Mapping and Applications of Linkage Disequilibrium and Association Mapping in Crop Plants. © FAO: http://www.fao.org

1. Aladdin Hamwieh
Mapping and Applications of Linkage
Disequilibrium and Association
Mapping in Crop Plants

2. independent assortment
and punnett square
A dihybrid cross produces
F2 progeny in the ratio 9:3:3:1.

3. Crossover
Independent assortment
produces a recombinant
frequency of 50 percent.

4. Linkage
• Loci that are close enough together on the
same chromosome to deviate from
independent assortment are said to display
genetic linkage
BUT
• The linked loci that are far from each others
are in danger of
CROSSINGOVER

5. Deviations from independent
assortment
In the early 1900s, William Bateson and R. C. Punnett
were studying inheritance of two genes in the sweet
pea.
In a standard self of a dihybrid F1, the F2 did not show
the 9:3:3:1 ratio predicted by the principle of
independent assortment.
In fact Bateson and Punnett noted that certain
combinations of alleles showed up more often than
expected, almost as though they were physically
attached in some way. They had no explanation for this
discovery.

6. Thomas Hunt Morgan found a similar deviation
from Mendel’s second law while studying two
autosomal genes in Drosophila. Morgan
proposed a hypothesis to explain the
phenomenon of apparent allele association.
One of the genes affected eye color (pr, purple, and pr, red), and
the other wing length (vg, vestigial, and vg, normal). The wild-
type alleles of both genes are dominant.
DEVIATIONS FROM INDEPENDENT ASSORTMENT

7. When two genes are close together on the same chromosome pair (i.e.,
linked), they do not assort independently.

9. • Chiasmata (the visible
manifestations of
crossing-over): a cross-
shaped structure
forming the points of
contact between non-
sister chromatides of
homologous
chromosomes.

11. Frequencies of recombinants arising from
crossing-over. The frequencies of such
recombinants are less than 50 percent.

12. Linkage maps (distance between the genes.)
• Recombinant frequencies are significantly lower
than 50 percent and the recombinant frequency
was 12.97 percent.
(146+157) * 100 / 2335 = 12.97
• Morgan studied
– linked genes,
– proportion of recombinant progeny
– varied considerably,
• Morgan concluded actual distances separating
genes on the chromosomes.
• Alfred Sturtevant suggested that we can use this
percentage of recombinants as a quantitative
index of the linear distance between two genes
on a genetic map, or linkage map.

13. • Sturtevant postulated the greater the distance
between the linked genes, the greater the chance
of crossovers in the region between the genes.
• Sturtevant defined one genetic map unit (m.u.)
as that distance between genes for which one
product of meiosis in 100 is recombinant. Put
another way, a recombinant frequency (RF) of
0.01 (1 percent) is defined as 1 m.u. A map unit is
sometimes referred to as a centimorgan (cM) in
honor of Thomas Hunt Morgan.
LINKAGE MAPS (DISTANCE BETWEEN THE GENES.)

15. A chromosome region containing three linked genes. Calculation of AB and
AC distances leaves us with the two possibilities shown for the BC distance.
Recombination between linked genes can be used to map their distance
apart on the chromosome. The unit of mapping (1 m.u.) is defined as a
recombinant frequency of 1 percent.

16. example
For the v and ct loci 89+94+3+5 =191
For the ct and cv, loci 45+40+3+5 = 93
For the v and cv, loci 45+40+89+94 = 268

18. Fig. 5.15

19. Mapping the
12
chromosomes
of tomatoes.

20. Morphological Markers
1. Small Number
2. Limited genomic coverage
3. Could be influence by environment
4. Most of them exhibit dominance nature

21. Linkage Mapping
• Genes are points on the genome and there are a
flanking regions around them link to these genes.
• The central idea of the linkage mapping is to put a
lot of points on the genome in order to get points
that linked to another interesting points (genes).
• These points that we add are called as:
“MARKERS”

22. Molecular Markers
• Dominant or Co-dominant nature in different types:
1. Protein-based
– Isozyme
– Allozyme
2. Hybridization-based
– RFLP
– DArT
3. PCR-based
– RAPD, AP-PCR
– AFLP
– STS (SSR, ISSR, SCAR, CAPS)
– RGA
4. Single Nucleotide Polymorphism (SNP)

