Transcript IBD Estimation in Pedigrees

Genetics and Human variation
Nick Martin
Queensland Institute of Medical Research
Boulder workshop: March 4, 2002
TC-1
TC-2
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YEAR
LOCATION
1987
1989
1990
1991
Leuven
TC-5
TC-6
TC-7
TC-8
TC-9
TC-10
TC-11
1993
1994
1995
1996
1997
1998
1998
TC-12
TC-13
TC-14
TC-15
1999
2000
2001
2002
Leuven
Boulder
Leuven
Boulder
Boulder
Helsinki
Boulder
Boulder
Boulder
Leuven
Boulder
Boulder
Boulder
Boulder
# FACULTY
# STUDENTS
10
11
11
14 Introductory
12 Advanced
24
41
28
49
13
16
10
10
10
12 Introductory
10 Introductory
13 Advanced
49
43
29
49
55
57
55
62
12 Advanced
12 Introductory
18 Advanced
Introductory
37
63
65
55
Attendance at twin workshops
Frequency of
Attendance
Faculty
Student
Total
1
2
4
8
337 127
345 131
3
4
5
6
7
8
9
13
15
16 TOTAL
1
27
1
12
2
3
2
1
4
0
1
0
1
0
1
0
1
0
6
0
32
507
28
13
5
3
4
1
1
1
1
6
539
People and Ideas
Galton (1865-ish)
Mendel
Correlation
Family Resemblance
Twins
Ancestral Heredity
Darwin (1858,1871)
(1865)
Natural Selection
Sexual Selection
Evolution
Particulate Inheritance
Genes: single in gamete
double in zygote
Segregation ratios
Spearman
Fisher (1918)
(1904)
Common Factor Analysis
Correlation & Mendel
Maximum Likelihood
ANOVA: partition of variance
Wright
(1921)
Path Analysis
Mather (1949) &
Thurstone (1930's)
Jinks (1971)
Multiple Factor Analysis
Biometrical Genetics
Model Fitting (plants)
Joreskog (1960)
Jinks & Fulker (1970)
Model Fitting applied to humans
Segregation
Linkage
Morton (1974)
Population
Genetics
Rao, Rice, Reich,
Cloninger (1970's)
Martin & Eaves (1977)
Neale (1990) Mx
Covariance
Structure Analysis
LISREL
Path Analysis &
Family Resemblance
Elston etc (19..)
Genetic Analysis of
Covariance Structure
Watson &
Crick (1953)
2000
Assortment
Cultural Inheritance
Molecular
Genetics
Paradigm clash ?


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
Genes which cause X, rather than genes
which cause variation in X
not necessarily same (e.g. having a
nose vs nose size ?) - but often so
physiologists, experimental
psychologists, sociobiologists vs. Quant
Genet, BG, GenEpi
see Baker BS, Taylor BJ, Hall JC (2001) Are complex behaviors specified
by dedicated regulatory genes ? Cell 105:13-24.
Individual differences




Physical attributes (height, eye color)
Disease susceptibility (asthma, anxiety)
Behavior (intelligence, personality)
Life outcomes (income, children)
Stature in adolescent twins
Women
700
600
500
400
300
200
Std. Dev = 6.40
100
Mean = 169.1
N = 1785.00
0
145.0
155.0
150.0
Stature
165.0
160.0
175.0
170.0
185.0
180.0
190.0
Continuous or Categorical ?

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Body Mass Index vs “obesity”
Blood pressure vs “hypertensive”
Bone Mineral Density vs “fracture”
Bronchial reactivity vs “asthma”
Neuroticism vs “anxious/depressed”
Reading ability vs “dyslexic”
Externalizing behavior vs “delinquent”
Central Limit Theorem


The normal distribution is
to be expected whenever
variation is produced by
the addition of a large
number of effects, nonpredominant
This plausibly holds quite
often
Polygenic Traits
1 Gene
2 Genes
3 Genes
4 Genes
 3 Genotypes
 3 Phenotypes
 9 Genotypes
 5 Phenotypes
 27 Genotypes
 7 Phenotypes
 81 Genotypes
 9 Phenotypes
3
3
2
2
1
1
0
0
7
6
5
4
3
2
1
0
20
15
10
5
0
Multifactorial Threshold Model
of Disease
Single threshold
unaffected
Disease liability
affected
Multiple
thresholds
normal
mild mod
Disease liability
severe
Genetic Epidemiology


Establishing the role of genes and
environment in variation in disease
and complex traits
Finding those genes
Genetically Complex Diseases

Imprecise phenotype

Phenocopies / sporadic cases

Low penetrance

Locus heterogeneity/ polygenic
effects
Complex Trait Model
Linkage
Marker
Gene1
Linkage
disequilibrium
Linkage
Association
Mode of
inheritance
Gene2
Disease
Phenotype
Individual
environment
Common
environment
Gene3
Polygenic
background
3 Stages of Genetic Mapping

Are there genes influencing this trait?


