Selective mapping and simulation study

high-density genome maps

Are used for:• Comparative mapping• Map-based cloning• Genome sequencing

But genotyping costs time and money

And density can surpass resolution because of cosegregation (i.e. bins)

X

bins and map resolution

random

X

selected

high-density mapping strategies

Selective mapping• Optimizes map resolution• Requires less genotyping

Bin mapping• Provides “honest” marker placement • Aids map integration

selective mapping

Genotype a base population

(many individuals, few markers)

Construct a precise framework map

Select a subsample with high resolution

Genotype subsequent markers on subsample

Vision et al. (2000) Genetics 155:407-420.

summarizing bin length distribution

Average (ABL)• Most breakpoints

Maximum (MBL)• Minimize areas of low resolution

Sum of Squares (SSBL)or Expected (EBL) = SSBL/G

discrete optimization strategies

Mathematical programming• Integer program for exact breakpoints

• Linear program• To derive lower bound

• Randomized rounding to obtain candidate samples

Semi-greedy algorithm• Avoids local optima

• Uses mixed objective function

comparing results

Performance Ratio (PR) = Lsample/Lpopulation

• Optimum is 1• Higher values are inferior

Also useful: Lsample/Lrandom

simulation 100 doubled haploids

1000 cM genome

per f

orm

ance

rat

i o (

MB

L)

simulation:cumulative bin length distribution

- whole pop.▼expected× maximum◊ averageΔ non-optimized

sample size=30

per f

orm

ance

rat

i o (

MB

L)

barley IGRI x Franka cross150 doubled haploids

1100 cM genome

data from http://wheat.pw.usda.gov/ggpages/maps.html

Simulation study

10

12

14

16

18

20

22

0 200 400 600 800 1000 1200

number of marker

numb

er o

f br

eakp

oint

cart2 t i mespedi gree

Number of breakpoint in different simulation

V2

3.983.90

3.823.74

3.663.58

3.493.41

3.333.25

3.173.09

3.012.93

2.852.77

2.692.61

2.532.44

2.362.28

2.202.12

2.041.96

1.881.80

1.721.64

1.561.47

1.391.31

1.231.15

1.07.99

.91.83

.75.67

.59.51

.42.34

.26.18

.10.02

HistogramFr

equency

800

600

400

200

0

Std. Dev = .49

Mean = .50

N = 10000.00

Additive effect: gamma(1,2)

V1

.99.97

.95.93

.91.89

.87.85

.83.81

.79.77

.75.73

.71.69

.67.65

.63.61

.59.57

.55.53

.51.49

.47.45

.43.41

.39.37

.35.33

.31.29

.27.25

.23.21

.19.17

.15.13

.11.09

.07.05

.03.01

HistogramFr

equency

140

120

100

80

60

40

20

0

Std. Dev = .29

Mean = .50

N = 10000.00

Epistasis effect: beta(1,1), only two level interaction

Total:

Sample:

Analysis:

Simulation procedure

500

100 50 100 10

LR IM LR IM LR IM LR IM

MapPop MapPop Random Random

Simulation:

Random:

1. 2QTL, h2:0.3,0.7,total size:500,marker:101;epi:0.5;

2. 10QTL, h2:0.3,0.7,total size:500, marker:101; epi:0.2;

3. Using QTL Cartographer to do 1,2.

Fixed QTL position:

1. 5QTL,h2:0.7,total size:500, marker:101; no epi

2. 5QTL ,h2:0.7, total size:1000, marker:101; no epi

3. 10 QTL h2:0.7, total size:500, marker:101; no epi

Set QTL far apart (100cM away form each other):

1. random 5 QTL position, h2:0.5,total size 500; marker:101;epi:0.3

2. Samiliar to 1, only difference is marker:201

3. Maker: 101 to 201.

4. Uning mean traits for each line (2,5,10,100);

Fixed population and samples to mapping different set of QTLs.

*each has 100 replicate; threhold values are gotten from 300 rounds under corresponding H0

How about the power

0

0. 5

1

1. 5

2

2. 5

500 m100 r100 m50 r50

QTL

Numb

er q203LRq203I Mq207LRq207I M

*2QTL, random position h2:0.3,0.7,total size:500,marker:101;epi:0.5;

Average number of QTL detected

012345

6789

10

500 m100 r100 m50 r50

QTL

Numb

er q1003LRq1003I Mq1007LRq1007I M

*10QTL, random position ,h2:0.3,0.7,total size:500,marker:101;epi:0.5;

Average number of QTL detected

How about the power with increased population size

*F5500: 5QTL,h2:0.7,total size:500, marker:101; no epi

*F51000: 5QTL ,h2:0.7, total size:1000, marker:101; no epi

0

1

2

3

4

5

6

total m100 r100 m50 r50

Numb

er o

f QT

L de

tect

ed

F5500LRF5500I MF51000LRF51000I M

Average number of QTL detected

How about the breakpoint number

*F500: total size is 500

*F1000: total size is 1000

Mean of breakpoi nt number f or each i ndi vi dual

0

5

10

15

20

25

total m100 r100 m50 r50

Numb

er o

f br

eakp

oint

F500F1000

How about the detected QTLposition

*5QTL far apart (100 cM away)

MSD of mappi ng posi t i on

0

0. 002

0. 004

0. 006

0. 008

0. 01

0. 012

500 m100 r100 m50 r50

Squa

re o

f mo

rgan

R5101MR5201M

How about the QTL effects

MSD of QTL eff ects

00. 10. 20. 30. 40. 50. 60. 70. 80. 9

1

500 m100 r100 m50 r50

addi

tive

effe

cts

R5101MR5201M

*5QTL far apart (100 cM away)

Fixed population and sample,mapping different trait genes

the mean of detected QTL number

0

1

2

3

4

5

500 m100 r100 m50 r50

QT

L n

umbe

r

R5101LRR5101I M

*5QTL;far apart(100cM away);h2:0.5;epi:0.3

MSD of mappi ng posi t i on

00. 0050. 01

0. 0150. 02

0. 0250. 03

0. 0350. 04

0. 045

500 m100 r100 m50 r50

Squa

red

morg

an

R5101I M

*5QTL;far apart(100cM away);h2:0.5;epi:0.3

MSD of QTL eff ects

0

2

4

6

8

10

12

14

500 m100 r100 m50 r50

Addi

tive

eff

ects

R5101I M

*5QTL;far apart(100cM away);h2:0.5;epi:0.3

Future work:

1. Power v.s. resolution.

2. Sample size needed to achieve same power in random.

3. Analyzing the breakpoint number v.s. resolution theoretically.

4. Simulating to see how MapPop works in fine mapping.