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The Causes of VariationLindon Eaves,
VIPBG, Richmond
Boulder,COMarch 2012
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Goals
• Summarize Causes of Variation• Provide some historical and conceptual background
• Introduce some of the ideas to be encountered this week
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“Genetics”
The Study of Variation and Heredity
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“Variation”“Why aren’t we all the same?”
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“Heredity”“Why do things run in families?”
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Conflicting Paradigms?Emerging Synthesis?
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Mendel(particulate inheritance)
Darwin (natural selection)
Galton (correlation
between relatives)
R.A. Fisher Sewall Wright
Quantitative GeneticsPolygenic
Population Genetics
Archibald Garod
“Human” GeneticsOligogenic
Sociobiology
Conflicting Paradigms
“Structural Modeling” (Twins etc.)
“Gene Hunting” (HGI) SYNTHESiS?
1865
2010
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Pretest
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Who are the Following People?
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“VARIATION”
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Continuous variation
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“Liberalism”
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Categorical Outcomes
Often called “threshold traits” because people “affected” if they fall above
some level (“threshold”) of a measured or hypothesized continuous trait.
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Probabilityof
Diagnosis
0
1
0 t
0.5
Liability(Trait Value)
∞
‐∞ +∞
Relationship between continuous normal “liability” and risk of “diagnosis”
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The Causes of Variation
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Path diagram for the effects of genes and environment on phenotype
P
G E
Measured variable
Latent variables
Genotype Environment
Phenotype
h e
r
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Path diagram for the effects of genes and environment on phenotype
P
E
Measured variable
Measured variables
Genotype Environment
Phenotype
h e
r
G E
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A Basic Model
Phenotype=Genotype+Environment
P=G+E {+f(G,E)}
f(G,E) = Genotype-environment interaction and correlation
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GENES (G)
• Contribution (“Heritability”)• Type of Action (“Additive”, “Dominant”, Epistatic”)
• Number, location and function
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Environment “E”
• Contribution (“1‐heritability”)• Type (Shared by family, unique to individual, remote, proximal,short‐, long‐term)
• Non‐genetic inheritance• Identification
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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.)
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“HEREDITY”
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Francis Galton (1822‐1911)
1869: Hereditary Genius1883: Inquiries into Human Faculty and its Development
1884‐5: Anthropometic Laboratory at “National Health Exhibition”
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Hereditary Genius (1869, p 317)
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Galton’s Anthropometric Laboratory:
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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
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Pearson and Lee’s diagram for measurement of “span” (finger‐tip to finger‐tip distance)
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From Pearson and Lee (1903) p.378
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From Pearson and Lee (1903) p.378
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From Pearson and Lee (1903) p.387
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From Pearson and Lee (1903) p. 373
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Modern DataThe Virginia 30,000
(N=29691)The Australia 22,000
(N=20480)
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ANZUS 50K: Extended Kinships of Twins
Twins
Parents of Twins
Offspring of Twins
Siblings of Twins
Spouses of Twins
© Lindon Eaves, 2009
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Overall sample sizes
Relationship # of pairsParent‐offspringSiblings
2501818697
Spouses 8287DZ TwinsMZ Twins
51204623
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00.050.10.150.20.250.30.350.40.450.5
USAustralia
Nuclear Family Correlations for Stature(Virginia 30,000 and OZ 22,000)
© Lindon Eaves, 2009
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00.10.20.30.40.50.60.70.8
USAustralia
Nuclear Family Correlations for Liberalism/Conservatism(Virginia 30,000 and Australia 22,000)
© Lindon Eaves, 2009
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The (Really!) BIG Problem
Families are a mixture of genetic and social
factors
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The Extended Phenotype
Me
World Parents
Siblings
Child
Spouse
Extended Phenotype
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DNA BrainEpi‐Genetics Behavior
Environment
MarkersSNPs
Candidate genes
ExpressionMethylation
CNVsHormonesMetabolitesProteins
Pre‐ and Peri‐Natal, Culture, Media, Parents,
Siblings, Peers, Teachers, Infection
Accidents, Life events, Habits,Life‐styles, SES
“Imaging”
Population structureStratificationAdmixture
AchievementAdaptation
Social/Anti‐socialDrugs
Depression AnxietySuicideEtc……
From Genes to Behavior: A Developmental Perspective
“Time and Age”
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P
G4G1 G2 G3 E1 E4E2 E3
GE
P1 P4P2 P3
G’4
E’4E’1 G’2 E’3
G’1
Measured Genotypes Measured Environments
Outcome Phenotype
Endophenotypes
TIME?
