Expected Frequency Example I
Liu, B.H. 1998. Statistical Genomics: Linkage, Mapping, and QTL Analysis.
CRC Press. pg 315.
Testcross progeny from AaBbCc F1
plant crossed to aabbcc tester. Coupling linkage, gene order A-B-C.
| |
observed |
Expected
Frequency |
| Genotype |
count |
with
double crossovers |
ignoring
double crossovers |
| AaBbCc |
f1 |
1/2(1-rAB-rBC+rABrBC) |
1/2(1-rAB-rBC) |
| AaBbcc |
f2 |
1/2(rBC-rABrBC) |
1/2rBC |
| AabbCc |
f3 |
1/2(rABrBC) |
0 |
| Aabbcc |
f4 |
1/2(rAB-rABrBC) |
1/2rAB |
| aaBbCc |
f5 |
1/2(rAB-rABrBC) |
1/2rAB |
| aaBbcc |
f6 |
1/2(rABrBC) |
0 |
| aabbCc |
f7 |
1/2(rBC-rABrBC) |
1/2rBC |
| aabbcc |
f8 |
1/2(1-rAB-rBC+rABrBC) |
1/2(1-rAB-rBC) |
Example:
Let rAB = 0.2 = rBC.
If we ignore double crossovers, then rAB
+ rBC
= rAC
0.2 + 0.2 = 0.4
If we consider double crossovers,
then rAC
= rAB
+ rBC
- 2rABrBC
rAC
= 0.2 + 0.2 - 0.08 = 0.32
rAB
= proportion of recombinant gametes between A and B loci.
1- rBC
= proportion of parental types of gametes for the B - C combination
Probability(recombinant gametes between A and B, but parental type
for B-C loci) = rAB
(1-rBC)
= rAB-rABrBC
Prob.(Abc and aBC gametes = rAB - rAB rBC)
Probability(Abc gamete) = Probability(aBC gamete)
= 1/2(rAB
-rABrBC)
Probability(Abc and aBC gametes) using Haldane's notation
= m(1-n) = m - mn
Probability (Abc gamete) = Probability(aBC gamete)
=1/2(m-mn)
