38 APPLICATION OP PETNCTPLES OF HEREDITY TO BEEEDING. 



lire 4, where four of the nine types increase and five decrease until, 

 in ten generations, the whole population consists of little more than 

 an equal mixture of the four homozygote types. Corn, being largely 

 but not completely cross-fertilized, would give a result intermediate 

 between those shown in figures 2 and 4. If the amount of cross- 

 fertilization in corn were fixed and definite, and if the average per- 

 centage of cross-fertilization could be determined, it would then be 

 possible to calculate the exact percentage of each type present in the 



population after the 

 relation between the 

 t}^es became con- 

 stant ; also the rate at 

 which each type 

 approached its ulti- 

 mate proportion of 

 the population. 



Figure 2 shows 

 what would happen 

 if corn were com- 

 pletely cross-fertil- 

 ized. This figure will 

 be understood when 

 it is explained that 

 the space between any 

 two adjacent horizon- 

 tal lines represents the 

 proportion of the pop- 

 ulation of the type 

 represented by the 

 formula in that space. 

 Here each of the nine 

 spaces maintains the 

 same width from gen- 

 eration to generation. This means that each of the nine t}^es present 

 tends to remain in the same proportion from generation to generation 

 under these conditions. 



One method of arriving at the data shown in figures 2, 3, 4, and 5 

 is illustrated immediately below, for tliose cases in wliich there is 

 complete cross-fertihzation, as in animals and in dioecious plants. 

 Generation in hybrids wliose parents differ in one Mendehan char- 

 acter only is IDZ), 2BR, IRR, where D represents the dominant and 

 E the recessive character. Hence one-fourth of generation Fg con- 

 sists of the type DD, two-fourths of type DR, and one-fourth of type 

 RR. But since males and females are equally numerous, one-fourtli 



w 



J. J- 



ss 





'/f6 











YY 



Ss 





% 











YY 



SS 















Yy 



ss 

















Ss 















Yy 

















yy 



SS 















yy 



Ss 















vv 



ss 





'//6 











Generat/ons. 



10 



Fig. 2.— Graphic illustration of ten generations of corn with no se- 

 lection, the first generation of which is 'YpSs.a The proportion 

 of each type is indicated by the vertical space between the hori- 

 zontal lines above and below the type symbols. Thus, YYSS 

 is one-sixteenth of the whole population. Under the conditions 

 mentioned each tjj>e tends to remain in the same proportion 

 from year to year. 



« Complete cross-fertilization is here assumed, 

 between tliose shown in figures 2 and 4. 



165 



The actual results are intermedial ( 