P5
G’5
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The (Really!) BIG Problem
Families are a mixture of genetic and social
factors
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Francis Galton (1822‐1911)
1869: Hereditary Genius1883: Inquiries into Human Faculty and its Development
1884‐5: Anthropometic Laboratory at “National Health Exhibition”
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Galton’s Solution:
Twins(Though Augustine may
have got there first –5th cent.)
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One (?ideal) solution
Twins separated at birth
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But separated MZs are rare
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An easier alternative:
Identical and non-identical twins reared together:
Galton (Again!)
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IDENTICAL TWINS• MONOZYGOTIC: Have IDENTICAL
genes (G)• Come from the same family (C)• Have unique experiences during life (E)
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FRATERNAL TWINS• DIZYGOTIC: Have DIFFERENT genes
(G)• Come from the same family (C)• Have unique experiences during life (E)
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-10 -5 0 5 10HTDEV1
-12
-7
-2
3
8
13
HTD
EV2
Scatterplot for corrected MZ stature
r=0.924
Data from the Virginia Twin Study of Adolescent Behavioral Development
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-16 -11 -6 -1 4 9 14HTDEV1
-20
-10
0
10
20
HTD
EV2
Scatterplot for age and sex corrected stature in DZ twins
r=0.535
Data from the Virginia Twin Study of Adolescent Behavioral Development
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Four scenarios
00.10.20.30.40.50.60.70.80.9
No G No C G and C G and I
MZDZ
Twin Correlation
Causes of Variation
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00.10.20.30.40.50.60.70.80.91
DZM DZF DZMF MZM MZF
USAustralia
Twin Correlations for Adult Stature(Virginia 30,000 and Australia 22,000)
© Lindon Eaves, 2009
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Four scenarios
00.10.20.30.40.50.60.70.80.9
No G No C G and C G and I
MZDZ
Twin Correlation
Causes of Variation
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00.10.20.30.40.50.60.70.80.91
DZM DZF DZMF MZM MZF
Stature USStature OZLiberal USLiberal OZ
Twin Correlations for Stature and Liberalism(Virginia 30,000 and Australia 22,000)
© Lindon Eaves, 2009
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Four scenarios
00.10.20.30.40.50.60.70.80.9
No G No C G and C G and I
MZDZ
Twin Correlation
Causes of Variation
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Twin correlations for gene expression
Correlation (Fisher's Z)
dens
ity
-1 0 1 2 3
0.0
0.2
0.4
0.6
0.8
1.0
-1 0 1 2 3
0.0
0.2
0.4
0.6
0.8
1.0 A
MZDZ
0.0 0.2 0.4 0.6 0.8 1.0
010
2030
4050
60
Broad sense heritability
B
York et al.
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“Quantitative Genetics”
Analysis of the patterns and mechanisms underlying variation in
continuous traits to resolve and identify their genetic and environmental causes.
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Gregor Mendel (1822‐1884)
1865: “Experiments in Plant Hybridization”
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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
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“Mendelian” Crosseswith Quantitative Traits
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Mendelian Basis of Continuous Variation?Experimental Breeding Experiments
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Experiments Show:
• Variation within inbred lines: Environment• F1’s typically show same within‐line variation• F2’s more variable: Mirrors Mendeliansegregation of Mendel’s classical hybridization experiments
• Average differences between individual F2plants continue to progeny generations (F3’s etc.)
