Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross...

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QTL ANALYSIS

Transcript of Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross...

Page 1: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

QTL ANALYSIS

Page 2: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

METHODS FOR MAPPING QTL

ð Single Marker Analysis

ð Interval Mapping

ð Composite Interval Mapping

ð Bayesian Methods

Page 3: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

QTL MAPPING

ð Methods based on linkage disequilibrium between markers

and QTL (line crossing or segregating population)

ð Requirements:

� Linkage (marker) maps

� Variation for the quantitative trait

M1 M2 M3 Mk-1 Mk

…r1 r2 r3 r(k-2) r(k-1)

QTL ?

Page 4: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

BC

QTL MAPPING Single Marker Analysis; Example with Backcross

× Purebreds, lines

80 40 F1

65

×

68 55 57 61 59

Page 5: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

QTL MAPPING Single Marker Analysis; Example with Backcross

65 68 55 57 61 59

Marker

59 61 55 57 68 65

Genotype 65

60

55

70

Page 6: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

QTL MAPPING Single Marker Analysis; Example with Backcross

65 68 55 57 61 59

Marker

61 59 55 68 57 65

Genotype 65

60

55

70

Page 7: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

SINGLE MARKER ANALYSIS

C Simple example with candidate gene and backcross population

Q1Q1 Q2Q2

Q1Q2 Q1Q1

Q1Q2 Q1Q1 δ

µ1

µ2

Q1Q2 Q1Q1

Genotype Obs. Mean STD Q1Q1 n1 m1 s1

Q1Q2 n2 m2 s2

ð H0: δ = 0 vs H1: δ ≠ 0

)2(

21

2

2121

~11

−+

⎟⎟⎠

⎞⎜⎜⎝

⎛+

−= nnt

nns

mmt

2nns)1n(s)1n(

s21

222

2112

−+

−+−=

2)( :)]1( ;[

21

2

)2/;2(12 21 −+±−− −+ nn

stmmCI nn ααδ

Page 8: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

SINGLE MARKER ANALYSIS

µ3

µ2

µ = (µ1 + µ3)/2

GG Gg gg

QTL genotypes

y α

α

τ

µ1 Additive

Dominance

Page 9: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

SINGLE MARKER ANALYSIS

C QTL and marker (M); recombination frequency = r

M1 M1 Q1 Q1

M1 M2 Q1 Q2

M1 M1 Q1 Q1

M1 M2 Q1 Q2

M1 M2 Q1 Q1

M1 M1 Q1 Q2

Genotype Freq. E[y] Marker group Freq. E[y] M1M1Q1Q1 (1-r)/2 µ1 M1M1 ½ M1M1Q1Q2 r/2 µ2 M1M2Q1Q1 r/2 µ1 M1M2 ½ M1M2Q1Q2 (1-r)/2 µ2

21 )1( µµ rr −+

21)1( µµ rr +−

Difference between marker group expected values

2121 )1()1( µµµµ rrrr −−−−+

δµµ )21())(21( 12 rr −=−−=

Page 10: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

SINGLE MARKER ANALYSIS

(EXAMPLE)

ð Brassica napus; Flowering time ð 10 Markers

(positions: 0, 8.8, 20.6, 27.4, 34.2, 42.9, 53.6, 64.1, 69.2, 83.9 cM)

ð 104 individuals; Double haploid

3.0204 -1 -1 -1 -1 -1 -1 -1 -1 -99 -1

2.9704 -1 -1 -1 -1 -99 -1 -1 -1 -1 1

2.7408 -1 -1 1 1 1 1 1 1 1 1

3.3673 1 1 1 1 -1 -1 -1 -1 -1 1

3.0681 1 1 1 1 -99 1 1 1 -1 -1

3.2771 -1 -99 -1 -1 -1 -1 -1 -1 -1 -1

(Satagopan et al. Genetics 144: 805-816, 1996)

Page 11: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

!

Chrom. Marker µ τ LRT F p-value!

!

1 1 3.184 -0.202 9.379 9.624 0.002 **!

1 2 3.204 -0.230 11.378 11.789 0.001 ***!

