Genetic Factors 



417 



found by Mendel himself and is due to a single pair of genes, tall being 

 dominant over short and segregating clearly in the F 2 . De Haan (1927, 

 1930) has shown that in addition to this gene there are two (perhaps 

 four) others that tend to inhibit growth. In this case a group of several 

 genes, all modifying the same trait, can be recognized and their indi- 

 vidual effects distinguished. In a considerable number of other cases it 

 can be shown that two, three, four, or more pairs of genes are concerned 

 in the inheritance of a size trait. Thus Quinby and Karper (1954) have 

 evidence that in cultivated sorghum varieties, ranging from 2 to 15 

 ft. in height, four pairs of genes are operative. 



Genes of this sort are cumulative in their effect. Sinnott (1937), Pow- 

 ers (1939), Charles and Smith (1939), and others have shown that 

 this additive effect is geometric rather than arithmetic, each gene 



Fig. 19-1. Geometric action of genes determining size. A, graph of fruit weight of an 

 F a population of cucurbit fruits consisting of 244 individuals plotted in arithmetically 

 equal classes. B, the same population plotted in classes equal logarithmically. The 

 first population is skewed, the second nearly symmetrical. ( From Sinnott. ) 



contributing not a certain definite amount of height or weight but a 

 certain percentage increase of the effect of the rest. This is shown by 

 the fact that the F x is closer to the geometric average of the parents than 

 to their arithmetic average and is thus somewhat nearer to the smaller 

 parent in size. Furthermore, if a segregating F 2 is plotted in classes that 

 are arithmetically equal, it skews toward the upper side, whereas if the 

 scale is a logarithmic one, the F 2 population is symmetrically distributed 

 around the geometric mean (Fig. 19-1). 



A developmental study of inherited size differences shows that some 

 are attained by differences in rate of growth and some in its duration. The 

 size differences between plants showing hybrid vigor and their parent 

 inbreds are related to a more rapid rate of growth, and some other size 

 differences also have their basis in genetically controlled growth rates. In 

 other cases the difference in size is due to longer duration of growth. 



