INTRODUCTION TO ASSOCIATION MAPPING

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INTRODUCTION TO ASSOCIATION MAPPING
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• We have a set of inbred lines or varieties
• We have genotyped them with a large set of
  markers
• We also have phenotypic data of the lines for
  several traits
• And now What?

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• We will take advantage of the Linkage
  Disequilibrium (LD) to identify genetic regions
  associated with our trait of interest
• Association mapping is also called Linkage
  Disequilibrium mapping

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Identify associations between markers and
phenotypes without the need to develop specific
populations
Marker Distance Line 1 Line 2 Line 3 Line 4 Line 5 Line 6 Line 7 Line 8 Line 9 Line 10 Line 11 Line 12 Line 13 Line 14 Line 15 Line 16
_3_0363_ 0 A B B A A A B A B B A B B B B B
_1_1061_ 0.8 A B B A A A B A B B A A A B B A
_3_0703_ 1.5 B A A B B B A B A A B B B B B B
_1_1505_ 1.5 B A A B B B A B A B B B B B B B
_1_0498_ 1.5 B B B B B B B B B B B B B B B A
_2_1005_ 3.8 A B B A A A B A B A A B B B B B
_1_1054_ 3.8 A A A A A A A A A B A A A A A A
_2_0674_ 6 A B B A A A B A B A A A A A A B
_1_0297_ 8.8 A A B B B B B A A A A A A A A B
_1_0638_ 10.7 A A B B B B B A A B A A A A A A
_1_1302_ 11.4 B A A A B B A A A B A B B B B A
_1_0422_ 11.4 B A A A B B A A A B A B B B B A
_2_0929_ 15.3 A B B B A A B B B A B A A A A B
_3_1474_ 15.4 A B B B A A B B B A B A A A A A
_1_1522_ 17.3 A B B B A A B B B A B A A A A A
_2_1388_ 17.3 A A A A A A A A A A A A A A A A
_3_0259_ 18.1 B B B B B B B B B B B A A A A A
_1_0325_ 18.1 B B B B B B B B B B B A A A A A
_2_0602_ 20.8 A A B A A A A B A B A A A A A A
_1_0733_ 23.9 B B B B B B B B B B B A A A A A
_2_0729 23.9 B B B B B B B B B B B A A A A A
_1_1272_ 23.9 A B B B A A B B B B B B B B B B
_2_0891_ 26.1 A A A A A A A A A B A A A A A A
_2_0748_ 26.6 B B B B B B B B B A B B B B B B
_3_0251_ 27.4 A B A A A B A A A B A A A B A A
_1_0997_ 35.5 B B A A A B B B B B B B B B B B
_1_1133_ 41.8 B B A A A B B B B A B A A A A A
_2_0500_ 42.5 A A A A A A A A A B A B B B B B
_3_0634_ 43.3 B B B B B B B B B A B A A A A A
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Desease severity
5
0
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• Definition of Linkage Disequilibrium is very
  simple
• is the non-random association of alleles at
  different loci

Equilibrium
Disequilibrium
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Equilibrium
Disequilibrium
Locus 1
Locus 2
Locus 3
Locus 4
Locus 5
Locus 1
Locus 2
Locus 3
Locus 4
Locus 5
Random mating population with loci segregating
independently

• Non random mating population LD due to selection,
  mutation, drift/sampling, population structure

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How do we measure LD?

• The LD is measured with a parameter called D.
• If alleles at different loci are not inherited
  independently, then
• PAB ? PA x PB and
  DAB PAB PA x PB
• (PA and PB are allele frequencies and PAB is the
  haplotype frequency)
• Standarized measures of LD D and r2

for D lt 0
for D gt 0
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Line

a a
A A
a a
a a
a a
a a
A A
a a
a a
a a
a a
a a
A A
a a
a a
A A
a a
A A
a a
A A
A A
a a
a a
a a
a a
a a
A A
a a
A A
A A

b b
B B
B B
b b
b b
b b
B B
b b
B B
b b
b b
B B
B B
b b
B B
B B
b b
B B
b b
B B
b b
b b
b b
b b
b b
B B
B B
B B
B B
B B
Locus 1
Locus 2

1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
10 10
11 11
12 12
13 13
14 14
15 15
16 16
17 17
18 18
19 19
20 20
21 21
22 22
23 23
24 24
25 25
26 26
27 27
28 28
29 29
30 30
Allele frequencies PA 10/30 Pa 20/30 PB
15/30 Pb 15/30
Haplotype frequencies PAB 9/30 PaB 6/30 PAb
1/30 Pab 14/30
DAB PAB PA x PB 9/30 (10/30 x 15/30)
0.13
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Spring barley Two rows Chromosome 5H
r2
Distance (bp)
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Extension of LD
Humans 80kb (Europeans) 5kb (Nigerians) Outcrossing
Cattle gt 10 cM Outcrossing
Arabidopsis 250 kb Selfing
Maize 1 kb (Diverse maize) 1.5 kb (diverse inbred lines) gt100 kb (Elite lines Outcrossing
Barley Up to 100kb Selfing
Flint-Garcia et al., Annu. Rev. Plant Biol. 2003.
5435774
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• Factors that increase LD
• mutation
• mating system (self-pollination),
• population structure
• admixture
• relatedness (kinship)
• small founder population size or genetic drift
• selection (natural, artificial, and balancing)

