Genome Evolution. Amos Tanay 2009 Genome evolution Lecture 9: Quantitative traits

Genome Evolution. Amos Tanay 2009

Genome evolution

Lecture 9: Quantitative traits


Every meaningful evolutionary traits is ultimately quantitative

F. Galton

Continuous traits: Weight, height, milk yeild, growth rate

Categorical traits: Number of offspring, petals, ears on a stalk of corn

Threshold traits: disease (the underlying liability toward the trait)

Ultimately, fitness is a quantitative trait, so what is special about it?

Historically, research on genetics and directed selection were distinct from evolutionary theory

Currently, a quantitative approach to molecular evolution and population genetics is a major frontier in evolutionary research


The basic observation: heritability

22 )()()( xExExVar

)()()(),( yExExyEyxCov

2)]([ bxayESS

A linear fit would try to minimize the mean square deviation:

0)]()()([2))((2

0))()((2)(2

2

xbExaExyEbxayxEb

SS

xbEayEbxayEa

SS

)()(

),(

)(

),(

0])()([)]()()([ 22

yVarxVar

yxCovr

xVar

yxCovb

xExEbyExExyE

2

2

1hb

Heritability is defined:

(dividing because only one parent is considered)

This is the “narrow sense” heritability


Artificial selection

Over 100 years of an ongoing selection experiments

12

12

48

%O

il

From 4.6% to 20.4% oil

What kinds of evolutionary dynamics allow for such rapid increase in the trait?


Artificial selection

Selection can work by exploiting existing polymorphic sites

SNP data suggest that at least 50 genes were involved in the corn selection

or by fixating new mutations

Theory suggest that fixation of all strong effects should occur rapidly – 20 generations. Later one should see fixation of alleles with smaller effect or new mutations

)2ln()/2( Nst Remainder- Theorem (Kimura):

One strong candidate for introducing mutations are repetitive elements.

The corn population is of tiny size (60)

Selection is enhanced due to the threshold effect


Limits to artificial selection

After some (variable number of) generations, artificial selection stop increasing the trait

One reason for that can be the exhaustion of polymorphismThis is frequently not the case, since reversing the selection is frequently shown to have an effect – meaning polymorphisms is present

Another reason for converging trait values is selection on other traits (fertility!)

Using many allele affecting the trait, artificial selection can reach trait values that are practically never observed in the original population

Not all traits can be artificially selected: in 1960, Maynard-Smith and Sondhi showed they could not select for asymmetric body plan in flies by choosing flies with excess of dorsal bristles on the left side

This suggest that some traits are strongly stabilized

Artificial selection can proceed non-linearly: starting and stoppingA main possible reason for that is that recombination of strongly linked alleles takes time

J. Maynard-Smith


Truncation selection

M

MS

S = MS - M

R = M’ - M

M’

Response:

Differential:

The selection differential is generally larger than the selection response

This is because some of the selected offsprings are of high trait value due to non-genetic effects

Another reason is that the genotype of the selected offspring is modified by segregation and recombination

ShR 2

We redefine (realized) heritability as the ratio between selection differential and selection response


Back to genetics: two loci

4

3

2 1 0

2

23

1

AA

Aa

aa

BB Bb bb

MS = 0.8Selecting class 0 and 1

1/161/16

1/16 1/16

2/16

2/16

2/16

2/16 4/16p(A)=p(B) = 0.2After selection:

M’ = 0.8Yielding:

Generally: M=2(p(A)+p(B))

Assume additive selected trait

h2 = 1and

4

4

2 2 0

4

24

2

AA

Aa

aa

BB Bb bb

MS = 12/7Selecting class 2

1/161/16

1/16 1/16

2/16

2/16

2/16

2/16 4/16

p(A)=p(B) =2/7After selection:

M’ =96/49Yielding:

Assume dominant selected trait

h2 =17/21=0.81and


Continuous traits

M

MS

BZ

T

(MS-M)/

AA

AA’

A’A’

2''AAAA mm

m

2''AAAA mm

a

mmd AA '

We now assume each genotype have a distribution of trait values

The variability may be a consequence of environmental factors or other loci

m – meana – additivityd = dominance

ammAA

amm AA ''dmmAA '

pqdaqpm

amqdmpqampM

2)(

)()(2)( 22

dpqpqpqa

ppqdaqpmpqdappm

)(22

)2](2)([222 2

Cov(pheno, number of A alleles)=

Var(number of A alleles)=22 )2(24 ppqp

dpqapq

dqppqpqab )(

2

)(22


Continuous traits

M

MS

BZ

T

(MS-M)/

AA

AA’

A’A’

2''AAAA mm

m

2''AAAA mm

a

mmd AA '

ammAA

amm AA ''

dmmAA '

aT dT

aT

Selecting on a threshold over the mean of the population (T)

