Genetic MappingbPb-63180.0BCD14341.1

DsT-66 1_04107.91_101111.1bPb-960812.22_122614.4[105102] [222208]17.8

MWG837B22.2

[223986]26.6

GBM100729.9

[105118] bPb-216633.2

bPb-481342.31_0760 [104834]46.8[221425]47.9bPb-5672 bPb-1231 bPb-1535 1_023851.3bPb-0482 [222328] bPb-2175 bPb-035752.32_0810 2_0427 2_0698 [223055]2_0912 bPb-9360 1_0438 1_13362_1312

57.9

1_1217 1_135961.2bPb-1193 BG36994062.32_1333 1_144465.6bPb-172367.81_104968.92_113170.02_0642 bPb-818372.2bPb-3389 1_000276.72_0696 1_046378.92_117680.01_0890 1_027983.2

1_046690.0

1_0535101.12_0769 JS10C 1_1439102.2

2_0754106.6

bPb-9180 1_0111 2_0613 1_1173112.3

[223108] KFP170119.2[221039]120.3

bPb-2063 bPb-5198124.7

1_1409128.0[221902]130.2

1_1457136.9MWG2028141.4ABC261142.5bPb-6065143.61_0903145.82_0383147.9WMC1E8151.21_1509153.42_0594154.5scssr04163 bPb-1487 bPb-5550156.7

1H

[223556]0.0[222367] bPb-0485 bPb-0611 bPb-5191bPb-0516 1_09701.1

2_14663.31_07184.4bPb-0471 [223937] bPb-02056.6[223539] bPb-7024 bPb-55198.81_105912.1[221686] bPb-0715 bPb-5444 bPb-9220bPb-429515.4

bPb-8374 [104949] 2_1423 bPb-4715bPb-649417.6

bPb-829219.8

bPb-4875 bPb-426146.5bPb-2501 1_0891 scssr07759 1_030749.81_084753.01_0919 Pox 2_0326 bPb-07221_083755.2

1_008456.31_048658.5bPb-5057 1_150562.91_0156 2_0688 bPb-022065.1scssr03381 [221628] 2_092966.21_152268.4bPb-6881 1_0927 2_0748 bPb-643870.6Hot1 2_064371.72_0500 1_0947 1_1288 2_14342_1286 1_1211 scssr02236 1_00991_0948 2_0378 2_0878 1_0154

72.8

1_138473.81_064077.12_0442 1_1430 2_147678.2bPb-7256 GBM1023 bPb-088580.4[222771] bPb-544082.6bPb-8100 bPb-724385.92_052887.0[222968]93.81_085997.11_110099.3vrs1100.31_0969104.8Bmag0125105.9

MWG503113.71_1285 bPb-4835 bPb-3563114.8KFP203115.91_0398119.21_0900120.3

1_1323 bPb-3653124.8

bPb-6822128.1

2_0064 1_0990 2_0955 bPb-38701_0128135.0

1_0429 1_0707136.1

1_0780142.8

bPb-7992 1_1365 2_1315147.32_1459 1_1486 [222960]149.5bPb-5412151.6[222464]152.7bPb-3858 1_0383156.11_1227158.3bPb-1505159.4

[223553]171.8bPb-8530 bPb-1566 GBM1019 bPb-5460[221407] bPb-4092172.9

2_0943174.0MWG720177.3bPb-1181 bPb-4601 bPb-4232180.6bPb-1085 bPb-6296 bPb-8698 [223337]185.0

2_1496188.3MWG949A190.5

2H

2_08580.0

2_0797 [223116] bPb-25533.31_14345.5

2_02528.8

1_1005 bPb-994513.22_097614.3[223396] [223877]16.52_1410 2_017219.82_0742 [221552]20.9bPb-3865 bPb-322923.1

2_055228.61_069129.72_1402 [221274] 2_096831.9[105024] bPb-996133.02_1268 bPb-303035.2bPb-5892 1_0968 bPb-7938 1_0081[220886] BCD706 [222320]38.5

1_1117 2_150648.71_1069 2_026455.5[224015] [223843]57.7alm58.82_086659.81_1283 2_0408 2_1062 Bmac02092_0439 2_1472 2_0591 1_14822_1435

63.1

2_044464.2bPb-649165.3ABC325 1_0653 1_085066.4DsT-6769.7bPb-475770.81_1342 2_1502 bPb-380571.92_130575.21_1314 bPb-007976.31_045278.52_052179.62_1194 bPb-7872 scssr25691 1_145482.91_1524 ABG37785.12_006391.8Bmag022592.9

1_0747104.5

2_0130115.1[221404]116.12_1381117.2

2_1493124.02_0009126.21_1392 2_1081127.3

1_0680136.2bPb-3630137.31_1330141.8bPb-1579142.9[223788] 2_1405145.1bPb-7785146.2

