Transcript Slide 1

The Causes of Variation
Lindon Eaves,
VIPBG, Richmond
Boulder,CO
March 2012
Goals
• Summarize Causes of Variation
• Provide some historical and conceptual
background
• Introduce some of the ideas to be
encountered this week
“Genetics”
The Study of
Variation and Heredity
“Variation”
“Why aren’t we all the same?”
“Heredity”
“Why do things run in families?”
Conflicting Paradigms?
Emerging Synthesis?
1865
Mendel
Galton
(particulate
inheritance)
(correlation
between relatives)
(natural selection)
Archibald
Garod
R.A. Fisher
Sewall Wright
“Human”
Genetics
Oligogenic
Quantitative
Genetics
Polygenic
Population
Genetics
Darwin
Sociobiology
Conflicting Paradigms
“Gene Hunting”
(HGI)
2010
SYNTHESiS?
“Structural
Modeling”
(Twins etc.)
Pretest
Who are the Following
People?
“VARIATION”
Continuous variation
“Liberalism”
Categorical Outcomes
Often called “threshold traits” because
people “affected” if they fall above
some level (“threshold”) of a measured
or hypothesized continuous trait.
∞
Relationship between continuous normal “liability”
and risk of “diagnosis”
Probability
of
Diagnosis
1
0.5
0
-∞
0
t
+∞
Liability
(Trait Value)
The Causes of Variation
Path diagram for the effects of genes and environment on phenotype
Environment
Genotype
r
G
h
Measured variable
E
Latent variables
e
P
Phenotype
Path diagram for the effects of genes and environment on phenotype
Environment
Genotype
r
G
Measured variables
h
Measured variable
e
P
Phenotype
EE
A Basic Model
Phenotype=Genotype+Environment
P=G+E {+f(G,E)}
f(G,E) = Genotype-environment
interaction and correlation
GENES (G)
• Contribution (“Heritability”)
• Type of Action (“Additive”, “Dominant”,
Epistatic”)
• Number, location and function
Environment “E”
• Contribution (“1-heritability”)
• Type (Shared by family, unique to individual,
remote, proximal,short-, long-term)
• Non-genetic inheritance
• Identification
Interactions and Correlations f(G,E)
• Mating system, population structure
• GxE interaction
• Multiple variables: Genetic and Environmental
Correlation
• Direction of Causation and Causal networks
• G x E interaction
• G – E correlation
• Remembering, Forgetting, Development (GxAge,
G x Time etc.)
“HEREDITY”
Francis Galton (1822-1911)
1869: Hereditary Genius
1883: Inquiries into Human Faculty and its Development
1884-5: Anthropometic Laboratory at “National Health Exhibition”
Hereditary Genius (1869, p 317)
Galton’s Anthropometric Laboratory:
Karl Pearson (1857-1936)
1903: On the Laws of Inheritance in Man: I Physical Characteristics (with Alice Lee)
1904: II Mental and Moral Characteristics
1914: The Life, Letters and Labours of Francis Galton
Pearson and Lee’s diagram for measurement of “span” (finger-tip to finger-tip distance)
From Pearson and Lee (1903) p.378
From Pearson and Lee (1903) p.378
From Pearson and Lee (1903) p.387
From Pearson and Lee (1903) p. 373
Modern Data
The Virginia 30,000
(N=29691)
The Australia 22,000
(N=20480)
ANZUS 50K: Extended Kinships of Twins
Parents of Twins
Siblings of Twins
Spouses of Twins
Twins
Offspring of Twins
© Lindon Eaves, 2009
Overall sample sizes
Relationship
Parent-offspring
Siblings
Spouses
DZ Twins
MZ Twins
# of pairs
25018
18697
8287
5120
4623
Nuclear Family Correlations for Stature
(Virginia 30,000 and OZ 22,000)
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
US
Australia
© Lindon Eaves, 2009
Nuclear Family Correlations for Liberalism/Conservatism
(Virginia 30,000 and Australia 22,000)
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
US
Australia
© Lindon Eaves, 2009
The (Really!) BIG
Problem
Families are a mixture of
genetic and social
factors
The Extended Phenotype
Parents
World
Me
Spouse
Siblings
Child
Extended Phenotype
From Genes to Behavior: A Developmental Perspective
Population structure
Stratification
Admixture
Pre- and Peri-Natal,
Culture, Media, Parents,
Siblings, Peers,
Teachers, Infection
Accidents, Life events, Habits,
Life-styles, SES
Environment
DNA
Epi-Genetics
Markers
SNPs
Candidate genes
Expression
Methylation
CNVs
Hormones
Metabolites
Proteins
Brain
“Imaging”
“Time and Age”
Behavior
Achievement
Adaptation
Social/Anti-social
Drugs
Depression Anxiety
Suicide
Etc……
Measured Genotypes
G1
G2
Measured Environments
G3
G4
E1
E2
E3
E4
G’4
G’1
Endophenotypes
P1
T
I
M
E
?
