Unpredictable selection in a structured population leads to local genetic differentiation in evolved reaction norms

Unpredictability during development of the optimum phenotype under future selection leads to a compromise reaction norm with a slope that is shallower than the slope of the optimum reaction norm. Unpredictability of selection can lead to an evolved curved reaction norm when genetic variation for curvature is available even if the optimum reaction norm is linear. This requires asymmetry in the frequency distribution of the habitats of selection; at small population size, stochasticity in the number of individuals per selection habitat is sufficient to generate such asymmetry. Unpredictability of selection in structured populations leads to local genetic differentiation of reaction norms. The mean habitat of a subpopulation is defined as the subpopulation's focal habitat. The evolved mean reaction norm of each subpopulation is anchored at the optimum genotypic value in its focal habitat. Linear reaction norms are parallel if the conditional distribution of adults around the focal habitats is the same for each subpopulation. Adult migration and absence of zygote dispersal represents the ultimate structured population, each habitat playing the role of focal habitat. Absence of zygote dispersal requires that the flow of individuals through the habitats is used instead of the habitats’ frequencies in the prediction of the evolved reaction norm. Adult migration in absence of zygote dispersal leads to an evolved pattern of locally differentiated reaction norms with optimum genotypic value anchored in the focal habitat and, for linear reaction norms, parallel slopes.     

The evolution of environmental and genetic sex determination in fluctuating environments

Twenty years ago, Bulmer and Bull suggested that disruptive selection, produced by environmental fluctuations, can result in an evolutionary transition from environmental sex determination (ESD) to genetic sex determination (GSD). We investigated the feasibility of such a process, using mutation-limited adaptive dynamics and individual-based computer simulations. Our model describes the evolution of a reaction norm for sex determination in a metapopulation setting with partial migration and variation in an environmental variable both within and between local patches. The reaction norm represents the probability of becoming a female as a function of environmental state and was modeled as a sigmoid function with two parameters, one giving the location (i.e., the value of the environmental variable for which an individual has equal chance of becoming either sex) and the other giving the slope of the reaction norm for that environment. The slope can be interpreted as being set by the level of developmental noise in morph determination, with less noise giving a steeper slope and a more switchlike reaction norm. We found convergence stable reaction norms with intermediate to large amounts of developmental noise for conditions characterized by low migration rates, small differential competitive advantages between the sexes over environments, and little variation between individual environments within patches compared to variation between patches. We also considered reaction norms with the slope parameter constrained to a high value, corresponding to little developmental noise. For these we found evolutionary branching in the location parameter and a transition from ESD toward GSD, analogous to the original analysis by Bulmer and Bull. Further evolutionary change, including dominance evolution, produced a polymorphism acting as a GSD system with heterogamety. Our results point to the role of developmental noise in the evolution of sex determination.     

Optimal reproductive allocation in annuals and an informational constraint on plasticity

In this computational study, we examined optimal reproductive allocation schedules in annual plants whose season lengths vary in predictability. We discuss relationships among season-length predictability, the form of the optimal allocation schedule, the degree of plasticity reflected in the optimal reaction norm, and the competitive consequences of plasticity and bet-hedging. We used an evolutionary algorithm to search the allocation-schedule space for optima, given different distributions of season length. The resulting schedules maximize geometric-mean fecundity under their selecting distributions. We then examined the relative fitness of these schedules in simulated competition among reaction norms optimized for different degrees of season-length predictability. Gradedness of optimal schedules decreases with increasing season-length predictability, and reaction norms comprising highly graded schedules reflect lesser plasticity than norms comprising schedules that are less graded. In simulations, competitively successful genotypes were those that reflected plasticity appropriate to the season-length predictability. Informational constraints in the form of low season-length predictability select for low plasticity and high bet-hedging in allocation. Because an environmental cue must mediate the relationship between environment and fitness, plasticity in reproductive allocation ought to be understood not as a direct response to the selective environment, but rather to cues that are correlated with relevant environmental parameters.     

