• The topic of this special issue is “Evolutionary or plastic responses to climate change”. The underlying question – whether observed responses have a genetic basis or are expressions of phenotypic plasticity – is an empirical one, to which evolutionary theory can only contribute indirectly.
• In particular, current theory is unable to make quantitative predictions about the magnitude of plastic responses. Furthermore, the challenges discussed in the introductory paper by Merilä and Hendry do not apply to
• Much of the relevant theory has not been developed with climate change specifically in mind (a notable exception being models of “evolutionary rescue”).

In which ways can evolutionary theory contribute to the question at hand?

• Identify factors that influence the response to environmental change.
• Make qualitative predictions about the effect of different environmental and genetic variables.
• Provide rough rules of thumb for the magnitude of genetic (but not plastic, wee above) changes.
• Make suggestions about measurements and scaling (e.g. Herford et al. 2004, Hansen and Houle 2008, Gingerich 2009)

Our review will have the following structure

• Genetic responses (focus on expected rates and evolutionary rescue)
  • Univariate case
  • Multivariate case
• Plastic responses

Consider now the case of gradual shift of a one-dimensional phenotypic optimum. Typically, a Gaussian fitness function is assumed:

<latex> w(z) = \exp\left(-\frac{(z-\theta_t)^2}{2\sigma_s^2}\right) </latex>

Here, z is the phenotype of an individual, theta_t is the optimum at time t, and the “variance” sigma^2 measures the width of the fitness function (i.e., selection is strong sigma^2 is small). Here and later on, our notation mainly follows … (Bürger and Lynch 1995?). Frequently, it is assumed that, at time 0, z = theta_0, that is, the population is perfectly adapted before the optimum stops moving. Movement of the optimum is typically assumed to the linear, potentially accompanied by stochastic white noise:

<latex> \theta_t = kt + \epsilon_t </latex>

where <latex>\epsilon_t</latex> is drawn from a normal distribution with mean 0 and variance <latex>\sigma_\theta^2</latex>. Setting <latex>\sigma_\theta^2 = 0</latex> recovers the deterministic case. This basic model has first(?) been analyzed by Lynch and Lande (1993) using a quantitative genetic framework, and later been extended by Bürger and Lynch (1995), … Since its behavior is highly instructive, we will describe it in some detail.

Assume that the trait z has a polygenic basis