F
Repulsion Data
| classes |
A_B_ |
A_bb |
aaB_ |
aabb |
| observed
# |
a |
a |
a |
a |
| expected
frequency |
2+p
4 |
1-p
4 |
1-p
4 |
p
4 |
The above table is for repulsion linkage from the cross
to get the F
progeny.
The equation to be maximized with respect to r is:
Using the chain rule that:
= 
= a(p
- p
)
+ 2p(-a
- a)
+ p(-a
- a)
+ 2a
- 2pa
+ pa
- pa
= 0
= -ap
- ap
- ap
- ap
+ ap
- 2ap
- 2ap
- 2ap
+ 2a
= 0
= p(-a
- a
- a
- a)
+ p(a
- 2a
- 2a
- 2a)
+ 2a
= 0
= -pn
+ p(a
- 2a
- 2a
-2a)
+ 2a
= 0
= pn
+ p(-a
+ 2a
+ 2a
+ 2a)
-2a4 = 0
We can solve for p using the quadratic equation in the form of rx2 +
sx + t = 0. r = +n, s = -a
+ 2a
+ 2a
+ 2a,
t = -2a
