Florida Agricultural Experiment Station


and omitting intermediate steps, it is possible to write for the
case of self-fertilization of a monohybrid,

 S
 q + q' -
 T
 Y 1
 qq' = -
 T w
 and for a dihybrid
 7S 2
 q + q =-- -
 3T 3
 7Y 1
 qq' = --
 T w
It is of no advantage to treat the dihybrid and monohybrid
progeny of the dihybrid separately, since they do not provide
independent equations. Also they cannot be separated accur-
ately without extensive progeny tests. They are combined in
S for this study. The best solutions obtained for these two
pairs of equations are the pairs of quadratic roots:

 S / fS2 4Y
 -- / --
 T V T Tw
 q or q'
 2
and
 7S 2 / 7S 212 28Y
 3T 3 V 3T 3 Tw
 q or q'
 2
In neither case has the necessary third condition or equation
to solve for three unknowns been found but the situation is
not entirely hopeless. Since the roots cannot be complex the
discriminant cannot be less than zero. Setting it equal to zero
provides a minimum limit on w in each case. Also the maxi-
mum limit on the larger root may be reasonably taken at one,
thus setting a maximum limit on w. Taking these limits for
the monohybrid,
 Y/T 4 Y/T
 Max. w = Min. w
 (S/T-1) (S/T)2
and for the dihybrid
 21Y 28 Y/T
 Max. w -- Min. w -
 (7S 5T) (7S/3T 2/3)2