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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 - PowerPoint PPT Presentation
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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
Your enlightening questions
