![Page 1: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/1.jpg)
Biometrical genetics
Pak C Sham
The University of Hong Kong
Manuel AR Ferreira
Queensland Institute for Medical Research
23rd International Workshop on Methodology of Twin and Family
Studies
2nd March, 2010
![Page 2: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/2.jpg)
Y1
A1D1E1
Y2
A2 D2 E2
1/0.25
1/0.5
e ac eca
ADE Model for twin dataMZ/DZ
![Page 3: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/3.jpg)
Biometrical Genetics
![Page 4: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/4.jpg)
Outline
1. Basic molecular genetics
2. Components of genetic model
3. Biometrical properties for single locus
4. Introduction to linkage analysis
![Page 5: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/5.jpg)
1. Basic molecular genetics
![Page 6: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/6.jpg)
A DNA molecule is a linear backbone of alternating sugar residues and phosphate groups
Attached to carbon atom 1’ of each sugar is a nitrogenous base: A, C, G or T
C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - GA - TC - GC - GT - AA - TG - CG - CC - GG - CA - TT - AA - TC - GT - AA - TA - TA - T
DNA
A gene is a segment of DNA which is translated to a peptide chain
Complementarity: A always pairs with T, likewise C with G
nucleotide
![Page 7: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/7.jpg)
23 chromosome pairs
22 autosomes, X,Y
~ 33,000,000,000 base pairs
Human genome
Other functional sequences
non-translated RNA
binding sites for regulatory molecules
~ 25,000 translated “genes”
![Page 8: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/8.jpg)
C - GA - TA - TT - AG - CC - GT - AT - AT - AG - CT - AA - TC - GG - CA - TC - GA - TC - GA - T (CA)nG - CG - CC - GG - CA - TT - AA - T C - G G - C T - GC - GT - AA - TA - TA - T
DNA sequence variation
(polymorphisms)
A
B
Microsatellites>100,000Many alleles, eg. (CA)n repeats, veryinformative, easily automated
Single nucleotide polymorphims (SNPs)11,883,685 (build 128, 03 Mar ‘08)Most with 2 alleles (up to 4), not veryinformative, easily automated
Copy Number polymorphisms Large-scale insertions / deletions
A
![Page 9: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/9.jpg)
Haploid gametes
♁
♂
♂ ♁
G1 phase
chr1
chr1
C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - G
C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - G
C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - G
S phase
Diploid zygote 1 cell
M phase
Diploid somatic cells
C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - G
♁♂ ♁
C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - G
C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - G
A -
B -
A -
B -
A -
B -
A -
B -
A -
B -
A -
B -
♂ ♁C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - G
C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - G
A -
B -
A -
B -
♂ ♁C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - G
C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - G
- A
- B
- A
- B- A
- B
- A
- B
C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - G
C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - G
Fertilization and mitotic cell
division
Mitosis
22 + 1 2 (22 + 1)
2 (22 + 1)
2 (22 + 1)
![Page 10: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/10.jpg)
Diploid gamete precursor cell
(♂) (♁)
C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - G
C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - G
C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - G
C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - G
C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - G
C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - G