1_1338150.7

1_0505 2_0343 2_0369156.22_0612157.3

bPb-8894 1_1328 2_0085168.7

MWG883173.1

bPb-2737 2_1386178.7bPb-2420 bPb-4748 1_1297180.9bPb-0789183.1bPb-7413184.22_0421187.6HVM62 bPb-0302188.7bPb-0200190.92_1237194.22_0605196.4bPb-4387198.6bPb-1411 1_0893199.7bPb-0164203.02_0176204.0bPb-3295 bPb-8962 [221662] bPb-77241_0215 [223314]208.4

3H

2_11170.0bPb-7534 bPb-69381.1

2_02749.0

[222436]23.91_0223 [104902]26.11_022127.21_1175 1_0562 2_0422 2_138531.52_077732.6scsnp0164833.2CDO12233.72_138938.11_034740.32_0011 bPb-6611 bPb-640441.4scssr2056943.6CDO795 1_079346.92_093949.12_0269 1_0667 scind04312a 1_04321_0607 1_0411 2_1303 2_05252_0853 1_1042 bPb-9504 2_10292_0426

52.4

1_0262 1_0527 1_0637 [105086]1_0881 scind01728 1_110854.6

2_0361 1_008659.12_1296 2_1273 1_1427 1_120761.3bPb-7987 bPb-429062.41_0052 2_0062 1_0639 2_072363.5[221608] bPb-421470.21_151371.3bPb-009872.31_0309 1_131975.72_133279.0scssr1407981.2bPb-7719 1_152682.31_1213 1_067083.4bPb-1999 2_0765 GBM105984.51_116892.5Ebmac070195.8MWG652B 1_066696.92_045499.1bPb-1166 bPb-9859102.41_1194104.6bPb-2677109.12_0701 bPb-1040110.21_1066111.3Hsh112.32_0224113.42_0760114.52_0272 1_0610115.6KFP241.1116.7

ABG601 bPb-5265126.1

4H

bPb-01700.02_05532.2

2_122111.6

MWG61821.9

ABC48326.32_136528.5

bPb-3830 2_1065 bPb-8072 bPb-740735.42_076137.6bPb-516639.8bPb-053640.8

2_084548.7ABG39549.8bPb-4273 bPb-227350.81_0481 1_0177 2_0101 2_10401_0240 2_0697 bPb-0949 2_10112_0179 2_1308 bPb-5584 1_1399bPb-1046 1_1462 bPb-8675 2_0481

58.8

bPb-5727 bPb-788159.92_005963.32_153665.51_1363 1_1512 2_0981 1_08991_115166.5

NRG045A 1_108968.7bPb-626069.82_1036 bPb-898770.91_1438 [223146] [222177]74.21_054881.11_095383.3bPb-2147 2_0818 [221220]86.6

ABC302 1_012792.21_0633 1_0140 2_024695.52_073696.6

1_1135103.2

1_0674107.7

1_0930112.11_1134 2_0449 1_0771114.3bPb-2869 bPb-5532115.4

1_0024126.71_0834 HvCBF9127.81_0871130.01_0477132.21_1341133.2

1_1245 [222196]141.4

bPb-0710 2_1422151.52_0045152.61_1456153.71_0228154.7

bPb-4084 2_0551 [221423]168.8

bPb-6578175.71_0004177.91_0104 2_0676179.02_0388 1_0080180.1[223182]182.32_0104183.4

1_0582 1_0741 1_0536 ABG496193.6

1_0336 1_1464 1_0273196.8

[222383]209.0E10757A212.32_0826213.4bPb-0618 ABG391216.72_0546217.8bPb-6179220.0[104899]221.1[223339] bPb-4621 [222776]223.31_0254 ABC622224.3bPb-9132 2_0189226.52_1393232.1bPb-8754233.2[222075]236.51_1413 1_0732238.7[221531]239.82_0402 bPb-7360 bPb-9244 2_1356240.9[221535]242.0

5H

2_0232 bPb-37800.0Bmac0316 2_08812.22_08823.3bPb-6511 2_0294 2_1204 [221458]5.5bPb-71936.5

bPb-5498 [222053] bPb-631120.0

[224154]25.7

[223325] 1_0023 2_124631.3

bPb-525234.6[222286]38.0[223808]40.2JS10A 2_074541.3

GBM102148.2[221169] bPb-6002 bPb-059749.3

1_1455 1_006158.2[223273]59.3bPb-537960.41_0817 1_0199 bPb-6142 1_08111_053961.5

bPb-2592 bPb-5270 2_067562.61_0497 2_1473 2_0656 bPb-91141_0962 2_1158 2_101467.0

1_1487 1_1140 [223845] [221391]scssr02093 1_1312 [223262] [224033][223207] 1_0848 Bmag0009 [224253]2_0142 1_1442

