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

Authors


Russell Lande, Division of Biology, Imperial College London, Silwood Park, Ascot, Berkshire SL5 7PY, UK.
Tel.: +44 (0)20759 42353; fax: +44 (0)20759 42236;
e-mail: r.lande@imperial.ac.uk

Abstract

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.

Introduction

The primary mechanisms of phenotypic adaptation are Darwinian evolution by natural selection on genetic variation, and phenotypic plasticity through environmental influence on individual development. Darwin (1859, 1868) and early naturalists including Lamarck, as well as animal and plant breeders and biometricians, were aware that both hereditary and environmental factors influence individual development, and that phenotypic plasticity often is adaptive (Provine, 1971). Baldwin (1896), Morgan (1896), Osborn (1897) and Osborn & Poulton (1897) proposed that after a change in environment plasticity of development can produce a partially adaptive phenotype, which subsequently becomes further adapted by natural selection, and that this process may be important for population persistence in an altered environment. The ‘Baldwin effect’ (Simpson, 1953) and phenotypic plasticity became neglected after the rediscovery of Mendelian inheritance in 1900. Interest in these topics eventually revived (Turesson, 1922; Clements, 1929; Hall, 1932; Clausen et al., 1940; Gause, 1947; Kirpichnikov, 1947; Schmalhausen, 1949; Waddington, 1953; Bateson, 1963) and they again became active topics of research (Via & Lande, 1985; Sultan, 1987; Wcislo, 1989; West-Eberhard, 1989, 2003; Schlichting & Pigliucci, 1998; Hall, 2001; Pigliucci, 2001; DeWitt & Scheiner, 2004; Ghalambor et al., 2007; Nussey et al., 2007).

Phenotypic adaptation to environmental fluctuations must frequently occur by preexisting plasticity, and recent models of the Baldwin effect usually assume that phenotypic plasticity itself does not evolve (e.g. Price et al., 2003; Price, 2006; Paenke et al., 2007). However, after an extreme environmental change, the evolution of phenotypic plasticity can greatly accelerate phenotypic evolution and adaptation. Paleoclimate data reveal that on rare occasions populations in situ experience sudden or very rapid major changes in average environment for ecologically important variables such as precipitation and temperature (Steffensen et al., 2008). During millions of years of existence, species repeatedly encounter extreme changes in average environment, and the capacity to accelerate phenotypic adaptation by transient evolution of plasticity may be crucial for long-term persistence. Rapid phenotypic adaptation may be necessary to prevent extinction of modern species subject to anthropogenic global warming, especially those with long generations such as large-bodied vertebrates and perennial plants, when natural barriers or artificial habitat destruction and fragmentation restrict opportunities for dispersal and change in geographical range (Peters & Lovejoy, 1994; Lovejoy, 2005; Parmesan, 2006; Gienapp et al., 2008).

Sudden environmental change often occurs at the start of natural biological invasions and colonizations, which are involved the evolutionary diversification of most major taxa, e.g. during host shifts by specialized pathogens, parasites and herbivores. The success of natural invasions, and artificial introductions for biocontrol, may depend on the evolution of increased plasticity during adaptation to novel environments outside the native range of a species (Richards et al., 2006; Yoshida et al., 2007; Price & Sol, 2008). Genetic variance in plasticity within and/or among populations has commonly been observed (Scheiner, 1993, 2002), and species invading novel or extreme environments often, but not always, display increased plasticity compared to populations from the native range (Chapman et al., 2000; Lee et al., 2003; Dybdahl & Kane, 2005;Chun et al., 2007; Cano et al., 2008; Lardies & Bozinovic, 2008;Lombaert et al., 2008).

Here I employ quantitative genetic models of phenotypic plasticity to analyse the dynamics of phenotypic adaptation to a sudden extreme environmental change. I derive conditions under which a rapid evolutionary increase in plasticity accelerates phenotypic adaptation, quickly bringing the mean phenotype close to a new optimum and recovering mean fitness, followed by slow genetic assimilation of the new phenotype.

Conceptual background

Selection and evolution of plasticity can be understood using genotypic norms of reaction that depict for each genotype its average phenotype as a function of the environment in which it develops. Here I define the reaction norm of a genotype as its breeding value, or total additive genetic effect determined by the mean phenotype of its offspring (under random mating) as a function of the environment in which offspring develop. With purely additive genetic variance these quantities are equivalent (Falconer & MacKay, 1996).