C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - G
(♂)
(♁)
C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - GHaploid
gamete precursors Hap. gametes
NR
NR
R
R
♁
A -
B -
- A
- B
A -
B -
- A
- B
A -
B -
- A
- B
A -
B -
- A
- B
♂ ♁C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - G
C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - G
A -
B -
A -
B -
- A
- B
- A
- B
C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - G
C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - G
C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - G
C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - G
C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - G
C - GA - TA - TT - AG - CC - GT - AT - AT - AA - TA - TG - CC - GG - CA - TT - AG - CT - AA - TC - G
Meiosis / Gamete
formation
Meiosis
2 (22 + 1)
2 (22 + 1)
22 + 1
22 + 1
chr1 chr1 chr1 chr1
chr1
chr1
chr1
chr1
chr1
chr1
![Page 11: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/11.jpg)
2. Components of genetic
model
![Page 12: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/12.jpg)
Segregation (Meiosis)
Mendel’s law of segregation
A3 (½) A4 (½)
A1 (½)
A2 (½)
Mother (A3A4)
A1A3 (¼)
A2A3 (¼)
A1A4 (¼)
A2A4 (¼)
Gametes
Father (A1A2)
A. Transmission
model
Offspring
Note: 50:50 segregation can be distorted (“meiotic drive”)
![Page 13: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/13.jpg)
Segregation (Meiosis)
B1 (½) B2 (½)
A1 (½)
A2 (½)
Locus B (B1B2)
A1B1 (1/4)
A2B1 (1/4)
A1B2 (1/4)
A2B2 (1/4)
Locus A (A1A2)
A. Transmission model: two unlinked
loci
Gametes
Phase: A1B1 / A2B2
![Page 14: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/14.jpg)
Segregation (Meiosis)
B1 (½) B2 (½)
A1 (½)
A2 (½)
Locus B (B1B2)
A1B1 ((1-)/2)
A2B1 (/2)
A1B2 (/2)
A2B2 ((1-)/2)
Locus A (A1A2)
A. Transmission model: two linked
loci
Gametes
Phase: A1B1 / A2B2
: Recombination fraction, between 0 (complete linkage) and 1/2 (free recombination)
![Page 15: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/15.jpg)
B: Population
modelFrequencies
aaAA
AA
AA
AAAAAA
Aa
Aa
Aa
aa aa
Genotype frequencies:
AA: PAa: Qaa: R
Allele frequencies:A: P+Q/2a: R+Q/2
![Page 16: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/16.jpg)
B: Population
model
AA Aa aa
AA AA AA:Aa
0.5:0.5
Aa
Aa AA:Aa
0.5:0.5
AA:Aa:aa
0.25:0.5:0.25
Aa:aa
0.5:0.5
aa Aa Aa:aa
0.5:0.5
aa
AA Aa aa
AA P2 PQ PR
Aa PQ Q2 QR
aa PR QR R2
Hardy-Weinberg Equilibrium (Hardy GH, 1908; Weinberg W, 1908)
Random mating
Offspring genotypic distribution
![Page 17: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/17.jpg)
B: Population
modelHardy-Weinberg Equilibrium (Hardy GH, 1908; Weinberg W, 1908)
Genotype Frequency
AA P2+PQ+Q2/4 = (P+Q/2)2
Aa 2PR+PQ+QR+Q2/2 = 2(P+Q/2)(R+Q/2)
aa R2+QR+Q2/4 = (R+Q/2)2
Offspring genotype frequencies
Allele Frequency
A (P+Q/2)2 + (P+Q/2)(R+Q/2) = P+Q/2
a (R+Q/2)2 + (P+Q/2)(R+Q/2) = R+Q/2
Offspring allele frequencies
![Page 18: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/18.jpg)
B. Population
model Panmixia (Random union of gametes)
A (p) a (q)
A (p)
a (q)
Maternal allele
Paternal alleleAA (p2)
aA (qp)
Aa (pq)
aa (q2)
P (AA) = p2
P (Aa) = 2pq
P (aa) = q2
Deviations from HWE Assortative mating Imbreeding Population stratification Selection
![Page 19: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/19.jpg)
C. Phenotype
modelClassical Mendelian (Single-gene) traits
Dominant trait - AA, Aa 1 - aa 0
Recessive trait - AA 1 - aa, Aa 0
Cystic fibrosis 3 bp deletion exon 10 CFTR gene
Huntington’s disease (CAG)n repeat, huntingtin gene
![Page 20: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/20.jpg)
C. Phenotype
model
0
1
2
3
1 Gene 3 Genotypes 3 Phenotypes
0
1
2
3
2 Genes 9 Genotypes 5 Phenotypes
01234567
3 Genes 27 Genotypes 7 Phenotypes
