8 PIEBALD RATS AND SELECTION. 



was adopted, which is shown at the top of Plate 1. Each young rat was 

 classed in that grade which it most nearly approached in amount of 

 pigmentation. Skins of rats graded from 3| to +4f are shown in 

 the middle and lower rows of Plate 1. The grading was done when 

 the rats were about three or four weeks old, at which time selected 

 individuals were reserved as the parents for a later generation, the 

 remainder being discarded. This method has been followed ever 

 since its adoption and the data thus obtained are summarized in the 

 tables, which cover the breeding operations of a little more than six 

 years, 1907-1913. 



The grouping of the young in a series of generations is only approx- 

 imately accurate, for practical considerations have often led us to mate 

 together animals which belonged to different generations of offspring. 

 When, for example, an animal of generation 2 was mated with one of 

 generation 4, the question would arise : To what generation do the off- 

 spring belong? In deciding this question we simply added one to the 

 mean of the generations to which the respective parents belonged. In 



2 -f- 4 



the foregoing case this would be -- L +l=4. 



& 



In case one parent belonged to generation 2 and the other to generation 



2 ~f" 3 



3, a fractional result would be obtained, thus ^-+l=3J. In making 



& 



up the summaries of the generations as given in the tables, offspring 

 like the foregoing, of generation 3|, were divided equally between gener- 

 ations 3 and 4, alternate litters of young as recorded in the ledger being 

 assigned to each. Offspring belonging to generations 2f and 3| were 

 tabulated in generation 3; those belonging to generations 3f and 4| 

 were tabulated in generation 4, etc. While, therefore, the genera- 

 tions as tabulated overlap, it is clear that they include groups of off- 

 spring of selected parents each the result of one additional selection over 

 the preceding group. 



The early generations include too few individuals to be of much 

 statistical value, but where the number of offspring rises to 500 or over, 

 the statistical constants acquire undoubted value. The data have been 

 given in the form of correlation tables which will repay careful study. 

 In the tables a single entry has been made for each individual offspring 

 in that row which corresponds with the mean grade of its two parents. 

 Thus, if one parent were of grade 2 and the other of grade 2|, the off- 

 spring would be entered in the row 2 1 along with the offspring of parents 

 both of grade 2|. Offspring of parents whose mean grade fell between 

 the rows given in the tables were divided equally between the adjacent 

 rows, alternate litters being assigned to each. Thus, if the mean grade 

 of the parents were 2, 1 ,., alternate litters of offspring would be entered in 

 row 2 and in row 2|. 