The phenotypic variance within plastic traits under migration-mutation-selection balance

How phenotypic variances of quantitative traits are influenced by the heterogeneity in environment is an important problem in evolutionary biology. In this study, both genetic and environmental variances in a plastic trait under migration-mutation-stabilizing selection are investigated. For this, a linear reaction norm is used to approximate the mapping from genotype to phenotype, and a population of clonal inheritance is assumed to live in a habitat consisting of many patches in which environmental conditions vary among patches and generations. The life cycle is assumed to be selection-reproduction-mutation-migration. Analysis shows that phenotypic plasticity is adaptive if correlations between the optimal phenotype and environment have become established in both space and/or time, and it is thus possible to maintain environmental variance (V(E)) in the plastic trait. Under the special situation of no mutation but maximum migration such that separate patches form an effective single-site habitat, the genotype that maximizes the geometric mean fitness will come to fixation and thus genetic variance (V(G)) cannot be maintained. With mutation and/or restricted migration, V(G) can be maintained and it increases with mutation rate but decreases with migration rate; whereas VE is little affected by them. Temporal variation in environmental quality increases V(G) while its spatial variance decreases V(G). Variation in environmental conditions may decrease the environmental variance in the plastic trait.     

Evolution of dispersal in spatially and temporally variable environments: The importance of life cycles

Spatiotemporal variability of the environment is bound to affect the evolution of dispersal, and yet model predictions strongly differ on this particular effect. Recent studies on the evolution of local adaptation have shown that the life cycle chosen to model the selective effects of spatiotemporal variability of the environment is a critical factor determining evolutionary outcomes. Here, we investigate the effect of the order of events in the life cycle on the evolution of unconditional dispersal in a spatially heterogeneous, temporally varying landscape. Our results show that the occurrence of intermediate singular strategies and disruptive selection are conditioned by the temporal autocorrelation of the environment and by the life cycle. Life cycles with dispersal of adults versus dispersal of juveniles, local versus global density regulation, give radically different evolutionary outcomes that include selection for total philopatry, evolutionary bistability, selection for intermediate stable states, and evolutionary branching points. Our results highlight the importance of accounting for life‐cycle specifics when predicting the effects of the environment on evolutionarily selected trait values, such as dispersal, as well as the need to check the robustness of model conclusions against modifications of the life cycle.     

GENERALISTS,SPECIALISTS, AND THE EVOLUTION OF PHENOTYPIC PLASTICITY IN SYMPATRIC POPULATIONS OF DISTINCT SPECIES

The evolution of phenotypic plasticity is studied in a model with two reproductively isolated “species” in a coarse-grained environment, consisting of two types of habitats. A quantitative genetic model for selection was constructed, in which habitats differ in the optimal value for a focal trait, and with random dispersal among habitats. The main interest was to study the effects of different selection regimes. Three cases were investigated: (1) without any limits to plasticity; (2) without genetic variation for plasticity; and (3) with a fitness cost for phenotypically plastic reactions. In almost all cases a generalist strategy to exploit both habitats emerged. Without any limits to plasticity, optimal adaptive reactions evolved. Without any genetic variation for plasticity, a compromise strategy with an intermediate, fixed phenotype evolved, whereas in the presence of costs a plastic compromise between the demands of the habitats and the costs associated with plasticity was found. Specialization and phenotypic differentiation was only found when selection within habitats was severe and optimal phenotypes for different habitats were widely different. Under soft selection (local regulation of population numbers in each habitat) the specialists coexisted; under hard selection (global regulation of population numbers) one specialist outcompeted the other. The prevalent evolutionary outcome of compromises rather than specialization implies that costs or constraints are not necessarily detectable as local adaptation in transplantation or translocation experiments.     

Reaction norms with bifurcations shaped by evolution

Two versions of a model for the evolution of seasonal polyphenism investigate the evolution of reaction norm bifurcation and branching. The first version is without a specific submodel for morphological development and the second has an explicit developmental map. Version 1 is evolutionarily relatively unconstrained: (i) reaction norms are specified by matrices containing the probabilities of occurrence of environment-phenotype combinations, (ii) all conceivable reaction norm matrices are reachable through a sequence of mutations, and (iii) small as well as large mutational effects occur. This version is used to find the evolutionarily stable strategy favoured by the population ecology that is characterized by stabilizing viability selection with a cyclically fluctuating selection optimum. When the strength of selection is large and when the lag between initiation of development and selection on mature phenotype is not a multiple of half the period of the environmental cycle, a branching reaction norm evolves. In the second model version, branching reaction norms occur for certain parameter combinations of the developmental submodel, but the evolution of this pattern is often constrained. The evolutionary trajectory becomes trapped in a local selective optimum for the parameters of the developmental system. Substantial developmental noise evolves, but mutations that produce a selectively advantageous branching pattern do not occur from there.     