0
5
10
15
20
4 Genes 81 Genotypes 9 Phenotypes
Central Limit Theorem Normal Distribution
Polygenic model
![Page 21: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/21.jpg)
Quantitative traits
Fra
ctio
n
Histograms by gqt
g==-1
0
.128205
g==0
-3.90647 2.7156g==1
-3.90647 2.7156
0
.128205
Fra
ctio
n
Histograms by gqt
g==-1
0
.128205
g==0
-3.90647 2.7156g==1
-3.90647 2.7156
0
.128205
Fra
ctio
n
Histograms by gqt
g==-1
0
.128205
g==0
-3.90647 2.7156g==1
-3.90647 2.7156
0
.128205
AA
Aa
aa
Fra
ctio
n
qt-3.90647 2.7156
0
.072
C. Phenotype
model
e.g. cholesterol levels
![Page 22: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/22.jpg)
d +a
P(X)
X
AA
Aa
aa
– a
Fisher’s model for single quantitative
trait locus (QTL)
Genotypic effects
D. Phenotype
model
2pq p2q2 Genotype frequencies
Assumption: Effect of allele independent of parental origin (Aa = aA)Violated in genomic imprinting
![Page 23: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/23.jpg)
3. Biometrical properties of
single locus
![Page 24: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/24.jpg)
Biometrical model for single biallelic
QTL1. Contribution of the QTL to the Mean (X)
aaAaAAGenotypes
Frequencies, f(x)
Effect, x
p2 2pq q2
a d -a
i
ii xfx
= m = a(p2) + d(2pq) – a(q2)Mean (X) = (p-q)a + 2pqd
Note: If everyone in population has genotype aa then population mean = -a change in mean due to A = ((p-q)a + 2pqd) – (-a) = 2p(a+qd)
![Page 25: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/25.jpg)
Biometrical model for single biallelic
QTL2. Contribution of the QTL to the Variance (X)
aaAaAAGenotypes
Frequencies, f(x)
Effect, x
p2 2pq q2
a d -a
= (a-m)2p2 + (d-m)22pq + (-a-m)2q2
Var (X)
i
ii xfxVar 2
= 2pq(a+(q-p)d)2 + (2pqd)2 = VQTL
Broad-sense heritability of X at this locus = VQTL / V Total
![Page 26: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/26.jpg)
Biometrical model for single biallelic
QTL2. Partitioning of QTL variance: additive component
A (p) a (q)
A (p)
a (q)
Maternal allele
Paternal allelea
d
d
-a
Average
pa+qd
pd-qa
Average pa+qd
pd-qa (p-q)a + 2pqd
Variance due to a single allele = p(q(d+a)-2pqd)2+q(p(d-a)-2pqd)2
= pq(a+(q-p)d)2
For both alleles, additive variance = 2pq(a+(q-p)d)2
![Page 27: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/27.jpg)
Biometrical model for single biallelic
QTL2. Partitioning of QTL variance: dominance component
Effect Additive effect
AA (p2)
Aa (2pq)
a
d
2(pa+qd)
(pa+qd)+(pd-qa)
-a 2(pd-qa)
Dominance variance due to QTL = p2(a-2(pa+qd))2
+2pq(d-(pa+qd+pd-qa))2
+q2(-a-2(pd-qa)
= (2pqd)2
Genotype
aa (q2)
![Page 28: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/28.jpg)
Biometrical model for single biallelic
QTL
Var (X) = Regression Variance + Residual Variance
-a
0
a
aa Aa AA aa Aa AA aa Aa AA
Additive Dominant Recessive
Genoty
pic
eff
ect
s
= Additive Variance + Dominance Variance
= VAQTL + VDQTL
![Page 29: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/29.jpg)
aa Aa AA aa Aa AA
+4 +4 +0.7 +0.4
log (x)
No departure from additivity
Significant departure from
additivity
Statistical definition of dominance is scale
dependent
![Page 30: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/30.jpg)
PracticalH:\ferreira\biometric\sgene.exe
![Page 31: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/31.jpg)
Practical
Aim Visualize graphically how allele frequencies, genetic effects, dominance, etc, influence trait mean and variance
Ex1a=0, d=0, p=0.4, Residual Variance = 0.04, Scale = 2.Vary a from 0 to 1.
Ex2a=1, d=0, p=0.4, Residual Variance = 0.04, Scale = 2.Vary d from -1 to 1.
Ex3a=1, d=0, p=0.4, Residual Variance = 0.04, Scale = 2.Vary p from 0 to 1.
Look at scatter-plot, histogram and variance components.
