42 GENETIC STOCKS AND BREEDING METHODS 



Dr. Wright : There are two main questions which arise in connection with such a 

 paper as that presented by Drs. Green and Doolittle : first, the question whether solution 

 of the mathematical problem is useful in genetics and, second, whether the results given 

 are correct. Dr. Green has brought out so clearly the importance of knowing how 

 many generations are required to bring about reasonable assurance of isogenicity in all 

 neutral genes under diverse systems of mating that no additional attention need be 

 given to this. With regard to correctness, I have found nothing with which to disagree. 

 I did not attempt to repeat the method of attack used by the authors. It seemed best 

 to compare their results with those of a wholly different method, path analysis, which I 

 have been applying to such problems since 1 92 1 . This leads to certain extensions. 



As applied to mating systems, this method consists in deducing the changes brought 

 about automatically in the correlations between gametes. As it is a correlation method, 

 it deals only with relations between two things at a time. Thus, it can deal with the 

 relative amount of heterozygosis expressed as a function of the correlation between 

 uniting gametes but cannot deal with the changes in frequency of types of mating where 

 this involves relations among four varying gametes. Thus, it does not give as complete 

 a picture as can be obtained from the matrix of mating types (the method of Bartlett 

 and Haldane 56 used by Green and Doolittle), but what it can do, it does more simply. 

 It may be noted that after a sufficient number of generations of a regular system of 

 mating in which the number of individuals in the inbreeding group is constant, all 

 diallelic mating types tend to fall off in frequency at the same limiting rate as does 

 heterozygosis, a rate which is easily obtained by path analysis. Because of its relative 

 simplicity, generalizations can be made by path analysis which have not been found 

 practicable in terms of mating types. I will devote most of my discussion to this 

 point. The method applies only to the effects of accidents of sampling and thus 

 only to neutral alleles. The joint effects of sampling, selection, recurrent mutation, and 

 occasional outcrossing have been dealt with in other ways. 1417 - 1422 



It is necessary to assume that genie frequencies remain constant in a hypothetical, 

 total population consisting of all possible inbreeding lines in order to have a constant 

 basis for comparison of the correlations within lines. In the case of the two alleles, it is 

 assumed that the frequency array in both ova (o) and spermatozoa (s) always remains 

 [(1 — q)a + qA] in this total population. The relation between uniting gametes is 

 represented below, in terms of the amount of heterozygosis, h. The values assigned to 

 a and A obviously make no difference in the correlation between them. It is con- 

 venient to assign to a and 1 to A. 



os a A Total 



A h/2 q- (h/2) q 



a 1 - q - (h/2) h/2 1 - q 



Total 1 — q 