Simple linear norms of reaction may differ among genotypes in elevation (breeding value) in a particular reference environment, and in slope which measures the degree of plasticity. Figure 1 (left panel) illustrates ‘phenotypic canalization’ in a range of environments around an initial average environment labelled 0. Genotypic norms of reaction tend to converge in elevation around the optimum phenotype in the average environment, but still vary in slope, so that genetic and phenotypic variances are minimized in the average environment. Canalization therefore implies plasticity (and vice versa), such that a large shift in the environment will produce an increased genetic variance in the new environment.

Figure 1.

 Norms of reaction and their evolution following a sudden change in average environment. In both panels the heavy line shows the optimum phenotype as a linear function of the environment with slope B. Left panel: Light lines are linear norms of reaction for 50 genotypes sampled at random from a population with a bivariate normal distribution of slope (plasticity) and elevation (breeding value) in the reference environment, 0. Minimum genetic and phenotypic variances occur in the reference environment, where reaction norm slope and elevation are uncorrelated. Background environmental fluctuations obey a stationary time series with variance inline image and autocorrelation ρ for developmental time lag τ. At time t = 0 the average environment suddenly changes from 0 to δ, shifting the distribution of background environment (insert at top of left panel). Right panel: Adaptation of the population mean norm of reaction to an extraordinary environmental change, assuming appreciable genetic variance for plasticity. The initial mean norm of reaction (t = 0) undergoes two phases of evolution. Parameters: inline image.

In a single environment natural selection on phenotypic variation has no direct impact on plasticity, which however can evolve as a correlated response to selection if an additive genetic correlation exists between reaction norm slope and elevation (de Jong, 1995; Via et al., 1995; Garland & Kelly, 2006). A change in environment, with a concomitant shift in the optimum phenotype, causes directional selection. After a small environmental change genetic variation is still due mostly to differences in reaction norm elevation in the original environment, whereas after a large environmental change (from 0 to δ in Fig. 1 left panel) genetic variation is caused mostly by differences in reaction norm slope. Therefore, although selection in any environment acts directly on phenotypes expressed there, it is equally valid to view selection as acting indirectly on a combination of plasticity and breeding values in a reference environment. For a character that is initially canalized, a major change in environment thus selects for increased plasticity, which can accelerate adaptive evolution of the mean phenotype (Gavrilets & Scheiner, 1993b; de Jong, 1995; Via et al., 1995).

Canalization resulting from stabilizing selection, and its implications for adaptive evolution are historically important topics (Waddington, 1942, 1960; Schmalhausen, 1949; Lerner, 1954; Bradshaw & Hardwick, 1989;Hoffmann & Parsons, 1993, 1997; Stearns & Kawecki, 1994) that until recently received little attention in population genetics theory (Wagner et al., 1997; Bergman & Siegal, 2003;de Visser et al., 2003; Hermisson & Wagner, 2004; Borenstein et al., 2006). For a quantitative (polygenic) character in a single environment, classical population genetics theory established that stabilizing selection towards an intermediate optimum phenotype tends to reduce genetic variance (Fisher, 1930, 1958, Chapter 5; Wright, 1935; Lande, 1975; Bürger, 2000). The larger the effective number of loci contributing to the additive genetic variance of a character, the more slowly stabilizing selection reduces the genetic variance (Crow & Kimura, 1970, p. 239; Lande, 1975; Bürger, 2000, p. 253). Stabilizing selection also can reduce the component of phenotypic variance due to micro-environmental variation and developmental noise (Lande, 1980; Bull, 1987; Gavrilets & Hastings, 1994).

The terms ‘genetic canalization’ and ’environmental canalization’ are sometimes applied to describe the reduction in genetic and environmental components of phenotypic variance by stabilizing selection (Stearns et al., 1995; Debat & David, 2001). However, nonparallel norms of reaction as depicted in Fig. 1 (left panel) constitute ‘genotype–environment interaction’ (Via & Lande, 1985) which, in heterogeneous or changing environments, complicates the assignment of canalization to these components of phenotypic variance. I therefore use ‘phenotypic canalization’, or just ‘canalization’, to describe the situation in Fig. 1 around environment 0.

