ESTIMATION OF AVERAGE DOMINANCE OF GENES 



511 



are not. The logical procedure is to compute <^ for various combinations of 

 values of r, c, and a. This is tedious but very useful if the three items are 

 varied over rational ranges. A set of values for 4> is presented in Table 30.8. 

 Choice of rational values for a presented no difficulty since, in this connec- 

 tion, we are not so much concerned with its actual value as with the smallest 

 for which sufficient data to make P = .50 are not beyond the reach of the 



experimenter. 



TABLE 30.8 



VALUE OF FOR r = 2 AND VARYING 

 V/VLUES OF c AND a 



Appropriate values for c will vary with the experimental material. The 

 range listed in the table was chosen for application to work with grain yield 

 of corn, a" is plot error variance which, judging from experience, will usually 

 be between 50 and 160 when yield is measured in bushels per acre.*^ This cor- 

 responds to a range of about 10 to 18 per cent for the coefficient of variation 

 if mean bushel yield is 70. 2m- is twice the additive genetic variance in the 

 Y'l population used. Robinson el al. (1949) worked with three F2 populations 

 and reported .0056 as an estimate of the average amount of additive genetic 

 variance where yield was measured as pounds per plant. Converted to 

 bushels per acre this figure becomes 78.4. More recent work at the North 

 Carolina Experiment Station has yielded estimates of the same order of mag- 

 nitude. From these results it appears that additive genetic variance will in 

 many cases be between 20 and 100 and hence that Zm^ will be between 40 

 and 200. The extreme values for c, if 0-- and '^u"- are within ranges suggested 

 above, ^ are 50/2(iO = .25 and 160/40 = 4.0. 



6. In work at the North CaroHna station it has been quite close to 50. 



7. Note that the suggested range for cr^ is off-center upwards and that for ^.ti^ is off- 

 center downwards with respect to estimates from North Carolina data. This was done 

 deliberately in an effort to be on the safe side. EfTiciency of the experiment suff'ers from 

 large <r^ or small Sm^. 



