106 GENETICS IN RELATION TO AGRICULTURE 



fore, the factors evidently segregate in the normal Mendelian fashion, 

 but the excess of purple starchy and white waxy kernels indicates that 

 the factors C and W which came from one parent and c and w which came 

 from the other have been distributed to the same gametes more often 

 than would occur on the basis of independent segregation. 



The ordinary gametic ratio for independent segregation in a hybrid 

 of the genetic constitution CcWw is 



lCW:lCw:lcW:lcw. 



In this particular case, however, the gametes were produced in about 

 the ratio 



3ACW:lCw:lcW:ZAcw. 



The factors, therefore, display partial linkage, i.e., the parental com- 

 binations of factors tend to remain together more frequently than they 

 tend to form new combinations. The factor W breaks away from C to 

 form a new combination with c only once in about 4.4 times, instead of 

 once in two times as is the case for independent segregation. Neces- 

 sarily whenever W breaks away from C to form a new combination with 

 c, w forms a new combination with C. This accounts for the symmetrical 

 relations displayed in the gametic ratio. In order to show that the two fac- 

 tors are linked, in this case we represent the genetic constitutions of the 

 parents as (CW)(CW), purple starchy, and (cw)(cw), white waxy; not 

 CCWW and ccww respectively, which is the form used to indicate inde- 

 pendent relations between the factors. Correspondingly the FI is 

 (CW )(cw), not CcWw, and the series of gametes which it forms is written 



3.4(C JF) : 1 (Cw) : 1 (cW) : 3.4(cw) . 



The method of deriving an F z ratio from such a gametic series is shown 

 in the checkerboard in Fig. 49. Here it is necessary to take into account 

 not only the genetic constitutions of the gametes, but also the coefficients 

 which represent their relative frequency. 



Summing up the totals for like phenotypes from this checkerboard, we 

 find the F 2 grains are distributed in the following ratio : 



50.28 with purple aleurone and starchy endosperm 

 7.8 with purple aleurone and waxy endosperm 

 7.8 with white aleurone and starchy endosperm 



11.56 with white aleurone and*waxy endosperm. 



The calculated results based on this ratio are given in Table XIX. They 

 show very close agreement with numbers actually observed, but in 

 judging the significance of this agreement it must be borne in mind that 

 a gametic ratio was arbitrarily selected which would give the closest 

 possible agreement with the observed results. 