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Description of East’s Experiment
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Ronald Fisher (1890‐1962)
1918: On the Correlation Between Relatives on the Supposition of Mendelian Inheritance1921: Introduced concept of “likelihood”
1930: The Genetical Theory of Natural Selection1935: The Design of Experiments
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Fisher developed mathematical theory that reconciled Mendel’s work with Galton and Pearson’s correlations
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0 1 2 3 4 5Y1
0.0
0.1
0.2
0.3
0.4
Distribution of scores produced by two genes(N=1000 subjects)
-2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5 5.5 6.5S1
0.0
0.1
0.2
0.3
0.4
The "smoothing" effect of the environment(N=1000 subjects, 2 gene model)
75 79 83 87 91 95 99 103 107 111 115 119 123Y1
0.00
0.02
0.04
0.06
Continuous distribution of polygenic trait (100 genes with small cumulative effects)
b.
c.
a.
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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
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Kenneth Mather 1911-1990 John Jinks 1929-1987
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Basic Model for Effects of a Single Gene on a Quantitative Trait
Mid‐homozygote
Homozygous effect
Dominancedeviation
Increasing Decreasing
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= Pathway blocked by mutant gene
A
B
BC
A
aa
bb
aa bb
Sequential (“complementary”) genesParallel (“duplicate”) genes
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Combining pathways
Dose of Bad Alleles
PhenotypicResponse
Complementary Genes
Duplicate Genes
Additive
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b. “Scalar” GxE
Environment (E)
PhenotypeGenotypes
c. “Non-scalar” GxE
Environment (E)
PhenotypeGenotypes
a. No GxE
Environment (E)
PhenotypeGenotypes
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Path diagram for the effects of genes and environment on phenotype
P
G E
Measured variable
Latent variables
Genotype Environment
Phenotype
h e
r
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Genetic AND Cultural inheritance?
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Multiple Variables
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N V S
F
USUVUN
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V2
G1
EV1
N2
N1 V1
S2
S1
Twin 2
Twin 1
G2
EN1ES1
ES2EV2EN2
gCommon Genes
Specific Environments
Specific Environments
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Development
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a. Genetic variation in developmental change: time series with common genes and time‐specific environmental “innovations”
T1T0 T2 T4 T5
G
E5E4E3E2E1
Genes
Environment
Age
hh h h
h
b b b b
ee e e
e
Phenotype
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a. Age change in genetic and environmental variance: genetic effect continuous across ages with age-specific environmental effects
Genetic variance
Environmental variance
Variance
Age
b. Age change in genetic and environmental variance: initial genetic effect decays with age with accumulating age-specific environmental
effects
Genetic variance
Environmental variance
Variance
Age
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Genetic differences in growth
Phenotype
Age
G1
G2
G3
Genotypes
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Attitudes over the life‐span
0
20
40
60
80
100
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
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“Mating”
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“Twins and Spouses”
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f(G,E)Genotype x Environment Interaction
(“GxE”)Genotype‐Environment Correlation
(“rGE”)
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GxE
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Effect of Strict Religious Upbringing on Expression of Genetic Differences in Behavioral Disinhibition Among Dutch Juveniles.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
MZ male MZ female DZ male DZ female DZ m-fRelationship
Correlation
ReligiousNon-religions
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Genetic Variance and Shared Life Events in Adolescent Females
00.5
11.5
22.5
33.5
44.5
0 1 2+
Number of life events
Gen
etic
Var
ianc
e
DepressionAnxiety
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Theory Model Data
Model‐building Study designData collection
Model‐Fitting
Fits?Revise Publishestimates
YESNO
“The Logic of Scientific Discovery”
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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
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Have fun!!!