The authors analyze developmental, genetic, and demographic mechanisms by which populations tolerate changing environments and discuss empirical methods for determining the critical rate of sustained environmental change that causes population extinction.

We study the dynamics of evolutionary recovery after an abrupt environmental shift in a density-regulated population with evolving plasticity. Maladaptation to the new environment initially causes the population to decline, until adaptive phenotypic plasticity and genetic evolution restore positive population growth rate. We assume that selection on a quantitative trait is densityindependent and that the initial cost of plasticity is much lower than the benefit of the initial plastic response. The initial partially adaptive plasticity reduces the effective magnitude of the environmental shift, whereas evolution of plasticity increases the rate of adaptation. Both effects greatly facilitate population persistence. In contrast, density dependence of population growth always hinders persistence. With θ-logistic population regulation, a lower value of θ produces a faster initial population decline and a higher extinction risk.

Phenotypic plasticity, if adaptive, may allow species to counter the detrimental effects of extreme conditions, but the infrequent occurrence of extreme environments and/or their restriction to low-quality habitats within a species range means that they exert little direct selection on reaction norms. Plasticity could, therefore, be maladaptive under extreme environments, unless genetic correlations are strong between extreme and non-extreme environmental states, and the optimum phenotype changes smoothly with the environment. Empirical evidence suggests that populations and species from more variable environments show higher levels of plasticity that might preadapt them to extremes, but genetic variance for plastic responses can also be low, and genetic variation may not be expressed for some classes of traits under extreme conditions. Much of the empirical literature on plastic responses to extremes has not yet been linked to ecologically relevant conditions, such as asymmetrical fluctuations in the case of temperature extremes. Nevertheless, evolved plastic responses are likely to be important for natural and agricultural species increasingly exposed to climate extremes, and there is an urgent need to collect empirical information and link this to model predictions.This article is part of the themed issue 'Behavioural, ecological and evolutionary responses to extreme climatic events'.

We model selection at a locus affecting a quantitative trait (QTL) in the presence of genetic variance due to other loci. The dynamics at the QTL are related to the initial genotypic value and to the background genetic variance of the trait, assuming that background genetic values are normally distributed, under three different forms of selection on the trait. Approximate dynamics are derived under the assumption of small mutation effect. For similar strengths of selection on the trait (i.e, gradient of directional selection b) the way background variation affects the dynamics at the QTL critically depends on the shape of the fitness function. It generally causes the strength of selection on the QTL to decrease with time. The resulting neutral heterozygosity pattern resembles that of a selective sweep with a constant selection coefficient corresponding to the early conditions. The signature of selection may also be blurred by mutation and recombination in the later part of the sweep. We also study the race between the QTL and its genetic background toward a new optimum and find the conditions for a complete sweep. Overall, our results suggest that phenotypic traits exhibiting clear-cut molecular signatures of selection may represent a biased subset of all adaptive traits.

In an island population receiving immigrants from a larger continental population, gene flow causes maladaptation, decreasing mean fitness and producing continued directional selection to restore the local mean phenotype to its optimum. We show that this causes higher plasticity to evolve on the island than on the continent at migration‐selection equilibrium, assuming genetic variation of reaction norms is such that phenotypic variance is higher on the island, where phenotypes are not canalized. For a species distributed continuously in space along an environmental gradient, higher plasticity evolves at the edges of the geographic range, and in environments where phenotypes are not canalized. Constant or evolving partially adaptive plasticity also alleviates maladaptation owing to gene flow in a heterogeneous environment and produces higher mean fitness and larger population size in marginal populations, preventing them from becoming sinks and facilitating invasion of new habitats. Our results shed light on the widely observed involvement of partially adaptive plasticity in phenotypic clines, and on the mechanisms causing geographic variation in plasticity.

Distributions of mutation fitness effects from evolution experiments are available in an increasing number of species, opening the way for a vast array of applications in evolutionary biology. However, comparison of estimated distributions among studies is hampered by inconsistencies in the definitions of fitness effects and selection coefficients. In particular, the use of ratios of Malthusian growth rates as ‘relative fitnesses’ leads to wrong inference of the strength of selection. Scaling Malthusian fitness by the generation time may help overcome this shortcoming, and allow accurate comparison of selection coefficients across species. For species reproducing by binary fission (neglecting cellular death), ln2 can be used as a correction factor, but in general, the growth rate and generation time of the wild-type should be provided in studies reporting distribution of mutation fitness effects. I also discuss how density and frequency dependence of population growth affect selection and its measurement in evolution experiments.

Genetic theories of adaptation generally overlook the genes in which beneficial substitutions occur, and the likely variation in their mutational effects. We investigate the consequences of heterogeneous mutational effects among loci on the genetics of adaptation. We use a generalization of Fisher's geometrical model, which assumes multivariate Gaussian stabilizing selection on multiple characters. In our model, mutation has a distinct variance-covariance matrix of phenotypic effects for each locus.Consequently, the distribution of selection coefficients s varies across loci. We assume each locus can only affect a limited number of independent linear combinations of phenotypic traits (restricted pleiotropy), which differ among loci, an effect we term "orientation heterogeneity." Restricted pleiotropy can sharply reduce the overall proportion of beneficial mutations. Orientation heterogeneity has little impact on the shape of the genomic distribution, but can substantially increase the probability of parallel evolution (the repeated fixation of beneficial mutations at the same gene in independent populations), which is highest with low pleiotropy. We also consider variation in the degree of pleiotropy and in the mean s across loci. The latter impacts the genomic distribution of s, but has a much milder effect on parallel evolution. We discuss these results in the light of evolution experiments.K E Y W O R D S : Adaptation, extreme value theory, genetic constraints, mutation, parallel evolution, pleiotropy, random matrix theory.

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