Other Explanations 353 



probably much truer. Smith expanded his study further to 

 include possible linkage relations between the various genes that 

 determine flower size and a number of genes that determine 

 flower color. Like East, Smith found that apparently a large 

 number of genes for flower size was involved and that they 

 acted as duplicate, cumulative genes of comparable magnitude. 

 Some, if not all, of these polymeric genes were nondominant. Each 

 of the color genes was linked with some of the size genes, and 

 some of the size genes were linked with the self-sterility alleles. 

 This case appears to be explainable on the basis of the multiple 

 factor hypothesis, for all these cumulative genes seemed to 

 have about equal value in determining size, and there was no 

 gene that had any pronounced major effect. 



Other Explanations 



Although the multiple factor hypothesis (or theory of poly- 

 mery) seems to be a very handy explanation for the inheritance 

 of quantitative characters, it has frequently been questioned by 

 geneticists on the grounds, largely, of its improbability. Dupli- 

 cate genes in which two or three loci are operating are recog- 

 nized beyond any dispute, but most quantitative characters de- 

 mand the simultaneous interaction of genes at considerably 

 larger numbers of loci, all of which genes are duplicates of each 

 other. The probability of the existence of so many duplicate 

 genes in one organism has been questioned. If they do exist, 

 they must have arisen in some way. If they arose independently 

 as gene mutations, we must assume that the same mutation 

 arose a number of times at different places on different chromo- 

 somes. If they did not arise independently, their presence must 

 be accounted for by assuming that a certain chromosomal 

 segment became incorporated a number of times into various 

 chromosomes by polyploidy and numerous translocations. For 

 Shull's duplicate genes for triangular capsule in Capsella, it has 

 been established that the species concerned are tetraploids and 

 have four instead of two genomes. It is possible, therefore, that 

 each gene for capsule shape is present four times instead of two. 

 It has been shown, also, that polyploidy exists in wheat and 

 that it might easily account for Nilsson-Ehle's cases of dupli- 

 cate genes in that genus. For most quantitative characters, how- 

 ever, so many genes must be present that too high a polyploid 



