1. INTRODUCTION TO ASSOCIATION MAPPING

2. 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?

3. 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

4. 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_ A B
_1_1061_
0.8
_3_0703_
1.5
_1_1505_
_1_0498_
_2_1005_
3.8
_1_1054_
_2_0674_ 6
_1_0297_
8.8
_1_0638_
10.7
_1_1302_
11.4
_1_0422_
_2_0929_
15.3
_3_1474_
15.4
_1_1522_
17.3
_2_1388_
_3_0259_
18.1
_1_0325_
_2_0602_
20.8
_1_0733_
23.9
_2_0729
_1_1272_
_2_0891_
26.1
_2_0748_
26.6
_3_0251_
27.4
_1_0997_
35.5
_1_1133_
41.8
_2_0500_
42.5
_3_0634_
43.3 10
Desease severity 5

5. Definition of Linkage Disequilibrium is very simple:
is the ‘non-random association of alleles at different loci’ A B b a
Locus 1
Locus 2 A B a b
Locus 1
Locus 2
Equilibrium
Disequilibrium

6. Random mating population with loci segregating independently
Disequilibrium
Equilibrium
Locus 1
Locus 2
Locus 3
Locus 4
Locus 5
Locus 1
Locus 2
Locus 3
Locus 4
Locus 5
Non random mating population LD due to selection, mutation, drift/sampling, population structure
Random mating population with loci segregating independently

7. 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 < 0
for D > 0

8. Haplotype frequencies: PAB= 9/30 PaB= 6/30 PAb= 1/30 Pab= 14/30
Line 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Locus 1 a A
Locus 2 b B
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

9. Spring barley – Two rows – Chromosome 5H
Distance (bp)

11. 1.5 kb (diverse inbred lines) >100 kb (Elite lines Barley
Extension of LD
Humans
80kb (Europeans)
5kb (Nigerians)
Outcrossing
Cattle
> 10 cM
Arabidopsis
250 kb
Selfing
Maize
1 kb (Diverse maize)
1.5 kb (diverse inbred lines)
>100 kb (Elite lines
Barley
Up to 100kb
Flint-Garcia et al., Annu. Rev. Plant Biol :357–74

12. Factors that increase LD: Factors that decrease 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

13. Allele b appears on gamete carrying A A and b will appear together
Mutation:
provides the original material for producing polymorphism that will be in LD A B a
Locus 1
Locus 2 A b
Allele b appears on gamete carrying A
A and b will appear together A B a

14. 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

15. Drift / Sampling Selection
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

16. LOD
LOD

17. LOD
LOD

19. 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

20. r2 r2 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

21. 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

22. 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_ A B
_1_1061_
0.8
_3_0703_
1.5
_1_1505_
_1_0498_
_2_1005_
3.8
_1_1054_
_2_0674_ 6
_1_0297_
8.8
_1_0638_
10.7
_1_1302_
11.4
_1_0422_
_2_0929_
15.3
_3_1474_
15.4
_1_1522_
17.3
_2_1388_
_3_0259_
18.1
_1_0325_
_2_0602_
20.8
_1_0733_
23.9
_2_0729
_1_1272_
_2_0891_
26.1
_2_0748_
26.6 10
Desease severity 5

23. 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_ A B
_1_1061_
0.8
_3_0703_
1.5
_1_1505_
_1_0498_
_2_1005_
3.8
_1_1054_
_2_0674_ 6
_1_0297_
8.8
_1_0638_
10.7
_1_1302_
11.4
_1_0422_
_2_0929_
15.3
_3_1474_
15.4
_1_1522_
17.3
_2_1388_
_3_0259_
18.1
_1_0325_
_2_0602_
20.8
_1_0733_
23.9
_2_0729
_1_1272_
_2_0891_
26.1
_2_0748_
26.6 10
Desease severity 5

24. Quality of the data: Minor allele frequency
Line
Locus 1
Locus 2
Line
Phenotype: heading date b B 21 20 19 18 17 26 25 24 23 22 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 63 58
154 64 57
153 60
149
151
152 59
150 62
Locus 1
Locus 2
Locus 1:
Average allele b: 78.8
Average allele B: 152
Locus 2:
Average allele b: 87.7
Average allele B: 89.3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 a A b B
Two loci can be completely unlinked and still show high LD

25. Quality of the data: Missing data
Line
Phenotype: heading date 21 20 19 18 17 26 25 24 23 22 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 63 58
154 64 57
153 60
149
151
152 59
150 62
Locus 1 B b
Locus 2
Locus 1:
Average allele b: 76.2
Average allele B: 102.8
Locus 2:
Average allele b: 87.7
Average allele B: 89.3 b - b b B b B b b B - b b - b B b b - b - b b b b b

26. 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

27. h2=Vgenotipic/Vphenotypic
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
h2=Vgenotipic/Vphenotypic

28. The problem of epistatic traits
Line
VRN1
VRN2
Phenotype: heading date 1 a c 62
VRN1 and VRN2 located in different chromosomes 2 A c
152 3 a c 59 4 a c 58 5 A D 60 6 a c 60
No association between individuals genes (VRN1 or VRN2) and heading date 7 a D 57 8 a c 64 9 A c
151 10 a D 59 11 a D 58 12 a c
152
However, late heading date only when haplotype Ac is present 13 a c 60 14 A c
151 15 a c 58 16 A c
149 17 A D 64 18 a c 58 19 A c
154 20 a c 58 21 a D 63 22 a c 60 23 A c
153 24 a c 58 25 a c 57 26 a c 64

29. 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

30. 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 Am. J.Hum. Genet. 43:520–26

31. 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

32. 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.

33. 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.

35. 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