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 = 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 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 = 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 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