hannes svardal - the role of environmental variance as adaptive response to fluctuating selection
TRANSCRIPT
Pourquoi suis-je ici?
Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 1 / 18
Does fluctuating selection favour an increase inenvironmental or in genetic variance?
Hannes Svardal, Claus Rueffler, and Joachim Hermisson
Institute of Mathematics, University of Vienna
1. Juni 2010
Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 2 / 18
Observations
Quantitative traits show considerable amounts of phenotypic variation
Variation could be adaptive (favoured by selection) or a constraint(mutation selection balance)
We are looking at adaptive sources of phenotypic variation
Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 3 / 18
Sources of phenotypic variance in a quantitative trait
phenotypic variance
genetic environmental
random GxE interaction
phenotypicplasticity
discretemorphs
Gaussiannoise
geneticpolymorphism
Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 4 / 18
Sources of phenotypic variance in a quantitative trait
phenotypic variance
genetic environmental
random GxE interaction
phenotypicplasticity
discretemorphs
Gaussiannoise
geneticpolymorphism
Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 4 / 18
Genetic polymorphism VS environmental decanalisation
phenotypic variance
genetic environmental
Gaussiannoise
geneticpolymorphism
genetically controlled viagenetic contribu-tion to a trait
degree of canali-sation of the trait
why adaptive?frequency depen-dent selection
as bet-hedgingstrategy
if both are adaptive:
? ?what
evolves?
Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 5 / 18
Genetic polymorphism VS environmental decanalisation
phenotypic variance
genetic environmental
Gaussiannoise
geneticpolymorphism
genetically controlled viagenetic contribu-tion to a trait
degree of canali-sation of the trait
why adaptive?frequency depen-dent selection
as bet-hedgingstrategy
if both are adaptive:
? ?what
evolves?
Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 5 / 18
Genetic polymorphism VS environmental decanalisation
phenotypic variance
genetic environmental
Gaussiannoise
geneticpolymorphism
genetically controlled viagenetic contribu-tion to a trait
degree of canali-sation of the trait
why adaptive?frequency depen-dent selection
as bet-hedgingstrategy
if both are adaptive:
? ?what
evolves?
Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 5 / 18
Genetic polymorphism VS environmental decanalisation
phenotypic variance
genetic environmental
Gaussiannoise
geneticpolymorphism
genetically controlled viagenetic contribu-tion to a trait
degree of canali-sation of the trait
why adaptive?frequency depen-dent selection
as bet-hedgingstrategy
if both are adaptive:
? ?what
evolves?
Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 5 / 18
Genetics
Clonal reproduction
Phenotype is a quantitative trait x
Phenotype is determined by genetic component µx and randomenvironmental effects (Gaussian noise with variance σ2x)
Amount of environmental canalisation genetically controlled:σx heritable
Probability that a genotype (µx, σx) produces a phenotype x:
µx
σx
x
prob
abili
ty
heritable canalisation
heritable genetic component
Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 6 / 18
canalised
a lot of noise
Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 7 / 18
The question
Most models treat fully canalised genotypes (µx, σx) = (x, 0)
x
We compare selection for genetic polymorphisms in µx to selection forincreased σx:
µx2
σx2
µx1
σx1
x
VS
µx
σx
x
In models where both – genetic polymorphism and environmental
decanalisation – are adaptive: What does evolve?Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 8 / 18
The Lottery model (Chesson and Warner 1981): Temporalvariation in selective optimum
Ecological assumptions:
discrete generations
maximum population size K
generation overlap γ⇒ ∼ (1− γ)K adults die each year, no selection on adults
Selection on juveniles:
selective optimum θ changes from year to year(but has stationary distribution with mean µθ, variance σ2θ)
Gaussian selection of strength 1/σ2s on distance |x− θ|surviving juveniles randomly compete to fill up the population sizeback to K
(equivalent to the seed bank model)
Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 9 / 18
Model ingredients
optimal phenotype θ
σθ
occurrence probability
θt
external environment:optima distribution withmean µθ and variance σ2θ
µθ
p
θ1
1− p
θ2
special caseexternal environment:optima distribution withmean µθ and variance σ2θ
µx
σx
phenotype x
heritablegenotypic values:µx and σx determine gene-tic contribution and noiselevel
freq
uen
cy
x
0 |x− θt|
σs
surv
ival
