4. A method of calculating gametic frequencies s
to z and coincidence from three‑point F_{2} data from an
individual heterozygous for three pairs of factors AaBbCc.
The observed zygotic F_{2} 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 
s^{2}+2sz+2sv+2st+2sw+2sy+2su+2sx+2vw+2tw+2wu+2ty+2tv+2xu 
b 
ABc 
t 
t^{2}+2tx+2vx+2tv+2tz 
c 
AbC 
u 
u^{2}+2uy+2vu+2vy+2uz 
d 
Abc 
v 
v^{2}+2vz 
e 
aBC 
w 
w^{2}+2wx+2wy+2wz+2xy 
f 
aBc 
x 
x^{2}+2xz 
g 
abC 
y 
y^{2}+2yz 
h 
abc 
z 
z^{2} 
The frequencies of the gametes s to z can then be
calculated as follows:
For z, z^{2}= h, then z = Ãh.
For y, (z+y)^{2} = h+g, or z+y = Ãh+g, and y
= Ãh+g ‑ z.
Similarly for v and x. x = Ãf+h  z and v = Ãd+h ‑ z. For w, h+f+g+e = (z+y+x+w)^{2} then w = Ãh+f+g+e  (z+y+x).
Similarly for t and u.
u =
Ãc+d+g+h ‑ (v+y+z) and 
t =
Ãb+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 
= 
Ãa+b+c+d+e+f+g+h ‑
(t+u+v+w+x+y+z). 
Corn was selected which was segregating for glossy,
liguleless and virescent_{4}, 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), virescent_{4} (v_{4}), and liguleless (lg), in F_{2}
GlV_{4}Lg 
GlV_{4}Lg 
Glv_{4}Lg 
Glv_{4}lg 
glV_{4}Lg 
glV_{4}lg 
glv_{4}Lg 
glv_{4}lg 
Total 
483 
256 
179 
108 
230 
6 
57 
1 
1320 
The analysis of these data follows:
z = 
Ã1 = 1 
y = 
Ã57+1 ‑ 1 = 6.6158 
x = 
Ã1+6 ‑ 1 = 1.6457 
v = 
Ã1+108 ‑ 1 = 9.4403 
w = 
Ã230+57+6+1 ‑
(x+y+z) = 7.8849 
u = 
Ã179+108+57+1 ‑
(v+y+z) = 1.5181 
t = 
Ã256+108+6+1 ‑
(v+x+z) = 7.1753 
s = 
Ã483+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 
v_{4} Gl lg 
v+w = 17.3252 
.4769 

V_{4} gl Lg 


Single crossovers in v_{4}‑gl 
v_{4} gl Lg 
x+y = 13.7911 
.3796 

V_{4} Gl lg 


Single crossovers in gl‑lg 
v_{4} Gl lg 
u+x = 3.1638 
.0870 

V_{4} gl Lg 


Double crossovers 
V_{4} Gl Lg 
s+z = 2.0517 
.0565 

v_{4} gl lg 

Crossing over in region 
1 = .4361 

2 = .1435 
Coincidence 
= 
observed doubles 
= 
.0565 
= 
.90 
expected doubles 
.0626 
Russell T. Johnson