432 E. J. WELLHAUSEN 



Which of the remaining three factors is the most important has not been de- 

 termined to date. 



Wright (1922) has shown that with random mating the vigor and produc- 

 tiveness of an F2 is less than that of the Fi by an amount equal to 1/nth of 

 the difference between the Fi and the average of the parental lines where n 

 is the number of parental lines involved. These theoretical conclusions of 

 Wright are adequately supported by experimental data from maize (Neal, 

 1935; Kiesselbach, 1933; Wellhausen and Roberts, 1949). 



In the past, in estimating the number of lines to use in a synthetic, appar- 

 ently it was assumed that the Fi mean in Wright's formula could be taken as 

 a constant value regardless of the number of lines involved. If this assump- 

 tion were correct, then the more lines involved the higher would be the yield 

 of the resulting synthetic. In actual practice, however, synthetics with a 

 large number of lines have yielded little more than the open-pollinated varie- 

 ties adapted to the same area. As indicated by Kinman and Sprague (1945), 

 the assumption of a constant mean yield for all Fi combinations seems un- 

 warranted. In any series in inbred lines, there are some that combine better 

 than others, and it is much easier to obtain four inbred lines that yield well 

 in all possible combinations than ten or sixteen. Therefore, to bring about the 

 highest mean yield of all possible single crosses, the use of relatively few lines 

 is indicated. 



It can be shown by holding the Fi yields as a constant that a better syn- 

 thetic might be made with four more productive lines than with eight less 

 productive. For example, assuming the mean yield of all single crosses in- 

 volved to be 120 per cent, an F2 of a synthetic involving four lines with a 

 mean yield of 80 per cent will be 110 per cent, while a synthetic involving 

 eight lines yielding only 30 per cent will yield 109 per cent in F2. Kinman and 

 Sprague (1945) concluded that in general the most efficient number of lines 

 to be included in a synthetic will vary with the range in combining ability 

 among the inbreds available as parents. However, on the basis of their study, 

 four to six lines appeared to be the most efficient number, the smaller number 

 being most efficient when more productive lines, yielding at least 75 per cent 

 of open-pollinated variety, were involved. 



Theoretically, therefore, the best synthetics would result from the use of 

 four to six lines which are as productive as possible and which are good com- 

 biners inter se. Certain practical aspects also must be taken into considera- 

 tion. If the inbred lines that are combined into a synthetic are greatly differ- 

 ent in type and maturity, the resulting Fo may be extremely variable for 

 these two characters. and may require considerable selection before distribu- 

 tion as a new variety. Variation is often a serious objection for many farmers 

 who have become used to their more-uniform highly selected old varieties. 

 The resistance of farmers to synthetic varieties which are variable and which 