68.0

[222527] [221245] 2_0202 2_1114[221874] 1_0513 1_027869.1

1_0803 bPb-551775.91_0964 2_0266 bPb-323078.1bPb-306878.5[224127] bPb-125679.22_0148 2_090483.7ABG388 2_071487.02_0892 1_059692.62_0784 scsnp2122693.7MWG82097.01_1246103.82_1404104.91_1147107.12_1025113.72_0972 1_0595119.31_0139120.42_0379122.6bPb-6477123.7GBM1022129.2bPb-3470130.3

[221063] bPb-5587138.3DsT-32B140.5

2_1455 2_1467 1_0645150.8DsT-28151.9bPb-5515153.0bPb-6677 bPb-2940155.21_1488 DsT-74156.3bPb-9890 [223186]159.5bPb-7146 bPb-4626 bPb-1621 1_0390160.6

6H

1_00360.01_0894 2_02012.2bPb-8272 bPb-8084 bPb-7559 bPb-73493.3[221346] bPb-44456.51_10358.7[223056] [221786]9.8bPb-920210.92_075513.1bPb-6453 bPb-372717.5

bPb-426621.9

MWG089 CDO47529.71_045130.8[221832] 2_0192 bPb-9601 bPb-5852bPb-253331.9

2_129238.8

1_036844.42_149147.62_132648.7

2_011355.41_040361.0[220928] [221740]62.11_065764.2bPb-4219 bPb-795267.61_102869.8bPb-805173.11_1257 1_1103 [221655] 1_12021_104574.2

1_0983 [222546]75.31_008379.72_0879 1_0115 bPb-5126 1_0581bPb-7915 bPb-2188 bPb-1770 1_06982_0200 2_0828 bPb-5599 1_00732_1335 bPb-8956 bPb-6975

80.8

1_0442 scsnp00703 1_1091 2_133089.72_0083 MWG203190.7[221574]91.8bPb-843994.01_1437 2_153095.1

bPb-6386 bPb-9912105.9

2_1201109.2

2_0808113.6bPb-1079 2_0103114.72_1464118.02_0824120.21_0362 DsT-30121.3

bPb-9908128.0[105081]129.11_1184132.5bPb-8498133.52_0217134.6

2_0354139.1

1_1279146.0[221079]147.1

bPb-7739157.41_0973 bPb-0917 bPb-4394 bPb-5923160.72_0753 bPb-3980 [220949]164.0[222528] 2_0452 bPb-8833 2_0414165.12_0640166.2[223928] bPb-9948 bPb-5898168.41_1275169.5GBM1065171.7

bPb-0328 KFP255195.6ThA1197.8

7H

Oregon Wolfe Barley Map (Szucs et al., 2009. The Plant Genome 2, 134-140)

Genetic Maps

• A genetic map or linkage map is a representation (table or figure) of the position of genes (or markers) within a linkage group.

• The map positions are inferred from recombination frequencies between genes (or markers).

Genetic Maps

• Crossovers tend to be randomly but not uniformly distributed along a chromosome. Crossovers are suppressed in some chromosomal regions.

- map distance ≠ physical distance

• Recombination frequency increases monotonically with a maximum of 50%.

- genetic mapping based on recombination frequencies should indicate the correct order of genes or markers on the chromosome

Uses of Genetic Maps

• Genomic architecture• Gene localization• Genetic dissection of complex traits

– Marker assisted selection• Starting point for map-based cloning• Starting point for genome sequencing

Mendelian Inheritance and Crossing OverAfter

DNA replicationPairing and

crossing over Anaphase IPre-meiotic

Heterozygous parent

21 43

A

B

A

B

a

b

a

b

21 43

A

B

A

B

a

b

a

b

1 2

A

B

a

b

21 43

A

b

A

B

a

b

a

B

2

1

4

3

A b

A B

a b

a B

Anaphase II4

a b

1A B

3a B

2A b

GametesNR

NR

R

R

4a b

1A B

3a B

2A b

Gametes

Non Recombinant n1

Non Recombinant n2

Recombinant n3

Recombinant n4

Total N

Recombination frequency

N

n4n3r

Parent

21 43

A

B

A

B

a

b

a

b

Linkage and recombination

• Two genes are said to be linked when they are located on the same chromosome.

• Linked genes tend to be passed together from parent to offspring.

• As a result of recombination during meiosis the alleles of a linked pair of genes may become ‘separated’, and non-parental combinations of alleles may be transmitted to the gametes (and to the offspring).

• The probability of a recombination event (crossing over) during meiosis depends on the distance between two gene loci. Therefore, the observed recombination frequency between loci is a measure for their ‘chromosomal distance’, or genetic map distance.

