324 CARL HALLQVIST 

to employ in the future in Lupinus. It is labour-saving, and an ana- 
lysis comprehensively enough may be made easier. 
The difficulties in the raising of a sufficient number of F,-families 
are remarkably reduced if the number of individuals in each family 
is intentionally decreased to a minimum. The question is to distinguish 
between the families segregating in the ratio 3:1 on the one hand, 
and the constant and the di-hybrids of different kinds on the other. 
A number of 32 individuals at the most in each family is required 
to make a sure discrimination — provided that the recessives are fully 
vital. The probability that a heterozygous plant shall give 32 domi- 
nants in succession is as 1: 10000. Thus even if an analysis is made 
comprising up to 10000 families probably only one family would be 
found to be erroneously grouped. Such a wrong grouping is of 
no account, however, as the rarer family-group has occurred often, even 
in cases of close linkage. There is no need of so great a precision in 
the case of low or moderately high linkage values. If the number 
of individuals in the F,-families are 24 throughout, one in 1000 families 
may be considered wrongly grouped. This precision may often be 
considered sufficiently accurate; indeed, a number of 20 individuals in 
‘ach family will be sufficient in certain cases. The number of plants 
in each family may thus be limited to 20—32 according to conditions. 
An F,-analysis of such a great number of families may mean too 
great a work to many, even if the task has been made easier through 
the limitations proposed above. However, the number of the indivi- 
duals may be still lowered in the following way. The sowing and 
the investigation of each family take place in different sets: only a 
few seeds of each family are sown the first time, for instance 4, the 
second portion may include another set of 4 seeds, and the rest, up 
to a maximum of 32 for instance, is sown the third time (if not a 
fourth set is tried). Families at once classed with certain segregating 
types — different in coupling and in repulsion already at the first 
sowing do not need to be repeated in the sowings made later. The 

last sowing includes then mainly one of the two groups of segregating 
types together with a small number of segregates belonging to the 
other group, which by a chance failed to expose its place in the first 
sowings made. The extent of the work depends apparently on the 
number of families left for the last sowings. Much labour-saving 
may therefore be made if the parent plants of the F,-families are selec- 
ted in the appropriate way. From the checker scheme, fig. 2 a, 
it is at once seen that it is inexpedient to use simplex recessive F,- 