23. Linkage mapping
populations
The mapping resolution and the genetic
diversity in the linkage mapping
populations will depend on the number
of founders, generations of inter-mating
and generations
of selfing.
AI-RILs, advanced intercross–
recombinant inbred lines
HIF, heterogeneous inbred family
MAGIC lines, multiparent
advanced generation intercross
lines
NIL, near-isogenic line
RILs, recombinant inbred lines
(Bergelson and Roux, 2010) Nature Review, Genetics (December), Vol 11: 867-879

24. Hamwieh et al. 2005
Molecular markers:
•RFLP
•AFLP
•RAPD
•SSR
•SNP
•STS
•ISSR
Genetic map of lentil
RAPD
AFLP
SSR

25. a b
b b a a b b b a a a a b b b a b b H
P1
P2

26. Plant
85
Plant
86
Marker 1
Marker 2
How to genotype?

28. Co-dominant Marker
P1 P2
1 2 3 4 5 6 7 8 9 10 11 12 13 14
DOMINANT MARKER
P1 P2
1 2 3 4 5 6 7 8 9 10 11 12 13 14

29. Chi-Square
• Obs.A=45 Exp.A=50
• Obs.B=55 Exp.B=50



Exp
ExpObs
x
2
2 )(
1
50
)5550(
50
)4550( 22
2




x

30. Chi-Square Table
DF 0,995 0,9500 0,100 0,050 0,025 0,010 0,005
1 0,000 0,004 2,706 3,842 5,024 6,635 7,879
2 0,010 0,103 4,605 5,992 7,378 9,210 10,597
3 0,072 0,352 6,251 7,815 9,348 11,345 12,838
4 0,207 0,711 7,779 9,488 11,143 13,277 14,860
5 0,412 1,146 9,236 11,071 12,833 15,086 16,750
6 0,676 1,635 10,645 12,592 14,449 16,812 18,548
7 0,989 2,167 12,017 14,067 16,013 18,475 20,278
8 1,344 2,733 13,362 15,507 17,535 20,090 21,955
9 1,735 3,325 14,684 16,919 19,023 21,666 23,589
10 2,156 3,940 15,987 18,307 20,483 23,209 25,188
11 2,603 4,575 17,275 19,675 21,920 24,725 26,757
12 3,074 5,226 18,549 21,026 23,337 26,217 28,300
13 3,565 5,892 19,812 22,362 24,736 27,688 29,819
14 4,075 6,571 21,064 23,685 26,119 29,141 31,319
15 4,601 7,261 22,307 24,996 27,488 30,578 32,801
16 5,142 7,962 23,542 26,296 28,845 32,000 34,267
17 5,697 8,672 24,769 27,587 30,191 33,409 35,718
18 6,265 9,390 25,989 28,869 31,526 34,805 37,156
19 6,844 10,117 27,204 30,144 32,852 36,191 38,582
20 7,434 10,851 28,412 31,410 34,170 37,566 39,997

31. Recombinant Fraction
P1 P2
1 2 3 4 5 6 7 8 9 10 11 12 13 14
M1
M2
CM3.14100
14
2


32. LOD Score
)5.0(
)5.0(
log_ 10





L
L
ScoreLOD
n
nmm
L
L
ratioLikelihood
5.0
)1(
)5.0(
)5.0(
_










33. Zmax
• N=35
• M=7
(0.20,2.92978)
-1
0
1
2
3
0 0.1 0.2 0.3 0.4 0.5
LODScore
Recombinant fraction





 


 n
nmm
Z
5.0
)1(
logmax 10
5.00
max


M:Recombinant
N: Total Number
M-N: Non Recombinant
θ 0.001 0.01 0.05 0.1 0.2 0.3 0.4
Z -6.0 -3.0 -1.1 -0.4 0.1 0.2 0.1
Zmax = maximum likelihood score (MLS)

34. Mapping Function
• Haldane
• Kosambi
0
50
100
150
200
0 0.1 0.2 0.3 0.4 0.5
Centimorgan
Recombinant fraction

Haldane
Kosambi
)21(5.0  LnM











21
21
25.0 LnM

35. Softwares
ProgramSystemLic.InterfacePop. TypesRef.
CARTHAGENEWin, UNIXFree
Graphical,
Command line
F2, backcross,
RIL, outcross
de Givry et al.
2005
CRIMAPWin, UNIXFreeCommand linepedigree
Green et al
1990
JOINMAPWinCom.Graphical
F2, backcross,
RIL, DH, outcross
Stam 1993
LINKMFEXWinFreeGraphicaloutcross
Danzann and
Gharbi 2001
MAPMAKER
Win,UNIX,
MAC
FreeCommand line
F2, backcross,
RIL, DH
Landr et al.
1987
MAPMANAGERWin, MACFreeGraphical
F2, backcross,
RIL
Manly and
Olson 1999

