4. A method of calculating gametic frequencies s
to z and coincidence from three‑point F2 data from an
individual heterozygous for three pairs of factors AaBbCc.
The observed zygotic F2 frequencies are
given the symbols a to h; their expected frequencies in terms of the gametic
frequencies s to z are given in table 1.
Table 1.
|
Observed zygotic frequency |
Phenotype |
Gametic frequency |
Phenotypes in terms of
gametic frequencies |
|
a |
ABC |
s |
s2+2sz+2sv+2st+2sw+2sy+2su+2sx+2vw+2tw+2wu+2ty+2tv+2xu |
|
b |
ABc |
t |
t2+2tx+2vx+2tv+2tz |
|
c |
AbC |
u |
u2+2uy+2vu+2vy+2uz |
|
d |
Abc |
v |
v2+2vz |
|
e |
aBC |
w |
w2+2wx+2wy+2wz+2xy |
|
f |
aBc |
x |
x2+2xz |
|
g |
abC |
y |
y2+2yz |
|
h |
abc |
z |
z2 |
The frequencies of the gametes s to z can then be
calculated as follows:
For z, z2= h, then z = �h.
For y, (z+y)2 = h+g, or z+y = �h+g, and y
= �h+g ‑ z.
Similarly for v and x. x = �f+h - z and v = �d+h ‑ z. For w, h+f+g+e = (z+y+x+w)2 then w = �h+f+g+e - (z+y+x).
Similarly for t and u.
|
u =
�c+d+g+h ‑ (v+y+z) and |
|
t =
�b+d+f+h ‑ (v+x+z). |
|
For s, a+b+c+d+e+f+g+h |
= |
(s+t+u+v+w+x+y+z)2 |
|
then s |
= |
�a+b+c+d+e+f+g+h ‑
(t+u+v+w+x+y+z). |
Corn was selected which was segregating for glossy,
liguleless and virescent4, on which this method could be tried.
Table 2 shows the classification of this material according to phenotype.
Table 2. Classification of corn seedlings
segregating for
glossy (gl), virescent4 (v4), and liguleless (lg), in F2
|
GlV4Lg |
GlV4Lg |
Glv4Lg |
Glv4lg |
glV4Lg |
glV4lg |
glv4Lg |
glv4lg |
Total |
|
483 |
256 |
179 |
108 |
230 |
6 |
57 |
1 |
1320 |
The analysis of these data follows:
|
z = |
�1 = 1 |
|
y = |
�57+1 ‑ 1 = 6.6158 |
|
x = |
�1+6 ‑ 1 = 1.6457 |
|
v = |
�1+108 ‑ 1 = 9.4403 |
|
w = |
�230+57+6+1 ‑
(x+y+z) = 7.8849 |
|
u = |
�179+108+57+1 ‑
(v+y+z) = 1.5181 |
|
t = |
�256+108+6+1 ‑
(v+x+z) = 7.1753 |
|
s = |
�483+256+179+108+230+6+57+1
‑ (t+u+v+w+x+y+z) = 1.0517. |
These calculated values may be arranged in a more orderly fashion as follows:
|
Class of gamete |
Gametes |
Relative frequency |
Actual frequency |
|
|
|||
|
Noncrossovers |
v4 Gl lg |
v+w = 17.3252 |
.4769 |
|
|
V4 gl Lg |
|
|
|
Single crossovers in v4‑gl |
v4 gl Lg |
x+y = 13.7911 |
.3796 |
|
|
V4 Gl lg |
|
|
|
Single crossovers in gl‑lg |
v4 Gl lg |
u+x = 3.1638 |
.0870 |
|
|
V4 gl Lg |
|
|
|
Double crossovers |
V4 Gl Lg |
s+z = 2.0517 |
.0565 |
|
|
v4 gl lg |
|
|
|
Crossing over in region |
1 = .4361 |
|
|
2 = .1435 |
|
Coincidence |
= |
observed doubles |
= |
.0565 |
= |
.90 |
|
expected doubles |
.0626 |
Russell T. Johnson