1 3 3.232 -0.266 14.706 15.485 0.000 ***!

1 4 3.229 -0.259 13.885 14.562 0.000 ***!

1 5 3.240 -0.276 15.554 16.446 0.000 ****!

1 6 3.259 -0.307 19.518 21.041 0.000 ****!

1 7 3.252 -0.302 19.747 21.312 0.000 ****!

1 8 3.257 -0.318 23.450 25.775 0.000 ****!

1 9 3.258 -0.330 25.156 27.884 0.000 ****!

1 10 3.252 -0.362 31.518 36.059 0.000 ****

0

5

10

15

20

25

30

35

40

0 10 20 30 40 50 60 70 80 90Position (cM)

F va

lues

Page 12: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

INTERVAL MAPPING

M QTL N

r1 r2

r

(Lander & Botstein, 1989)

M m N n

Backcross

M m Q q N n

m m q q n n

m m n n

M m n n

m m N n

δ µ

QQ Qq

iii qy εδµ ++=

phenotype QTL genotype

residual

0 , if qq 1 , if Qq qi =

Page 13: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

INTERVAL MAPPING

),0(~ 2σε Ni ) ,(~| 2σδµ iii qNqy +If

⎭⎬⎫

⎩⎨⎧ −−−= 2

22)(

21exp

21)|( δµ

σπσiiii qyqyp

[ ]∏=

==+==∝N

iiiiiii qqyfqqyfL

1

2 )1Pr()1|()0Pr()0|()|,,,,( yqλσδµ

∏=⎢⎣

⎡=

⎭⎬⎫

⎩⎨⎧ −−∝

N

iii qyL

1

222

2 )|0Pr()(21exp1)|,,,,( λµσσ

λσδµ yq

⎥⎦

⎤=

⎭⎬⎫

⎩⎨⎧ −−−+ )|1Pr()(21exp1 222

λδµσσ

ii qyQTL position

Page 14: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

INTERVAL MAPPING

Marker Genotypes Pr(qi = QQ) Pr(qi = Qq)

M,N (1 - r1)(1 - r2)/(1 - r) r1 r2 /(1 – r)

M,n (1 - r1) r2 / r r1 (1 - r2 )/ r

m,N r1 (1 - r2 )/ r (1 - r1) r2 / r

m,n r1 r2 /(1 - r) (1 - r1)(1 - r2 )/(1 - r)

)|Pr( λiq is modeled in terms of recombinations between flanking markers and QTL:

Markers Pr(qi = QQ) Pr(qi = Qq)

M,N 1 0

M,n (1 - p) p

m,N p (1 - p)

m,n 0 1

Approximation: (no double recombination)

rrp 1=

Page 15: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

INTERVAL MAPPING

ð Likelihood estimation: EM algorithm to estimate parameters, including λ (position of QTL).

ð Alternatively: Fix λ (grid search) and evaluate LOD.

⎥⎦

⎤⎢⎣

==

)0,|ˆ,ˆ,ˆ(L)|ˆ,ˆ,ˆ,ˆ(LlogLOD 2

2

10 δσµσδµ

λ yqyq

C A QTL is detected whenever the LOD score gets larger than a threshold; estimated position of the QTL maximizes LOD.

Page 16: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

INTERVAL MAPPING

REGRESSION APPROACH (Haley & Knott, 1992)

εXβy +=

⎥⎥⎥⎥

⎢⎢⎢⎢

+⎥⎦

⎤⎢⎣

⎥⎥⎥⎥

⎢⎢⎢⎢

=

⎥⎥⎥⎥

⎢⎢⎢⎢

NNNN pp

pppp

y

yy

ε

ε

ε

µ

µ

2

1

2

1

21

2221

1211

2

1⎥⎥⎥⎥

⎢⎢⎢⎢

+⎥⎦

⎤⎢⎣

⎥⎥⎥⎥

⎢⎢⎢⎢

=

⎥⎥⎥⎥

⎢⎢⎢⎢

NNN p

pp

y

yy

ε

ε

ε

δ

µ

2

1

2

22

12

2

1

1

11

yXXXβ ')'(ˆ 1−=

yXβyy ''ˆ'RSS −=

Residual Sum of Squares:

Estimated position of the QTL minimizes RSS.

alternatively

Page 17: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

GENE MAPPING Interval Mapping; Example with Backcross 65 68 55 57 61 59

Chromosome, marker positions (cM)

Test

sta

tistic

s (e

vide

nce

for Q

TL)

M1 M2 M3 M4 M5 M6

Page 18: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

INTERVAL MAPPING

ð COMMENTS:

� Backcross to both parental lines, or use F2 design, to estimate additive and dominance effects.

