FLOWER AND SEED COLOUR IN LUPINUS 319 
e 

TABLE 2. 
Ass. coeff. of the phenotypic ratios corresponding to 
various gametic ratios. 
Gametic ratio Coupling Repulsion 
Poe d 0,3494 0,3425 
os 0,5575 0,5422 
Re | 0,6845 0,6646 
3.0.1 0,7656 0,7445 
ES AE | 0,8198 0,7986 
Ao: À 0,3575 0,8373 
4,5 : 1 0,8847 0,8659 
5,0 : 1 0,9049 0,8875 
35:4 0,9114 0,9043 
The linkage values: obtained may be further tested with the help 
of the standard error of the ass. coeff. determined according to YULE 
(1900) and listed in table 1, col. 7, and with the help of the table of 
the association coefficients for a series of gametic ratios (table 2). Both 
coupling and repulsion values answering to about 3 : 1 and 1 : 3 respec- 
tively are obtained if the threefold standard error is subtracted from the 
association coefficient of the observed values. This value marks the 
lower limit, and it is very improbable that the numerical values corre- 
spond to a gametic ratio lower than this. The corresponding upper limit 
lies higher. The ass. coeff. of repulsion reaches a value differing 
from the ass. coeff. by three times the standard error first at the ga- 
metic ratio 1 : 5,5, and the limit lies still higher in question of coupling 
values. When the simple standard error is used, the corresponding 
limits are 1: 3,5 and 1: 4,3. 2 
Thus it is seen that the standard errors allow great fluctuations 
of the linkage values, and the reliance of these may be questioned. 
It is very significant, however, that the gametic ratios of the coupling 
and the repulsion values show such a close correspondence, in the 
former case n=3,, in the latter n=3,s. It is very improbable, 
indeed, that the two different cases should give extreme deviations 
from a common middle value in the same direction in both 
cases. The allowed range of fluctuation diminishes greatly in such 
cases, and the linkage values obtained from the numerical relations 
of the different phenotypes, therefore, must be considered more 
reliable than is indicated in the above control. 
