Florida Agricultural Experiment Station
It should be noted, however, that these limits may be strictly
imposed only on expected values of w. Random deviations be-
yond the limits may readily occur. The entire mathematical
treatment given here deals expressly with the expected values.
Utility of the solutions obtained must be judged by their sam-
pling variances finally. These limits set on w have proven to
be of considerable value in the analysis of the present case
while further treatment has been fruitless. However, it seems
desirable to present the further treatment briefly because ac-
curate evaluations of q, q', and w should prove of great value
preliminary to cytological investigations of such cases as the
present one.
The segregating F2 plants from a dihybrid F, are dihybrids
and monohybrids in the proportions
2+q+q' 2(q + q')
+ -1.
2+q+q'+2(q+q') 2 + q+ q'+ 2(q+ q')
It seemed that this relation might provide the necessary third
condition for a definite solution for q, q', and w in the F3 gen-
eration. Such data were available with cross 1 x 14. However,
it was learned from the Jacobian determinant that no solution
was possible. This test was kindly made by Dr. L. W. Gaddum
of the Florida Experiment Station, who then suggested that a
combination of the data in three separate cases should provide
three independent equations and a definite solution for q, q',
and w. The first choice for this attack was the ratio of re-
cessives to the total number of progeny in each of three cases,
since the error involved in experimentally determining these
ratios is least. Classification into true breeding and segregating
is hazardous unless very large progenies are grown. The ratios
of recessive to total progenies in a monohybrid, a dihybrid, and
in the F3 progeny of segregating F2 plants from a dihybrid F,
were designated as a, b, and c respectively. Solution of the
three equations resulted in:
9b 8ab a 6ab
S+ q' =-- qq' =
a + 2ab 3b (a + 2ab 3b)w
c(b-2ab+a) (21b-20ab-a) b(a-2ac+c) (3b-4ab+a) -
W -
c(1-a) (1-b) (21b-20ab-a) b(1-c) (1-a) (3b-4ab+a) -
2a(b---2bc+c) (9b-8ab-a)
2a(1-c) (1-b) (9b--ab-a)