QTL mapping in animals - PowerPoint PPT Presentation

QTL mapping in animals. QTL mapping in animals. It works. QTL mapping in animals. It works It’s c

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QTL mapping in animalsQTL mapping in animals
  • It works
QTL mapping in animals
  • It works
  • It’s cheap
QTL mapping in animals
  • It works
  • It’s cheap
  • It’s relevant to human studies
Genomic resource

Nature December 5 2002

No more crosses?In silico mappingMethodMethod

F0 Parental Generation

F1 Generation

F2 Generation

Interbreeding for approximately 20 generations to produce recombinant inbreds

Recombinant InbredsRI strain phenotypesRI strain genotypesQTL for airway responsivenessPower

n -2 = (ta + tb)2/(s2QTL/s2RES)

ta and tb are values on the t distribution corresponding to the desired a value

s2QTL is the phenotypic variance explained by a QTL

s2RES the unexplained variance.

Experimentally verified QTL for airway responsiveness

Zhang, Y. et al.A genome-wide screen for asthma-associated quantitative trait loci in a mouse model of allergic asthma. Hum. Mol. Genet. 8, 601-605 (1999).

Inbred Strain CrossQuantitative Trait Locus Detection Marker QTL

M

r

Q

m

q

Marker QTL

M

r

Q

m

q

MM QQ Qq qq

Mm QQ Qq qq

mm QQ Qq qq

Marker QTL

MM QQ

Mm QQ

Mm QQ

P (QQ | MM) = (1-r)2

P (Qq | MM) = 2r(1-r)

P (qq | MM) = r2

(1-r)2 + 2r(1-r) + r2

QTL Genotypic values

Alleles at the QTL: q and Q

Additive value: a

Degree of dominance: d

mQQ = m + 2a

mQq = m + a(1+d)

mqq = m

Mean values for marker genotypesMean values for marker genotypesTwo things follow
  • Contrasts of single marker means can be used to detect QTL
Example

QTLeffects.xls

Example

REAL_DATA/Real data.xls

Two things follow
  • Contrasts of single marker means can be used to detect QTL
  • Estimates of position and effect are confounded
Additive and dominance estimatesFlanking markers

M1

M2

m1

m2

Flanking markers

M1

M2

m1

m2

M1M1 M2M2

M1M1 M2m2

M1M1 m2m2

M1m1 M2M2

M1m1 M2m2

M1m1 m2m2

m1m1 M2M2

m1m1 M2m2

m1m1 m2m2

M1

Q

M2

m1

q

m2

Interval mapping

r12

r1

r2

M1

Q

M2

m1

q

m2

Interval mapping

r12

r1

r2

r2 =( r12 – r1)/(1-2r1) No interference

r2 = r12- r1 Complete interference

M1

Q

M2

m1

q

m2

Interval mapping

r12

r1

r2

M1M1 M2M2

p(M1QM2 | M1QM2) = ((1-r1) (1-r2)/2)2

M1

Q

M2

m1

q

m2

Interval mapping

r12

r1

r2

p(QQ|M1M1M2M2) = ((1-r1) 2(1-r2)2)/(1-r12)2

p(Qq|M1M1M2M2) = (2r1r2(1-r1) (1-r2) )/(1-r12)2

p(qq|M1M1M2M2) = (r12r22)/(1-r12)2

Significance thresholdsPermutation tests to establish thresholds

Empirical threshold values for quantitative trait mapping

GA Churchill and RW Doerge

Genetics, 138, 963-971 1994

An empirical method is described, based on the concept of a permutation test, for estimating threshold values that are tailored to the experimental data at hand.

Permutation tests

Trait values are randomly reassigned to genotypes

10,000 re-samplings for 1% value

Permutation tests
  • Robust to departures from normality
  • Robust to missing or erroneous data
  • Easy to implement
Significance Thresholds

Lander, E. Kruglyak, L. Genetic dissection of complex traits: guidelines for interpreting and reporting linkage resultsNature Genetics. 11, 241-7, 1995

Maximum likelihood methodsMaximum likelihood methodsMaximum likelihood methods

M1

Q

M2

M1

q

M2

Interval mapping

r12

r1

r2

M1

Q

M2

M1

q

M2

Interval mapping

r12

r1

r2

Maximum likelihoodTest statisticExample

SIMULATED_DATA

WinQTL

Linear modelsLinear models

mQQ = m + a mQq = m + d mqq = m - a

Linear models

mQQ = m + a mQq = m + d mqq = m - a

zj = m + a . x (Mj) + d . y (Mj) + ej

Linear models

mQQ = m + a mQq = m + d mqq = m - a

zj = m + a . x (Mj) + d . y (Mj) + ej

x (Mj) = p(QQ | Mj) – p (qq| Mj)

y (Mj) = p(Qq | Mj)

(1-r1) 2(1-r2)2 -(r12r22)

x(M1M1M2M2)

=

(1-r12)2

Linear models

x (Mj) = p(QQ | Mj) – p (qq| Mj)

(1-r1) 2(1-r2)2 -(r12r22)

x(M1M1M2M2)

=

(1-r12)2

2r1r2(1-r1) (1-r2)

y(M1M1M2M2)

=

(1-r12)2

Linear models

x (Mj) = p(QQ | Mj) – p (qq| Mj)

y (Mj) = p(Qq | Mj)

Significance test

LR = n ln (SST/SSE) = -n ln (1-r2)

Degrees of freedom are the number of estimated QTL parameters, plus one for the map position

Matrix statement of Haley Knott regression

br1 = (XTr1 Xr1) -1 XTr1 z

ith row of matrix Xr1: (1,x(Mi,r1), y(Mi,r1))

Example

Regression example.xls

Problems of QTL detection
  • Linked QTLs corrupt the position estimates
  • Unlinked QTLs decreases the power of QTL detection
Extensions to linear regression
  • Composite interval mapping
  • Multiple interval mapping
Composite interval mapping

ZB Zeng Precision mapping of quantitative trait loci

Genetics, Vol 136, 1457-1468, 1994

http://statgen.ncsu.edu/qtlcart/cartographer.html

Composite interval mappingComposite interval mapping

Q

M1

Q

M2

Q

M1

M2

Composite interval mapping

Q

M-1

M1

Q

M2

M3

Q

M-1

M1

M2

M3

Composite interval mapping

Q

M-1

M1

Q

M2

M3

Q

M-1

M1

M2

M3

zj = m + a . x (Mj) + d . y (Mj)

S

+

bk . xkj + ej

k=i, i+1

Example

SIMULATED_DATA

WinQTL

Multiple Interval MappingMultiple Interval MappingMultiple Interval MappingExample?

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