vice versa; but that (2) 

 the somatic character of an individual is not a j)erfect index of its ger- 

 minal character, since the offspring of aberrant individuals are less 

 aberrant than themselves, i. e., the offspring regress toward the mean of 

 the race; yet that (3) by selection of plus variations we can displace, in a 

 plus direction, not only the mean of the race, but also the upper and 

 lower limits of its variation, the total amount of variability (standard 

 deviation) being thereby only slightly decreased. 



MINUS SELECTION SERIES. 



This series begins with selected parents ranging in grade from — 1.25 

 to — 1.87. Their average, if each pair is weighted in proportion to the 

 number of its offspring, is —1.46. The offspring (Table 16), like the 

 offspring of the original plus selections, regress toward grade 0. They 

 range in grade from +0.25 to —2.00, their mean being —1.00. The 

 total number of offspring recorded in this generation is only 55, this 

 being too small to warrant the calculation of a correlation coefficient. 



Generation 2 (Table 17) is somewhat larger, but still too small to 

 make statistical constants based upon it of much consequence. The 

 offspring show substantially the same range of variation as in the pre- 

 vious generation, but with a slightly higher average ( — 1.07). The 

 coefficient of correlation ( — 0.03) is negative, but too small to be signifi- 

 cant. The record of the next eleven generations will be found summar- 

 ized in Tables 18 to 28, or in more condensed form in Tables 29 and 30. 

 Generation 13 (Table 28) is still incomplete. 



The mean of the parents steadily rises from — 1.56 in generation 3 to 

 — 2.50 in generation 13. The mean of the offspring rises by like incre- 

 ments from — 1 . 18 in generation 3 to — 2.39 in generation 13. There is 



