Mean Value of Each Marker Class
Marker
Genotype |
Prob(QTL/marker) |
Marker
Mean |
| pi |
QQ |
Qq |
qq |
| AA |
1/4 |
(1-r)2 |
2r(1-r) |
r2 |
uAA |
| Aa |
1/2 |
r(1-r) |
(1-r)2+r2 |
r(1-r) |
uAa |
| aa |
1/4 |
r2 |
2r(1-r) |
(1-r)2 |
uaa |
QTL
mean |
u1 |
u2 |
u3 |
|
The QTL mean for each marker genotype is equal to the frequency of
each QTL type times the value of each QTL type, given the marker genotype.
The following is used for single marker-QTL association only:
uAA = (1-r)2u1 + 2r(1-r)u2
+ r2u3
uAa = r(1-r)u1 + [(1-r)2 + r2]u2
+ r(1-r)u3
uaa = r2u1 + 2r(1-r)u2
+ (1-r)2u3
We have 3 equations and four unknowns. The unknown parameters are u1,
u2, u3, and r. This shows that QTL effects and
position are confounded. We can solve for the QTL effects (means) only
by fixing r. Mapmaker will not calculate a lod score for only one marker!