When three traits make a line: evolution of phenotypic plasticity and genetic assimilation through linear reaction norms in stochastic environments

Genetic assimilation emerges from selection on phenotypic plasticity. Yet, commonly used quantitative genetics models of linear reaction norms considering intercept and slope as traits do not mimic the full process of genetic assimilation. We argue that intercept–slope reaction norm models are insufficient representations of genetic effects on linear reaction norms and that considering reaction norm intercept as a trait is unfortunate because the definition of this trait relates to a specific environmental value (zero) and confounds genetic effects on reaction norm elevation with genetic effects on environmental perception. Instead, we suggest a model with three traits representing genetic effects that, respectively, (i) are independent of the environment, (ii) alter the sensitivity of the phenotype to the environment and (iii) determine how the organism perceives the environment. The model predicts that, given sufficient additive genetic variation in environmental perception, the environmental value at which reaction norms tend to cross will respond rapidly to selection after an abrupt environmental change, and eventually becomes equal to the new mean environment. This readjustment of the zone of canalization becomes completed without changes in genetic correlations, genetic drift or imposing any fitness costs of maintaining plasticity. The asymptotic evolutionary outcome of this three‐trait linear reaction norm generally entails a lower degree of phenotypic plasticity than the two‐trait model, and maximum expected fitness does not occur at the mean trait values in the population.     

Neuroendocrine control of life histories: what do we need to know to understand the evolution of phenotypic plasticity?

Almost all life histories are phenotypically plastic: that is, life-history traits such as timing of breeding, family size or the investment in individual offspring vary with some aspect of the environment, such as temperature or food availability. One approach to understanding this phenotypic plasticity from an evolutionary point of view is to extend the optimality approach to the range of environments experienced by the organism. This approach attempts to understand the value of particular traits in terms of the selection pressures that act on them either directly or owing to trade-offs due to resource allocation and other factors such as predation risk. Because these selection pressures will between environments, the predicted optimal phenotype will too. The relationship expressing the optimal phenotype for different environments is the optimal reaction norm and describes the optimal phenotypic plasticity. However, this view of phenotypic plasticity ignores the fact that the reaction norm must be underlain by some sort of control system: cues about the environment must be collected by sense organs, integrated into a decision about the appropriate life history, and a message sent to the relevant organs to implement that decision. In multicellular animals, this control mechanism is the neuroendocrine system. The central question that this paper addresses is whether the control system affects the reaction norm that evolves. This might happen in two different ways: first, the control system will create constraints on the evolution of reaction norms if it cannot be configured to produce the optimal reaction norm and second, the control system will create additional selection pressures on reaction norms if the neuroendocrine system is costly. If either of these happens, a full understanding of the way in which selection shapes reaction norms must include details of the neuroendocrine control system. This paper presents the conceptual framework needed to explain what is meant by a constraint or cost being created by the neuroendocrine system and discusses the extent to which this occurs and some possible examples. The purpose of doing this is to encourage endocrinologists to take a fresh look at neuroendocrine mechanisms and help identify the properties of the system and situations in which these generate constraints and costs that impinge on the evolution of phenotypic plasticity.     

EXPERIMENTAL EVIDENCE FOR THE EVOLUTION OF INDIRECT GENETIC EFFECTS: CHANGES IN THE INTERACTION EFFECT COEFFICIENT,PSI (Ψ), DUE TO SEXUAL SELECTION

Indirect genetics effects (IGEs)—when the genotype of one individual affects the phenotypic expression of a trait in another—may alter evolutionary trajectories beyond that predicted by standard quantitative genetic theory as a consequence of genotypic evolution of the social environment. For IGEs to occur, the trait of interest must respond to one or more indicator traits in interacting conspecifics. In quantitative genetic models of IGEs, these responses (reaction norms) are termed interaction effect coefficients and are represented by the parameter psi (Ψ). The extent to which Ψ exhibits genetic variation within a population, and may therefore itself evolve, is unknown. Using an experimental evolution approach, we provide evidence for a genetic basis to the phenotypic response caused by IGEs on sexual display traits in Drosophila serrata. We show that evolution of the response is affected by sexual but not natural selection when flies adapt to a novel environment. Our results indicate a further mechanism by which IGEs can alter evolutionary trajectories—the evolution of interaction effects themselves.     