Where are those genes?


Genetic epidemiological studies
Linkage analysis
What are those genes?

Association analysis
Sources of variance

Additive genetic - A

Interaction between alleles at same locus
(dominance) or different loci (epistasis) – D

Common environmental influences shared by
members of the same family – C

Non-shared environmental influences unique
to the individual – E

Measurement error (confounded with E)
unless replicate test-retest sample
Designs to disentangle G + E
Resemblance between relatives caused by:

shared Genes (G = A + D)

environment Common to family
members (C)
Differences between relatives caused by:

nonshared Genes

Unique environment (U or E)
Designs to disentangle G + E

Family studies – G + C confounded

MZ twins alone – G + C confounded


MZ twins reared apart – rare, atypical,
selective placement ?
Adoptions – increasingly rare, atypical,
selective placement ?

MZ and DZ twins reared together

Extended twin design
Designs to disentangle G + E

Family studies – G + C confounded

MZ twins alone – G + C confounded


MZ twins reared apart – rare, atypical,
selective placement ?
Adoptions – increasingly rare, atypical,
selective placement ?

MZ and DZ twins reared together

Extended twin design
MZ concordance for human conditions

Asthma
45%

Eczema
84%

Diabetes (type I)
56%

Schizophrenia
50%

Cleft lip/palate
30%

Club foot
23%

Homosexuality (M)
18%

Homosexuality (F)
23%
Designs to disentangle G + E

Family studies – G + C confounded

MZ twins alone – G + C confounded


MZ twins reared apart – rare, atypical,
selective placement ?
Adoptions – increasingly rare, atypical,
selective placement ?

MZ and DZ twins reared together

Extended twin design
MZ twins reared apart - note the same way of
supporting their cans of beer
Body postures of MZ twins reared apart
Body postures of DZ twins reared apart
Designs to disentangle G + E

Family studies – G + C confounded

MZ twins alone – G + C confounded


MZ twins reared apart – rare, atypical,
selective placement ?
Adoptions – increasingly rare, atypical,
selective placement ?

MZ and DZ twins reared together

Extended twin design
Percentage of adoptees convicted of violent and
property offenses by biological parents’ convictions

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
Denmark
14,427 nonfamilial
adoptions 1927-47
Court convictions
available for
biological and
adoptive parents
Mednick et al (1984)
Science 224:891-4
Designs to disentangle G + E

Family studies – G + C confounded

MZ twins alone – G + C confounded


MZ twins reared apart – rare, atypical,
selective placement ?
Adoptions – increasingly rare, atypical,
selective placement ?

MZ and DZ twins reared together

Extended twin design
Placentation and zygosity
Dichorionic
Two placentas
Dichorionic
Fused placentas
Monochorionic
Diamniotic
Monochorionic
Monoamniotic
MZ 19%
DZ 58%
MZ 14%
DZ 42%
MZ 63%
DZ 0%
MZ 4%
DZ 0%
Identity at marker loci except for rare mutation
MZ and DZ twins:
determining zygosity using
ABI Profiler™ genotyping
(9 STR markers + sex)
MZ
DZ
DZ
Twin studies that changed the
world




Multiple sclerosis
Autism
ADHD
Schizophrenia
Total mole count for MZ and DZ twins
DZ twins - 199 pairs, r = 0.60
400
400
300
300
Twin 1
Twin 1
MZ twins - 153 pairs, r = 0.94
200
200
100
100
0
0
0
100
200
300
Twin 2
400
0
100
200
300
Twin 2
400
Decomposing variance
E
Covariance
A
C
0
Adoptive
Siblings
0.5
DZ
1
MZ
Path analysis



allows us to diagrammatically represent linear
models for the relationships between
variables
easy to derive expectations for the variances
and covariances of variables in terms of the
parameters of the proposed linear model
permits translation into matrix formulation
(Mx)
Variance components
Unique
Environment
Shared
Environment
Additive
Genetic
Effects
C
A
E
c
Dominance
Genetic
Effects
D
a
e
d
Phenotype
P = eE + aA + cC + dD
ACE Model for twin data
1
MZ=1.0 / DZ=0.5
E
C
e
c
PT1
A
a
A
C
a
c
PT2
E
e
Fit of ACE model to mole count
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A = 64%, C = 30%, E = 6%
drop A, Χ21= 124.0 (P < .001)
drop C, Χ21 = 13.2 (P < .001)
therefore can’t drop A or C
and can’t drop E !
Structural equation modeling
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Both continuous and categorical variables
Systematic approach to hypothesis testing
Tests of significance
Can be extended to:



