RECURRENT SELECTION AND OVERDOMINANCE 465 



and Fi yields are strictly comparable and b-i is negative, are: 2.25, 1.50, 1.88 

 (2.18), i.83, 1.78, 2.45, 1.41, 2.25, 1.69. The 1.88 (2.18) entry is Fi and F2 re- 

 spectively of Stringfield's example. Table 1. The value 1.09 from F2 data was 

 doubled to correct for the effect of inbreeding. 



If these independent estimates of k should be unbiased operationally, we 

 must still be cautious in attempting any unique physiological interpretation. 

 All of the several types of apparent overdominance listed here and others too 

 may be operating in corn yield. 



Estimates of backcrosses 5, and B, may be written by inspection of (1) 

 and (2). Fi is transformed to F2 (by selfing Fi) by multiplying the coefficient 

 of each k term in (1) by h. This provides three linear sets Fi, Fo, bar P; Fi, 

 Bi, P„-and F:, Bj, Fj, on the assumption of no epistasis. Fi, F2, and P are 

 alike in gene frequency. They differ only in frequency of heterozygosity. 

 Differences in the backcross comparisons arise from both gene frequency and 

 frequency of heterozygosity. 



GRAPHIC TRANSFORMATIONS TO REMOVE EPISTASIS 

 Where the two intervals in any one of the three comparisons are not equal, 

 epistasis may be suspected and a transformation of data may help to elimi- 

 nate some of its effects. No transformation of the corn yield data would be 

 warranted by all of the considerable amount of published data I have found, 

 since the data fit the linear hypothesis very closely with F2 and backcross 

 comparisons. 



Where transformation is clearly indicated, I may suggest a graphical de- 

 termination of the best function. Plot the data. Pi, Pj, P, Fi, F2, Bi, Bj, and 

 B on the vertical axis, and the same values on the horizontal axis linearly 

 with no dominance, with any arbitrary scale. If the plotted points do not 

 seem to provide a smooth curve, move Fi to the right a trial distance. Move 

 F2, B^, Bj, and B the same direction one-half as far. Move to the right or left 

 (Fi twice as far as the others each move) until the best fit visually to a 

 smooth curve is found as the best transformation function. The only excuse 

 for suggesting such a crude process is that if it is carefully carried out with 

 good data the function is so much more refined than any arbitrarily chosen 

 function for the purpose of correcting a complex of different kinds of epistasis 

 together. 



The transforming function determined by the above process with all avail- 

 able data on grain yield of corn would not differ sensibly from a straight line. 

 From this I have said earlier that epistasis is unimportant in corn yield. Con- 

 siderable amounts of increasing and decreasing returns types of epistasis may 

 be effectively balanced, of course. In that case, epistasis would provide no ex- 

 planation of the disparity of inbred and crossbred yields. 



MAXIMUM YIELDS FROM CROSSING HIGH BY LOW? 

 For four loci with v and w = f , the gametes are aiAiAsAi, Aia^A^Ai, 

 AiAiazAi, AiAiAidi. Equations (1) or (3) with appropriate substitutions 