� Threshold; multiple testing; false positives

� Confidence intervals

� Multiple QTL, ghost QTL

Page 19: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

COMPOSITE INTERVAL MAPPING

(Zeng, 1993, 1994)

ð Interval analysis adding marker cofactors (to account for the effects of unlinked QTLs); combination of single interval mapping and multiple linear regression.

Mj

QTL

λ

Mj-1 Mj+1 Mj+2

Flanking markers

Cofactors Cofactors

Page 20: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

COMPOSITE INTERVAL MAPPING

(Zeng, 1993, 1994)

ijjk

ikkiji wxy εβββ +++= ∑+≠ 1,

*0

Intercept Genetic effect of the putative QTL

(between markers j and j+1)

Dummy variables

⎥⎥⎥⎥⎥

⎢⎢⎢⎢⎢

=

NpNNj

pj

pj

wwx

wwxwwx

1

2212

1111

1

11

X

εXβy +=

yXXXβ ')'(ˆ 1−=

Page 21: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

(EXAMPLE)

ð Brassica napus; Flowering time (Satagopan et al., 1996)

INTERVAL MAPPING

0

5

10

15

20

25

30

35

40

0 10 20 30 40 50 60 70 80 90Position (cM)

LRT

Page 22: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

(EXAMPLE)

ð Brassica napus; Flowering time (Satagopan et al., 1996)

COMPOSITE INTERVAL MAPPING

0

2

4

6

8

10

12

14

16

18

0 10 20 30 40 50 60 70 80 90Position (cM)

LRT

Page 23: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

EXAMPLES

Page 24: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

MARKER ASSISTED SELECTION

Page 25: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

ð MAS: Use of genetic markers to improve the efficiency of genetic selection

ð Basic idea behind of MAS:

MARKER ASSISTED SELECTION

• Most traits of economic importance are controlled by a fairly large number of genes

•  Some of these genes, however, with larger effect

•  Following the pattern of inheritance of such genes might assist in selection

Phenotype Genotype

Page 26: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

(Kinghorn &

van der Werf, 2000)

BASIC IDEA BEHIND MAS

ð MAS can potentially improve genetic gain by: 1) Increasing accuracy of genetic prediction, 2) Increasing selection intensity, and 3) Decreasing generation interval.

Page 27: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

TYPES OF GENETIC MARKERS

Direct Markers: loci that code for the functional mutation

LD Markers: loci that are in population-wide LD with the functional mutation

LE Markers: loci that are in population LE with the mutation

M QTL

r = 0

Direct Markers:

(e.g. Halothane gene in pigs, double muscling gene in cattle)

M QTL

r

Indirect Markers:

Page 28: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

INDIRECT MARKERS

Let: Marker M (alleles M1 and M2) and QTL Q (alleles Q1 and Q2)

Recombination rate: rMQ

Allelic frequencies: Pr(M1) = p1; Pr(Q1) = q1

If linkage equilibrium:

Pr(M1Q1) = p1q1

Pr(M1Q2) = p1(1 - q1)

Pr(Q1|M1) = q1

Pr(Q2 |M1) = (1 - q1)

Page 29: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

MAS MAY HELP IMPROVE

� Low heritability traits

� Phenotypes that can be measured on one sex only

� Characteristics that are not measurable before sexual maturity

� Traits that are difficult to measured or require sacrifice

� Size (effect) of QTL

� Frequency of favorable allele

� Recombination rate between marker(s) and QTL

EFFICIENCY OF MAS

Page 30: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

Lir

Yr/BV BVEBV;TBV σ××=Δ

interval GenerationVariationIntensityAccuracyYr/BV ××

GENETIC GAIN; THE KEY EQUATION

ð MAS can improve genetic gain by: 1) increasing accuracy of genetic prediction, 2) increasing selection intensity, and 3) decreasing generation interval.