The strongest evidence of canalization comes from meristic or threshold traits that are nearly invariant in natural populations, using major mutations or environmental perturbations to experimentally decanalize the trait (Rendel, 1967, 1968; Scharloo, 1991; Rutherford & Lindquist, 1998; de Visser et al., 2003; Flatt, 2005). Phenotypic canalization is evident in natural variation of some meristic traits such as ray floret number in Chrysanthemum segatum, in which the distance between the thresholds around the modal number substantially exceeds that between thresholds around other numbers (Wright, 1968, pp. 262–263). Similarly, the frequency of abnormal vertebrae in herring fish increases markedly for vertebrae numbers well above or below the mean (Fisher, 1958, p. 129).

Little evidence of canalization exists for most quantitative characters, and extreme environments or intense artificial directional selection to change the mean phenotype has produced mixed results concerning the increased genetic variance predicted by canalization (Hoffmann & Parsons, 1993, 1997; Wagner et al., 1997; Hermisson & Wagner, 2004; Mery & Kawecki, 2004; Flatt, 2005; Garland & Kelly, 2006). However, intense artificial stabilizing (or disruptive) selection produced a substantial decrease (or increase) in both the genetic and environmental components of phenotypic variance in quantitative characters that were artificially decanalized by a major mutation (Scharloo, 1964, 1972, 1991; Scharloo et al., 1967). Artificial disruptive selection generally increased genetic and environmental components of variance, but artificial stabilizing selection produced relatively small reductions in the variances in wild-type populations (Gibson & Thoday, 1963; Gibson & Bradley, 1974; Kaufman et al., 1977), which presumably were already subject to stabilizing natural selection.

Another classical topic neglected in population genetics theory involves the evolution of plasticity by ‘genetic assimilation’ (Waddington, 1953, 1961; Schlichting & Pigliucci, 1998; Pigliucci & Murren, 2003). In Waddington's experiments a new phenotype initially expressed as a plastic response to an altered environment is artificially selected in the altered environment until it becomes regularly expressed even in the original environment. Adding to the confusion in concepts of plasticity (Crispo, 2007), Waddington apparently misinterpreted his selection experiments on threshold characters, which do not necessarily involve the evolution of plasticity (Scharloo, 1991; Falconer & MacKay, 1996, pp. 309–310; de Jong, 2005). Here I define genetic assimilation in an altered environment as the reduction in plasticity and its replacement by genetic evolution, while maintaining the phenotype initially produced by plasticity in the altered environment. This is a potentially important process following the evolution of increased plasticity during adaptation to environmental change. Reduction in plasticity during genetic assimilation is often attributed to fitness costs of plasticity.

Quantitative genetic models describing evolution of phenotypic plasticity were analysed by several authors (Via & Lande, 1985, 1987; van Tienderen, 1991, 1997; Gomulkiewicz & Kirkpatrick, 1992; Gavrilets & Scheiner, 1993a,b; de Jong, 1995, 1999, 2005; de Jong & Gavrilets, 2000; Tufto, 2000). These models established that in the absence of constraints, when individuals are selected in the environment where they develop, plasticity should evolve to produce the optimum phenotype in every environment to which a population is repeatedly exposed in space and/or time. They also showed that the evolution of adaptive phenotypic plasticity can be constrained by genetic correlations among characters in different environments, or in parameters of their plasticity, as well as by costs of plasticity.

An important insight from quantitative genetic models of plasticity concerns the role of environmental predictability over time spans required for individual development (Gavrilets & Scheiner, 1993a; Scheiner, 1993; de Jong, 1999; de Jong & Gavrilets, 2000). The environments in which individuals develop often differ from those in which they are selected, due to temporal environmental fluctuations or individual dispersal in space. The slope of the population norm of reaction is then selected to be to a fraction of the slope of the optimum phenotype as a function of the environment, reduced by the correlation between the environments of development and selection. Discounting the environment during development by its predictability over the time lag until selection puts the average phenotype achieved by plasticity closest to the expected optimum phenotype at the time of selection. Such selection for mean plasticity less than the slope of the optimum phenotype actually is optimal, though common parlance labels this ‘partially adaptive’. The distinction is emphasized by considering a population subject to seasonal cycles, for which a negative environmental autocorrelation over a developmental time lag can select a norm of reaction with slope of opposite sign to that of the optimum phenotype as a function of the environment. This could be called ‘nonadaptive’ or ‘maladaptive’ plasticity, although again it is actually optimal. However, in some cases plasticity may be truly maladaptive (Grether, 2005; Ghalambor et al., 2007). Imperfect predictability of spatial and temporal environmental variation provides the most general explanation of why phenotypic plasticity typically is ‘partially adaptive’, even when genetic constraints and costs of plasticity are weak or absent (DeWitt et al., 1998; Van Buskirk & Steiner, 2009). It may also be one of the main causes for evolutionary decrease in plasticity during genetic assimilation.

