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 
1CW:1 Cw:1cW: 1cew. 
In this particular case, however, the gametes were produced in about 
the ratio 
3.4CW :1Cw:1ceW:3.4cw. 
The factors, therefore, display partial linkage, 7.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 gameticratio. Inorderto 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 F is 
(CW) (cw), not CcWw, and the series of gametes which it forms is written 
3.4(CW):1(Cw):1(cW) :3.4 (ew). 
The method of deriving an F, 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, 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. 
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