Thresh relative to AA normal distrib

Thresh relative to AA’ normal distrib

Thresh Relative to A’A’ normal distrib

The “fitness” equals the ratio between the areas beyond the threshold

Assuming small differences we have rectangular areas:

)())()((1211 daZaTdTZww

)())()((2212 daZdTaTZww


Allele frequency change

M

MS

BZ

T

(MS-M)/

AA

AA’

A’A’

2''AAAA mm

m

2''AAAA mm

a

mmd AA '

ammAA

amm AA ''

dmmAA '

We showed before (lecture 3):

)())()((1211 daZaTdTZww

)())()((2212 daZdTaTZww

wwwqwwppqp /)]()([ 22121211

BdaqZdapZpqp /)]()([

Average fitness is the area B:

])([)/( dpqapqBZp

SelectionIntensity

Allelefrequency

Phenotype to genotyperegression


Mean Phenotype

M

MS

BZ

T

(MS-M)/

AA

AA’

A’A’

2''AAAA mm

m

2''AAAA mm

a

mmd AA '

ammAA

amm AA ''

dmmAA 'pdpqaM

ppqaamqdmpqamp

ampqdmpqppamppM

])([2

)]([2)()(2)(

)()())()((2)()('22

22

])([)/( dpqapqBZp

SelectionIntensity

Allelefrequency

Phenotype to genotyperegression

22

22

2

/])([2

/])([2)(

])([2)/(

])([2'

dpqapqSR

dpqapqMM

dpqapqBZ

pdpqaMM

S

222 /])([2 dpqapqh


Phenotype variation

Phenotypes in natural environment can be modeled as a combination of genotype and environmental effects:

EGP

More carefully, the genotype effect on phenotype may is a function of the environment, and the additive form may be wrong

For example, gene expression of stress related genes depends on the genotype differently for different stresses

Understanding QTL evolution

Mapping phenotypes to QTL


Genetic analysis of genome-wide variation in human gene expression (Morely et al. 2004)

14 CEPH families (of ~8 members each)

3554 variable expression genes (in lymphoblastoid cells)

2756 SNPs (just a few!)

Alternatively: 94 unrelated CEPH grandfathers

Testing linkage of expression and SNPs in the large family trees yield linkage for ~1000 phenotypes

The test on families use the genealogical structure (SIBPAL - http://darwin.cwru.edu/)

Alternative test on unrelated individuals use simple correlation of the 0,1,2 individual

Difficulties: multiple testing vs low resolution

Reporting on loci that are linked with many QTLs


Variability in B-cells response to irradiation

Mapped eQTL15 CEPH families (of ~8 members each)

Low resolution ~3000 SNPS, and high resolution HapMap SNPS,

3280 responding genes – different time points during irradiation

Follow up molecular biology experiments

Genetic analysis of radiation-induced changes in human gene expression (Smirnov 2009)


Genetic Dissection of Transcriptional Regulation in Budding Yeast (Brem et al 2002)

Crossing two budding yeast strains

Fully genotyping, testing expression (later in different conditions)

Hundred of variably expressed genes

Using the compact yeast genome help deciding linkage

Using the well-characterized biology of yeast helps explain linkage


Building association to groups of genes instead of single genes (Litvin et al 2009)

©2009 by National Academy of Sciences

Identifying regulatory mechanisms using individual variation reveals key role for chromatin modification (Lee et al 2008)


Schadt EE et al. 2005 (and many publications following it)

R – expressionL – locus genoetype

C - phenotype

Looking for gene expression traits that explain QTLs – stands between genetic loci and some disease trait of interest

Applied to obesity linkage (in mice)

Further development use more data (not just expression), or gene subnetworks

Ultimate goal is to build a model explaining phenotype by genotype through molecular phenotypes

Possible modes of causality or interaction

Positive correlation suggests linked eQTLs

Correlation between genetic distance and correlation suggests LD effect


(a) The horizontal axis shows the frequency from the NMR spectrum expressed as chemical shift from right to left ( , ppm). The vertical axis indicates genetic locations (cM) on chromosomes 1 to X. The lod scores between each genotype and each metabolite are color coded. Significant linkages between genomic locations and regions of the plasma NMR profile are present in the aliphatic region (0.5 to 4.5 ppm) and the aromatic region (>5.5 ppm). Resonances corresponding to the anesthetics and their degradation products were withdrawn as described in Methods. (b,c) Genome-wide linkage mapping across the full metabonomic spectrum for marker D14Wox10 (b) and linkage data across the genome for the metabolite 7.86 (c).

Direct quantitative trait locus mapping of mammalian metabolic phenotypes in diabetic and normoglycemic rat models (Dunas et al. 2007)

Crossing two rat strains: diabitic and normal

2000 microsatellite and SNP markers

Using NMR to perform metabolic profiling – looking for linkage explaining metabolic abnormalities

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Genome Evolution. Amos Tanay 2009 Genome evolution Lecture 9: Quantitative traits