52 GENETIC STUDIES ON A CAVY SPECIES CROSS. 



In actual breeding experiments one would undoubtedly meet with 

 much deviation from a perfect blend of quantitative characters in the 

 Fi generation, or from such a distribution of r2 classes according to 

 the formula (1+1)^°, as in the hypothetical case used above as an 

 illustration. This is particularly true of size-characters in which the 

 theory of multiple factors, incompletely dominant, is most often invoked ; 

 for external conditions affect growth and size very easily. Further- 

 more, there are many other misleading circumstances in such a complex 

 that render analysis difficult. How often could we be sure that a parent 

 race possessed, or was homozygous in, each one of the multiple factors 

 affecting a character; or how often would we find them so, especially 

 in animals? Different individuals in the parent strains might appear 

 alike in a certain character and yet carry different sets of genes for this 

 character. Hayes (1912) had a case in tobacco which could be inter- 

 preted in this way. He crossed two varieties of Nicotiana tahacum, 

 both having about the same mode, mean, and low coefficient of vari- 

 ability with regard to number of leaves. The Fi was like the parents, 

 but the Fz showed such a marked increase in variability that he was 

 led to believe there had been a recombination of several factors for 

 leaf-number. The argument involved in his explanation is essentially 

 as follows: one parent might have a formula AABBccdd and the other 

 parent aabbCCDD. They would be of the same leaf-number, since 

 each had the cumulative effect of a double dose of two factors, and 

 they would breed true because each was homozygous. The Fi genera- 

 tion, AaBbCcDd, would also be of the same leaf-number, having the 

 cumulative effect of four factors. But when the Fi plants were 

 crossed, the F2 generation could have recombinations ranging from 

 AABBCCDD to aabbccdd. The frequency distribution of the classes 

 would be obtained by expanding the binomial (1-f 1)*. Hence, plants 

 occurred with much larger and with much smaller leaf-numbers than 

 in the parental forms or the Fi generation. Thus, in actual breeding 

 experiments, one might use parent plants which were of identical 

 appearance but of different zygotic formulae. 



In the simple illustrations of the theory, we suppose that one dose 

 of each factor, such as Ai, lends an effect about equal to that of any 

 other factor, such as A2, A3, A4 . . . . A^. But we do not really know 

 for how much influence each factor might be responsible, or whether any 

 one factor always causes the same result under all conditions. Factors 

 in a heterozygous condition may act more vigorously (East and Hayes 

 1912), or the vigor due to heterozygosis might raise the size of certain 

 classes only. Sterility or partial sterility of one sex might also impair 

 any sort of an analysis on the theoretical scheme suggested. 



Environmental influence might affect certain individuals subject by 

 chance, or they might regularly affect individuals of a particular zygotic 

 formula. 



