The role of ecology in the adaptive process

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The role of ecology in the adaptive process

• Joachim Hermisson
• Mathematics MFPL, University of Vienna

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How does adaptive evolution proceed?
Origin of Species (1859) Adaptive evolution is
the product of natural selection on heritable
variation
Charles Darwin
Thomas Huxley
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How does adaptive evolution proceed?
Origin of Species (1859) Adaptive evolution is
the product of natural selection on heritable
variation
Charles Darwin
Thomas Huxley
Natural selection uses everyday variation and
evolution proceeds in many small steps
Small variants will get lost. Selection uses
occasional larger mutations
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How does adaptive evolution proceed?
Origin of Species (1859) Adaptive evolution is
the product of natural selection on heritable
variation
Charles Darwin
Thomas Huxley
Natural selection uses everyday variation and
evolution proceeds in many small steps
Small variants will get lost. Selection uses
occasional larger mutations
Many small steps or fewer larger steps?
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How does adaptive evolution proceed?
1900 1920s Biometricians vs. Mendelians
William Bateson
Karl Pearson

• Classical Darwinian view
• selection acts on small variation
• that is continuously produced
• Evolutionary gradualism

• Mendelian inheritance
• important role of discrete,
• large, and rare mutations
• Evolutionary saltationism

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How does adaptive evolution proceed?

• Modern Synthesis (1930s)
• Key points
• Mendelian inheritance
• Evolutionary gradualism

Ronald A. Fisher
Phenotypic adaptation proceeds through natural
selection on a large number of mutations of very
small effect
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How does adaptive evolution proceed? Fishers
geometric model
trait 2
optimum
Ronald A. Fisher
trait 1
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How does adaptive evolution proceed? Fishers
geometric model
trait 2
fitness w f(d)
d
Ronald A. Fisher
trait 1
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How does adaptive evolution proceed? Fishers
geometric model
trait 2
Ronald A. Fisher
trait 1
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How does adaptive evolution proceed? Fishers
geometric model
trait 2
Ronald A. Fisher
trait 1
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How does adaptive evolution proceed? Fishers
geometric model
trait 2
Ronald A. Fisher
trait 1
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How does adaptive evolution proceed? Fishers
geometric model
trait 2
Ronald A. Fisher
trait 1
Adaptation proceeds in many small steps
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How does adaptive evolution proceed?
?
Fisher / Darwin
Huxley
Small variants will get lost. Selection needs
occasional larger mutations to act on
Adaptation proceeds in many small steps
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How does adaptive evolution proceed?
?
Fisher / Darwin
Huxley / Kimura
Small variants will get lost. Selection needs
occasional larger mutations to act on
Adaptation proceeds in many small steps
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How does adaptive evolution proceed?
We need to distinguish new mutations and fixed
mutations
Selection and drift during the fixation
process act as a stochastic sieve
Motoo Kimura
stochastic
sieve
effect size
Distribution of beneficial mutations
Distribution of adaptive substitutions
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How does adaptive evolution proceed? State of
the art consensus

• Order of step sizes
• large adaptive steps before small steps
• Distribution of step sizes
• exponential distribution of adaptive
  substitutions

H.A. Orr Model calculations for the adaptive
response to a single sudden change of the
environment
Golf picture of adaptive evolution
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Adaptation to a variable environmentAn
ecologists view of the problem
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Adaptation to a variable environmentAn
ecologists view of the problem

• So far purely geneticists view of the adaptive
  process
• trivial ecology single and sudden
  environmental change
• constant selection
• But real selection pressures arise from variable
  environments

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Adaptation to a variable environmentAn
ecologists view of the problem

• So far purely geneticists view of the adaptive
  process
• trivial ecology single and sudden
  environmental change
• constant selection
• But real selection pressures arise from variable
  environments

Set of ecological sieves
?
effect size
Distribution of beneficial mutations
Distribution of adaptive substitutions
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Adaptation to a variable environmentA model
Quantitative trait with moving optimum
selection strength
moving optimum
fitness w
trait z
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Adaptation to a variable environmentA
physicists' perspective

• Dissecting the fixation process
• How does ecology affect the model?
• Ecology introduces a new time-scale in the
  fixation process
• Ecology important?
• For parameter values where the ecological
  time-scale dominates