Quantitative genetics of reaction norm evolution

For simplicity, I assume that the genotypic reaction norms and the optimum phenotype are linear functions of the environment. All individuals in the population in a given generation are assumed to experience the same environment. The adult phenotype of an individual subject to selection in generation t is

image( (1a))

Here a is the elevation (or intercept) of the genotypic reaction norm, giving the additive genetic effect (breeding value) in the reference environment, ɛ = 0 and b is the slope of the plastic phenotypic response to the environment. Generations are discrete and nonoverlapping, but the environment is assumed to change continuously, with time t measured in generations. Juveniles of generation t are exposed to environment ɛtτ during a critical period of development a fraction of a generation τ before the adult phenotype is expressed and subjected to natural selection. An independent residual component of phenotypic variation, e, caused by genetic dominance, developmental noise and micro-environmental variation unrelated to the macro-environment, is assumed to be normally distributed with constant mean inline image = 0 and variance inline image among individuals in every generation. The units of a and e are the same as for the character, z, whereas b is measured in character units per environmental unit.

Reaction norm elevation in the reference environment a and slope b are assumed to have a bivariate normal distribution in the population, with additive genetic variances, Gaa and Gbb, and covariance Gab that remain constant during evolution of the means, inline image and inline image. Thus in any generation the individual breeding values and adult phenotypes before selection also are normally distributed. Given the environment at time t - τ, the phenotypic mean and variance before selection in generation t are (Gavrilets & Scheiner, 1993a,b)

image( (1b))
image( (1c))

With linear norms of reaction plasticity b has identical additive genetic variance in all environments, Gbb. In contrast, the reaction norm elevation a + bɛtτ has additive genetic variance given by the first three terms on the right-hand side of eqn  (1c), which is a quadratic function of the environment of development, ɛtτ.

To model evolution of a canalized character I assume that that the population has long evolved under stabilizing selection in a typical range of environments centred around a reference environment, ɛ = 0, in which the additive genetic and phenotypic variances are minimized (as in Fig. 1 left panel). However, eqn  (1c) implies that these variances are minimized in environment ɛ = −Gab/Gbb. Therefore, reaction norm elevation in the reference environment and plasticity must be uncorrelated, Gab = 0. Then within any other environment reaction norm elevation and slope have covariance Gbbɛ. The genetic correlation between reaction norm elevation and slope thus reverses sign in environments above vs. below the reference environment. Similarly, de Jong (1990) and Stearns et al. (1991) showed that plasticity can change the magnitude and sign of genetic correlation between characters in different environments.

The optimum phenotype, θt, also is assumed to be a linear function of the environment at time t, and in each environment stabilizing selection towards the optimum phenotype is described by a Gaussian function having ‘width’ω,

image( (2a))
image( (2b))

Averaging over the phenotype distribution p(zt) yields the mean fitness

image( (2c))

where inline image.

The change per generation in mean reaction norm slope and elevation in the reference environment

image( (3a))

is the product of the additive genetic variance-covariance matrix for a and b and the selection gradient, β, which can be derived by substituting eqns  (1b,c, 2a) into eqn  (2c) and differentiating (Lande, 1979; Gavrilets & Scheiner, 1993a,b;de Jong, 1995, 1999)

image( (3b))

The subsequent analysis concerns the expected evolution of the mean reaction norm in a stochastic environment. Background environmental fluctuations follow a stationary autocorrelated process ɛt = ξt with mean inline image, variance inline image and autocorrelation ρ over time interval τ. For simplicity, the width of the fitness function is assumed to be substantially greater than the phenotypic standard deviation in environments experienced by the population, E(inline image) << ω2, so that γ ≈ 1/ω2 is approximately constant. Either before or after a sudden change in the average environment at time t = 0, eqns  (3a,b) governing the stochastic evolution of inline image and inline image, when averaged over the stationary distribution of background environmental fluctuations, will produce linear dynamic equations with constant coefficients for the expected mean reaction norm parameters, E(inline image) and E(inline image).