selection: depends on diffe-rence optimum⇔phenotype
Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 10 / 18
Model ingredients
optimal phenotype θ
σθ
occurrence probability
θt
external environment:optima distribution withmean µθ and variance σ2θ
µθ
p
θ1
1− p
θ2
special case
external environment:optima distribution withmean µθ and variance σ2θ
µx
σx
phenotype x
heritablegenotypic values:µx and σx determine gene-tic contribution and noiselevel
freq
uen
cy
x
0 |x− θt|
σs
surv
ival
selection: depends on diffe-rence optimum⇔phenotype
Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 10 / 18
Model ingredients
optimal phenotype θ
σθ
occurrence probability
θt
external environment:optima distribution withmean µθ and variance σ2θ
µθ
p
θ1
1− p
θ2
special case
external environment:optima distribution withmean µθ and variance σ2θ
µx
σx
phenotype x
heritablegenotypic values:µx and σx determine gene-tic contribution and noiselevel
freq
uen
cy
x
0 |x− θt|
σs
surv
ival
selection: depends on diffe-rence optimum⇔phenotype
Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 10 / 18
Model ingredients
optimal phenotype θ
σθ
occurrence probability
θt
external environment:optima distribution withmean µθ and variance σ2θ
µθ
p
θ1
1− p
θ2
special case
external environment:optima distribution withmean µθ and variance σ2θ
µx
σx
phenotype x
heritablegenotypic values:µx and σx determine gene-tic contribution and noiselevel
freq
uen
cy
x
0 |x− θt|
σs
surv
ival
selection: depends on diffe-rence optimum⇔phenotype
Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 10 / 18
The two possibilities independently
selected if
decanalisation (σx > 0) σ2θ > σ2s
σ2θ
σ2s noise
genetic polymporphism(disruptive selection in µx)
γσ2θ > σ2s
γσ2θ
σ2s genetic p.
Now: analysis of evolution in the 2D”genotype-space“ (µx, σx):
σx
µxµθ
Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 11 / 18
The two possibilities independently
selected if
decanalisation (σx > 0) σ2θ > σ2s
σ2θ
σ2s noise
genetic polymporphism(disruptive selection in µx)
γσ2θ > σ2s
γσ2θ
σ2s genetic p.
Now: analysis of evolution in the 2D”genotype-space“ (µx, σx):
σx
µxµθ
Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 11 / 18
Adaptive dynamics of the genotypic values µx, σx
Growth rate of mutant (µxm, σxm) in resident population (µxr, σxr):
λ(µxm, σxm, µxr, σxr) =
1− (1− γ)
1−
√σ2s + σ2xr exp
((θ−µxr)22(σ2
s+σ2xr)− (θ−µxm)2
2(σ2s+σ
2xm)
)√σ2s + σ2xm
Invasion fitness of mutant m = (µxm, σxm):
w(m, r) =
∫ln(λ(m, r|θ))h(θ)dθ
⇒ Calculate zeros of selection gradient ∇w and investigate stability
Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 12 / 18
Results
Noise will evolve to its optimum: σ2x = σ2θ − σ2sAdditional genetic polymorphism (branching) are selected if:
γ > 4
gθ+4+√
8µ23θ+g2θ
µ3θ ... skewness of optima distributiongθ ... kurtosis of optima distribution
I optima distribution sufficiently asymmetricI optima distribution has fatter tails than Gaussian (extremes more likely)
⇒ If noise can evolve, genetic polymorphisms are only selected if theoptima distribution is sufficiently different from Gaussian
Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 13 / 18
Examples of optima distributions
optima distribution example branching branching in
sum of smalleffects
never -
number ofpredation
events
γ > 4λ1+4λ+
√1+8λ
µx, σx
? γ > 2/5 σx
µθ
p 1− p
occurence ofthunderstorm
γ > 2p(1−p)1−2p(1−p) µx, σx
Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 14 / 18
Two possible optima
evolutionary convergenceto optimal noise level
if asymmetric:further genetic branching
σx
µxµθ
σx
µxµθθ1 θ2
p = 0.8 1− p = 0.2
If genetic polymorphism evolve, mostly both, µx AND σx, divergebetween the populations (cf. Doebeli and Ispolatov 2010)
Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 15 / 18
Simulation Results: Two possible optima
γ =0.5 general observations:
↑ γ stabilises (lhs)↑ σs stabilises↑ p destabilises
conclusion:
polymorphism oftenunstable
γ =0.75
γ =0.95 parametres: p = 0.8, σs = 0.1,
µθ = −0.3, σ∗x = 0.39, γ′ = 0.47
Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 16 / 18
Conclusion
Under temporally fluctuating selection noise evolves easier thangenetic polymorphisms
Genetic branching at optimal noise level ifI optima distribution sufficiently asymmetricI optima distribution has fatter tails than Gaussian
Polymorphism of divergent genotypes often unstable
In sexual populations: selection for increased genetic variance
Predictions about the heritability of traits under different forms offluctuating selection could be made
Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 17 / 18
Thanks for your attention!
Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 18 / 18