Can heritability be modeled as a function of DNA marker sharing at a particular chromosomal location using pihat?

1
Can heritability be modeled as a function of DNA
marker sharing at a particular chromosomal
location using pihat?
2
rMZ rDZ 1
rMZ 1, rDZ 0.5
E
E
rMZ 1, rDZ 0, 0.5 or 1
C
C
e
e
A
A
c
c
a
a
Q
Q
q
q
Twin 1
Twin 2
4 group linkage analysis (3 IBD DZ groups and 1
MZ group)
3
Pihat

• Merlin estimates the 3 IBD probabilities for each
  sib pair at each location
• Remember pibd2 pibd1 pibd0 1
• Pihat pibd21 pibd10.5 pibd00
• Estimate of the probability of sharing alleles
  identical by descent
• Proxy additive genetic correlation at the locus

4
rMZ rDZ 1
rMZ 1, rDZ 0.5
E
E

rMZ 1, rDZ ?
C
C
e
e
A
A
c
c
a
a
Q
Q
q
q
Twin 1
Twin 2
5
Pihat Mx Script for 1 marker

• !QTL analysis via Pihat method
• !Using marker1
• !Using MZ and DZ twins
• !Analysis of LDL
• !Dutch Adults
• define nvar 1 !different for
  multivariate
• define nsib 2 !number of siblings
• NGroups 3
• G1 Parameter Estimates
• G2 Monozygotic twins
• G3 Dizygotic twins

6
Group 1 specify parameters

• Begin Matrices
• X Lower nvar nvar Free !additive genetic
  parameter
• Y Lower nvar nvar Free !shared environmental
  parameter
• Z Lower nvar nvar Free !unique environmental
  parameter
• L Full nvar 1 Free !QTL effect
• Begin Algebra
• A XX' !additive
  genetic variance
• C YY' !shared
  environmental variance
• E ZZ' !unique
  environmental variance
• Q LL' !variance due
  to QTL
• V ACQE !total variance
• T ACQE !parameters in one
  matrix for standardizing
• S T_at_V !standardized
  variance component estimates

7
Group 2 MZ twins

• See Group 1
• M Full 1 nvar Free !means
• U Unit 1 nsib
• include lipidmz.dat
• Select ldl1 ldl2
• Begin Matrices Group 1
• Means U_at_M
• Covariance ACQE ACQ _
• ACQ ACQE
• End

8
Group 3 DZ twins

• include lipiddz.dat
• Select ibd0m1 ibd1m1 ibd2m1 ldl1 ldl2
• Definition ibd0m1 ibd1m1 ibd2m1
• Begin Matrices Group 1
• K Full 3 1 !IBD
  probabilities (from Merlin)
• J Full 1 3 !coefficients
  0,0.5,1 for pihat
• End Matrices
• Specify K ibd0m1 ibd1m1 ibd2m1
• Matrix J 0. 0.5 1.0
• Begin Algebra
• P JK !estimate of
  pihat
• End Algebra

9
Group 3 End Multiple Fit

• Means U_at_M
• Covariance ACQE H_at_ACP_at_Q _
• H_at_ACP_at_Q ACQE
• Start 1 All
• Start 2.8 M 1 1 1
• Option NDecimals3
• Option Multiple Issat
• End
• ! Test significance of QTL effect
• Drop L 1 1 1
• End

10
Exercise

• Fit ACEQ model to MZ/DZ data for one location at
  a time
• Fit ACE model to (drop Q)
• Is the QTL effect significant?
• Plot the results

11
Basic script and data (LDL)

• ACEQ model in MZ/DZ twins lipidpihatmzdz1.mx
• f\hmaes\a16\martin\linkage
• IBD probabilities every 2 cM gt 54 locations
• Rectangular files DZ lipiddz.rec
• MZlipidmz.rec
• Dat files DZ lipiddz.dat
• MZ lipidmz.dat
• FEQ model for DZ twins only lipidpihat1.mx

12
Fit to marker number according to table position
1 16 17 32 33
2 15 18 31 34
3 14 19 30 35
4 13 20 29 36
5 12 21 28
6 11 22 27
7 10 23 26
8 9 24 25
13
Chi-square for all locations
14
Pihat Mx Script for N locations

• repeat 54 !total number of
  markers N
• Begin Script
• Group 3
• include lipiddz.dat
• include seldefrepeat_number
• Select ibd0m? Ibd1m? Ibd2m? ldl1 ldl2
• Definition ibd0m? ibd1m? Ibd2m?
• include specifyrepeat_number
• Specify K ibd0m? ibd1m? ibd2m?
• Rest Script
• end repeat

15
Extended script and data (LDL)

• ACEQ model in MZ/DZ twins lipidpihatmzdz54.mx
• IBD probabilities every 2 cM gt 54 locations
• Rectangular files DZ lipiddz.rec
• MZlipidmz.rec
• Dat files DZ lipiddz.dat
• MZ lipidmz.dat
• Help files seldef1 seldef54
• specify1 specify54
• FEQ model for DZ twins only lipidpihat54.mx

16
Get summary of results

• Unix commands in Cygwin on PC
• grep Difference Chi-squared lipidpihat54.mxo gt
  chi54
• awk print 4 chi54 gt chisq54
• pico chisq54