• The map distance between two loci of the same chromosome may be so large that these loci behave as if they were unlinked: they segregate independently, as if they were on different chromosomes.

• The unit of genetic map distance is the centimorgan. One centimorgan (cM) corresponds to 1% recombination frequency.

Linkage and recombination

Detection of Linkage

• The most direct way to detect linkage would be to observe the genotypes, and their frequencies, of gametes produced by a parent that is heterozygous at two linked loci.

• This is not possible in most plant species (an exception are doubled haploids (DH).)

• Therefore, we need to apply indirect ways of observation, which means not observing individual gametes but the result of fused gametes, i.e. the diploid offspring of a diheterozygous parent, or two diheterozygous parents. In practice, linkage of gene loci is inferred from the observation that among the offspring traits are associated (‘go together’) rather than segregating independently.

Detection of Linkage

• The most classical and easiest way to indirectly observe gamete genotypes and their frequencies is the testcross or backcross. (there is a one-to-one relation between genotype of gametes produced by the double heterozygous parent and the phenotype of the offspring).

X

Parent 1 AB/AB Parent 2 ab/ab

F1 AB/ab

X

Parent 2 ab/ab

A

BB

A a

bb

a

a

bB

A a

bb

a

a

bB

A a

bb

aa

bb

A a

bB

aTest Cross Offspring

NR: AB/ab NR: ab/abR: Ab/ab R: aB/ab

(tester)

coupling linkage phase

Locus A: Seed Color (A>a)

Allele A: GreenAllele a: Yellow

Locus B: Seed Shape (B>b)

Allele B: SphericAllele b: Dented

BACKCROSS (test cross)

a

bB

A a

bb

aa

bb

A a

bB

aTest Cross Offspring

NR: AB/ab NR: ab/abR: Ab/ab R: aB/ab

expected frequency

f112--- 1 r– =

f212---r=

f312---r=

f412--- 1 r– =

r = 0 r = 0.5

0.5 0.25

0.0 0.25

0.0 0.25

0.5 0.25

Non Recombinant

Recombinant

AB/ab

Ab/ab

aB/ab

ab/ab Non Recombinant

Recombinant

Estimation of recombination frequency

• In the testcross the frequencies of recombinant and non-recombinant gametes can be obtained by simply counting the two classes of phenotypes.

• In many other cases, there is no such a one-to-one relation between phenotype of offspring and the gamete genotype that gave rise to this phenotype.

• There is a universally applicable method to obtain an estimate of recombination frequency from observed phenotype frequencies among the offspring. This method is known as the maximum likelihood method.

• Let a sample of N gametes contain k recombinant and N-k non-recombinant gametes.

• For any value of r this sample composition has a probability or likelihood, the binomial probability.

Estimation of recombination frequency

kNk rrk

NrL

)1()(

For any value of r (0 ≤ r ≤ 1) this probability can be calculated. There is one,unique, value of r for which L is largest. This value of r maximizes thelikelihood of the sample composition (hence ‘maximum likelihoodestimation’, ML). This value of r can be obtained by taking the derivative of Lwith respect to r and equating this to zero:

0r

L

0)(Ln

r

L

Easier to take the derivative of Ln(L)

Since ln(L) is monotonic, the value of r that maximizes ln(L) also maximizes L.

01

)(Ln

r

kN

r

k

r

L

Application of the above yields

Solving for r yields

r

kN

r

k

1

orN

kr

Linkage PhaseCoupling - cis

Repulsion - trans

A B

BA

a b

ba

A B

ba

Parent 1 (AB/AB) Parent 2 (ab/ab) F1 (AB/ab)

A b

bA

a B

Ba

A b

Ba

Parent 1 (Ab/Ab) Parent 2 (aB/aB) F1 (Ab/aB)

X

X

X

Parent 1 Ab/Ab Parent 2 aB/aB

F1 Ab/aB

X

Parent 2 aB/aB

A

bb

A a

BB

a

a

Bb

A a

BB

a

a

Bb

A a

BB

aa

BB

A a

Bb

aBackCross Offspring

NR: Ab/aB NR: aB/aBR: AB/aB R: ab/aB

Repulsion linkage phase

Locus A: Seed Color (A>a)

Allele A: GreenAllele a: Yellow

Locus B: Seed Shape (B>b)

Allele B: SphericAllele b: Dented

BACKCROSS

expected frequency

f112--- 1 r– =

f212---r=

f312---r=

f412--- 1 r– =

r = 0 r = 0.5

0.5 0.25

0.0 0.25

0.0 0.25

0.5 0.25

Non Recombinant

Recombinant

Ab/aB

AB/aB

ab/aB

aB/aB Non Recombinant

Recombinant

a

Bb

A a

BB

aa

BB

A a

Bb

aBackCross Offspring

NR: Ab/aB NR: aB/aBR: AB/aB R: ab/aB