One Marker In Duplex Coupling
And One Marker In Simplex Coupling
Hackett, C.A. et al. 1998. Linkage analysis in tetraploid
species: a simulation study. Genet. Res. Comb. 71:143-154.
XXxx
Yyyy
Situation A - coupling
| X Y (A) |
|
X y(C) |
| o |
|
o |
|
(B) |
|
(D) |
| o |
|
o |
| x y |
|
x y |
Situation B - repulsion
We will consider coupling phase linkage (Situation
A).
| X Y |
|
X y |
|
| o |
|
o |
Case
1 |
| |
|
|
A+B |
| o |
|
o |
C+D |
| x y |
|
x y |
|
| X Y |
|
x y |
|
| o |
|
o |
Case
2 |
| |
|
|
A+C |
| o |
|
o |
B+D |
| X y |
|
x y |
|
| X Y |
|
x y |
|
| o |
|
o |
Case
3 |
| |
|
|
A+D |
| o |
|
o |
B+C |
| x y |
|
X y |
|
There is observable recombination in cases 1 and 3,
but not in case 2.
Situation A - Coupling phase.
Case
1 Gametes
|
| |
(1/2)Xy |
(1/2)xy |
| [(1-r)/2]XY |
[(1-r)/4]XXYy |
[(1-r)/4]XxYy |
| [(1-r)/2]xy |
[(1-r)/4]Xxyy |
[(1-r)/4]xxyy |
| (r/2)Xy |
(r/4)XXyy |
(r/4)Xxyy |
| (r/2)xY |
(r/4)XxYy |
(r/4)xxYy |
Case
2 Gametes
|
| |
1xy |
| (1/2)XY |
(1/2)XxYy |
| (1/2)Xy |
(1/2)Xxyy |
Case
3 Gametes
|
| |
(1/2)xy |
(1/2)Xy |
| [(1-r)/2]XY |
[(1-r)/4]XxYy |
[(1-r)/4]XXYy |
| [(1-r)/2]xy |
[(1-r)/4]xxyy |
[(1-r)/4]Xxyy |
| (r/2)Xy |
(r/4)Xxyy |
(r/4)XXyy |
| (r/2)xY |
(r/4)xxYy |
(r/4)XxYy |
Now we will add the probabilities of each type of gamete
across cases 1, 2, and 3. We weight each probability
by a factor of 1/3 so that the total probability across
all three cases will add to unity.
| Gametes |
Probability |
Observed
Number |
| XXYy |
 |
|
| Xxyy |
 |
|
| XxYy |
 |
|
| Xxyy |
|
|
| XxYy |
|
|
| xxyy |
|
|
We can double check our results by adding the probabilities
of each type of gamete.
| Gametes |
Probability |
Observed
Number |
| X_Y_ |
 |
a |
| Xxyy |
 |
b |
| xxY_ |
 |
c |
| xxyy |
 |
d |
Now we can set up the likelihood expression [L(r)],
take the Log L(r), take the derivative of Log L(r),
set this derivative equal to zero, and solve for r.
Solve for r by substituting the actual numbers for
a, b, c, and d, then plot f(r) as r is varied. Where
f(r) crosses the line at Y = 0 is a solution for r.
If 0< r < 0.5, then r is for coupling.
