The Possibility of QTL Detection with Allele Frequency Fluctuation in a Single Selective Line
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Transcript of The Possibility of QTL Detection with Allele Frequency Fluctuation in a Single Selective Line
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The Possibility of QTL Detection with Allele Frequency Fluctuation
in a Single Selective LineDr. Xijiang Yu
Shandong Agricultural University
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Background
Agencies that affect gene frequency
Selection Mutation Migration Random drift
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Background
In a selective line
Selection Mutation Mutation Migration Migration Random drift
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The problem
Can we distinguish the signal Directional frequency change due to selection
From the noises Fluctuation due to random drift ?
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Theories
Wright-Fisher model Markov chain with transition probability matrix
The diffusion approximation
Ni
jNjjNij
p
qpCT
2
22
with
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Calculation of null distribution
sgeneration
)12()12()12()12()12()12(
12
1states Initial
n
NNijNNijNNij
N
ne
neeeee
e
TTT
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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.
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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
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About Ne
fm nnfm
fm
fm
nn
nn
nnNe
4
The calculation only involves those reproduce.Hence selection ratio is accounted for.
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Approximate simulation
N
pqUpp
2
312
Kimura, 1980
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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
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Objectives
Feasible marginal parameters for candidate loci and selection association
Power @ these scenarios
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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?
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Answer
The 99% confidential intervals under the null hypothesis is: (0.234, 0.770)
0.9 is beyond this scope.
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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
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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
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A general package
General assumptions of previous theories: Random mating among breeding animals.
The brute-force method
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Brute-force method
Using gene-dropping To account for violations of assumptions
mentioned previously. Non-random mating Generation overlapping Multiple co-segregating loci Inbreeding …
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Acknowledgement
Funded by NSFC, 863, & my university
Your enlightening questions