The Possibility of QTL Detection with Allele Frequency Fluctuation in a Single Selective Line

1. 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 • Directional frequency change due to selection • From the noises • Fluctuation due to random drift ?

5. Theories • Wright-Fisher model • 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 • Heritability @ 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 • Power @ 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