Page 31: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

LONG TERM MAS

ð Selection Index that combines the EBV of the QTL with the EBV for polygenes :

)q()u(

uqI +=

uqbI +=

(Soller, 1978)

(Dekkers and van Arendonk, 1998)

Phe

noty

pe

Generation

MAS

Polygenes

Page 32: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

εβ +++= ZuWqXy

),0(~ 2uANu σ

phenotype

fixed effects (environmental)

QTL effects

Polygenic effects

residual ),0(~ 2

εσε IN

MODELING EFFECTS AT THE QTL GENOTYPE

Page 33: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

ð Two-step iterative scheme:

� Calculating QTL genotype probabilities using

segregation analysis

� Regressing phenotypes on these probabilities

(Kinghorn et al., 1993), or carrying out regression

weighted by these probabilities (Meuwissen and

Goddard, 1997)

QTL-GENOTYPE AS A FIXED EFFECT

Page 34: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

ð Useful when limited number of genotypic effects at the QTL (i.e. limited number of alleles, and effect of different genotypes are equal across families/herds)

ð Easily accommodates dominance at the QTL (and epistasis if more than one QTL)

ð Incidence matrix W: genotype probabilities at the QTL

ð With QTL genotype as fixed effect: E[Wq] = Wq and Var[Wq] = 0

CONSIDERATIONS

Page 35: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

(Fernando and Grossman, 1989)

The effect of a QTL is modeled as the sum of the two gametic effects:

εβ +++= ZuWvXy

⎟⎟⎟

⎜⎜⎜

=⎟⎟⎟

⎜⎜⎜

2

2

2

000000

εσ

σ

σ

ε IA

Guv

Var u

vv

Dimension: 2n (for each animal: paternal and maternal gametic effects)

Gametic relationship matrix

QTL-GENOTYPE AS A RANDOM EFFECT

Page 36: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

This approach can be used to calculate animal EBV’s at the QTL, much as we use coefficients of

relationship to estimate ‘polygenic’ breeding values

⎟⎟⎟

⎜⎜⎜

=⎟⎟⎟

⎜⎜⎜

⎟⎟⎟

⎜⎜⎜

+

+−

yWyZyX

vu

GWWZWXWWZAZZXZWXZXXX

vv

u

'''

'''''''''

1

1

β

α

α

MIXED MODEL EQUATIONS

Page 37: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

ð Gives the probabilities of identity between each of the two alleles in each individual

ð Example with and without marker information:

105.5.00601005.5.55.0100045.00100305.0010205.00011654321Site

12 34

56

QTL

109.1.00601001.9.59.0100041.00100301.0010209.00011654321Site

12 AB

34 AC

56 AC

QTL

Marker (alleles A, B, C)

r = 0.1

GAMETIC RELATIONSHIP MATRIX

Page 38: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

Conditions that favor QTL detection F High heritability, i.e. small environmental influence F Genetic differences caused by few loci F Large family sizes F Large data base of phenotypic information

When is MAS most useful as an adjunct to conventional selection for polygenic traits? F Traits with low heritability F Sex limited traits (expressed in one sex) F Phenotypes costly to measure F Phenotypes expressed late in life F Phenotypes cannot be measured in breeding

animals, e.g. carcass traits

Notice: Conditions that optimize MAS are often opposite to those that favor QTL detection.

Page 39: Part 6 QTL Analysis - USP€¦ · BC QTL MAPPING Single Marker Analysis; Example with Backcross Purebreds, × lines 80 40 F1 65 × 57 68 55 61 59

POTENTIAL PROBLEMS IN MAS

ð Favorable QTL allele(s) fixed/absent for a specific herd/commercial population

ð QTL effect may depend on genetic background (in general, QTL have stronger effects in the genetic background in which they were detected)

ð QTL with unfavorable effect(s) on other trait(s)

ð Cost, etc.

(QTL detected in resource population)