• Factors that decrease LD
• high recombination and mutation rate
• recurrent mutations
• outcrossing

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Mutation provides the original material for
producing polymorphism that will be in LD
Allele b appears on gamete carrying A A and b
will appear together
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• Mating system
• Generally LD decays more rapidly in outcrossing
  species compared to selfing, where individuals
  are likely to be homozygous
• In selfing species, most recombination occurs
  between identical haplotypes, as a result of high
  individual homozygosity, and thus these events do
  not reduce LD
• Selfing reduces the rate at which LD breaks down
• When loci are closely linked in a selfing
  population they remain in high LD for many
  generations

Selfing, little or no recombination
Outcrossing 0.00 Selfing 0.99
Little recombination 0.05 High recombination
0.5
Outcrossing, high recombination
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• Drift / Sampling
• In small populations the effects of genetic drift
  results in the loss of rare allelic combination,
  which increases LD.
• Sampling increases or reduces certain allelic
  combinations by chance

• Selection
• Strong selection at a locus is expected to reduce
  diversity and increase LD in the surrounding
  region
• Selection operating on a gene will increase LD
  and reduce diversity in the vicinity of that
  gene. Alleles flanking the selected gene will be
  fixed.
• Can cause LD also between unlinked loci typical
  result of coselection of loci during breeding for
  multiple traits

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LOD
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• What information we need to know the association
  mapping analysis?
• Genotypic
• Linkage disequilibrium decay
• Number of markers and Marker density
• Quality of the data missing values, minor allele
  frequency
• Phenotypic
• Quantitative or qualitative traits
• Heritability of the trait, repeatability
• Population
• Structure
• Kinship

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• Genotypic Information
• Linkage disequilibrium decay.
• The power of detection is highly influenced by
  the LD between the QTL and the marker

r2
r2
10 kb
100 kb
Physical distance
Physical distance
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• Marker density
• The extend of LD shows the expected r2 at a given
  distance
• According to it, it is important to chose an
  adequate marker density to increase the power of
  detection

r2
r2
10 kb
100 kb
Physical distance
Physical distance
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• Quality of the data
• Number of individuals with small samples sizes,
  the probability of a significant association
  between maker and QTL is high.

Marker Distance Line 1 Line 2 Line 3 Line 4 Line 5 Line 6 Line 7 Line 8 Line 9 Line 10 Line 11 Line 12 Line 13 Line 14 Line 15 Line 16
_3_0363_ 0 A B B A A A B A B B A B B B B B
_1_1061_ 0.8 A B B A A A B A B B A A A B B A
_3_0703_ 1.5 B A A B B B A B A A B B B B B B
_1_1505_ 1.5 B A A B B B A B A B B B B B B B
_1_0498_ 1.5 B B B B B B B B B B B B B B B A
_2_1005_ 3.8 A B B A A A B A B A A B B B B B
_1_1054_ 3.8 A A A A A A A A A B A A A A A A
_2_0674_ 6 A B B A A A B A B A A A A A A B
_1_0297_ 8.8 A A B B B B B A A A A A A A A B
_1_0638_ 10.7 A A B B B B B A A B A A A A A A
_1_1302_ 11.4 B A A A B B A A A B A B B B B A
_1_0422_ 11.4 B A A A B B A A A B A B B B B A
_2_0929_ 15.3 A B B B A A B B B A B A A A A B
_3_1474_ 15.4 A B B B A A B B B A B A A A A A
_1_1522_ 17.3 A B B B A A B B B A B A A A A A
_2_1388_ 17.3 A A A A A A A A A A A A A A A A
_3_0259_ 18.1 B B B B B B B B B B B A A A A A
_1_0325_ 18.1 B B B B B B B B B B B A A A A A
_2_0602_ 20.8 A A B A A A A B A B A A A A A A
_1_0733_ 23.9 B B B B B B B B B B B A A A A A
_2_0729 23.9 B B B B B B B B B B B A A A A A
_1_1272_ 23.9 A B B B A A B B B B B B B B B B
_2_0891_ 26.1 A A A A A A A A A B A A A A A A
_2_0748_ 26.6 B B B B B B B B B A B B B B B B
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Desease severity
5
0
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• Quality of the data
• Number of individuals with small samples sizes,
  the probability of a significant association
  between maker and QTL is high.

