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Adaptation in polygenic traits Criteria for sweeps and shifts - - PowerPoint PPT Presentation

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS Adaptation in polygenic traits Criteria for sweeps and shifts Joachim Hermisson Mathematics & Biology, University of Vienna POLYGENIC ADAPTATION: SWEEPS & SHIFTS Adaptation in polygenic

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Joachim Hermisson

Mathematics & Biology, University of Vienna

Adaptation in polygenic traits

Criteria for sweeps and shifts

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Adaptation in polygenic traits

Ilse Hölliger

University of Vienna

Pleuni Pennings

San Francisco State University

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Adaptive scenarios

“Sweeps“

  • adaptation due to

independent large changes at single loci

  • clear molecular footprint

“Shifts“

  • adaptation due to

small collective shifts at many loci

  • no clear sweep pattern

molecular popgen quantitative genetics

Pritchard et al. 2010

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Adaptive scenarios

“Sweeps“

  • adaptation due to

independent large changes at single loci

  • clear molecular footprint

“Shifts“

  • adaptation due to

small collective shifts at many loci

  • no clear sweep pattern

molecular popgen quantitative genetics

Pritchard et al. 2010

Which scenario should we expect

?

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Adaptive scenarios

Assume:

  • panmictic population, new selection pressure
  • adaptation from mutation-selection-drift balance

new mutation standing genetic variation few loci many loci weak selection strong selection weak mutation strong mutation

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Adaptive scenarios

Assume:

  • Which scenario is favored under which conditions ?
  • panmictic population, new selection pressure
  • adaptation from mutation-selection-drift balance

new mutation standing genetic variation few loci many loci weak selection strong selection weak mutation strong mutation

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS trait Z fitness W Zopt

𝑋 𝑎 = exp −𝜏

2(𝑎 − 𝑎opt)2

Z0

𝑗=1 𝑀 𝛿𝑞𝑗

𝑎 =

Additive quantitative trait

under stabilizing selection

  • 𝑂 haploids, 𝑀 biallelic loci
  • recurrent mutation 𝜄𝑗 = 2𝑂𝑣𝑗
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POLYGENIC ADAPTATION: SWEEPS & SHIFTS trait Z fitness W Zopt

𝑋 𝑎 = exp −𝜏

2(𝑎 − 𝑎opt)2

Z0

𝑗=1 𝑀 𝛿𝑞𝑗

𝑎 =

Additive quantitative trait

under stabilizing selection

  • 𝑂 haploids, 𝑀 biallelic loci
  • recurrent mutation 𝜄𝑗 = 2𝑂𝑣𝑗
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POLYGENIC ADAPTATION: SWEEPS & SHIFTS trait Z fitness W Zopt

𝑋 𝑎 = exp −𝜏

2(𝑎 − 𝑎opt)2

Z0

𝑎

Z1

𝑗=1 𝑀 𝛿𝑞𝑗

𝑎 =

Additive quantitative trait

under stabilizing selection

  • 𝑂 haploids, 𝑀 biallelic loci
  • recurrent mutation 𝜄𝑗 = 2𝑂𝑣𝑗
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POLYGENIC ADAPTATION: SWEEPS & SHIFTS trait Z fitness W Zopt

𝑋 𝑎 = exp −𝜏

2(𝑎 − 𝑎opt)2

Z0

𝑎

Z1

“Architecture of polygenic adaptation”

joint distribution

  • f allele frequencies 𝑞𝑗:

𝑗=1 𝑀 𝛿𝑞𝑗

𝑎 =

Additive quantitative trait

under stabilizing selection

  • 𝑂 haploids, 𝑀 biallelic loci
  • recurrent mutation 𝜄𝑗 = 2𝑂𝑣𝑗
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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

  • 𝑂 haploids, 𝑀 biallelic loci
  • recurrent mutation 𝜄𝑗 = 2𝑂𝑣𝑗
  • fitness function (e.g. resistance):

1+ sb # mut. 2 1 3 1 fit. # mut. 2 1 3 1 fit. 1- sd before env. change after env. change wt mutant phenotype

Binary trait

with complete redundancy

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

  • 𝑂 haploids, 𝑀 biallelic loci
  • recurrent mutation 𝜄𝑗 = 2𝑂𝑣𝑗
  • fitness function (e.g. resistance):

1+ sb # mut. 2 1 3 1 fit. # mut. 2 1 3 1 fit. 1- sd before env. change after env. change wt mutant phenotype

Binary trait

with complete redundancy

𝑋 𝑎 = 1 ± 𝑡𝑐,𝑒 𝑎

  • freq. of mutant phenotype

𝑎 = 1 −

𝑗=1 𝑀

(1 − 𝑞𝑗)

