July 29, 1921] 



SCIENCE 



95 



posite this will be found the number of fac- 

 tors indicated. 



Let us take a specific example. Emerson 

 and East- (1913, p. 59) studied (among other 

 quantitative characters) the inheritance of 

 weight of seed in crosses of two varieties of 

 maize. The mean weight of a seed in one 

 parent variety was 2.Y grams; in the other 

 variety, it was 8.3 grams, a difference of 5.6 

 grams. The seeds of Fj plants had a mean 

 weight of 4.6 grams and a standard deviation 

 in weight of .639 grams. The mean seed 

 weight of Eg plants was 6.0 grams and the 

 standard deviation for F^ was 1.17 grams. 

 The difference between the standard deviations 

 of Ej and F, is 1.17 — .639 = .531 grams. 

 This is to be divided by the difference between 

 the parental means, which was 5.6 grams. 

 ISTow .531/5.6 = .0948, which multiplied by 100 

 gives 9.48 per cent. Looking in the column 

 " standard deviation " in Table II., we find 

 the indicated number of factors to be 14. 



Emerson and East made two other crosses 

 between these same varieties of maize, but 

 used different individuals as the parents in 

 'each cross. The results for the other two 

 crosses may be compared with the case just 

 discussed to test the reliability of the method. 

 In one case, the standard deviation of F„ was 

 1.089, making the difference between F^ and 

 Fj .45. Now (.45/5.6) X 100 = 8.03 per cent., 

 which corresponds with the result expected 

 from about 19 factors. In the other case the 

 standard deviation of F., was 1.23, making the 

 difference between Fj and F^ .591. But 



~ ' ' The inieritance of quantitative characters in 

 maize, ' ' Ses. Bull., 2, Agr. Exp. Station, Nebraska. 



(.591/5.6) X 100 = 10.55 per cent, indicating 

 11 factors. The three different lots of F^ 

 individuals thus indicate the factorial differ- 

 ences between the parents crossed to have been 

 in one case, 11 factors; in a second case, 14 

 factors; and in a third case, 19 factors. It 

 is rather probable that the parent races were 

 not homozygous, maize rarely is. But the 

 indicated mean difference between the parent 

 races would be about 15 factors. 



It is evident that the method has some seri- 

 ous limitations in its applicability. It ap- 

 plies perfectly only to cases in which the 

 parents are genetically pure, that is, are homo- 

 zygous for all factors affecting the character 

 under investigation. Such material is rarely 

 met with even in self fertilizing plants. If 

 either of the parent races is in any degree 

 variable genetically (heterozygous), Fj^ will 

 be variable in like degree. This will tend to 

 decrease the difference in variability between 

 Fj and F, and so to increase the indicated 

 number of factorial differences between the 

 parents. This difficulty can be offset in part 

 by raising an Fj generation derived from all 

 classes of F^ in the proportion of their oc- 

 currence. It is obvious that when a variable 

 Fj is obtained, various classes of Fj indi- 

 viduals should be tested as to their genetic 

 character, and if they are found to be gen- 

 etically diverse, each should have proportion- 

 ate representation in the F, population. 



The theory of multiple factors in blending 

 inheritance assumes that each factor is equal 

 to every other factor in its influence on the 

 character affected. It is improbable that this 

 is strictly true, but no other assumption will 



'Estimation of the Number of Genetic Factors Influencing Weight Involved in Crosses of Cer- 

 tain Races of Raibits 