36. QTL mapping
• genotype and phenotype individuals
• look for statistical correlation between
genotype and phenotype

37. Quantitative trait loci (QTL) analysis:
Correlate segregation of the
quantitative trait with that of
qualitative trait, i.e., markers

38. Marker Distance
Line1
Line2
Line3
Line4
Line5
Line6
Line7
Line8
Line9
Line10
Line11
Line12
Line13
Line14
Line15
Line16
_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
0
10
5Disease
severity

39. Ref.Software
Lander et al. 1987MapMaker/QTL
Basten et al. 1999QTL Cartographer
Broman et al. 2003R/qtl
Mester et al. 2004MultiQTL
van Ooijen and Maliepaard 1996MapQTL
Seaton et al. 2002QTL Express
Utz and Melchinger 1996PLABQTL
Meer et al. 2004MapManager/QTX
Wang et al. 2003WebQTL
Yang et al. 2005QTLNetwork
QTL Detection Softwares

40. Statistical Models
1. Interval Mapping (IM)
2. Composite Interval Mapping (CIM)
3. Multiple Interval Mapping (MIM)
4. Bayesian Interval Mapping (BIM)
5. single Marker Regression (MR)
6. Statistical Machine Learning (SML)

41. Association mapping
Comparison of Different Plant Breeding
Materials for Association Mapping

45. Hamwieh, A., Udupa, S., Sarker, A., Jung, C. and Baum, M. (2009). Development of new microsatellite markers and their application in the
analysis of genetic diversity in lentils. Breeding Science 59: 77-86.
Project 2: Genetic diversity in lentils

46. 300 accessions2915 accessions
Chickpea Reference Set (GCP)
Upadhyaya HD, Dwivedi SL, Baum M, Varshney RK, Udupa SM, Gowda CLL, Hoisington D and Singh S (2008) Genetic structure, diversity, and
allelic richness in composite collection and reference set in chickpea (Cicer arietinum L.). BMC Plant Biology 8: 106.

47. Allele frequency
–frequency (A) = p,
–frequency (B) = q,
then the next generation will have:
–frequency of the AA genotype = p2
–The frequency of the AB genotype = 2pq
–The frequency of the BB genotype = q2

48. Allele and Genotype Frequencies in H-
W equilibrium
p2 (AA)
2pq (Aa)
q2 (aa)

49. Hardy-Weinberg Equilibrium
Hardy–Weinberg equilibrium
Females
A (p) a (q)
Males
A (p) AA (p2) Aa (pq)
a (q) Aa (pq) aa (q2)
(p2) + (2pq) + (q2) = 1
P= AA + ½ Aa
q= aa + ½ Aa
where p is the frequency of the A allele, q is the frequency of the a allele, and p + q= 1.

50. Basic Descriptors of
Linkage Disequilibrium

51. • LD is measuring non
random association
between alleles
m2
m3
m4
m5
m6
m7
m8
m9m1

52. Hardy–Weinberg equilibrium
p + q = 1
p2 + 2pq + q2 = 1
Example
p: is the frequency of the dominant allele.
p: is the frequency of the recessive allele.
p2:is the frequency of individuals with the homozygous dominant genotype.
2pq: is the frequency of individuals with the heterozygous genotype.
q2 :is the frequency of individuals with the homozygous recessive genotype.

53. Hardy–Weinberg equilibrium
p + q = 1
p2 + 2pq + q2 = 1
The frequency of white fruits is 160, the homozygous recessive genotype, as they have
only one genotype, (bb). Black fruits can have either the genotype (Bb) or the genotype
(BB), and therefore, the frequency cannot be directly determined. Population size is 1000.
𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑒 𝑜𝑓 𝑖𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙 =
𝐼𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙
𝑇𝑜𝑡𝑎𝑙 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛
160
1000
= 0.16
bb = q2 = 0.16  q = 0.4  p = 1 – q  p = 1 – 0.4 = 0.6
 2pq = 2 X 0.6 X 0.4 = 0.48  p2 = 0.62 = 0.36
q2 X total population = 0.16 X 1000 = 160 White fruits, bb genotype
p2 X total population = 0.36 X 1000 = 360 Black fruits, BB genotype
2pq X total population = 0.48 X 1000 = 480 Black fruits, Bb genotype

54. MarkerB
A
A
marker B
Linkage equilibrium : random association
Linkage disequilibrium : there is a correlation between loci