Natural selection and genetic variation for reproductive reaction norms in a wild bird population

Many morphological and life-history traits show phenotypic plasticity that can be described by reaction norms, but few studies have attempted individual-level analyses of reaction norms in the wild. We analyzed variation in individual reaction norms between laying date and three climatic variables (local temperature, local rainfall, and North Atlantic Oscillation) of 1126 female collared flycatchers (Ficedula albicollis) with a restricted maximum likehood linear mixed model approach using random-effect best linear unbiased predictor estimates for the elevation (i.e., expected laying date in the average environment) and slope (i.e., adjustment in laying date as a function of environment) of females' reaction norms. Variation in laying date was best explained by local temperature, and individual females differed in both the elevation and the slope of their laying date-temperature reaction norms. As revealed by animal model analyses, there was weak evidence for additive genetic variance of elevation (h2 +/- SE = 0.09 +/- 0.09), whereas there was no evidence for heritability of slope (h2 +/- SE = 0.00 +/- 0.01). Selection analysis, using a female's lifetime production of fledglings or recruits as an estimate of her fitness, revealed significant selection for a lower phenotypic value and breeding value for elevation (i.e., earlier laying date at the average temperature). There was selection for steeper phenotypic values of slope (i.e., greater plasticity in the adjustment of laying date to temperature), but no significant selection on the breeding values of slope. Although these results suggest that phenotypic laying date is influenced by additive genetic factors, as well as by an interaction with the environment, selection on plasticity would not produce an evolutionary response.     

Selection on skewed characters and the paradox of stasis

Observed phenotypic responses to selection in the wild often differ from predictions based on measurements of selection and genetic variance. An overlooked hypothesis to explain this paradox of stasis is that a skewed phenotypic distribution affects natural selection and evolution. We show through mathematical modeling that, when a trait selected for an optimum phenotype has a skewed distribution, directional selection is detected even at evolutionary equilibrium, where it causes no change in the mean phenotype. When environmental effects are skewed, Lande and Arnold's (1983) directional gradient is in the direction opposite to the skew. In contrast, skewed breeding values can displace the mean phenotype from the optimum, causing directional selection in the direction of the skew. These effects can be partitioned out using alternative selection estimates based on average derivatives of individual relative fitness, or additive genetic covariances between relative fitness and trait (Robertson–Price identity). We assess the validity of these predictions using simulations of selection estimation under moderate sample sizes. Ecologically relevant traits may commonly have skewed distributions, as we here exemplify with avian laying date — repeatedly described as more evolutionarily stable than expected — so this skewness should be accounted for when investigating evolutionary dynamics in the wild.     

EVOLUTION OF GENERALISTS AND SPECIALISTS IN SPATIALLY HETEROGENEOUS ENVIRONMENTS

Quantitative genetic models are used to investigate the evolution of generalists and specialists in a coarse-grained environment with two habitat types when there are costs attached to being a generalist. The outcomes for soft and hard selection models are qualitatively different. Under soft selection (e.g., for juvenile or male-reproductive traits) the population evolves towards the single peak in the adaptive landscape. At equilibrium, the population mean phenotype is a compromise between the reaction that would be optimal in both habitats and the reaction with the lowest cost. Furthermore, the equilibrium is closer to the optimal phenotype in the most frequent habitat, or the habitat in which selection on the focal trait is stronger. A specialist genotype always has a lower fitness than a generalist, even when the costs are high. In contrast, under hard selection (e.g., for adult or female-reproductive traits) the adaptive landscape can have one, two, or three peaks; a peak represents a population specialized to one habitat, equally adapted to both habitats, or an intermediate. One peak is always found when the reaction with the lowest cost is not much different from the optimal reaction, and this situation is similar to the soft selection case. However, multiple peaks are present when the costs become higher, and the course of evolution is then determined by initial conditions, and the region of attraction of each peak. This implies that the evolution of specialization and phenotypic plasticity may not only depend on selection regimes within habitats, but also on contingent, historical events (migration, mutation). Furthermore, the evolutionary dynamics in changing environments can be widely different for populations under hard and soft selection. Approaches to measure costs in natural and experimental populations are discussed.     

