FLOWER AND SEED COLOUR IN LUPINUS 325 


plants as parent plants in the case of repulsion. The majority of these 
are constants — the greater the repulsion, the greater their number — 
and the main part of the families from these plants would be left for 
the last sowing. Thus the simplex recessives should be excluded as 
parent plants in the case of repulsion; these should instead be taken 
from the duplex dominant group. The last sowing will then include 
only the 3:1-segregates, now in minority, together with the very few 
constant duplex dominants, and the di-hybrids, which have not yet 
shown their di-hybrid character. In the case of coupling, on the 
other hand, only the simplex recessive F,-plants are selected; the ex- 
periment gets freed from the constant double dominants as well as 
from the families passing into repulsion. The total number of the 
individuals necessary in F, may be limited considerably in this way. 
Although seemingly paradoxical the statement holds true that the 
greater the coupling the easier the work, due to the fewness of the 
groups necessary in the last sowing. 
The advantage of this procedure may be readily demonstrated by 
the following example. We assume that the gametic ratio in a case 
of repulsion, otherwise identical with cross 9, is 1:30:30:1. We 
assume, further, that F, segregates in 1000 blue, 500 violet and 500 
bluish red for instance. The gametic ratio, then, is not to be found 
from the numerical relations in F,; the F,-analysis becomes necessary. 
As the fixing of the gametic ratio becomes surer the greater the num- 
ber of families, 480 families for instance are raised. The following 
total number of plants has to be raised in the case of such an analysis. 
As it is a case of repulsion only blue individuals are used as parent 
plants. The constant blue group from the upper left corner of the 
periphery of the scheme and the groups passing into coupling, which 
groups in all represent the expectation */, family in a total of 480 
families, are ignored. The families from the middle groups of the 
periphery, segregating in the ratio 3 : 1, have naturally to be included 
in the last sowing. Their number should be 30. The total number 
of individuals to be raised becomes 960, as 32 seeds from each of these 
30 parent plants have to be sown successively. A number of 450 di- 
hybrid families, segregating 1 : 2 : 1, has further to be expected. The 
first sowing of these will then include 1800 plants in all. According to 
probability 43 % of these families will show their di-hybrid character, 
while 57 % have to be sown again. This makes 256 families and 1024 
plants. When the result is combined with the numerical relations ob- 
tained in the first sowing 65 % of these 256 families are found to 