E’1
P2
P3
G’2
P4
E’3
E’4
P5
G
E
P
Outcome Phenotype
G’5
The (Really!) BIG
Problem
Families are a mixture of
genetic and social
factors
Francis Galton (1822-1911)
1869: Hereditary Genius
1883: Inquiries into Human Faculty and its Development
1884-5: Anthropometic Laboratory at “National Health Exhibition”
Galton’s Solution:
Twins
(Though Augustine may
have got there first –
5th cent.)
One (?ideal) solution
Twins separated at
birth
But separated MZs are rare
An easier alternative:
Identical and non-identical
twins reared together:
Galton (Again!)
IDENTICAL TWINS
• MONOZYGOTIC: Have IDENTICAL
genes (G)
• Come from the same family (C)
• Have unique experiences during life (E)
FRATERNAL TWINS
• DIZYGOTIC: Have DIFFERENT genes
(G)
• Come from the same family (C)
• Have unique experiences during life (E)
Scatterplot for corrected MZ stature
13
HTDEV2
8
3
-2
r=0.924
-7
-12
-10
-5
0
5
10
HTDEV1
Data from the Virginia Twin Study of Adolescent Behavioral Development
Scatterplot for age and sex corrected stature in DZ twins
20
HTDEV2
10
0
r=0.535
-10
-20
-16
-11
-6
-1
4
9
14
HTDEV1
Data from the Virginia Twin Study of Adolescent Behavioral Development
Four scenarios
Twin
Correlation
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
MZ
DZ
No G
No C
G and C G and I
Causes of Variation
Twin Correlations for Adult Stature
(Virginia 30,000 and Australia 22,000)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
US
Australia
DZM
DZF
DZMF
MZM
MZF
© Lindon Eaves, 2009
Four scenarios
Twin
Correlation
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
MZ
DZ
No G
No C
G and C G and I
Causes of Variation
Twin Correlations for Stature and Liberalism
(Virginia 30,000 and Australia 22,000)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Stature US
Stature OZ
Liberal US
Liberal OZ
DZM
DZF
DZMF
MZM
MZF
© Lindon Eaves, 2009
Four scenarios
Twin
Correlation
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
MZ
DZ
No G
No C
G and C G and I
Causes of Variation
B
50
60
A
0.8
1.0
Twin correlations for gene expression
0
0.0
10
0.2
20
0.4
30
density
0.6
40
MZ
DZ
-1
0
1
C orrelation (Fisher' s Z)
2
3
0.0
0.2
0.4
0.6
0.8
1.0
B road sense heritability
York et al.
“Quantitative Genetics”
Analysis of the patterns and
mechanisms underlying variation in
continuous traits to resolve and identify
their genetic and environmental causes.
Gregor Mendel (1822-1884)
1865: “Experiments in Plant Hybridization”
Karl Pearson (1857-1936)
1903: On the Laws of Inheritance in Man: I Physical Characteristics (with Alice Lee)
1904: II Mental and Moral Characteristics
1914: The Life, Letters and Labours of Francis Galton
“Mendelian” Crosses
with Quantitative Traits
Mendelian Basis of Continuous Variation?
Experimental Breeding Experiments
Experiments Show:
• Variation within inbred lines: Environment
• F1’s typically show same within-line variation
• F2’s more variable: Mirrors Mendelian
segregation of Mendel’s classical hybridization
experiments
• Average differences between individual F2
plants continue to progeny generations (F3’s
etc.)
Description of East’s Experiment
Ronald Fisher (1890-1962)
1918: On the Correlation Between Relatives on the Supposition of Mendelian Inheritance
1921: Introduced concept of “likelihood”
1930: The Genetical Theory of Natural Selection
1935: The Design of Experiments
Fisher developed mathematical theory
that reconciled Mendel’s work with
Galton and Pearson’s correlations
a.