Selection experiments and the study of phenotypic plasticity1

Abstract Laboratory selection experiments are powerful tools for establishing evolutionary potentials. Such experiments provide two types of information, knowledge about genetic architecture and insight into evolutionary dynamics. They can be roughly classified into two types: (1) artificial selection in which the experimenter selects on a focal trait or trait index, and (2) quasi‐natural selection in which the experimenter establishes a set of environmental conditions and then allows the population to evolve. Both approaches have been used in the study of phenotypic plasticity. Artificial selection experiments have taken various forms including: selection directly on a reaction norm, selection on a trait in multiple environments, and selection on a trait in a single environment. In the latter experiments, evolution of phenotypic plasticity is investigated as a correlated response. Quasi‐natural selection experiments have examined the effects of both spatial and temporal variation. I describe how to carry out such experiments, summarize past efforts, and suggest further avenues of research.     

Diapause and bet-hedging strategies in insects: a meta-analysis of reaction norm shapes

Many organisms escape from lethal climatological conditions by entering a resistant resting stage called diapause, which needs to be optimally timed with seasonal change. As climate change exerts selection pressure on phenology, the evolution of mean diapause timing, but also of phenotypic plasticity and bet-hedging strategies is expected. The potential of the latter strategy as a means of coping with environmental unpredictability has received little attention in the climate change literature. Populations should be adapted to spatial variation in local conditions; contemporary patterns of phenological strategies across a geographic range may hence provide information about their evolvability. We thus extracted 458 diapause reaction norms from 60 studies. First, we correlated mean diapause timing with mean winter onset. Then we partitioned the reaction norm variance into a temporal component (phenotypic plasticity) and among-offspring variance (diversified bet-hedging) and correlated this variance composition with variability of winter onset. Mean diapause timing correlated reasonably well with mean winter onset, except for populations at high latitudes, which apparently failed to track early onsets. Variance among offspring was, however, limited and correlated only weakly with environmental variability, indicating little scope for bet-hedging. The apparent lack of phenological bet-hedging strategies may pose a risk in a less predictable climate, but we also highlight the need for more data on alternative strategies.     

EVOLUTION OF DISPERSAL RATES IN METAPOPULATION MODELS: BRANCHING AND CYCLIC DYNAMICS IN PHENOTYPE SPACE

We study the evolution of dispersal rates in a two patch metapopulation model. The local dynamics in each patch are given by difference equations, which, together with the rate of dispersal between the patches, determine the ecological dynamics of the metapopulation. We assume that phenotypes are given by their dispersal rate. The evolutionary dynamics in phenotype space are determined by invasion exponents, which describe whether a mutant can invade a given resident population. If the resident metapopulation is at a stable equilibrium, then selection on dispersal rates is neutral if the population sizes in the two patches are the same, while selection drives dispersal rates to zero if the local abundances are different. With non-equilibrium metapopulation dynamics, non-zero dispersal rates can be maintained by selection. In this case, and if the patches are ecologically identical, dispersal rates always evolve to values which induce synchronized metapopulation dynamics. If the patches are ecologically different, evolutionary branching into two coexisting dispersal phenotypes can be observed. Such branching can happen repeatedly, leading to polymorphisms with more than two phenotypes. If there is a cost to dispersal, evolutionary cycling in phenotype space can occur due to the dependence of selection pressures on the ecological attractor of the resident population, or because phenotypic branching alternates with the extinction of one of the branches. Our results extend those of Holt and McPeek (1996), and suggest that phenotypic branching is an important evolutionary process. This process may be relevant for sympatric speciation.     

Giving‐up densities and ideal pre‐emptive patch use in a predatory benthic stream fish

1. We used observational and experimental field studies together with an individual‐based simulation model to demonstrate that behaviours of mottled sculpin (Cottus bairdi) were broadly consistent with the expectations of Giving‐Up Density theory and an Ideal Pre‐emptive Distribution habitat selection model. 2. Specifically we found that: (i) adult mottled sculpin established territories within patches characterised by significantly higher prey densities and prey renewal rates than patches occupied by juveniles or randomly selected patches; (ii) patches abandoned by adult sculpin possessed significantly lower prey densities than newly occupied patches, although this was not true for juveniles; (iii) the observed giving‐up density (GUD) for adult sculpin (i.e. average prey density in patches recently abandoned) increased linearly with increasing fish size up to the average prey density measured in randomly selected patches (i.e. 350 prey items per 0.1 m²) and decreased with increasing sculpin density and (iv) juveniles rapidly shifted their distribution towards the highest quality patches following removal of competitively dominant adult sculpin. 3. These results provide the first evidence of the applicability of GUD theory to a stream‐dwelling organism, and they elucidate the underlying factors influencing juvenile and adult sculpin habitat selection and movement behaviours. Furthermore, optimal patch use, ideal pre‐emptive habitat selection and juvenile ‘floating’ provide behavioural mechanisms linking environmental heterogeneity in the stream benthos to density‐dependent regulation of mottled sculpin populations in this system.     

