Simplex Repulsion
Hackett, C.A. et al. 1998. Linkage analysis in tetraploid species:
a simulation study. Genet. Res. Comb. 71:143-154.
The four homologous chromosomes have the following genotypes:
Xy = A
xY = B
xy = C
xy = D
When A pairs with C or D, there is no observed recombination. When
B pairs with C or D, there is no observed recombination. Only when A
and B pair, would observed recombination occur.
| X y |
|
xy |
|
| o |
|
o |
Case
1 |
| |
|
|
A+B |
| o |
|
o |
C+D |
| x Y |
|
xy |
|
| X y |
|
xY |
|
| o |
|
o |
Case
2 |
| |
|
|
A
+ C |
| o |
|
o |
B
+ D |
| x y |
|
xy |
|
| X y |
|
xY |
|
| o |
|
o |
Case
3 |
| |
|
|
A
+ D |
| o |
|
o |
B
+ C |
| x y |
|
xy |
|
Of the six possible bivalent pairs, only when A pairs with B would
recombination be observable. When A and B pair, the combinations produced
would be:
When C pairs with D, the combinations produced
would be: (xy)
For Case 1 we would have the following gametes:
r/2XYxy:r/2xyxy
When A pairs with C, the combinations would be:
which reduces to:
When B pairs with D, the combinations would be:
which reduces to ½ xY: ½ xy.
For Case 2 we would have the following gametes:
¼ XyxY: ¼ Xyxy: ¼xyxY: ¼ xyxy.
For Case 3 we would have the following gametes:
¼ XyxY: ¼ Xyxy: ¼ xyxY: ¼ xyxy:
| To
summarize |
| Case |
Gametes |
| 1 |
 |
| 2 |
¼
XxYy: ¼ Xxyy: ¼ xxYy: ¼ xxyy |
| 3 |
¼
XxYy: ¼ Xxyy: ¼ xxYy: ¼ xxyy |
| Gametes |
Probability |
Observed
Number |
| Xxyy |
 |
b |
| xxYx |
|
c |
| XxYy |
 |
a |
| xxyy |
|
d |
The probability of observing a, b, c, and d of each class is:
We can solve for r by taking the derivative of the log of this function
with respect to r and setting the derivative equal to zero. The log-likelihood,
L, is given by:
2a + 2d - ra- rd = b + c + br + cr
2a - b - c + 2d = r(a+b+c+d)
2a - b - c + 2d = rn, because n = a + b + c + d
= r; which is the solution
Copyright
2000©, Ted Helms
| 
