2. experimental design - evolutionary...

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2. Experimental design

1. parent-offspring regression2. cross-foster designs3. common garden designs4. breeding designs5. artificial selection6. pedigree analysis7. QTL mapping

Not treated are: molecular approaches (e.g., candidate gene, mutation screen, knock-out/down, etc.).

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The genetic covariance between relatives

Relationship r VD VI(A,A)

Parent-offspring

Grandparent-grandchild

Great grandparent-great grandchild

Full sibs, dizygotic twins

Half-sibs (maternal or paternal)

Aunt(uncle)-niece(nephew)

First cousins

Monozygotic twins / Individual(Repeatability)

1/2

1/4

1/8

1/2

1/4

1/4

1/8

1

1/2

1/4

1/8

1/2

1/4

1/4

1/8

1

0

0

0

1/4

0

0

0

1

VA

1/4

1/16

1/64

1/4

1/16

1/16

1/64

1

r: coefficient of genetic relatedness

1. Parents and their offspring live in similar environments

2. Siblings live in similar environments, and receive similar amounts/qualities of resources from their parents

3. Generally speaking: when the set of relatives that are compared also tend to live in similar environments (jargon: when there is a genotype x environment correlation)

4. The environment also includes pre-birth (maternal) effects, such as non-genetic influences during gestation and lactation (mammals) or in the egg (birds, ectotherms) and during incubation (birds)

5. The offspring trait is not exactly the same as the one measured in the parents (relevant for parent-offspring regression): consider e.g. body size: at what age should the body size of offspring be measured when regressed on the parents’ body size?

1. Parents and their offspring live in similar environments

2. Siblings live in similar environments, and receive similar amounts/qualities of resources from their parents

3. Generally speaking: when the set of relatives that are compared also tend to live in similar environments (jargon: when there is a genotype x environment correlation)

4. The environment also includes pre-birth (maternal) effects, such as non-genetic influences during gestation and lactation (mammals) or in the egg (birds, ectotherms) and during incubation (birds)

5. The offspring trait is not exactly the same as the one measured in the parents (relevant for parent-offspring regression): consider e.g. body size: at what age should the body size of offspring be measured when regressed on the parents’ body size?

Simply comparing individuals belonging to a certain category of relatives is usually a poor way to estimate components of genetic variation and heritabilities because these categories are usually confounded by non-genetic sources of variation. For example:

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Parent-offspring regression

Parent Offspring

Generation: t t+1

Trait measured on parent and offspringCaution: trait should be measured at the same stage/age to be certain that the trait is really identical

Trait measured on parent and offspringCaution: trait should be measured at the same stage/age to be certain that the trait is really identical


Although tarsus length (a measure of structural size in birds) is usually measured during the nestling stage in offspring, it was repeatedly confirmed that this trait does not change anymore later in life.

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Sibling analysis / ANOVA

Generation: t t

Sibship 1Sibship 2

0.25<r<0.50.25<r<0.5

Trait measured on individuals of same generation only, no parental trait measurements involvedCaution: trait should be measured at the same stage/age among sibships

Trait measured on individuals of same generation only, no parental trait measurements involvedCaution: trait should be measured at the same stage/age among sibships

Sibling analysis / ANOVA

Sibship ID

Body

wei

ght (

14 d

ays)

ModelErrorC. Total

Source72

446518

DF1639.4043513.9620

2153.3664

Sum ofSquares

22.76951.1524

Mean Square19.7587F Ratio

<.0001*Prob > F

Analysis of Variance

Parus major

SS: sum of squaresMS: mean squareDF/d.f.: degrees of freedom

Confounded by rearing environment

Sibships

5

Cross-fostering designs:1) complete cross-fostering

Beforeexperimental manipulation

After experimental manipulation


Good for parent-offspring regression. For sibling analysis, the common rearing environment still confounds genetic sources of similarity.

Cross-fostering designs:2) partial cross-fostering



Parent-offspring regressionand/or full-sib analysis

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Sibling analysis in cross-fostering designs→ Nested analysis of variance

Nest-pair

Nest of rearing

Nest of origin

Example: Pied flycatcher (Ficedula hypoleuca)

Merilä, J. 1996. Functional Ecology 10, 465-474.

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Example: Pied flycatcher (Ficedula hypoleuca) body condition

Rearing environment has strong effect on nestling condition. Effect of nest of origin also significant, and slightly larger in enlarged broods.

Origin(Rearing)

Origin(Rearing)

Cross-fostering designs:2) partial cross-fostering continued



Parent-offspring regressionand/or

full-sib analysis

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Example: Great tit (Parus major) begging call intensity

Kölliker et al. 2000. Proc R Soc Lond B 267, 2127-2132.

Group: group of three nests hatching on same day

Without additional experimental manipulations, it is impossible to be certain that there indeed are no environmental differences between the environments of the different individuals.

