1. Dr. Xijiang Yu Shandong Agricultural University
The Possibility of QTL Detection with Allele Frequency Fluctuation in a Single Selective Line
Dr. Xijiang Yu
Shandong Agricultural University

2. Background Agencies that affect gene frequency Selection Mutation
Migration
Random drift

3. Background In a selective line Selection Mutation Migration
Random drift

4. The problem Can we distinguish the signal From the noises
Directional frequency change due to selection
From the noises
Fluctuation due to random drift ?

5. Theories Wright-Fisher model The diffusion approximation
Markov chain with transition probability matrix
The diffusion approximation

6. Calculation of null distribution

7. A sample Markov process
Real matrix can be constructed using the relationship between binomial CDF and incomplete beta function instantly [which has minor bias]. And one matrix for all if Ne keeps constant.

8. Assumptions of model of random genetic drift
Diploid organism
Sexual reproduction
Non-overlapping generations
Many independent subpopulations, each of constant size N
Random mating within each subpopulation
No migration between subpopulations
No mutation
No selection

9. About Ne The calculation only involves those reproduce.
Hence selection ratio is accounted for.

10. Approximate simulation
Kimura, 1980

11. Scenario parameters Effective population size, Ne
To determine the null distribution
the locus
Power issues.
Initial allele frequency
Still involved with power
Number of loci considered
Multiple tests

12. Objectives
Feasible marginal parameters for candidate loci and selection association
these scenarios

13. Case study I
In a selective population with constant Ne = 100, random mating is applied to the breeding individuals. An allele with frequency of 0.5 changed to 0.9 after nine generation of selection.
Is this allele affected by the selection?

14. Answer The 99% confidential intervals under the null hypothesis is:
(0.234, 0.770)
0.9 is beyond this scope.

15. Case study II
A diallelic locus with initial h2 = 0.1, what is the power of detecting it?
Ne = 100,
Selection rate = 0.5
No. of generations = 10,
Pure additive model.
Random mating of breeding individuals

16. Answer
The 95% & 99% confidential intervals under the null hypothesis are: []
[.234, .770]
The probability of one allele frequency exceed [threshold] is ?? [the power]
.919 [100k permutations]
.659 when h2 = 0.05

17. A general package General assumptions of previous theories:
Random mating among breeding animals.
The brute-force method

18. Brute-force method Using gene-dropping
To account for violations of assumptions mentioned previously.
Non-random mating
Generation overlapping
Multiple co-segregating loci
Inbreeding …

19. Acknowledgement Funded by NSFC, 863, & my university
Your enlightening questions