Hannes Svardal - The role of environmental variance as adaptive response to fluctuating selection
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Hannes Svardal - The role of environmental variance as adaptive response to fluctuating selection

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  • 1. Pourquoi suis-je i¸i? c Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 1 / 18
  • 2. Does fluctuating selection favour an increase in environmental 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
  • 3. 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
  • 4. Sources of phenotypic variance in a quantitative trait phenotypic variance genetic environmental random GxE interaction genetic Gaussian discrete phenotypic polymorphism noise morphs plasticity Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 4 / 18
  • 5. Sources of phenotypic variance in a quantitative trait phenotypic variance genetic environmental random GxE interaction genetic Gaussian discrete phenotypic polymorphism noise morphs plasticity Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 4 / 18
  • 6. Genetic polymorphism VS environmental decanalisation phenotypic variance genetic environmental genetic Gaussian polymorphism noise Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 5 / 18
  • 7. Genetic polymorphism VS environmental decanalisation phenotypic variance genetic environmental genetic Gaussian polymorphism noise genetic contribu- degree of canali- genetically controlled via tion to a trait sation of the trait Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 5 / 18
  • 8. Genetic polymorphism VS environmental decanalisation phenotypic variance genetic environmental genetic Gaussian polymorphism noise genetic contribu- degree of canali- genetically controlled via tion to a trait sation of the trait frequency depen- as bet-hedging why adaptive? dent selection strategy if both are adaptive: Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 5 / 18
  • 9. Genetic polymorphism VS environmental decanalisation phenotypic variance genetic environmental genetic Gaussian polymorphism noise genetic contribu- degree of canali- genetically controlled via tion to a trait sation of the trait frequency depen- as bet-hedging why adaptive? dent selection strategy if both are adaptive: what ? evolves? ? Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 5 / 18
  • 10. Genetics Clonal reproduction Phenotype is a quantitative trait x Phenotype is determined by genetic component µx and random 2 environmental effects (Gaussian noise with variance σx ) Amount of environmental canalisation genetically controlled: σx heritable Probability that a genotype (µx , σx ) produces a phenotype x: probability σx heritable canalisation µx x heritable genetic component Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 6 / 18
  • 11. a lot of noise canalised Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 7 / 18
  • 12. The question Most models treat fully canalised genotypes (µx , σx ) = (x, 0) x We compare selection for genetic polymorphisms in µx to selection for increased σx : σx1 σx2 σx VS µx1 µx2 x µx 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
  • 13. The Lottery model (Chesson and Warner 1981): Temporal variation 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 2 (but has stationary distribution with mean µθ , variance σθ ) 2 Gaussian selection of strength 1/σs on distance |x − θ| surviving juveniles randomly compete to fill up the population size back to K (equivalent to the seed bank model) Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 9 / 18
  • 14. Model ingredients occurrence probability external environment: σθ optima distribution with 2 mean µθ and variance σθ optimal phenotype θ Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 10 / 18
  • 15. Model ingredients p special case 1−p occurrence probability σθ optimal phenotype θ θ1 µθ θ2 Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 10 / 18
  • 16. Model ingredients occurrence probability external environment: σθ optima distribution with 2 mean µθ and variance σθ optimal phenotype θ heritable frequency genotypic values: σx µx and σx determine gene- tic contribution and noise µx phenotype x level Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 10 / 18
  • 17. Model ingredients occurrence probability external environment: σθ optima distribution with 2 mean µθ and variance σθ θt optimal phenotype θ heritable frequency genotypic values: σx µx and σx determine gene- tic contribution and noise µx x phenotype x level survival σs selection: depends on diffe- rence optimum⇔phenotype 0 |x − θt | Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 10 / 18
  • 18. The two possibilities independently selected if 2 σθ decanalisation (σx > 0) 2 2 σθ > σs 2 σs noise 2 γσθ genetic polymporphism 2 2 γσθ > σs (disruptive selection in µx ) 2 genetic p. σs Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 11 / 18
  • 19. The two possibilities independently selected if 2 σθ decanalisation (σx > 0) 2 2 σθ > σs 2 σs noise 2 γσθ genetic polymporphism 2 2 γσθ > σs (disruptive selection in µx ) 2 genetic p. σs Now: analysis of evolution in the 2D genotype-space“ (µx , σx ): ” σx µθ µx Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 11 / 18
  • 20. Adaptive dynamics of the genotypic values µx , σx Growth rate of mutant (µxm , σxm ) in resident population (µxr , σxr ): λ(µxm , σxm , µxr , σxr ) = (θ−µxr )2 (θ−µxm )2   2 2 σs + σxr exp − 2 2 2(σs +σxr ) 2 2 2(σs +σxm ) 1 − (1 − γ) 1 −  2 2 σs + σxm 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
  • 21. Results 2 2 2 Noise will evolve to its optimum: σx = σθ − σs Additional genetic polymorphism (branching) are selected if: √4 γ> gθ +4+ 8˜2 +gθ µ3θ 2 µ3θ ... skewness of optima distribution ˜ gθ ... kurtosis of optima distribution optima distribution sufficiently asymmetric optima distribution has fatter tails than Gaussian (extremes more likely) ⇒ If noise can evolve, genetic polymorphisms are only selected if the optima distribution is sufficiently different from Gaussian Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 13 / 18
  • 22. Examples of optima distributions optima distribution example branching branching in sum of small never - effects number of 4λ predation γ> √ 1+4λ+ 1+8λ µx , σx events ? γ > 2/5 σx p 1−p occurence of 2p(1−p) γ> 1−2p(1−p) µx , σx thunderstorm µθ Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 14 / 18
  • 23. Two possible optima evolutionary convergence if asymmetric: to optimal noise level further genetic branching σx σx µθ µx µθ µx θ1 θ2 p = 0.8 1 − p = 0.2 If genetic polymorphism evolve, mostly both, µx AND σx , diverge between the populations (cf. Doebeli and Ispolatov 2010) Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 15 / 18
  • 24. Simulation Results: Two possible optima γ= 0.5 general observations: ↑ γ stabilises (lhs) ↑ σs stabilises ↑ p destabilises conclusion: γ= polymorphism often 0.75 unstable γ= parametres: p = 0.8, σs = 0.1, 0.95 ∗ µθ = −0.3, σx = 0.39, γ = 0.47 Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 16 / 18
  • 25. Conclusion Under temporally fluctuating selection noise evolves easier than genetic polymorphisms Genetic branching at optimal noise level if optima distribution sufficiently asymmetric 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 of fluctuating selection could be made Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 17 / 18
  • 26. Thanks for your attention! Hannes Svardal (Vienna) environmental vs. genetic variance 1. Juni 2010 18 / 18