JOHANNSEN 



summary and conclusions 



All that will be discussed here 

 gives at one and the same time a com- 

 plete confirmation and a total elucida- 

 tion of Galton's well-known law of 

 regression, which concerns the rela- 

 tionship between parent and offspring. 

 Other regression relationships do not 

 concern us here. 



Insofar as my research material is 

 concerned, it agrees very well with 

 Galton's Law. This law states that in- 

 dividuals differing from the average 

 character of the population produce 

 offspring which, on the average, differ 

 to a lesser degree but in the same direc- 

 tion from the average as their parents. 

 Selection within a population causes a 

 greater or lesser shift in the direction 

 of the selection of the average for the 

 characteristics around which the in- 

 dividuals concerned are fluctuating. 



While as a consequence of this I am 

 not able to continue to regard the 

 population as completely uniform, 

 nevertheless my material can be bro- 

 ken up into "pure lines." It has been 

 demonstrated that in all cases within 

 the pure lines the retrogression men- 

 tioned above has been completed: Se- 

 lection within the pure lines has pro- 

 duced no new shift in genotype. 



The shift in the average for a char- 

 acteristic, which selection in a popula- 

 tion can usually produce, is thus an 

 indication that the total population— at 

 least in my material— consists of differ- 

 ent "lines" whose genotypes can be 

 more or less differentiated. In the 

 course of ordinary selection a popula- 

 tion would become impure; this result 

 is a consequence of the incomplete 

 isolation of these lines, whose geno- 

 rs'pes cause deviation of the average 

 character of the population in their 

 directions. 



The typical, well-known results of 

 selection, that is, step-wise progress in 



21 



the direction of the selection in the 

 course of each generation, therefore 

 depends upon step-wise progression in 

 each generation of the differing lines 

 concerned. It is now easily understood 

 that the action of selection cannot go 

 beyond the known limits— it must stop 

 when the purification, or, practically 

 speaking, the isolation of the most 

 strongly divergent pure line is com- 

 plete, in this connection it must be 

 pointed out that one can never ascer- 

 tain with certainty the existence of 

 only a single genotype in a sample 

 solely on the basis of concordance be- 

 tween the table or curve of variation 

 shown by that sample and the numer- 

 ical proportions of the binomial for- 

 mula. The variation curve of indi- 

 viduals, representing a racially pure 

 population in the ordinary sense, 

 frequently, indeed perhaps in most in- 

 stances, can be shown to be the result 

 of numerous genotypes representing 

 the various pure lines of the popula- 

 tion. The average value thus does not 

 always have the significance of a true 

 genotype. A great deficiency of a 

 purely statistical approach is obvious 

 in this regard. 



For this reason, I have attempted 

 throughout this paper to distinguish 

 sharply between the concept of the 

 mean (average character, average 

 values, and so on) and the concept of 

 the genotype. The confusion of these 

 two thoroughly different concepts has 

 only too frequently caused misunder- 

 standing and erroneous inferences, 

 perhaps not only in the field of hered- 

 ity. It must be conceded that it can 

 often be extremely difficult to dis- 

 tinguish between these two concepts 

 without detailed analysis; and in pure 

 lines the two concepts frequently 

 cover the same area. The numerical 

 expression of a genotype is frequently, 

 but by no means always, an average 

 value. 