Before a change in the average environment (for t < 0), the expected evolution of the mean norm of reaction is a product of the additive genetic variance–covariance matrix and the expected selection gradient conditioned on the state of the population (eqns  3a,b). The expected selection gradient, given inline image and inline image, is

image( (3c))

Gavrilets & Scheiner (1993a) and de Jong & Gavrilets (2000) previously analysed this model for spatial rather than temporal environmental variation, and assumed (for simplicity) that Gab = 0 in the reference environment. Supposing that the population has adapted to the background environmental stochasticity, before the change in average environment the expected mean reaction norm parameters are

image( (3d))

and the expected mean phenotype coincides with the expected optimum phenotype, E(inline image.

  Thus before the sudden change in average environment the optimal norm of reaction has a slope lower by a factor ρ than the slope of the optimum phenotype as a function of the environment. Although termed ‘partially adaptive’, this represents the optimal plasticity. The reason is revealed by the prediction equation for the optimum phenotype at selection, given the environment at development. Assuming environmental fluctuations with a stationary Gaussian distribution having mean inline image = 0, the prediction equation for the environment at selection is E[ɛt|ɛtτ] = ρɛtτ (Kendall & Stuart, 1973). Conditioning eqn  (2a) on the environment at development and taking expectations then yields the prediction equation for the optimum phenotype, E[θt|ɛtτ] = A + ρBɛtτ, which has a slope lower than in eqn  (2a) by a factor ρ.

Sudden change in a stochastic environment

Let the environment be composed of two parts,

image(4)

The unit step function Ut (which changes from 0 to 1 at t = 0) governs the sudden change in average environment by amount δ at time 0. Background environmental stochasticity ξt constitutes a stationary autocorrelated process described above. This model is illustrated in Fig. 1 (upper left panel).

After the sudden change in average environment (for t ≥ 0), the expected selection gradient, given inline image and inline image, is

image( (5a))

Gavrilets & Scheiner (1993b) derived a special case of this formula with no stochasticity to analyse the response to directional selection in a constant environment. Here I analyse the expected evolution with continued background environmental stochasticity.

Long after the sudden change in average environment, the eventual evolutionary equilibrium of the probability distribution of inline image and inline image occurs when the expected selection gradient in eqn (5a) vanishes. This yields the final expected mean reaction norm parameters after adaptation to the new environment is completed,

image( (5b))

Then, using eqns  (1b, 2a), the final expected mean phenotype coincides with the expected optimum in the new environment, inline image. Comparison of eqns  (3d) and (5b) shows that the expected mean reaction norm slope (mean plasticity) undergoes no net change from beginning to end, whereas the mean reaction norm elevation eventually increases to achieve the expected optimum phenotype in the new environment, finally producing a total change in the expected mean phenotype of inline image.

I now show that after a sudden major change in the average environment selection produces a rapid transient increase in mean plasticity, followed by slow genetic assimilation decreasing the mean plasticity. I calculate the maximum proportion of the total adaptive change in mean phenotype achieved by the transient increase in plasticity before it is lost by genetic assimilation.

From eqns  (3a) and (5a,b) the expected evolution of the mean reaction norm parameters for t ≥ 0 obeys

image( (6a))

The expected dynamics can be solved using eigenvalues, λ, and eigenvectors, v, of the matrix (Searle, 1966),

image( (6b))

where c1 and c2 are constants determined by the initial conditions at t = 0 (eqn  3d).

It is informative to consider approximate results for a sudden environmental change of magnitude much greater than the usual range of background environmental fluctuations. Results then take the form of series in the small parameter, inline image << 1. Eigenvalues of the matrix are to first order

image( (6c))
image( (6d))

where φ = Gbbδ2/(Gaa + Gbbδ2) is the proportion of the additive genetic variance in the new environment due to additive genetic variance in plasticity (eqn  1c). Associated with each eigenvalue is an eigenvector describing a direction of change in the expected mean reaction norm parameters, which are to first order

image( (6e))

Using the assumption that inline image (after eqn  3b), the geometric terms in eqn  (6b) can be approximated as exponential functions, (1 + λi)t ≈ eλit, producing the time scales for these components to approach equilibrium, ti ≈ −1/λi for i=1,2. By comparison the time scale for Darwinian evolution alone (or for the Baldwin effect with constant plasticity, after the initial plastic response) is tD ≈ −1/(γGaa) (Lande, 1976). Ratios of the time scales are to leading order

image( (6f))

For an extraordinary change in environment, with inline image << 1 and φ near 1, Phase 2 is far slower than Phase 1. Under these conditions Phase 1 also occurs much faster than Darwinian evolution alone (with plasticity absent or constant). The great difference in these time scales allows separation of the expected dynamics into two distinct phases of evolution, depicted in Fig. 2, with durations denoted as ‘order of magnitude’O(t1) and O(t2) representing a few multiples of t1 and t2.