55. Introduction to Linkage Disequilibrium
B b Total
A PAB PaB PA
a PaB Pab Pa
Total PB Pb 1.0
A B
A b
a B
a b
A, B: major alleles
a, b: minor alleles
PA: probability for A alleles at SNP1
Pa: probability for a alleles at SNP1
PB: probability for B alleles at SNP2
PB: probability for b alleles at SNP2
PAB: probability for AB haplotypes
Pab: probability for ab haplotypes
SNP1 SNP2

56. Linkage Equilibrium
• PAB = PAPB
• PAb = PAPb = PA(1-PB)
• PaB = PaPB = (1-PA) PB
• Pab = PaPb = (1-PA) (1-PB)
B b Total
A PAB PAb PA
a PaB Pab Pa
Total PB Pb 1.0
SNP1
SNP2

57. Linkage Disequilibrium
PAB ≠ PAPB
DAB=PAB-PAPB

A1 A2 Total
B1 p1q1+D p2q1-D q1
B2 p1q2-D p2q2+D q2
Total p1 p2

Allele frequencies

58. Linkage Disequilibrium
PAB ≠ PAPB DAB=PAB-PAPB
D’ = D/DmaxWhen D≥ 0 
Dmax is the smaller of p1q2 and p2q1
D’ = D/DminWhen D≤ 0 
Dmin is the larger of -p1q2 and -p2q1

59. Linkage Disequilibrium
Another LD measure is r2 and this is calculated as the following:
r2= D2/(p1p2q1q2)
0 ≤ r2 ≤ 1
r2 = 0: Loci in complete linkage equilibrium
r2 = 1: Loci are in complete linkage disequilibrium

60. Haplotype Observed Frequency
A1B1 0.6
A1B2 0.1
A2B1 0.2
A2B2 0.1
Example
SNP locus A: A1 = T, A2 = C
SNP locus B: B1 = A, B2 = G
Allele Symbol Allelic freq.
A1 p1 0.7
A2 p2 0.3
B1 q1 0.8
B2 q2 0.2
D=0.6-(0.7 * 0.8) D = 0.04 D>0 then we use Dmax
p1q2 = 0.14
p2q1 = 0.24
D’ = 0.04/0.14 = 0.286
r2= (0.04)^2/(0.7*0.3*0.8*0.2)
r2= 0.048

61. Examples

63. Disease
Linkage Disequilibrium

64. Likelihood ratio test for HWE

65. 65
An Example of LD Bins (1/3)
• SNP1 and SNP2 can not form an LD bin.
– e.g., A in SNP1 may imply either G or A in SNP2.
Individual SNP1 SNP2 SNP3 SNP4 SNP5 SNP6
1 A G A C G T
2 T G C C G C
3 A A A T A T
4 T G C T A C
5 T A C C G C
6 T G C T A C
7 A A A T A T
8 A A A T A T

66. 66
An Example of LD Bins (2/3)
• SNP1, SNP2, and SNP3 can form an LD bin.
– Any SNP in this bin is sufficient to predict the values of others.
Individual SNP1 SNP2 SNP3 SNP4 SNP5 SNP6
1 A G A C G T
2 T G C C G C
3 A A A T A T
4 T G C T A C
5 T A C C G C
6 T G C T A C
7 A A A T A T
8 A A A T A T

67. 67
An Example of LD Bins (3/3)
• There are three LD bins, and only three tag SNPs are required to
be genotyped (e.g., SNP1, SNP2, and SNP4).
Individual SNP1 SNP2 SNP3 SNP4 SNP5 SNP6
1 A G A C G T
2 T G C C G C
3 A A A T A T
4 T G C T A C
5 T A C C G C
6 T G C T A C
7 A A A T A T
8 A A A T A T

68. 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100 120 140 160 180
LD(R2)
Distance
Short LD extend

69. Long LD extend

73. Genome-Wide Association Studies (GWAS): Hunting for Genes in
the New Millennium
•GWAS scan the
genomes of thousands of
individuals who have a
particular phenotype for
DNA sequences that they
share, but are much
rarer in individual who
do not have the trait
•GWAS: to identify of
new regions containing
no a priori candidate
genes, and potentially
enhancing the
knowledge of complex
traits.
Accessions with disorder Accessions without disorder
The new way to track genes (Genome wide association)

74. Advantages of combining association and
traditional linkage mapping methods.
(Bergelson and Roux, 2010) Nature Review, Genetics(December), Vol 11: 867-879

75. (Bergelson and Roux, 2010) Nature Review, Genetics(December), Vol 11: 867-879

76. Thank you