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