VARIATION IN THERMAL PERFORMANCE AND REACTION NORMS AMONG POPULATIONS OF DROSOPHILA MELANOGASTER

The major goal of evolutionary thermal biology is to understand how variation in temperature shapes phenotypic evolution. Comparing thermal reaction norms among populations from different thermal environments allows us to gain insights into the evolutionary mechanisms underlying thermal adaptation. Here, we have examined thermal adaptation in six wild populations of the fruit fly (Drosophila melanogaster) from markedly different natural environments by analyzing thermal reaction norms for fecundity, thorax length, wing area, and ovariole number under ecologically realistic fluctuating temperature regimes in the laboratory. Contrary to expectation, we found only minor differences in the thermal optima for fecundity among populations. Differentiation among populations was mainly due to differences in absolute (and partly also relative) thermal fecundity performance. Despite significant variation among populations in the absolute values of morphological traits, we observed only minor differentiation in their reaction norms. Overall, the thermal reaction norms for all traits examined were remarkably similar among different populations. Our results therefore suggest that thermal adaptation in D. melanogaster predominantly involves evolutionary changes in absolute trait values rather than in aspects of thermal reaction norms.     

The genetics of phenotypic plasticity. VII. Evolution in a spatially-structured environment

Previous models of the evolution of phenotypic plasticity have, for the most part, not considered the effects of genetic architecture and spatial structure. I examine those factors with an individual-based simulation model. With regard to genetic architecture, I considered how the presence of different types of loci would affect medium-term evolutionary outcomes. The types of loci differed in how the environment determined phenotypic expression and included loci that were insensitive to the environment (non-plastic loci), sensitive in a linear fashion, and sensitive in a quadratic fashion (both plastic loci). With regard to spatial structure, I investigated the affects of migration patterns. These simulations demonstrated that two general conditions are necessary for phenotypic plasticity to be selected. (1) The environment must have a strong influence on genotypic expression. (2) The between-generation changes in the environment must be large and predictable, in the current instance because of migration in a spatially-structured (clinal) environment. Responses to selection were not simple, however. Rarely were pure strategies — genetic specialization or phenotypic plasticity — selected for. Instead, the existence of multiple types of loci led to mixed genetic outcomes. The result of this mixed outcome were individuals with reaction norms that were less steep than the optimal reaction norm (when non-plastic and linear-plastic loci were present) or individuals with curved reaction norms when the optimal reaction norms was linear (when all three types of loci were present). A pure plasticity strategy had the highest global fitness because plastic individuals would match the optimal phenotype everywhere. The reason that the metapopulation did not achieve this global fitness optimum is that local selection is stronger than global selection. Each deme is driven to a local fitness peak based on the combined, locally additive effects of the non-plastic and plastic loci. Plasticity is only selected globally, so plasticity becomes more highly favored with high migration rates. This effect was greatest in parts of the cline where the plasticity loci were not being expressed and, thus, not locally selected upon. That is, in these demes local selection was weak or absent allowing global fitness effects to predominate.     

Adaptation to an extraordinary environment by evolution of phenotypic plasticity and genetic assimilation

Adaptation to a sudden extreme change in environment, beyond the usual range of background environmental fluctuations, is analysed using a quantitative genetic model of phenotypic plasticity. Generations are discrete, with time lag τ between a critical period for environmental influence on individual development and natural selection on adult phenotypes. The optimum phenotype, and genotypic norms of reaction, are linear functions of the environment. Reaction norm elevation and slope (plasticity) vary among genotypes. Initially, in the average background environment, the character is canalized with minimum genetic and phenotypic variance, and no correlation between reaction norm elevation and slope. The optimal plasticity is proportional to the predictability of environmental fluctuations over time lag τ. During the first generation in the new environment the mean fitness suddenly drops and the mean phenotype jumps towards the new optimum phenotype by plasticity. Subsequent adaptation occurs in two phases. Rapid evolution of increased plasticity allows the mean phenotype to closely approach the new optimum. The new phenotype then undergoes slow genetic assimilation, with reduction in plasticity compensated by genetic evolution of reaction norm elevation in the original environment.