Epistasis / Multi-locus Modelling - PowerPoint PPT Presentation

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Epistasis / Multi-locus Modelling

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Title: Epistasis / Multi-locus Modelling Author: Shaun Purcell Last modified by: Shaun Purcell Created Date: 2/6/2001 10:07:33 PM Document presentation format – PowerPoint PPT presentation

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Title: Epistasis / Multi-locus Modelling


1
Epistasis / Multi-locus Modelling
  • Shaun Purcell, Pak Sham
  • SGDP, IoP, London, UK

2
I
3
Single locus model
T
QTL1
4
Multilocus model
QTL1 QTL2
T
5
GENE x GENE Interaction
  • GENE x GENE INTERACTION Epistasis
  • Additive genetic effects
  • alleles at a locus and across loci independently
    sum to result in a net phenotypic effect
  • Nonadditive genetic effects
  • effects of an allele modified by the presence of
    other alleles (either at the same locus or at
    different loci)

6
Nonadditive genetic effects
  • Dominance
  • an allele ? allele interaction occurring within
    one locus
  • Epistasis
  • an interaction occurring between the alleles at
    two (or more) different loci
  • Additionally, nonadditivity may arise if the
    effect of an allele is modified by the presence
    of certain environments

7
Separate analysis
  • locus A shows an association with the trait
  • locus B appears unrelated

Locus B
Locus A
8
Joint analysis
  • locus B modifies the effects of locus A

9
Genotypic Means
  • Locus A
  • Locus B AA Aa aa
  • BB ?AABB ?AaBB ?aaBB ?BB
  • Bb ?AABb ?AaBb ?aaBb ?Bb
  • bb ?Aabb ?Aabb ?aabb ?bb
  • ?AA ?Aa ?aa ?

10
Partitioning of effects
  • Locus A
  • Locus B

M
P
M
P
11
4 main effects
M
Additive effects
P
M
P
12
6 twoway interactions
M
P
?
Dominance
M
P
?
13
6 twoway interactions
M
M
?
Additive-additive epistasis
P
P
?
M
P
?
P
M
?
14
4 threeway interactions
M
P
M
?
?
Additive-dominance epistasis
P
P
M
?
?
M
P
M
?
?
M
P
P
?
?
15
1 fourway interaction
Dominance-dominance epistasis
M
M
P
P
?
?
?
16
One locus
  • Genotypic
  • means
  • AA m a
  • Aa m d
  • aa m - a

0
d
a
-a
17
Two loci
  • AA Aa aa
  • BB
  • Bb
  • bb

dd
18
Research questions
  • How can epistasis be modelled under a variance
    components framework?
  • How powerful is QTL linkage to detect epistasis?
  • How does the presence of epistasis impact QTL
    detection when epistasis is not modelled?

19
Variance components
  • QTL linkage single locus model
  • P A D S N
  • Var (P) ?2A ?2D ?2S ?2N

Under H1 Cov(P1,P2) ??2A z?2D
?2S where ? proportion of alleles shared
identical-by- descent (ibd) between siblings
at that locus z probability of complete allele
sharing ibd between siblings at that locus
Under H0 Cov(P1,P2) ½?2A ¼?2D
?2S where ½ proportion of alleles shared
identical-by- descent (ibd) between
siblings ¼ prior probability of complete allele
sharing ibd between siblings
20
Covariance matrix
  • Sib 1 Sib 2
  • Sib 1 ?2A ?2D ?2S ?2N ??2A z?2D ?2S
  • Sib 2 ??2A z?2D ?2S ?2A ?2D ?2S ?2N

Sib 1 Sib 2 Sib 1 ?2A ?2D ?2S
?2N ½?2A ¼?2D ?2S Sib 2 ½?2A ¼?2D
?2S ?2A ?2D ?2S ?2N
21
  • QTL linkage two locus model
  • P A1 D1 A2 D2
  • A1A1 A1D2 D1A2 D1D2
  • S N
  • Var (P) ?2A ?2D ?2A ?2D
  • ?2AA ?2AD ?2DA ?2DD
  • ?2S ?2N

22
  • Under linkage
  • Cov(P1,P2) ??2A z?2D ??2A z?2D
  • ???2A ?z?2AD z??2DA zz?2DD
  • ?2S
  • Under null
  • Cov(P1,P2) ½?2A ¼?2D ½?2A ¼?2D
  • E(??)?2AE(?z)?2AD E(z?)?2DA E(zz)?2DD
  • ?2S

