10 PIEBALD RATS AND SELECTION. 



low range of the offspring in Table 2, which extends from 1.00 to 

 + 3.75. The parents' range (means of pairs) extends from 2.00 to 3.12. 

 The grand average of the parents is 2.52, that of the offspring is 1.92. 

 The correlation between grade of parents and grade of offspring is 0.32. 



From this point on in the series no new stock was added and each 

 generation of offspring furnished the parents for the following genera- 

 tion, except for the slight overlapping of generations when parents of 

 different generations were mated with each other, as has already been 

 explained. 



In generation 3, Table 3, the parents ranged from 2.12 to 3.37 in 

 grade, the offspring from 0.75 to 4.00. The mean of the parents was 

 2.73, that of the offspring 2.51. The degree of correlation between 

 parents and offspring is expressed by the coefficient 0.33 (a perfect 

 correlation would give 1.00). 



In generation 4, Table 4, the selection of parents became considerably 

 more rigid; most of the parental pairs were of grade 3 or higher, their 

 average being 3.09. The average grade of the offspring was 2.73, their 

 range extending from 0.75 to 3.75. The correlation in this generation 

 fell very low, to 0.07, not because of a lessened regression but rather 

 because of a very high regression on the part of the offspring of high- 

 grade parents. 



In generation 5, Table 5, the grade of the selected parents ranged 

 from 2.75 to 4.12, its mean being 3.33. The offspring, showing the 

 usual regression, ranged from 0.75 to 4.25, their mean grade being 2.90. 

 The correlation between parents and offspring in this generation was 

 0.16. The number of individuals comprising this generation of off- 

 spring was 610. 



It is scarcely necessary to discuss separately the correlation table 

 for each of the next eight generations, Tables 6 to 13. The number of 

 offspring rises to a maximum (1,408) in generation 8, Table 8; then 

 declines to less than 200 in generation 13. But as this generation and 

 the preceding one are still being produced, it is probable that the num- 

 ber recorded will be considerably increased before the generation is 

 complete. The means of parents and offspring and the other statistical 

 constants for the several generations can be most easily compared by 

 reference to Table 14. Leaving out of consideration the exceptional 

 generation, 2, the following will be observed: 



(1) The mean of the selected parents has steadily advanced through- 

 out the scries, as has also that of their offspring. 



(2) The variability (standard deviation) of the parents as a group 

 has decreased somewhat as increase in numbers made a more rigid selec- 

 tion possible; that of the offspring has undergone a similar change. 



(3) The correlation between parents and offspring has not materially 

 changed. The average of the correlation coefficients for the entire 

 series is 0.194, for the last throe general ions it is 0.175, for the three pro- 