Distribution of scores produced by two genes
b.
(N=1000 subjects)
The "smoothing" effect of the environment
(N=1000 subjects, 2 gene model)
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0.0
0.0
-2.5
0
1
2
3
4
c.
Y1
-1.5
-0.5
0.5
5
Continuous distribution of polygenic trait
0.06
0.04
0.02
0.00
79
83
87
2.5
S1
(100 genes with small cumulative effects)
75
1.5
91
95
99
Y1
103
107
111
115
119
123
3.5
4.5
5.5
6.5
Fisher (1918): Basic Ideas
• Continuous variation caused by lots of genes
(“polygenic inheritance”)
• Each gene followed Mendel’s laws
• Environment smoothed out genetic differences
• Genes may show different degrees of “dominance”
• Genes may have many forms (“mutliple alleles”)
• Mating may not be random (“assortative mating”)
• Showed that correlations obtained by e.g. Pearson
and Lee were explained well by polygenic inheritance
Kenneth Mather 1911-1990
John Jinks 1929-1987
Basic Model for Effects of a Single Gene on a Quantitative Trait
Mid-homozygote
Decreasing
Increasing
Dominance
deviation
Homozygous effect
Parallel (“duplicate”) genes
Sequential (“complementary”) genes
A
A
aa
B
bb
aa
bb
B
C
= Pathway blocked by mutant gene
Combining pathways
Complementary Genes
Phenotypic
Response
Additive
Duplicate Genes
Dose of Bad Alleles
a. No GxE
Phenotype
Genotypes
Environment (E)
b. “Scalar” GxE
c. “Non-scalar” GxE
Phenotype
Phenotype
Genotypes
Environment (E)
Genotypes
Environment (E)
Path diagram for the effects of genes and environment on phenotype
Environment
Genotype
r
G
h
Measured variable
E
Latent variables
e
P
Phenotype
Genetic AND Cultural inheritance?
Multiple Variables
F
N
V
S
UN
UV
US
Specific
Environments
EN1
EV1
ES1
N1
V1
S1
Twin 1
G1
g
Common Genes
G2
Twin 2
Specific
Environments
N2
V2
S2
EN2
EV2
ES2
Development
a. Genetic variation in developmental change: time series with common
genes and time-specific environmental “innovations”
Genes
h
h
Phenotype
T0
b
G
T1
h
b
T2
b
T4
Age
e
E1
h
h
e
e
e
E2
E3
E4
Environment
b
T5
e
E5
a. Age change in genetic and environmental variance: genetic effect
continuous across ages with age-specific environmental effects
Variance
Genetic variance
b. Age change in genetic and environmental variance: initial genetic
effect decays with age with accumulating age-specific environmental
effects
Variance
Genetic variance
Environmental variance
Environmental variance
Age
Age
Genetic differences in growth
G1
Phenotype
G2
Genotypes
G3
Age
Attitudes over the life-span
100
80
60
40
20
0
9.5
11
12.5
14
15.5
17
18-20 21-25 26-30 31-35 36-40 41-45 46-50 51-55 56-60 61-65 66-70 71-75 75+
MZ
DZ
“Mating”
“Twins and Spouses”
f(G,E)
Genotype x Environment Interaction
(“GxE”)
Genotype-Environment Correlation
(“rGE”)
GxE
Effect of Strict Religious Upbringing on Expression of Genetic
Differences in Behavioral Disinhibition Among Dutch Juveniles.
Correlation
0.7
Religious
Non-religions
0.6
0.5
0.4
0.3
0.2
0.1
0
MZ male
MZ female
DZ male
Relationship
DZ female
DZ m-f
Genetic Variance
Genetic Variance and Shared Life Events
in Adolescent Females
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
Depression
Anxiety
0
1
Number of life events
2+
“The Logic of Scientific Discovery”
Revise
NO
YES
Fits?
Publish
estimates
Model-Fitting
Theory
Data
Model
Model-building
Study design
Data collection
Statisical approach
“Likelihood” (Fisher)
Some models and values of quantities
(“parameters”, VA, VD etc) are “unlikely” to
produce the data.
Choose those parameters values for that make
the data “most likely”, i.e. maximum likelihood.
General statistical approach: applied widely in
genetics
Have fun!!!