316 CARL HALLQVIST 


Assuming a relative frequency between recombinated gametes and non- 
recombinated ones (the former category not yet found in this case) 
of 1:10:10:1 (BF: Bf: bF: bf) a number of 6,5 double recessives 
would originate, and the probability of their non-appearance is about 
1: 1000. Thus it is very improbable that the non-recombinated game- 
tes are less than 10 times the recombinated ones. They are rather 
much more numerous. This belief is strengthened when the numerical 
relations of the F,-families are considered. 
The F,-method for determining gametic ratios will be further 
treated in the following, where a case of partial linkage is discussed 
(pag. 323). As it is shown here the gametic ratio may be determined 
by the proportions between F,-families of two different groups 
belonging to different types of segregation. — 
A number of 60 segregating families of repulsion type, 22 constant 
violets and 44 constant tinged blue have been obtained in the present 
cross. They all belong to one of the family-groups just mentioned, the 
other group, where the families segregating in the ratios 3:1 form 
the bulk, is altogether absent. As in the »F,-analysis» the minimal 
value of the strength of the linkage may thus be determined and 
it is found that the F,-method gives much better result. The mini- 
mum ratio 1:10 just calculated is, according to the F,-analysis, out 
of question; the ratio 1 : 36 may be assumed with just the same proba- 
bility to be the minimum. The gametic representation would neces- 
sitate 7 families out of the 126 grown belonging to the absent group, 
and the probability that all these are excluded is about 1: 1000. It is 
therefore rather safe to assume a higher frequency of the non-recom- 
binated gametes. The probability of the exclusion of the said families 
is about 1:25 at a gametic frequency of 1:100; the probability of 
their exclusion and their presence are equal first at a gametic fre- 
quency of 1:300, when the total number of families is 126. These 
calculations show clearly the advantage of using the F,-method in cases 
of repulsion. It has been found to give much greater precision than 
the analysis of the F,, even when the number of the families has 
been relatively small. It is clear that the present case is a case of 
close linkage, and it is of great interest to continue the cross. 
The result of the examination of the seed colour in this cross 
gave: 40 violets with rust-brown seeds, 87 blue and 59 tinged blue 
with earth-brown seeds. | 
