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

The Possibility of QTL Detection with Allele Frequency Fluctuation

in a Single Selective LineDr. Xijiang Yu

Shandong Agricultural University

Background

Agencies that affect gene frequency

Selection Mutation Migration Random drift

Background

In a selective line

Selection Mutation Mutation Migration Migration Random drift

The problem

Can we distinguish the signal Directional frequency change due to selection

From the noises Fluctuation due to random drift ?

Theories

Wright-Fisher model Markov chain with transition probability matrix

The diffusion approximation

Ni

jNjjNij

p

qpCT

2

22

with

Calculation of null distribution

sgeneration

)12()12()12()12()12()12(

12

1states Initial

n

NNijNNijNNij

N

ne

neeeee

e

TTT

A sample Markov process

0625.25.375.25.0625.

10000

316.422.211.047.004.

0625.25.375.25.0625.

004.047.211.422.316.

00001

00100

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

fm nnfm

fm

fm

nn

nn

nnNe

4

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

Approximate simulation

N

pqUpp

2

312

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

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