![Page 32: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/32.jpg)
Some conclusions
1. Additive genetic variance depends on
allele frequency p
& additive genetic value a
as well as
dominance deviation d
2. Additive genetic variance typically greater than dominance variance
![Page 33: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/33.jpg)
Biometrical model for single biallelic
QTL
3. Contribution of the QTL to the Covariance (X,Y)
2. Contribution of the QTL to the Variance (X)
1. Contribution of the QTL to the Mean (X)
![Page 34: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/34.jpg)
Biometrical model for single biallelic
QTL
i
iiYiXi yxfyxYXCov ,),(
AA
Aa
aa
AA Aa aa(a-m) (d-m) (-a-m)
(a-m)
(d-m)
(-a-m)
(a-m)2
(a-m)
(-a-m)
(d-m)
(a-m)
(d-m)2
(d-m)(-a-m) (-a-m)2
3. Contribution of the QTL to the Cov (X,Y)
![Page 35: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/35.jpg)
Biometrical model for single biallelic
QTL
i
iiYiXi yxfyxYXCov ,),(
AA
Aa
aa
AA Aa aa(a-m) (d-m) (-a-m)
(a-m)
(d-m)
(-a-m)
(a-m)2
(a-m)
(-a-m)
(d-m)
(a-m)
(d-m)2
(d-m)(-a-m) (-a-m)2
p2
0
0
2pq
0 q2
3A. Contribution of the QTL to the Cov (X,Y) – MZ twins
= (a-m)2p2 + (d-m)22pq + (-a-m)2q2 Cov(X,Y)
= VAQTL + VDQTL
= 2pq[a+(q-p)d]2 + (2pqd)2
![Page 36: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/36.jpg)
Biometrical model for single biallelic
QTL
AA
Aa
aa
AA Aa aa(a-m) (d-m) (-a-m)
(a-m)
(d-m)
(-a-m)
(a-m)2
(a-m)
(-a-m)
(d-m)
(a-m)
(d-m)2
(d-m)(-a-m) (-a-m)2
p3
p2q
0
pq
pq2 q3
3B. Contribution of the QTL to the Cov (X,Y) – Parent-Offspring
![Page 37: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/37.jpg)
• e.g. given an AA father, an AA offspring can come from either AA x AA or AA x Aa parental mating types
AA x AA will occur p2 × p2 = p4
and have AA offspring Prob()=1
AA x Aa will occur p2 × 2pq = 2p3q
and have AA offspring Prob()=0.5
and have Aa offspring Prob()=0.5
Therefore, P(AA father & AA offspring) = p4 + p3q
= p3(p+q)
= p3
![Page 38: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/38.jpg)
Biometrical model for single biallelic
QTL
AA
Aa
aa
AA Aa aa(a-m) (d-m) (-a-m)
(a-m)
(d-m)
(-a-m)
(a-m)2
(a-m)
(-a-m)
(d-m)
(a-m)
(d-m)2
(d-m)(-a-m) (-a-m)2
p3
p2q
0
pq
pq2 q3
= (a-m)2p3 + … + (-a-m)2q3 Cov (X,Y)
= ½VAQTL= pq[a+(q-p)d]2
3B. Contribution of the QTL to the Cov (X,Y) – Parent-Offspring
![Page 39: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/39.jpg)
Biometrical model for single biallelic
QTL
AA
Aa
aa
AA Aa aa(a-m) (d-m) (-a-m)
(a-m)
(d-m)
(-a-m)
(a-m)2
(a-m)
(-a-m)
(d-m)
(a-m)
(d-m)2
(d-m)(-a-m) (-a-m)2
p4
2p3q
p2q2
4p2q2
2pq3 q4
= (a-m)2p4 + … + (-a-m)2q4 Cov (X,Y)
= 0
3C. Contribution of the QTL to the Cov (X,Y) – Unrelated individuals
![Page 40: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/40.jpg)
Biometrical model for single biallelic
QTL
Cov (X,Y)
3D. Contribution of the QTL to the Cov (X,Y) – DZ twins and full sibs
¼ genome
¼ (2 alleles) + ½ (1 allele) + ¼ (0 alleles)
MZ twins P-O Unrelateds
¼ genome ¼ genome ¼ genome
# identical alleles inherited
from parents
01(mother)
1(father)
2
= ¼ Cov(MZ) + ½ Cov(P-O) + ¼ Cov(Unrel) = ¼(VAQTL
+VDQTL) + ½ (½ VAQTL
) + ¼
(0) = ½ VAQTL + ¼VDQTL
![Page 41: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/41.jpg)
Summary so far…
![Page 42: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/42.jpg)
Biometrical model predicts contribution of a QTL to the mean, variance and covariances of a trait
Var (X) = VAQTL + VDQTL
Cov (MZ) = VAQTL + VDQTL
Cov (DZ) = ½VAQTL + ¼VDQTL
On average!
0 or 10, 1/2 or 1
IBD estimation / Linkage
Mean (X) = a(p-q) + 2pqdAssociation
analysis
Linkage analysis
For a sib-pair, do the two sibs have 0, 1 or 2 alleles in common?
![Page 43: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/43.jpg)
4. Introduction to Linkage
Analysis
![Page 44: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/44.jpg)
For a heritable trait...
localize region of the genome where a QTL that regulates the trait is likely to be harboured
identify a QTL that regulates the trait
Linkage:
Association:
Family-specific phenomenon: Affected individuals in a family share the same ancestral predisposing DNA segment at a given QTL
Population-specific phenomenon: Affected individuals in a population share the same ancestral predisposing DNA segment at a given QTL
![Page 45: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/45.jpg)
Linkage Analysis: Parametric vs.