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Adaptation to a variable environmentA
physicists' perspective
zopt(t) vt
Phenotype
A
Mutation at rate m
a
Time t
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Adaptation to a variable environmentA
physicists' perspective
zopt(t) vt
Frequency
Phenotype /
A
Mutation at rate m
a
Time t
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Adaptation to a variable environmentA
physicists' perspective
Fixation time TF
Waiting time TW
Lag time TL
Frequency
Phenotype /
A
Mutation at rate m
a
Time t
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Adaptation to a variable environmentA
physicists' perspective
Fixation time TF
Waiting time TW
Lag time TL
mutation selection
selection
ecology (speed v)
Frequency
Phenotype /
A
Mutation at rate m
a
Time t
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Adaptation to a variable environmentA race to
fixation
Frequency
Phenotype /
A
small
a
TWA gt TWB
TLA lt TLB
TFA gt TFB
vs.
Frequency
Phenotype /
B
large
b
Time
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Adaptation to a variable environmentFast
change Mutation limited regime
large v
Frequency
Phenotype /
A
a
Frequency
B
Phenotype /
b
Time
TW TF gtgt TL Advantage large (classical case)
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Adaptation to a variable environmentSlow
change Environmentally limited regime
small v
Frequency
Phenotype /
A
a
Frequency
B
Phenotype /
b
Time
TL gtgt TWTF Small allele fixes earlier
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Adaptation to a variable environmentDerivation
single locus

• Selection coefficient s(t), mutation parameter Q
• Main problem
• Waiting time Poisson process with inhomogeneous
  rate

Fixation probability for moving optimum selection
mutation input per generation
(x initial allele frequency)
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Adaptation to a variable environmentDerivation
single locus

• Problem Fixation under time-dependent selection
• Approach Diffusion theory
• describe fixation probability Pfix(t,x) by
  backward diffusion

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Adaptation to a variable environmentDerivation
single locus

• Problem Fixation under time-dependent selection
• Approach Diffusion theory
• describe fixation probability Pfix(t,x) by
  backward diffusion

ecology leads to time inhomogeneous equation
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Adaptation to a variable environmentDerivation
single locus

• Problem Fixation under time-dependent selection
• Approach Diffusion theory
• Approximate solution Branching process limit
  (small x)

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ResultsI. Order of adaptations Who is fastest?

single mutation z ? z a
optimum z(t) vt
Fastest mutation at a a defines the boundary
between the classical regime (larger faster)
and the environmentally limited regime.
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ResultsI. Order of adaptations Who is fastest?

speed v
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ResultsI. Order of adaptations Who is fastest?

• Small mutations favored for
• slow environmental change v
• large mutation rate Q
• strong selection s

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ResultsII. Distribution Who is most frequent?
Step sizes during an adaptive walk
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ResultsII. Distribution Who is most frequent?

• Model Multilocus trait with continuum of alleles
• Given distribution of new mutations
• e.g. uniform, Gaussian, exponential
• What is the distribution of adaptive
  substitutions?

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ResultsII. Distribution Who is most frequent?

• Model Multilocus trait with continuum of alleles
• Given distribution of new mutations
• e.g. uniform, Gaussian, exponential
• What is the distribution of adaptive
  substitutions?
• Approach Two time-scales
• Successful mutations affected by lag time and
  waiting time
• Fixation time can be ignored for the distribution
  problem

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ResultsII. Distribution The sieve function
stochastic
p(a)
a p(a)
sieve
a
a
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ResultsII. Distribution The sieve function
Uniform distribution of new mutations ? Sieve
stochastic
p(a)
a p(a)
sieve
a
a
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ResultsII. Distribution The sieve function
Uniform distribution of new mutations ? Sieve
Kimura sieve for sudden change Pfix a
a
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ResultsII. Distribution The sieve function
Uniform distribution of new mutations ? Sieve
1-dim family of sieves, depending on
parameter g v / Q s
a
Sieve maximally permeable at most favored
mutation
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ResultsII. Distribution of Adaptive
Substitutions
Mutation distribution
uniform
Gaussian
exponential
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ResultsII. Distribution of Adaptive
Substitutions
Mutation distribution
uniform
Gaussian
exponential

• Distribution of adaptive substitutions never
  exponential !

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ResultsII. Distribution of Adaptive
Substitutions
Slow environment environmentally limited
Fast environment mutationally limited
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ResultsII. Distribution of Adaptive
Substitutions
Exponential distribution p(a) exp(- a)
environm. limited
independent of p(a)
mutation limited
Kimura a p(a)
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ResultsPredictions and Data

• Most favored mutation
• Fastest mutation

same composite parameter
g v / Q s
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ResultsPredictions and Data

• typically in the range of observed
  mutations

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Summary3 Messages for Theoreticians

• Ecology matters !
• New phenomena in variable environments
• Small mutations can outcompete large mutations
• Non-exponential distribution of adaptive
  substitutions
• Time scales useful concept
• Fixation in a variable environment is governed by
  3 time scales
• More work needed for alternative ecological
  scenarios
• Collection of ecological stochastic sieves

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Summary3 Messages for Experimentalists

• Ecology matters !
• Do not rely on consensus predictions
• In particular distribution of adaptations not
  necessarily exponential
• Look for the following pattern Many small steps
  favored
• for slow change, strong mutation, strong
  selection
• small composite parameter g v / (Q s)
• Do experimental evolution with variable
  environment
• Slow / fast increase of temperature, salinity,
  etc

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Thanks !

• Michael Kopp
• ... and

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Effects of linkage
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Effects of linkage
(Q 20)
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Limited movement of the optimum