No. 551] THE MENDELIAN NOTATION 



647 



I shall speak first of the case least open to objection from the geno- 

 type point of view, which requires : 



1. That no cross breeding shall attend or shortly precede the selection 

 experiment, lest modifying units may unconsciously have been intro- 

 duced, and 



2. That only a single unit-character shall be involved in the experiment. 

 These requirements are met by a variety of hooded rat which shows a 



particular black and white coat pattern. This pattern has been found 

 to behave as a simple Mendelian unit-character alternative to the self- 

 condition of all black or of wild gray rats, by the independent investi- 

 gations of Doncaster, MacCurdy and myself. The pigmentation how- 

 ever in the most carefully selected race fluctuates in extent precisely as 

 it does in Holstein or in' Dutch Belted cattle. Selection has now been 

 made by Dr. John C. Phillips and myself through 12 successive genera- 

 tions without a single out-cross. In one series selection has been made 

 for an increase in the extent of the pigmented areas; in the other series 

 the attempt has been made to decrease the pigmented areas. The result 

 is that the average pigmentation in one series has steadily increased, in 

 the other it has steadily decreased. The details of the experiment can 

 not be here presented, but it may be pointed out (1) that with each 

 selection the amount of regression has grown less, i. e., the effects of 

 selection have become more permanent; (2) that advance in the upper 

 limit of variation has been attended by a like recession of the lower 

 limit; the total range of variation has therefore not been materially 

 affected, but a progressive change has been made in the mode about 

 which variation takes place. 



3. The plus and minus series have from time to time been crossed 

 with the same wild race. Each behaves as a simple recessive unit giving 

 a 3:1 ratio among the grandchildren. But the extracted plus and the 

 extracted minus individuals are different; the former are the more 

 extensively pigmented. 



4. The series of animals studied is large enough to have significance. 

 It includes more than 10,000 individuals. 



The conclusion seems to me unavoidable that in this case selection has 

 modified steadily and permanently a character unmistakably behaving 

 as a simple Mendelian unit. 



This conclusion, from the writer's standpoint, is not 

 only avoidable, but unnecessary. No direct or implied 

 denial of these facts is made, but a shift is made in the 

 point of view. It seems to me a logical necessity that 

 hypothetical units used as measurement or descriptive 

 standards be fixed. The problem to be solved is the 

 simplest means of thus expressing the facts. If the most 



