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 F repulsion progeny data we have the following:

classes	A_B_	A_bb	aaB_	aabb	Total
observed #	a	a	a	a	n
expected #	n(2+p) 4	n(1-p) 4	n(1-p) 4	np  4	n

The above table is for repulsion phase linkage. The maximum likelihood estimate of 'p' is:

Example

because: -a + 2a + 2a + 2a = 571 = s
because: n = 1415 = r
because  -2a = -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 F progeny from F individuals, we can just use the product method to estimate p.