Aladdin Hamwieh

Mapping and Applications of Linkage Disequilibrium and Association

Mapping in Crop Plants

independent assortment and punnett square

A dihybrid cross produces F2 progeny in the ratio 9:3:3:1.

Crossover

Independent assortment produces a recombinant frequency of 50 percent.

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

Deviations from independent assortment

In the early 1900s, William Bateson and R. C. Punnettwere 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.

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

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

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

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

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.

• 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.)

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.

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

Fig. 5.15

Mapping the12 chromosomes

of tomatoes.

Morphological Markers

1. Small Number2. Limited genomic coverage3. Could be influence by environment4. Most of them exhibit dominance nature

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”

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)

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 generationsof selfing.

AI-RILs, advanced intercross–recombinant inbred linesHIF, heterogeneous inbred familyMAGIC lines, multiparent advanced generation intercross linesNIL, near-isogenic lineRILs, recombinant inbred lines

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

Hamwieh et al. 2005

Introducti on

Molecular markers:•RFLP•AFLP•RAPD•SSR•SNP•STS•ISSR

Genetic map of lentil

RAPDAFLPSSR

How to genotype?

a bb b a a b b b a a a a b b b a b b H

P1 P2

Plant 85

Plant 86

Marker 1

Marker 2

How to genotype?

Qualitati ve traits:

Co-dominant MarkerP1 P2

1 2 3 4 5 6 7 8 9 10 11 12 13 14

DOMINANT MARKERP1 P2

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Chi-Square

• Obs.A=45 Exp.A=50• Obs.B=55 Exp.B=50

Exp

ExpObsx

22 )(

150

)5550(

50

)4550( 222

x

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

Recombinant Fraction

P1 P2 1 2 3 4 5 6 7 8 9 10 11 12 13 14

M1

M2

CM3.1410014

2

LOD Score

)5.0(

)5.0(log_ 10

L

LScoreLOD

n

nmm

L

LratioLikelihood

5.0

)1(

)5.0(

)5.0(_

Zmax

• N=35• M=7

0 0.1 0.2 0.3 0.4 0.5

-1

0

1

2

3(0.20,2.9

2978)

Recombinant fraction

LOD

Sco

re

n

nmm

Z5.0

)1(logmax 10

5.00max

M:RecombinantN: Total NumberM-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

θ 0.05 0.1 0.15 0.2 0.25 0.3 04

Σ(Z) 28.2 31.2 30.4 27.8 24.0 19.4 9.0

Zmax = maximum likelihood score (MLS)

Mapping Function

• Haldane

• Kosambi

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

50

100

150

200

qHaldaneKosambi

Recombinant fraction

Centi

mor

gan

)21(5.0 LnM

21

2125.0 LnM

Softwares

Program System Lic. Interface Pop. Types Ref.

CARTHAGENE Win, UNIX FreeGraphical,

Command line

F2, backcross, RIL, outcross

de Givry et al. 2005

CRIMAP Win, UNIX Free Command line pedigreeGreen et al

1990

JOINMAP Win Com. GraphicalF2, backcross ,

RIL, DH, outcrossStam 1993

LINKMFEX Win Free Graphical outcrossDanzann and Gharbi 2001

MAPMAKERWin,UNIX,

MACFree Command line

F2, backcross, RIL, DH

Landr et al. 1987

MAPMANAGER Win, MAC Free GraphicalF2, backcross,

RILManly and Olson 1999

QTL mapping

• genotype and phenotype individuals• look for statistical correlation between

genotype and phenotype

Quanti tati ve traits:

Quantitative trait loci (QTL) analysis:Correlate segregation of thequantitative trait with that ofqualitative trait, i.e., markers

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 1

6 _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

Ref. Software

Lander et al. 1987 MapMaker/QTL

Basten et al. 1999 QTL Cartographer

Broman et al. 2003 R/qtl

Mester et al. 2004 MultiQTL

van Ooijen and Maliepaard 1996 MapQTLSeaton et al. 2002 QTL Express

Utz and Melchinger 1996 PLABQTL

Meer et al. 2004 MapManager/QTX

Wang et al. 2003 WebQTL

Yang et al. 2005 QTLNetwork

QTL Detection Softwares

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)

Association mapping

Comparison of Different Plant Breeding Materials for Association Mapping

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

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.

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

Allele and Genotype Frequencies in H-W equilibrium

p2 (AA)2pq (Aa)q2 (aa)

Hardy-Weinberg Equilibrium

Hardy–Weinberg equilibriumFemalesA (p) a (q)

MalesA (p) AA (p2) Aa (pq)a (q) Aa (pq) aa (q2)

(p2) + (2pq) + (q2) = 1

P= AA + ½ Aaq= aa + ½ Aa

where p is the frequency of the A allele, q is the frequency of the a allele, and p + q= 1.

Basic Descriptors ofLinkage Disequilibrium

• LD is measuring non random association between alleles

m2m3

m4m5

m6m7

m8m9m1

Hardy–Weinberg equilibrium p + q = 1p2 + 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.

Hardy–Weinberg equilibriump + q = 1p2 + 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.

𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑒𝑜𝑓 𝑖𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙=𝐼𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙

𝑇𝑜𝑡𝑎𝑙 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛160

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 genotypep2 X total population = 0.36 X 1000 = 360 Black fruits, BB genotype2pq X total population = 0.48 X 1000 = 480 Black fruits, Bb genotype

Mar

ker B

A

A

marker B

Linkage equilibrium : random associationLinkage disequilibrium : there is a correlation between loci

Introduction to Linkage Disequilibrium

B b Total

A PAB PaB PA

a PaB Pab Pa

Total PB Pb 1.0

A BA ba Ba 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

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

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

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

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

Haplotype Observed FrequencyA1B1 0.6

A1B2 0.1

A2B1 0.2

A2B2 0.1

ExampleSNP locus A: A1 = T, A2 = CSNP 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 = 0.14p2q1 = 0.24

D’ = 0.04/0.14 = 0.286r2= (0.04)^2/(0.7*0.3*0.8*0.2)

r2= 0.048

Examples

Dis

ease

Linkage Disequilibrium

Likelihood ratio test for HWE

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

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

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

0 20 40 60 80 100 120 140 160 1800

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Distance

LD(R

2)Short LD extend

Long LD extend

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)

Advantages of combining association andtraditional linkage mapping methods.

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

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

Thank you