Figure 2.

 Dynamics of (a) the expected mean phenotype E(inline image) and log mean fitness in the average environment inline image, with (b) expected mean reaction norm slope (plasticity) E(inline image) and elevation in the reference environment E(inline image), following a sudden extraordinary change in average environment. Solid lines: Two-phase adaptation with evolution of plasticity occur on time scales t1 and t2. Dashed lines: Adaptation with constant partially adaptive plasticity followed by natural selection (Baldwin effect). Dotted lines: Adaptation by natural selection alone with no plasticity. Left panels depict short-term dynamics including Phase 1. Right panels illustrate long-term dynamics including Phase 2 with time plotted logarithmically.

Phase 1: 0 < t ≤ O(t1)

After the sudden change in average environment Phase 1 begins with a precipitous decrease in mean fitness and a jump in the mean phenotype by expression of partially adaptive plasticity during the first generation in the new environment. The expected initial direction of evolution in mean reaction norm parameters produces contributions to the expected change in the mean phenotype proportional to (Gaa,Gbbδ2)T where superscript T indicates transposition (eqns  3d, 5b, 6a). This agrees to leading order with the direction implied by the first eigenvector, v1 (eqn  6e), and accords with previous results for directional selection in a constant environment (Gavrilets & Scheiner, 1993b). Thus the proportion of the initial response of the mean phenotype at the beginning of Phase 1 due to evolution of increased plasticity is φ.

With a strong separation of time scales (eqn  6f), at the end of Phase 1 the component of change from the first eigenvector has nearly vanished, (1 + λ1)O(t1) ≈ 0 whereas that from the second eigenvector remains nearly unchanged, (1 + λ2)O(t1) ≈ 1. To leading order the constants are c1 ≈ − B, c2 ≈ − φB. Using eqns  (5b, 6b,e) and ignoring small terms, the expected mean reaction norm elevation and slope at the end of Phase 1 are then

image( (7a))
image( (7b))

In generation t = 1, after the initial expression of phenotypic plasticity in the new environment but before selection on adults, the adaptive phenotypic change that remains to be completed is (1 − ρ)Bδ. By the end of Phase 1 a fraction near φ of this has occurred by a transient increase in plasticity, and a fraction near 1 − φ occurred by evolution of reaction norm elevation in the reference environment. These terms when added give nearly the expected optimum phenotype in the new environment. More accurately, at the end of Phase 1 a small fraction of the total adaptive change in the expected mean phenotype still remains to be completed during the long second phase. To first order this is (from eqn  6b)

image( (7c))

Empirical observations suggest that the heritability of plasticity may usually be much smaller than that of the breeding value in the average environment (Scheiner, 1993). Nevertheless, an extraordinary change in average environment, with φ near 1, is sufficient for the new expected optimum to be nearly achieved at the end of Phase 1 predominantly by a transient increase in mean plasticity, with relatively little change in the mean breeding value in the reference environment.

This condition also implies a substantial increase in genetic variance (eqn  1c) after a major change in the average environment and throughout the subsequent phases. The reaction norm elevation and slope that were uncorrelated in the original average environment become strongly correlated in the new average environment. Under weak stabilizing selection the increased genetic variance in the new average environment slightly reduces the mean fitness (eqn  2c), even after the mean phenotype has nearly achieved the new expected optimum.

Phase 2: O(t1) < t ≤ O(t2)

The expected direction of change in the mean reaction norm elevation and slope during Phase 2, v2 (eqn  6e), produces contributions to change in the expected mean phenotype of nearly equal magnitude but opposite sign, (δ, − δ)T. The increased plasticity gained at the end of the previous phase becomes slowly reduced by genetic assimilation to the original level determined by the predictability of environmental fluctuations over the time lag for individual development. This involves gradual reduction in slope of the mean reaction norm, with a compensatory increase in reaction norm elevation in the reference environment. During Phase 2 the expected mean phenotype slowly undergoes the last small fraction of adaption to the new expected optimum (eqn  7c). The small distance to the optimum remaining at the end of Phase 1 (barely visible in the upper right panel of Fig. 2) eventually disappears in Phase 2 and would be obscured by background environmental fluctuations in a realization of the full stochastic process.

