466 FRED H. HULL 



calculate the mean of the 16 Fi combinations of four gametes of equal gene 

 frequency. Deviations of the individual Fi's from the mean are not predict- 

 able from parent phenotypes. They are due to specific combinability arising 

 from varying frequencies of heterozygosity. No more than two loci can be 

 heterozygous in this example. But iiv= f , w = j, six of the sixteen Fi's are 

 heterozygous at all four loci. In the event of overdominance ^g of high X low 

 combinations may exceed the best high X high combination. If 1 < ^ < 2, 

 and V = I, the mean of high X high is greater than the mean of high X low. 

 From the general combinability viewpoint we see only the difference of 

 means. Selection of the very few elites among specific Fi's would, however, 

 find them more frequently in high X low combinations. Hayes and Immer 

 (1942, Table 21) present data of Johnson and Hayes which seem to agree 

 with this interpretation in that the mean of high X high is best, but the 

 highest specific combination is more likely in high X low. 



EQUILIBRIUM FREQUENCIES OF GENES 



We may substitute for v in equation (1) the mean gene frequency of a 

 group of lines or of a variety, a general tester, to be held constant. Then if 

 V is less than (1 + k)/2k, and ^ > 1, regression of Fi on w is positive. Selec- 

 tion for general combinability with the same tester should continue to fixa- 

 tion of A except for reverse mutation. But if selected lines are recombined 

 for each cycle and the recombination is the tester for the next cycle, selection 

 comes to equilibrium when gene frequency of the tester reaches (1 -\- k)/2k, 

 short of fixation if ^ > 1. 



If concurrent with the foregoing process there should be selection of the 

 high specific combinations (high X low) with lower gene frequencies, the 

 combined effect on gene frequency may be nil. It may even be to degrade 

 gene frequency when gene frequency is so near the equilibrium that herita- 

 bility of general combinability is weak. From this view we may expect in the 

 event of overdominance to find the equilibrium zone nearer the upper end of 

 the range of data, providing some degree of positive heritability, some de- 

 gree of positive regression of Fi's on inbred parents. 



Ear-to-row selection should have progressed toward equilibrium gene fre- 

 quencies except for the counter effect of selection of superior plants within 

 ear-rows and within recombinations, selections of elite specific combinations 

 of two gametes with above-average heterozygosity and lower gene frequency. 



Modern corn breeding is failing largely beyond the first cycle for the same 

 reasons that caused the failure of ear-to-row selection, except that inbred 

 lines provide for a more efficient identification of elite specific combinations 

 which may have the lower gene frequencies. 



The whole of the evidence fits the generalized Mendelian model neatly 

 enough if we may accept overdominance and otherwise proceed without 

 prejudice to those conclusions more consistent with the data. 



