462 FRED H. HULL 



ed to disappear with inbreeding of the crosses. The first two examples in 

 Table 28.1 are the two more extensive of the three cases which include F2, 

 and it is apparent that the negative trend of Fi has decreased or become posi- 

 tive in F2. It is positive in F2 of the third case also with a strong negative 

 trend in Fi. 



The regularity of regression trends apparent in the first two examples in 

 Table 28.1 is by no means so readily apparent in any of the other twenty- 

 three cases. The eight cases with positive trends do not appear worse in this 

 respect than the others. 



The possibility that the 10 inbred lines of Kinman and Sprague do not 

 comprise a representative sample has been tested by dividing the 10 into two 

 groups of 5 each in various ways. This provides a 5 X 5 table in each case 

 with a unique sample of 25 F/s from the total of 45. These 5X5 tables do 

 not have vacant cells which arise when one parent line is included on both 

 margins of a table. Each tester in one group is rated with the same five lines 

 in the other group. Estimates of b^ and Pc from such 5X5 tables have con- 

 sistently substantiated those reported in Table 28.1, for the 10 X 10 table. 



Analyses of six of the twenty-five cases have been done also with loga- 

 rithms of P and Fi records, with results generally in agreement with those of 

 the original data. 



Most or all of the individual values of bp and 62 are not statistically sig- 

 nificant. The distribution of the twenty-five 62's is distinctly bi-modal. Eight 

 are positive indicating dominance of low yield, one is negative and small 

 enough to indicate intermediate dominance of high yield. Sixteen are nega- 

 tive and decidedly in the overdominance range. No explanation of the bi- 

 modality is apparent now. The eight positive values of 62 are in some degree 

 suspect since they are inconsistent with so many facts. All of these tests could 

 be repeated with the same unique samples of genotypes insofar as the parent 

 lines were homozygous and are still available. We need more comprehensive 

 and precise data. 



Present evidence from regression analysis is slightly in favor (2 to 1) of the 

 conclusion that a zone of nearly level regression, nearly zero heritability, 

 exists near the upper end of the range of present data. This conclusion would 

 be more consistent with the failure of selection for general combinability if 

 it should be that selection for specific combinability should favor aA over 

 AA, and thus tend to degrade gene frequencies below that equilibrium where 

 heritability and regression change from positive to negative. 



GENETIC INTERPRETATION OF THE REGRESSIONS 



The problem of genetic interpretations of bp and 62 may be approached 

 first with the simpler case of no epistasis. Consider the multiple gene set 

 aiAi to OnAn- Let {I — v) and v be relative frequencies of a and A in the 

 gametes of P, with respect to the n loci, and w similarly for Pj. The product 