More complex questions
Multiple variables
Other relatives
SEM : more complex questions

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Are the same genes acting in males and
females ? (sex limitation)
Role of age on (a) mean (b) variance (c)
variance components
Are G & E equally important in age, country
cohorts ? (heterogeneity)
Are G & E same in other strata (e.g.
married/unmarried) ? ( G x E interaction)
E
G
VAR 1
G
VAR 2
E
G
VAR 3
E
G
E
Sources of variation in male sexual orientation
EC
AC
Homosexuality
Orientation of
sexual
feelings
AF
EF
Attitude to
sex with a
man
Number of
same-sex
partners
AA
AP
EA
EP
Direction of causation modeling
with cross-sectional twin data
Model
Full Bivariate
Reciprocal
Distress Parenting
Parenting Distress
No causation
Final
c2
145.66
146.00
161.74
146.71
376.29
151.26
A
AIC
-69.34
.34
-70.00
16.08 -56.26
1.05
-71.29
230.63 156.29
5.60
-80.74
A
E
.45
.38
DISTRESS
.63
C
.55
.56
ANX
E
.20
.25
PARENTING
+ .18
.49
.67
DEP
C
Dc2
df
107
108
109
109
110
116
SOM
COLD
E
A
E
A
E
.36
.13
.21
.11
.40
C
.52
.16
OVERP
E
.17 .26
A
C
E
.21 .14 .49
AUTON
C
E
.11 .37
Designs to disentangle G + E

Family studies – G + C confounded

MZ twins alone – G + C confounded


MZ twins reared apart – rare, atypical,
selective placement ?
Adoptions – increasingly rare, atypical,
selective placement ?

MZ and DZ twins reared together

Extended twin design
cm
cm
cf
Gendercommon
Additive
Genes
mf
mm
Malespecific
Additive
Genes
Female
Unique
Environment
Malespecific
Additive
Genes
cm
0.5
0.5
ef
Female Twin
Environment
0.5
hfc
em
sf
tm
Male parent
Environment
wmm
dm
wff
Female
Dominant
Genes
Gendercommon
Additive
Genes
hfc
Male
Dominant
Genes
Female
Unique
Environment
Malespecific
Additive
Genes
Malespecific
Additive
Genes
Male Unique
Environment
hmm
ef
rt
tf Female Twin
Male Twin
Environment
Environment
Female twin
hmc
tm
Male twin
sf
df
em
Gendercommon
Additive
Genes
sm
Female
Sibling
Environment
rs
Female
Dominant
Genes
rd
Male Sibling
Environment
Male
Dominant
Genes
dm
Extended
kinship
model
• twins
sm Male Sibling
wfm
wmf
df
Male Twin
Environment
hmc

Female parent
0.5
0.5
0.5
tf
Female
Sibling
Environment
0.5
hmm
0.5
Gendercommon
Additive
Genes
Male Unique
Environment
• siblings
• parents
• children
• grandparents
• aunts, uncles
• cousins
3 Stages of Genetic Mapping

Are there genes influencing this trait?


Where are those genes?


Epidemiological studies
Linkage analysis
What are those genes?

Association analysis
Linkage analysis
Linkage = Co-segregation
A3A4
A1A2
A1A3
A1A2
A1A4
A2A4
A3A4
A2A3
A3A2
Marker allele A1
cosegregates with
dominant disease
Linkage Analysis

Sharing between relatives

Identifies large regions


Include several candidates
Complex disease




Scans on sets of small families popular
No strong assumptions about disease alleles
Low power
Limited resolution
rMZ = rDZ = 1
rMZ = 1, rDZ = 0.5
E
e
E
^
rMZ = 1, rDZ = 
C
c
C
A
a
Twin 1
mole
count
A
Q
Q
q
q
a
Twin 2
mole
count
c
e
Flat mole count - genome scan in 274 twin families
3 Stages of Genetic Mapping

Are there genes influencing this trait?


Where are those genes?


Epidemiological studies
Linkage analysis
What are those genes?

Association analysis
Association Analysis

Sharing between unrelated individuals


Trait alleles originate in common ancestor
High resolution



Powerful if assumptions are met


Recombination since common ancestor
Large number of independent tests
Same disease haplotype shared by many patients
Sensitive to population structure
First (unequivocal)
positional cloning of a
complex disease QTL !
but can we find the God gene?
Time will tell….