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Maths of polygenic adaptation

Evolutionary trajectories (2 loci, schematic):

1st locus 2nd locus sampling rapid phenotypic adaptation slow change (neutral) time

(SGV or)

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS establishment phase stochastic: mutation & drift competition phase deterministic: selection & epistasis

Maths of polygenic adaptation

Evolutionary trajectories (2 loci, schematic):

1st locus 2nd locus sampling rapid phenotypic adaptation slow change (neutral) time

(SGV or)

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

  • track only mutant copies destined for establishment, prob. 𝑞est(𝑡𝑐, 𝑡𝑒; 𝜏, 𝛿)

locus 1 locus 2

  • split rate (reproduction) ~ 𝑞est

~ 𝜄𝑗 ∙ 𝑞est

  • new lines (mutation)

per line per locus 𝑜1, 𝑜2, … copies at all loci time

Establishment phase (both models): Yule branching process

Maths of polygenic adaptation

mutation and drift during establishment create stochastic differences among loci

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

  • ratios

independent of

  • track only mutant copies destined for establishment, prob. 𝑞est(𝑡𝑐, 𝑡𝑒; 𝜏, 𝛿)

locus 1 locus 2

  • split rate (reproduction) ~ 𝑞est

~ 𝜄𝑗 ∙ 𝑞est

  • new lines (mutation)

per line per locus 𝑜1, 𝑜2, … copies at all loci time 𝑦𝑗 = 𝑜𝑗/𝑜1 𝑡𝑐/𝑒; 𝜏, 𝛿

Establishment phase (both models): Yule branching process

Maths of polygenic adaptation

mutation and drift during establishment create stochastic differences among loci

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

  • ratios

independent of

  • joint distribution of frequency ratios 𝑦𝑗

depends only on mutation rates 𝜄𝑗:

  • track only mutant copies destined for establishment, prob. 𝑞est(𝑡𝑐, 𝑡𝑒; 𝜏, 𝛿)

locus 1 locus 2

  • split rate (reproduction) ~ 𝑞est

~ 𝜄𝑗 ∙ 𝑞est

  • new lines (mutation)

per line per locus 𝑜1, 𝑜2, … copies at all loci time 𝑦𝑗 = 𝑜𝑗/𝑜1 𝑡𝑐/𝑒; 𝜏, 𝛿

Establishment phase (both models): Yule branching process

Maths of polygenic adaptation

mutation and drift during establishment create stochastic differences among loci

(inverted Dirichlet distribution)

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Competition phase: binary trait model

  • deterministic dynamics

𝑞𝑗 = 𝑞𝑗𝑡𝑐 1 − 𝑎

⟹ 𝑒 𝑒𝑢 𝑞𝑗 𝑞𝑘 = 0

  • maintains ratios
  • zooms up differences

Maths of polygenic adaptation

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Competition phase: binary trait model

  • deterministic dynamics

𝑞𝑗 = 𝑞𝑗𝑡𝑐 1 − 𝑎

⟹ 𝑒 𝑒𝑢 𝑞𝑗 𝑞𝑘 = 0

  • maintains ratios
  • zooms up differences

Maths of polygenic adaptation

  • joint distribution of mutant frequencies 𝑞𝑗 at

𝑎 = 1 − 𝑔

𝑥 :

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Competition phase: binary trait model

  • deterministic dynamics

𝑞𝑗 = 𝑞𝑗𝑡𝑐 1 − 𝑎

⟹ 𝑒 𝑒𝑢 𝑞𝑗 𝑞𝑘 = 0

  • maintains ratios
  • zooms up differences

Maths of polygenic adaptation

  • joint distribution of mutant frequencies 𝑞𝑗 at

𝑎 = 1 − 𝑔

𝑥 :

  • depends only on mutation rates 𝜄𝑗
  • independent of selection strength 𝑡𝑐, 𝑡𝑒
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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Competition phase: quantitative trait

Maths of polygenic adaptation

  • deterministic dynamics (LE and weak selection)

𝑞𝑗 = 𝑞𝑗 1 − 𝑞𝑗 𝜏𝛿 𝑎opt − 𝑎 + 𝜏𝛿2(2𝑞𝑗 − 1)

directional selection disruptive selection

[DeVladar/Barton 2014 Jain/Stephan 2017]

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Competition phase: quantitative trait

Maths of polygenic adaptation

  • deterministic dynamics (LE and weak selection)

𝑞𝑗 = 𝑞𝑗 1 − 𝑞𝑗 𝜏𝛿 𝑎opt − 𝑎

directional selection

[DeVladar/Barton 2014 Jain/Stephan 2017]