Even if the zone of canalization around the reference environment ɛ = 0 does not coincide with the original average environment, inline image, the expected dynamics would resemble that described here, provided that the deviation of the new average environment from the reference environment, δ, substantially exceeds both the magnitude of background environmental fluctuations and the deviation of the original average environment from the reference, inline image. This would still entail an increase in genetic variance in the new average environment compared to the original one.

On a long time scale, possibly commensurate with t2, stabilizing selection around the expected optimum in the new average environment would re-canalize the genetic variance, and diminish the genetic correlation between reaction norm elevation and slope towards zero in the new average environment. These effects, not included in the present model, would facilitate genetic assimilation during Phase 2, which nevertheless should remain a slow process.

Figure 1 (right panel) depicts the phases in the expected evolution of the population mean norm of reaction for a canalized character following a sudden extraordinary change in the average environment. For parameter values in the figure caption φ = 0.9 is near 1, and inline image as well as inline image are small, satisfying the assumptions of the model, under which evolution of plasticity greatly accelerates phenotypic adaptation to a sudden environmental change.

Figure 2 illustrates the expected dynamics of the mean phenotype, the loss and recovery of mean fitness in the average environment (assuming constant Wmax in eqn  2c), and evolution of the mean reaction norm parameters, compared to the expected dynamics for natural selection alone with no plasticity, and to the Baldwin effect with constant plasticity. Parameters in Fig. 1 give the approximate time scales t1 = 10 and t2 = 2780 generations.

Discussion

The assumption of linear norms of reaction entails that if a quantitative character is canalized, with minimum genetic and phenotypic variance in its average environment, then reaction norm slope (plasticity) and elevation (breeding value) in the average environment must be uncorrelated, as in Fig. 1 (left panel). This genetic architecture determines the expected dynamics of phenotypic adaptation for a canalized character. After a sudden extraordinary environmental change, substantially exceeding typical background environmental fluctuations, a key parameter in the expected dynamics is φ, the proportion of the additive genetic variance in the new average environment due to additive genetic variance in plasticity. The greater the change in the average environment the larger the increase in additive genetic variance, making φ closer to 1. The expected dynamics occurs in two phases, illustrated for an example with φ near 1 in Fig. 1 (right panel) and Fig. 2.

The expected mean phenotype initially coincides with the optimum in the original average environment. The initial mean plasticity is partially adaptive, lower than the slope of the optimum phenotype as a function of the environment by a factor ρ, the predictability of background environmental fluctuations over the time lag for individual development. After a sudden major change in average environment, Phase I begins with a precipitous drop in mean fitness ameliorated by a jump in mean phenotype through expression of partially adaptive plasticity, and increased additive genetic variance, during the first generation in the new environment.

Transient evolution of increased plasticity accelerates phenotypic adaptation during Phase 1. The time scale for the mean phenotype to closely approach the optimum in the new average environment is 1 − φ times shorter than by Darwinian evolution alone (with no plasticity) or by the Baldwin effect (with constant plasticity). Under the Baldwin effect the proportion of the total adaptive change due to plasticity is ρ. Allowing evolution of plasticity, this increases to nearly ρ + φ(1 − ρ) at the end of Phase 1. Thus for φ near 1 most of the phenotypic adaptation is initially achieved by a combination of preexisting plasticity and transient evolution of increased plasticity. At the end of this phase the mean norm of reaction has only slightly increased its elevation in the original average environment, but markedly increased its slope.

Phase 2 involves a slow process of genetic assimilation with reduction in plasticity nearly compensated by evolution of breeding value in the reference environment, while the remaining small fraction of the adaptive change in the expected mean phenotype is completed. The mean plasticity gradually returns to a value determined by the predictability of background environmental fluctuations, ρ. The mean norm of reaction slowly increases in elevation in the reference environment while decreasing in slope, maintaining the mean phenotype near the optimum in the new average environment.

Accelerated phenotypic adaptation during Phase 1 can alternatively be interpreted as resulting from increased genetic variance in the new environment (eqns  1c, 6c). This also entails an increased magnitude of genetic correlation between reaction norm slope and elevation in the new environment (after eqn  1c), which retards genetic assimilation in Phase 2. Stabilizing selection in the new range of environments should eventually readjust the zone of canalization, reducing the genetic variance and diminishing the correlation between reaction norm slope and elevation in the new average environment. Such re-canalization, or a small cost of plasticity, would facilitate genetic assimilation but this should remain a slow process.

