Snippets

• What can theory contribute to the study of adaptation to climate change?
  • Identify important parameters
  • Make rough predictions about quantitative change
  • Suggest measures and scalings
• What theory cannot do
  • Predict the ratio of genetic vs. genetic responses
  • Make exact quantitative predictions
• Scope of this paper
  • Phenotypic evolution of quantitative change
  • Simple selective scenarios
  • Focus on rates

• How should evolutionary change be measured?
  • Darwins, haldanes, haldane numerators
  • mean- vs. variance standardization (Herford et al. 2004)
  • extrapolation to per-generation rates (Gingerich)
• How to model phenotypic evolution?
  • Quantitative genetics (adaptation from standing genetic variation)
  • population genetics (adaptation by single large mutations)
  • adaptive walks (new mutations only)
  • optimality, game theory (not needed for simple scenarios considered here; relevant for evolution of plasticity)
  • adaptive dynamics (for evolution of plasticity, eco-evolutionary feedbacks)
• Which scenarios of environmental change have been considered?
  • sudden change,
  • moving optimum,
  • stochastic fluctuations
  • increased variability
  • range shifts????

• Standing variation vs. new mutations
• Small or large mutation

(Difficult to discuss details here; maybe just use as announcement, or combine with modeling approaches)

• Rate of adaptation
  • From new mutations: fixation probability (Haldane, Kimura, Gomulkiewicz and Kirkpatrick, Orr and Uncless, Uecker and Hermisson)
  • From standing variation (quantitative genetic models): Lande's equation
    • Additive genetic variance (under mutation-selection balance and during evolution); when will additive variance be exhausted?
    • Selection gradients
• Evolutionary rescue
  • from standing variation or new mutations
  • in models with sudden change
  • in models with moving optimum
  • critical rates of environmental change
• phenotype vs. fitness

• How to model multivariate evolution?
  • Multivariate Lande's/breeders' equation
  • Fisher's geometric model
  • Pleiotropic side effects
• How many traits? (Organismal complexity)
• What are the effects of multivariate mutation and selection?
  • G-matrix, M-matrix
  • Evolution of G-matrix
  • Genetic line of least resistance
  • multivariate constraints
  • evolution of mean fitness
• Evolvability

• How to model plasticity?
• How plastic are organisms?
• How does plasticity interact with genetic evolution?
• Does plasticity evolve during adaptation?
• How does plasticity contribute to evolutionary rescue?

• Evolutionary change in a community context
  • Effects of plasticity (trait-mediated indirect effects etc.)
  • Eco-evolutionary dynamics

In all cases, the answer may be quantitative, or may contain a list of factors that influence the result.

• Overall questions:
  • How fast can adaptation happen?
  • Plastic or genetic adaptation?
  • Evolutionary rescue?
• How much due to plasticity? (no general answers)
• Adaptation from standing variation or new mutations?
• Small or large mutations?
• How much standing genetic variation?
• What happens to genetic variance during adaptation?
• What constrains adaptation?
• What determined evolvability?
• Maximal rate of genetic adaptation?
• Evolutionary rescue due to genetic adaptation?
• How much plasticity?
• Will plasticity evolve?
• Can plasticity enhance genetic adaptation?
• Evolutionary rescue with plasticity?
• What happens at the community level?

• We might ask: What is possible with genetic change only?

• Most likely yes:-)
• Approaches: Lande 2009, earlier models from 1990s, Draghi and Whitlock
• Baldwin effect etc.

• How fast without plasticity?
• Factors determining speed:
  • Genetic variance (large literature here)
  • Selection gradient
  • Multivariate constraints
  • Evolvability, complexity etc.
• Evolutionary rescue
  • critical rates: explain
  • Explain Lynch and Lande (1993)
  • Key factors: selection gradient vs. mean fitness
  • Strong selection is a good thing with a moving optimum
  • additional factors: demographic and environmental stochasticity

• Different theoretical approaches/traditions
• Quantitative genetics vs. adaptive walks
• Some results from quantitative genetics (Hill…)
• Open questions

• Lots of recent interest in models of adaptive walks (from new mutations only)
• Kopp and Hermisson 2009b: at least in univariate case, adaptive walk predictions are good approximations to quantitative genetic model

• models on maintenance of genetic variation

• multivariate constraints
• Fisher's model etc.

• trade-offs?

• Starting point: Lande's equation: selection gradient and additive variance
• Lot's of literature on additive variance
• Selection gradient vs. mean fitness: depends on fitness function
  • double exponential fitness function: selection gradient constant
• Problem: How to deal with phenotypic variance and sampling error? For an observed change to be significant, the difference in haldanes must be <latex>(\bar x - \bar y)/\sigma_p > 1.96\sqrt(2/n)</latex>; for n = 100, this is 0.087.
• check out Lande 1976, Hendry and Kinnison 1999, Gingerich 2009 for this
• essentially dividing the Lande equation by sigma_p leads to standardized selection gradients, discussed and critized in Herford et al. 2004

• Multivariate Lande's equation
• critized by Morrisey et al. 2010
• Multivariate constraints: Walsh and Blows 2009

What happens when a populations experiences environmental change, and which theoretical problems do we encounter along the way?

• Before the change: maintenance of genetic variation (mutation-selection balance, fluctuating selection …)
• Different kinds of environmental change
• Adaptation from standing genetic variation
• Adaptation from new mutations (unlikely)
• Evolutionary rescue?
• Plasticity
• Which factors favor adaptation: genetic variation, plasticity, evolvability, modularity, lack of complexity