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Competition phase: quantitative trait

Maths of polygenic adaptation

  • deterministic dynamics (LE and weak selection)

𝑞𝑗 = 𝑞𝑗 1 − 𝑞𝑗 𝜏𝛿 𝑎opt − 𝑎

⟹ 𝑒 𝑒𝑢 𝑧𝑗 𝑧𝑘 = 0

𝑧𝑗 ≔

𝑞𝑗 1−𝑞𝑗

[DeVladar/Barton 2014 Jain/Stephan 2017]

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Competition phase: quantitative trait

Maths of polygenic adaptation

  • deterministic dynamics (LE and weak selection)

𝑞𝑗 = 𝑞𝑗 1 − 𝑞𝑗 𝜏𝛿 𝑎opt − 𝑎

⟹ 𝑒 𝑒𝑢 𝑧𝑗 𝑧𝑘 = 0

𝑧𝑗 ≔

𝑞𝑗 1−𝑞𝑗

  • joint distribution of mutant frequencies 𝑞𝑗 at

𝑎 = 𝑎1 = 𝛿𝑑𝑎 :

[DeVladar/Barton 2014 Jain/Stephan 2017]

  • depends only on mutation rates 𝜄𝑗
  • independent of locus effect and selection strength 𝛿, 𝜏
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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Results: binary trait

  • equal loci, 𝜄𝑗 = 𝜄
  • start in mutation-selection-drift balance
  • adaptation until 95% mt phenotypes (

𝑎 = 1 − 𝑔

𝑥 = 0.95)

  • loci ordered according to their contribution to the adaptive

response:

– locus with largest frequency: major locus – all other loci: minor loci

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

𝜄

𝑞< 𝑞>

Relative adaptive response (2 loci)

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

𝜄

𝑞< 𝑞>

Relative adaptive response (2 loci)

N = 10000, sampling at 95% mt. phenotype

sbN = sdN = 1000, LE

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

𝜄

𝑞< 𝑞>

Relative adaptive response (2 loci)

N = 10000, sampling at 95% mt. phenotype

sbN = sdN = 1000, LE

homogeneous heterogeneous individual collective

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Influence of selection?

Relative adaptive response (2 loci)

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

𝜄

𝑞< 𝑞>

Relative adaptive response (2 loci)

N = 10000, sampling at 95% mt. phenotype

sbN = 1000 sbN = 100

sdN = 1000

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

How about adaptation from standing genetic variation?

Relative adaptive response (2 loci)

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

𝜄

𝑞< 𝑞>

Relative adaptive response (2 loci)

N = 10000, sampling at 95% mt. phenotype

sbN = 1000

low SGV; sd N = 1000 high SGV; sd N = 10

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Architecture of polygenic adaptation

allele frequencies with complete redundancy

2 loci 10 loci 100 loci allele frequency

N = 10000, sb = sd = 0.1, LE

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

𝜄 = 0.01

Architecture of polygenic adaptation

allele frequencies with complete redundancy

minor locus major locus

sweep @ single major locus

2 loci 10 loci 100 loci allele frequency

N = 10000, sb = sd = 0.1, LE

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

𝜄 = 0.01

Architecture of polygenic adaptation

allele frequencies with complete redundancy

minor locus major locus 9 minors 1 major 99 minors 1 major

sweep @ single major locus

2 loci 10 loci 100 loci allele frequency

𝜄bg = 𝑀 − 1 𝜄 = 0.01

(≈ “genome-wide 𝜄”)

N = 10000, sb = sd = 0.1, LE

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Architecture of polygenic adaptation

allele frequencies with complete redundancy

minor major

partial sweeps & strong major/minor structure

2 loci 10 loci 100 loci allele frequency

𝜄bg = 𝑀 − 1 𝜄 = 1

1 major sum over 9 minors sum over 99 minors 1 major

N = 10000, sb = sd = 0.1, LE

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Architecture of polygenic adaptation

allele frequencies with complete redundancy partial sweeps & strong major/minor structure

2 loci 10 loci 100 loci allele frequency 2nd 3rd 1st 2nd 3rd 1st 1st

𝜄bg = 𝑀 − 1 𝜄 = 1

N = 10000, sb = sd = 0.1, LE

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Architecture of polygenic adaptation

allele frequencies with complete redundancy partial sweeps & strong major/minor structure

2 loci 10 loci 100 loci allele frequency

𝜄bg = 1, Yule approximation

N = 10000, sb = sd = 0.1, LE

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Architecture of polygenic adaptation

allele frequencies with complete redundancy partial sweeps & strong major/minor structure