Remarkably, the end result is almost the same as evolution by natural selection without plasticity, or by the Baldwin effect with constant plasticity (Fig. 2). One long-lasting effect of transient evolution of increased plasticity might be larger genetic variance and increased genetic correlation between reaction norm slope and elevation in the new average environment. The most permanent effect may be that the population still persists when it would have gone extinct without rapid phenotypic adaptation allowed by transient evolution of plasticity. The phenotypic plasticity that finally evolves in the new environment may be larger or smaller that in the original environment due to a change in environmental autocorrelation, or evolution of the population life history, altering the predictability of environmental fluctuations. These considerations help to explain inconsistent findings in empirical tests for increased plasticity in invasive species in their new range compared to their native range (references in Introduction). Whether increased plasticity is observed depends on the magnitude of change in the average environment, the genetic variance in plasticity, the predictability of environmental fluctuations in native and nonnative ranges, and the time scale for genetic assimilation in the new environment, in comparison with the time of observation.

Preexisting plasticity must frequently contribute to adaptive phenotypic evolution in response to small or slow environmental changes. In contrast, transient evolution of increased plasticity and genetic assimilation are predicted only during adaptation of a canalized character to an extraordinary environmental change, exceeding the usual background environmental fluctuations. Qualitatively similar dynamics would occur whenever a canalized character adapts to a major environmental change that happens more rapidly than the time scale for evolution by Darwinian natural selection alone or by the Baldwin effect with constant plasticity. The qualitative dynamics do not depend on the population being initially centred in a zone of canalization, but only on genetic variance in plasticity causing a substantial increase in genetic variance in the new environment.

The existence of canalization, regardless of its cause, must be addressed empirically by testing whether a minimum of phenotypic and genetic variances exist in an intermediate environment. For continuously varying quantitative characters tests for canalization must be performed on an appropriate scale of measurement on which the phenotypic variance is not correlated with the mean phenotype among populations in different environments, for example by use of a generalized logarithmic transformation (Wright, 1977, Chapters 11 and 12; Falconer & MacKay, 1996; Lynch & Walsh, 1998). Observations on the environmental dependence of phenotypic and genetic variances, in conjunction with analysis of genetic variability in reaction norms, can test for canalization and the potential for accelerated phenotypic adaptation by evolution of plasticity after an extraordinary environmental change.

The present model assumes that genetic variability in reaction norm parameters is maintained during adaptation to a new environment. Initial population sizes often are large for natural populations in situ, and in deliberate species introductions for biocontrol (Gurr et al., 2002; Heikki & Lynch, 2003; Hawkins & Cornell, 2008), accidental translocations and natural invasions (Mooney & Hobbs, 2000; Carleton & Ruiz, 2003; Mooney et al., 2005; Boorsma et al., 2006). Even a small founding population can contain a high fraction of the heterozygosity and additive genetic variance in quantitative characters that existed in a large source population (Lewontin, 1965; Lande, 1980). Populations of invasive species outside their native range usually maintain substantial genetic variance (Sexton et al., 2002; Clements et al., 2004; Gilchrist & Lee, 2007), although in some cases they are genetically depauperate (e.g. Pan et al., 2006).

Experiments on newly established small populations show that intense artificial selection can rapidly create large phenotypic changes, often altering the mean phenotype by several standard deviations within a few dozen generations (Wright, 1977; Robertson, 1980; Falconer & MacKay, 1996). The most important impact of restricted population size may be the elimination of rare (formerly deleterious) alleles that could be advantageous in a new environment. For extremely large populations undergoing sudden environmental change in situ, sustained intense directional selection can cause adaptation by a rare allele of major effect, as often occurs in the evolution of pesticide resistance in natural populations (Roush & McKenzie, 1987;Roush & Tabashnik, 1990;) but if the major gene has a large homozygote disadvantage that prevents fixation in the new environment, it may eventually be replaced (assimilated) by quantitative genetic changes (Lande, 1983). Population bottlenecks during species introductions, or following extraordinary environmental change in situ, tend to eliminate rare alleles and predispose populations towards quantitative genetic evolution, if substantial genetic variation is maintained through the bottleneck or created by high rates of spontaneous polygenic mutation (Lande, 1975; Bürger, 2000).

Acknowledgments

I thank G. Mace, A. Hendry, F. Galis, J. Tufto, A.M. Lister, L.-M. Chevin and S. Engen for discussions. This work was supported by a Royal Society Research Professorship.

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