23
IBD locus 1 2 Expected Sib
Correlation
0 0 ?2S
0 1 ?2A/2 ?2S
0 2 ?2A ?2D ?2S
1 0 ?2A/2 ?2S
1 1 ?2A/2 ?2A/2 ?2AA/4 ?2S
1 2 ?2A/2 ?2A ?2D ?2AA/2 ?2AD/2 ?2S
2 0 ?2A ?2D ?2S
2 1 ?2A ?2D ?2A/2 ?2AA/2 ?2DA/2 ?2S
2 2 ?2A ?2D ?2A ?2D ?2AA ?2AD ?2DA
?2DD ?2S
24
Joint IBD sharing for two loci
  • For unlinked loci,
  • Locus A
  • 0 1 2
  • Locus B 0 1/16 1/8 1/16 1/4
  • 1 1/8 1/4 1/8 1/2
  • 2 1/16 1/8 1/16 1/4
  • 1/4 1/2 1/4

25
Joint IBD sharing for two linked loci
? at QTL 1
? at QTL 2
0
1/2
1
0
1/2
1
26
Potential importance of epistasis
  • a genes effect might only be detected within
    a framework that accommodates epistasis
  • Locus A
  • A1A1 A1A2 A2A2 Marginal
    Freq. 0.25 0.50 0.25
  • B1B1 0.25 0 0 1 0.25
  • Locus B B1B2 0.50 0 0.5 0 0.25
  • B2B2 0.25 1 0 0 0.25
  • Marginal 0.25 0.25 0.25

27
Power calculations for epistasis
  • Specify
  • genotypic means,
  • allele frequencies
  • residual variance
  • Calculate
  • under full model and submodels
  • variance components
  • expected non-centrality parameter (NCP)

28
Submodels
  • Apparent variance components
  • - biased estimate of variance component
  • - i.e. if we assumed a certain model (i.e. no
    epistasis) which, in reality, is different from
    the true model (i.e. epistasis)
  • Enables us to explore the effect of misspecifying
    the model

29
Detecting epistasis
  • The test for epistasis is based on the difference
    in fit between
  • - a model with single locus effects and epistatic
    effects and
  • - a model with only single locus effects,
  • Enables us to investigate the power of the
    variance components method to detect epistasis

30
(No Transcript)
31
- DD VA1 VD1 VA2 VD2 VAA VAD VDA -
- AD VA1 VD1 VA2 VD2 VAA - - -
- AA VA1 VD1 VA2 VD2 - - - -
- D VA1 - VA2 - - - - -
- A VA1 - - - - - - -
H0 - - - - - - - -
32
Example 1 epi1.mx
  • Genotypic Means B1B1 B1B2 B2B2
  • A1A1 0 0 1
  • A1A2 0 0.5 0
  • A2A2 1 0 0
  • Allele frequencies A1 50 B1 50
  • QTL variance 20
  • Shared residual variance 40
  • Nonshared residual variance 40
  • Sample N 10, 000 unselected pairs
  • Recombination fraction Unlinked (0.5)

33
Example 2 epi2.mx
  • Genotypic Means B1B1 B1B2 B2B2
  • A1A1 0 1 2
  • A1A2 0 1 2
  • A2A2 2 1 0
  • Allele frequencies A1 90 B1 50
  • QTL variance 10
  • Shared residual variance 20
  • Nonshared residual variance 70
  • Sample N 2, 000 unselected pairs
  • Recombination fraction 0.1

34
Exercise
  • Using the module, are there any configurations of
    means, allele frequencies and recombination
    fraction that result in only epistatic components
    of variance?
  • How does linkage between two epistatically
    interacting loci impact on multilocus analysis?

35
Poor power to detect epistasis
  • Detection reduction in model fit when a term is
    dropped
  • Apparent variance components soak up variance
    attributable to the dropped term
  • artificially reduces the size of the reduction

36
Epistasis as main effect
  • Epistatic effects detected as additive effects
  • Main effect versus interaction effect blurred
  • for linkage, main effects and interaction effects
    are partially confounded

37
  • Probability Function Calculator
  • http//statgen.iop.kcl.ac.uk/bgim/
  • Genetic Power Calculator
  • http//statgen.iop.kcl.ac.uk/gpc/
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