2 loci 10 loci 100 loci allele frequency 2nd 3rd 1st 2nd 3rd 1st

𝜄bg = 1, Yule approximation

N = 10000, sb = sd = 0.1, LE

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Architecture of polygenic adaptation

allele frequencies with complete redundancy shifts @ many loci

2 loci 10 loci 100 loci allele frequency

𝜄bg = 𝑀 − 1 𝜄 = 100

N = 10000, sb = sd = 0.1, LE

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Results: quantitative trait

  • equal loci, 𝜄𝑗 = 𝜄
  • start from mutation-selection-drift balance with some initial

trait optimum 𝑎0

  • adaptation from SGV and new mutations until mean

phenotype reaches a threshold value, 𝑎 = 𝑎1 < 𝑎opt

  • loci ordered according to their contribution to the adaptive

response

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Adaptive architecture

additive trait: single adaptive step

4 loci, 𝑎 𝛿 : 2 → 3 10 loci, 𝑎 𝛿 : 5 → 6 100 loci, 𝑎 𝛿 : 50 → 51

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Adaptive architecture

additive trait: single adaptive step

4 loci, 𝑎 𝛿 : 2 → 3 10 loci, 𝑎 𝛿 : 5 → 6 100 loci, 𝑎 𝛿 : 50 → 51

“sweeps” “partial sweeps” “shifts”

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Adaptive architecture

additive trait: adaptation over larger distances

10 loci, 𝑎opt/𝛿: 0 → 10

𝑎 𝛿 = 1 𝑎 𝛿 = 3 𝑎 𝛿 = 9 𝑎 𝛿 = 6

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Adaptive architecture

additive trait: adaptation over larger distances

10 loci, 𝑎opt/𝛿: 0 → 10, effective 𝜄𝑐𝑕 = (𝑀 − 𝑎/𝛿)𝜄 : decreasing redundancy

𝑎 𝛿 = 1 𝑎 𝛿 = 3 𝑎 𝛿 = 9 𝑎 𝛿 = 6 𝜄𝑐𝑕 = 0.001 𝜄𝑐𝑕 = 0.01 𝜄𝑐𝑕 = 0.1

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Adaptive architecture

additive trait: adaptation over larger distances

10 loci, 𝑎opt/𝛿: 0 → 10, effective 𝜄𝑐𝑕 = (𝑀 − 𝑎/𝛿)𝜄 : decreasing redundancy

𝑎 𝛿 = 1 𝑎 𝛿 = 3 𝑎 𝛿 = 9 𝑎 𝛿 = 6 𝜄𝑐𝑕 = 0.001 𝜄𝑐𝑕 = 0.01 𝜄𝑐𝑕 = 0.1

full model?

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Adaptive architecture

additive trait: adaptation over larger distances

10 loci, 𝑎opt/𝛿: 0 → 10, effective 𝜄𝑐𝑕 = (𝑀 − 𝑎/𝛿)𝜄 : decreasing redundancy

𝑎 𝛿 = 1 𝑎 𝛿 = 3 𝑎 𝛿 = 9 𝑎 𝛿 = 6 𝜄𝑐𝑕 = 0.001 𝜄𝑐𝑕 = 0.01 𝜄𝑐𝑕 = 0.1

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Summary: limitations & generalizations

Analytical approximation for joint distribution of mutant frequencies … at loci with equal effect on the trait assuming linkage equilibrium

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

𝑋 𝑎 = exp −𝜏(𝑢)

2 (𝑎 − 𝑎opt(𝑢))2

Summary: limitations & generalizations

Analytical approximation for joint distribution of mutant frequencies … at loci with equal effect on the trait assuming linkage equilibrium

  • locus mutation rates can differ
  • selection strength / trait optimum can depend on time
  • background variation due to loci of arbitrary effect

𝑗=1 𝑀 𝛿𝑞𝑗 + 𝑎𝐶(𝑢)

𝑎 =

focal QTL background

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

𝑋 𝑎 = exp −𝜏(𝑢)

2 (𝑎 − 𝑎opt(𝑢))2

Summary: limitations & generalizations

Analytical approximation for joint distribution of mutant frequencies … at loci with equal effect on the trait assuming linkage equilibrium

  • locus mutation rates can differ
  • selection strength / trait optimum can depend on time
  • background variation due to loci of arbitrary effect

𝑗=1 𝑀 𝛿𝑞𝑗 + 𝑎𝐶(𝑢)

𝑎 =

focal QTL background

Adaptive architecture as function of mean phenotype

  • independent of selection strength

𝜏, 𝛿, 𝑎opt (resp. 𝑡𝑐,𝑡𝑒)