Nonparametric
QM
Phe
A
D
C
E
Genetic factors
Environmental factors
Mode of inheritanc
e
Recombination
Correlation
ChromosomeGene
Adapted from Weiss & Terwilliger 2000
Dominant trait1 - AA, Aa0 - aa
![Page 46: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/46.jpg)
Approach
Parametric: genotypes marker locus & genotypes trait locus
(latter inferred from phenotype according to a specific disease model)
Parameter of interest: θ between marker and trait lociNonparametric: genotypes marker locus & phenotype
If a trait locus truly regulates the expression of a phenotype, then two
relatives with similar phenotypes should have similar genotypes at a
marker in the vicinity of the trait locus, and vice-versa.
Interest: correlation between phenotypic similarity and marker genotypic
similarityNo need to specify mode of inheritance, allele frequencies, etc...
![Page 47: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/47.jpg)
Phenotypic similarity between relatives
Squared trait differencesSquared trait sumsTrait cross-product
221 XX
221 XX
21 XX
Trait variance-covariance matrix
221
211
XVarXXCov
XXCovXVar
Affection concordance
T2
T1
![Page 48: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/48.jpg)
Genotypic similarity between relatives
IBS Alleles shared Identical By State “look the same”, may have the
same DNA sequence but they are not necessarily derived from a
known common ancestorIBD Alleles shared
Identical By Descent
are a copy of the
same
ancestor
allele
M1
Q1
M2
Q2
M3
Q3
M3
Q4
M1
Q1
M3
Q3
M1
Q1
M3
Q4
M1
Q1
M2
Q2
M3
Q3
M3
Q4
IBS IBD
2 1
Inheritance vector (M)
0 0 0 1 1
![Page 49: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/49.jpg)
Genotypic similarity between relatives -
M1
Q1
M3
Q3
M2
Q2
M3
Q4
Number of alleles shared IBD
0
M1
Q1
M3
Q3
M1
Q1
M3
Q4
1
M1
Q1
M3
Q3
M1
Q1
M3
Q3
2
Proportion of alleles shared IBD
-0
0.5
1
Inheritance vector (M)
0 0 1 1
0 0 0 1
0 0 0 0
![Page 50: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/50.jpg)
x0/x1 x0/x1
x0/x0
x0/x0
x0/x0
x0/x0
x0/x1
x0/x1
x0/x1
x0/x1
x1/x0
x1/x0
x1/x0
x1/x0
x1/x1
x1/x1
x1/x1
x1/x1
x0/x0
x0/x1
x1/x0
x1/x1
x0/x0
x0/x1
x1/x0
x1/x1
x0/x0
x0/x1
x1/x0
x1/x1
x0/x0
x0/x1
x1/x0
x1/x1
Inheritance vector
0000000100100011010001010110011110001001101010111100110111101111
Prior probability
1/161/161/161/161/161/161/161/161/161/161/161/161/161/161/161/16
IBD
2110120110210112
A1/A3 A1/A2
Posterior probability
01/400
1/4000000
1/400
1/40
A1A3 A1A2
Posterior probability
01/121/121/121/12
01/121/121/121/12
01/121/121/121/12
0
1 2
3 4
A1A2 A3A2
A1/A2
Posterior probability
A1/A3
A1/A2 A3/A2
0100000000000000
P (IBD=0)P (IBD=1)P (IBD=2)
1/41/21/4
1/32/30
010
010
Genotypic similarity between relatives -
21
210 22
2
2
1
2
0ˆ
22n
A B C D
![Page 51: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/51.jpg)
Var (X) = VAQTL + VDQTL
Cov (MZ) = VAQTL + VDQTL
Cov (DZ) = ½VAQTL + ¼VDQTL
On average!
Cov (DZ) = VAQTL + VDQTL
For a given twin pair
2
![Page 52: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/52.jpg)
Cov (DZ) = VAQTL
Cov (DZ) = VAQTL
Genotypic similarity ( )
Phenoty
pic
sim
ilari
ty
0 0.5 1
Slope ~ VAQTL
![Page 53: Biometrical genetics Pak C Sham The University of Hong Kong Manuel AR Ferreira Queensland Institute for Medical Research 23 rd International Workshop on](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649d5d5503460f94a3c865/html5/thumbnails/53.jpg)
Statistics that incorporate both phenotypic and genotypic similarities to test VQTL
Regression-based methods
Variance components methods
Mx, MERLIN, SOLAR, GENEHUNTER
Haseman-Elston, MERLIN-regress