514 



R. E. COMSTOCK AND H. F. ROBINSON 



of plots, lir = 2. If male groups per progeny set are 4.0, in Experiment I, as 

 in the work of Robinson et al., there would also be 16 progenies per set and 

 degrees of freedom for M12 would be 12/32 of the number of plots. 



Experiment III is obviously the most powerful and I the least powerful of 

 the three. In the three cases examined, the plot requirement for I is from ten 

 to twelve times that of III. Experiment II is intermediate, requiring from 

 two to four times the data needed in III. It may be of interest that in the 



work reported by Robinson et al. (1949) in which Experiment I was used in 

 studying corn yield there were about 500 degrees of freedom for Mn- The esti- 

 mate of a was 1.64 and, by the approximate F test, was just significant at the 

 5 per cent point. 



Before leaving the subject, it should be noted that the problem of data re- 

 quired has been dealt with under the original assumptions. If what have been 

 called estimates of a are biased upward by linkage or epistasis, their expected 

 values are larger than a, and the foregoing has relevance to the expected 

 values of the estimates rather than to a itself. To exemplify, suppose that a 

 were 1.2, but as a result of bias from epistasis and linkage the expected value 

 of the Experiment III estimate were 1.2. Then assuming c = .25 and r = 2, 

 the probability of the estimate being significantly above 1.0 would be .50 if 

 the data furnished 168 degrees of freedom (Table 30.9), the same number re- 

 quired if a were 1.0 and the estimate unbiased. Thus, we see that the proba- 

 bility of an estimate significantly greater than one is a function of the expect- 

 ed value of the estimate rather than of a when the two are not equal. The 

 corollary, that an estimate (obtained as described) significantly greater than 

 one is not final proof of overdominance at the locus level, has been indicated 

 in preceding sections. 



CONCLUDING REMARKS 



To attempt a general discussion of what has been presented appears un- 

 wise. It would almost certainly lead to some unnecessary repetition and could 

 do more to confuse than to clarify. However, certain comments seem in order. 



With regard to the experiments themselves, III appears definitely the 

 most useful (1) because it is the most powerful, and (2) because it can be em- 

 ployed to learn something about the effect of linkage on the estimate of a. 



