The Causes of VariationLindon Eaves,

VIPBG, Richmond

Boulder,COMarch 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?

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

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.

Probabilityof

Diagnosis

0

1

0 t

0.5

Liability(Trait Value)

∞

‐∞ +∞

Relationship between continuous normal “liability” and risk of “diagnosis”

The Causes of Variation

Path diagram for the effects of genes and environment on phenotype

P

G E

Measured variable

Latent variables

Genotype Environment

Phenotype

h e

r

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

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 Genius1883: 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 DataThe Virginia 30,000 

(N=29691)The Australia 22,000

(N=20480)

ANZUS 50K:  Extended Kinships of Twins

Twins

Parents of Twins

Offspring of Twins

Siblings of Twins

Spouses of Twins

© Lindon Eaves, 2009

Overall sample sizes

Relationship # of  pairsParent‐offspringSiblings

2501818697

Spouses 8287DZ TwinsMZ Twins

51204623

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

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

The (Really!) BIG Problem

Families are a mixture of genetic and social

factors

The Extended Phenotype

Me

World Parents

Siblings

Child

Spouse

Extended Phenotype

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”

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

The (Really!) BIG Problem

Families are a mixture of genetic and social

factors

Francis Galton (1822‐1911)

1869: Hereditary Genius1883: 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)

-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

-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

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

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

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

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

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

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. 

“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” Crosseswith 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 Mendeliansegregation of Mendel’s classical hybridization experiments

• Average differences between individual F2plants 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 Inheritance1921: Introduced concept of “likelihood”

1930:  The Genetical Theory of Natural Selection1935:  The Design of Experiments

Fisher developed mathematical theory that reconciled Mendel’s work with Galton and Pearson’s correlations

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.

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

Homozygous effect

Dominancedeviation

Increasing Decreasing 

= Pathway blocked by mutant gene

A

B

BC

A

aa

bb

aa bb

Sequential (“complementary”) genesParallel (“duplicate”) genes

Combining pathways

Dose of Bad Alleles

PhenotypicResponse

Complementary Genes

Duplicate Genes

Additive

b. “Scalar” GxE

Environment (E)

PhenotypeGenotypes

c. “Non-scalar” GxE

Environment (E)

PhenotypeGenotypes

a. No GxE

Environment (E)

PhenotypeGenotypes

Path diagram for the effects of genes and environment on phenotype

P

G E

Measured variable

Latent variables

Genotype Environment

Phenotype

h e

r

Genetic AND Cultural inheritance?

Multiple Variables

N V S

F

USUVUN

V2

G1

EV1

N2

N1 V1

S2

S1

Twin 2

Twin 1

G2

EN1ES1

ES2EV2EN2

gCommon Genes

Specific Environments

Specific Environments

Development

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

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

Genetic differences in growth

Phenotype

Age

G1

G2

G3

Genotypes

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

“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.

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

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

Theory Model Data

Model‐building Study designData collection

Model‐Fitting

Fits?Revise Publishestimates

YESNO

“The Logic of Scientific Discovery”

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!!!