Common-garden designs

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From Roff, 1997

Common-garden designs

Breeding designs

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Diallel Crosses Among Inbred Lines (or among Genotypes); „North Carolina Designs“

♂

♀

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

XXXXXXXXXXXXXXXX

Full (factorial) diallel cross

L1 L2 L3 L4

L1

L2

L3

L4

♀

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

0000000

000

XXXXXX

Partial diallel cross

L1 L2 L3 L4

Paternal half-sib design

♂

♀ (female family ID, genotype)

⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

000

0000

000

000

0000

000

000

000

0000

0000

000

000

XXXX

XXXXXXX

X

XXXXXX

XXXXXX

1 2 3 4 5 6 7 8

1

2

3

4

5

6

7

8

Mal

e fa

mily

ID, g

enot

ype

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Breeding designs

♂♂♀♀ ♀♀

Full sibs

Paternal half-sibs

Breeding designs (improved design)→ in particular if there is maternal/paternal care

♂♂♀♀ ♀♀

Cross-fostering

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Combined Designs

• Common Garden + cross-fostering• Parent-offspring regression + cross-fostering• diallel-crosses + cross-fostering + parent-

offspring regression• sib-sib analyses among different types of sibs

(half-sibs versus full-sibs versus dizigotictwins versus monozygotic twins)

• Common Garden + cross-fostering• Parent-offspring regression + cross-fostering• diallel-crosses + cross-fostering + parent-

offspring regression• sib-sib analyses among different types of sibs

(half-sibs versus full-sibs versus dizigotictwins versus monozygotic twins)

Synergies among combinations of single approaches

Synergies among combinations of single approaches

Variance Components

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Variance components

Composition of phenotypic variance:

VP = VA + VD + VI + VE(model of phenotypic expression)

Composition of phenotypic variance:

VP = VA + VD + VI + VE(model of phenotypic expression)

Observational variance components (e.g., σ2

S, σ2D, σ2

W ):

proportion of phenotypic variance accounted for by particular sets of related individuals

(depends on experimental design)

Observational variance components (e.g., σ2

S, σ2D, σ2

W ):

proportion of phenotypic variance accounted for by particular sets of related individuals

(depends on experimental design)

Variance components

Causal variance components:

Estimates for VA, VD, VI and VE based on observational variance components

(depends on experimental design and the structure of genetic relatedness in the sample)

Causal variance components:

Estimates for VA, VD, VI and VE based on observational variance components

(depends on experimental design and the structure of genetic relatedness in the sample)

2

2

1σ

σ

rV

rV

A

A

=→

=

P

A

VVh =2

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ModelErrorC. Total

Source72

446518

DF1639.4043513.9620

2153.3664

Sum ofSquares

22.76951.1524

Mean Square19.7587F Ratio

<.0001*Prob > F

Analysis of Variance σ2A: obs. Varcomp among sibships

n: 519 chicksd: 73 nests (sibships)k: 7.11 chicks / sibship

MSA: mean square „Among“MSW: mean square „Within“

Calculation of variance componentsExample: full-sibling analysis

AmongWithin

dnk

kMSMS WA

A =−

= ;2σ

SS MS

Parus major body weight(see earlier example)

nestbox&RandomResidualTotal

Component3.0421291.1523814.19451

VarComp Est

72.52627.474

100.000

Percentof Total

These estimates based on equating Mean Squares to Expected Value

Variance Component Estimates

Observational Variance Component

AmongWithin

EcDAA VVV ++=41

212σ

Parus major body weight(see earlier example)

Calculation of variance componentsExample: full-sibling analysis

If we ASSUME siblings to be full-siblings, and dominance and common rearing environment variance to be negligible, we can estimate heritability as:

VEc: Variance due to common rearing environment

45.119.408.62 2

22 ===

Total

Ahσσ

Which is an impossible value. Thus, clearly the assumptions above are violated. Chicks in the same nest resemble each other more in terms of body weight than genetic relatedness could cause.In particular VEc is well-known to have strong impact -> cross-fostering experiments

Causal variance component

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Calculation of variance componentsExample: paternal half-sib breeding design

Calculation of variance componentsExample: paternal half-sib breeding design

(Chrysomelidae; Blattkäfer)

Iva frutescens: marsh elder(native to Florida‘s marshs)

Sire variance component

Dam variance component

Causal components of variance

Narrow-sense heritability

11.091.2*84.183.042.12 =

−=

−=

dkMSMS DS

Sσ

15.091.239.083.02 −

=−

=k

MSMS WDDσ

EcDAD

AS

VVV

V

++=

=

41

4141

2

2

σ

σ

68.039.015.011.0

11.0*44222

22 =

++=

++=

WDS

Shσσσ

σ

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Comparison of Experimental Designs

Heritability can depend on the environment

The environmental variancecomponent is part of thedenominator of the heritability

The environment can affectthe expressed geneticvariance (GxE interaction)

h2 = VA/VP

To widespread misconceptions about heritability:1. A heritability of 0 does not mean genes do not affect the expression of the

trait (example: number of legs in humans has a heritability of 0)2. A heritability of 1 does not mean the environment cannot affect the trait. A

change in the environment can still affect the mean of the trait (or change the heritability itself)

To widespread misconceptions about heritability:1. A heritability of 0 does not mean genes do not affect the expression of the

trait (example: number of legs in humans has a heritability of 0)2. A heritability of 1 does not mean the environment cannot affect the trait. A

change in the environment can still affect the mean of the trait (or change the heritability itself)

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Technical issues of design-optimization→ Multiple measurements of traits

r: „True“ (but usually unknown, here assumed)repeatabilities

Gain in accuracy from multiple measurements of each individual:The lower the accuracy of a single measure, or the more flexible the

trait, the more important to make multiple measurements

(n)

Varia

nce

of th

e m

ean

of n

mea

sure

men

ts a

s a

prop

ortio

n of

a s

ingl

e m

easu

rem

ent

0.1

0.25

0.5

0.75

Falconer & Mackay 1996

Technical issues of design-optimization→ Statistical Power and the trade-off between number and size of families


Statistical power (1-β): The likelihood of finding a significanteffect, if thehypothesized effect(here heritability) istruly present

Arnold 1994

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