  • only depends on the mutation rate

𝜄bg = (𝑀 − 1)𝜄

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Three scenarios of polygenic adaptation

for adaptation from mutation-selection-drift balance 𝜄bg: “effective redundancy”, measures competition due to potential adaptation at alternative loci

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

  • 𝜄bg ≲ 0.1 ∶

sweep @ single major locus

  • usually hard sweep from new mutation
  • 0.1 ≲ 𝜄bg ≲ 10 ∶ major-minor locus pattern of adaptation
  • (almost) completed sweep from SGV at major locus
  • partial (hard or soft) sweeps at several minor loci
  • 𝜄bg ≳ 10 ∶

small frequency shifts @ many loci

  • no clear selection footprint in linked variation

Three scenarios of polygenic adaptation

for adaptation from mutation-selection-drift balance 𝜄bg: “effective redundancy”, measures competition due to potential adaptation at alternative loci

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

How should we explain evidence for adaptation by small shifts (size / weight / yield traits)?

Scenarios of polygenic adaptation

by small frequency shifts

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Scenarios of polygenic adaptation

by small frequency shifts

How should we explain evidence for adaptation by small shifts (size / weight / yield traits)?

  • really “small shifts”?
  • “slow sweeps” at small-effect loci ?
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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

How should we explain evidence for adaptation by small shifts (size / weight / yield traits)?

  • really “small shifts”?
  • “slow sweeps” at small-effect loci ?
  • 𝜄bg ≈ 2𝑀𝑂𝑓𝑣 is large:
  • large “omnigenic” basis 𝑀 > 10000 ?
  • large “short-term 𝑂𝑓” ?

Scenarios of polygenic adaptation

by small frequency shifts

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

How should we explain evidence for adaptation by small shifts (size / weight / yield traits)?

  • really “small shifts”?
  • “slow sweeps” at small-effect loci ?
  • 𝜄bg ≈ 2𝑀𝑂𝑓𝑣 is large:
  • large “omnigenic” basis 𝑀 > 10000 ?
  • large “short-term 𝑂𝑓” ?
  • initial allele frequencies more homogeneous than predicted

by mutation-selection-drift balance

  • balancing selection ? (but implies constraint)
  • spatial structure or admixture ?

Scenarios of polygenic adaptation

by small frequency shifts

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

More than sweeps or shifts

Pattern of stalled partial sweeps:

  • predicted in large and relevant parameter region
  • strongly heterogeneous even among loci with identical effect
  • should also be heterogeneous among replicates / for parallel

adaptation (“zoomed-up stochasticity”)

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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

More than sweeps or shifts

Pattern of stalled partial sweeps:

  • predicted in large and relevant parameter region
  • strongly heterogeneous even among loci with identical effect
  • should also be heterogeneous among replicates / for parallel

adaptation (“zoomed-up stochasticity”)

Evidence ?

  • a lot of evidence for partial sweeps
  • strong completed sweeps are rare
  • plateauing of allele trajectories in experimental evolution
  • strongly heterogeneous among replicates
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POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Thanks!

Ilse Hölliger Pleuni Pennings

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SLIDE 60

POLYGENIC ADAPTATION: SWEEPS & SHIFTS Equal levels of SGV at many loci … 𝑂 𝑣 𝑡𝑒 = 𝜄 2𝑡𝑒 … should lead to equal proportions after adaptation 𝑜𝑗/𝑜𝑘

Relative adaptive response (2 loci)

slide-61
SLIDE 61

POLYGENIC ADAPTATION: SWEEPS & SHIFTS Equal levels of SGV at many loci … 𝑂 𝑣 𝑡𝑒 = 𝜄 2𝑡𝑒 … should lead to equal proportions after adaptation 𝑜𝑗/𝑜𝑘 But: levels of SGV in mutation-selection-drift balance are stochastic and have a large variance

frequency

  • no. of copies

𝜄 2𝑡𝑒

𝜄 = 0.1; 𝑡𝑒 = 0.01; 𝑡𝑐 = 0.1

  • Same major-minor locus structure

as for new mutation

Relative adaptive response (2 loci)

slide-62
SLIDE 62

POLYGENIC ADAPTATION: SWEEPS & SHIFTS

How about linkage disequilibrium ?

Relative adaptive response (2 loci)

slide-63
SLIDE 63

POLYGENIC ADAPTATION: SWEEPS & SHIFTS

Relative adaptive response (2 loci)

𝑞< 𝑞>

𝜄

sbN = sdN = 1000

N = 10000, sampling at 95% mt. phenotype