Marker Distance Line 1 Line 2 Line 3 Line 4 Line 5 Line 6 Line 7 Line 8
_3_0363_ 0 A B B A A A B A
_1_1061_ 0.8 A B B A A A B A
_3_0703_ 1.5 B A A B B B A B
_1_1505_ 1.5 B A A B B B A B
_1_0498_ 1.5 B B B B B B B B
_2_1005_ 3.8 A B B A A A B A
_1_1054_ 3.8 A A A A A A A A
_2_0674_ 6 A B B A A A B A
_1_0297_ 8.8 A A B B B B B A
_1_0638_ 10.7 A A B B B B B A
_1_1302_ 11.4 B A A A B B A A
_1_0422_ 11.4 B A A A B B A A
_2_0929_ 15.3 A B B B A A B B
_3_1474_ 15.4 A B B B A A B B
_1_1522_ 17.3 A B B B A A B B
_2_1388_ 17.3 A A A A A A A A
_3_0259_ 18.1 B B B B B B B B
_1_0325_ 18.1 B B B B B B B B
_2_0602_ 20.8 A A B A A A A B
_1_0733_ 23.9 B B B B B B B B
_2_0729 23.9 B B B B B B B B
_1_1272_ 23.9 A B B B A A B B
_2_0891_ 26.1 A A A A A A A A
_2_0748_ 26.6 B B B B B B B B
10
Desease severity
5
0
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Quality of the data Minor allele frequency
Line
Locus 2
Locus 1

a a
a a
a a
a a
a a
a a
a a
a a
a a
a a
a a
a a
a a
a a
a a
A A
a a
a a
a a
a a
a a

b b
b b
b b
b b
b b
b b
b b
b b
b b
b b
b b
B B
b b
b b
b b
b b
b b
b b
b b
b b
b b

1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
10 10
11 11
12 12
13 13
14 14
15 15
16 16
17 17
18 18
19 19
20 20
21 21
Two loci can be completely unlinked and still
show high LD
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Quality of the data Missing data
b
-
b
b
B
b
B
b
b
B
-
b
b
-
b
B
b
b
-
b
-
b
b
b
b
b
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• What information we need to know the association
  mapping analysis?
• Genotypic
• Linkage disequilibrium decay
• Number of markers and Marker density
• Quality of the data missing values, minor allele
  frequency
• Phenotypic
• Quantitative or qualitative traits
• Heritability of the trait, repeatability
• Population
• Structure
• Kinship

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• Phenotypic
• Quantitative or qualitative traits
• One or more QTL involved
• The higher the effect of the QTL, the higher the
  power of detection
• Quantitative traits usually many genes involved
  of small effect
• The problem of epistatic traits

Heritability of the trait, repeatability
h2Vgenotipic/Vphenotypic
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The problem of epistatic traits
Phenotype heading date
Line
VRN1
VRN2
1
62
a
c
VRN1 and VRN2 located in different chromosomes
2
152
A
c
3
59
a
c
4
58
a
c
5
60
A
D
6
60
No association between individuals genes (VRN1 or
VRN2) and heading date
a
c
7
57
a
D
8
64
a
c
9
151
A
c
10
59
a
D
11
58
a
D
12
152
However, late heading date only when haplotype Ac
is present
a
c
13
60
a
c
14
151
A
c
15
58
a
c
16
149
A
c
17
64
A
D
18
58
a
c
19
154
A
c
20
58
a
c
21
63
a
D
60
a
22
c
153
A
23
c
58
a
24
c
57
a
25
c
64
a
26
c
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• What information we need to know the association
  mapping analysis?
• Genotypic
• Linkage disequilibrium decay
• Number of markers and Marker density
• Quality of the data missing values, minor allele
  frequency
• Phenotypic
• Quantitative or qualitative traits
• Heritability of the trait, repeatability
• Population
• Structure
• Kinship

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Population Structure
The classical example of interference by
population structure

• Study of type 2 diabetes in 2 tribes of Native
  Americans from Arizona
• A correlation between a haplotype at the
  immunoglobulin G locus and reduced diabetes
• However on further analysis it was found that
  those with diabetes had a lower proportion of
  European ancestry
• And that the haplotype associated with reduced
  diabetes was more prevalent in Europeans
• When the analysis was restricted to individuals
  with similar European ancestry, the association
  was no longer detected.

Knowler WC, et al. 1988. Am. J.Hum. Genet.
4352026
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• Population Structure
• Similar structure exists in plants
• Breeding history of many important crop species
  and limited gene flow have created complex
  stratification within the germplasm.
• Different geographic origin of the germplasm
  causes population structure (usually natural
  selection tends to fix alleles at many loci
  related to adaptation).
• Also the destination of the crop, growth habit,
  certain morphological traits.
• This is a common cause of spurious associations

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• How can we allocate individuals to
  sub-populations?
• First, we need to know in advance how many
  sub-populations there are.
• If unknown, this can be estimated
• The allocation process is repeated for different
  possible numbers and the best fitting selected.

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• The computer program STRUCTURE
• Uses computationally intensive methods to
  partition individuals into populations.
• Many individuals or lines will not belong
  uniquely to one, but will be the descendents of
  crosses between two or more ancestral
  populations.
• STRUCTURE also estimates the proportion of
  ancestry attributable to each population.

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The effect of kinship
y Xß Qv Zu e
Xß includes all fixed effects population means,
environments, and marker allele effects
Q is a subpopulation incidence matrix v are
estimates of subpopulation mean effects
There is a degree of relatedness not captured by
population structure u is the polygenic effect
gnerated by othre loci unlinked to the one being
tested