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

Background Agencies that affect gene frequency Selection Mutation Migration Random drift

Background In a selective line Selection Mutation Migration Random drift

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

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

Calculation of null distribution

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.

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

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

Approximate simulation Kimura, 1980

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

Objectives Feasible marginal parameters for candidate loci and selection association Power @ these scenarios

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?

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

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

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

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

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

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