Summary
We use calculus to find a 'p' value that maximizes the probability
that the observed data fits the model. For testcross
data the maximum likelihood of p is nr/n which is the
number of recombinant progeny divided by the total number
of progeny.
For F2
repulsion progeny data we have the following:
| classes |
A_B_ |
A_bb |
aaB_ |
aabb |
Total |
| observed
# |
a1 |
a2 |
a3 |
a4 |
n |
| expected
# |
n(2+p2)
4 |
n(1-p2)
4 |
n(1-p2)
4 |
np2
4 |
n |
The above table is for repulsion phase linkage. The maximum likelihood
estimate of 'p' is:
Example
| class |
A_B_ |
A_bb |
aaB_ |
aabb |
Total |
| observed
# |
753 |
292 |
351 |
19 |
1415 |
because: -a1
+ 2a2
+ 2a3
+ 2a4
= 552 = s
because: n = 1415 = r
because -2a4
= -38 = t
When we used the product method 
= 0.245 for the same F2 repulsion phase linkage data.
The conclusion is that except for special cases, such
as progeny testing F3
progeny from F2
individuals, we can just use the product method to estimate
p.
