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Keywords:

  • environmental change;
  • labile trait;
  • mixed model;
  • phenotypic plasticity;
  • random regression;
  • reaction norm;
  • vertebrate;
  • wild population

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Variation in individual reaction norms
  5. Ecological and evolutionary causes of reaction norm variation
  6. Using random regression to measure I × E and G × E
  7. Analyses of individual plasticity in wild vertebrate populations
  8. Predicting a population's response to the environment: a reaction norm perspective
  9. Future directions and applications
  10. Conclusions
  11. Acknowledgments
  12. References

The ability of individual organisms to alter morphological and life-history traits in response to the conditions they experience is an example of phenotypic plasticity which is fundamental to any population's ability to deal with short-term environmental change. We currently know little about the prevalence, and evolutionary and ecological causes and consequences of variation in life history plasticity in the wild. Here we outline an analytical framework, utilizing the reaction norm concept and random regression statistical models, to assess the between-individual variation in life history plasticity that may underlie population level responses to the environment at both phenotypic and genetic levels. We discuss applications of this framework to date in wild vertebrate populations, and illustrate how natural selection and ecological constraint may alter a population's response to the environment through their effects at the individual level. Finally, we present future directions and challenges for research into individual plasticity.


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Variation in individual reaction norms
  5. Ecological and evolutionary causes of reaction norm variation
  6. Using random regression to measure I × E and G × E
  7. Analyses of individual plasticity in wild vertebrate populations
  8. Predicting a population's response to the environment: a reaction norm perspective
  9. Future directions and applications
  10. Conclusions
  11. Acknowledgments
  12. References

Phenotypic plasticity is classically defined as occurring when the phenotype expressed by a given genotype alters as environmental conditions change (Pigliucci, 2001). It has typically been modelled and empirically examined using the ‘reaction norm’ concept (Via et al., 1995). A reaction norm is simply a function (or series of functions) describing the change in a genotype's phenotype across an environmental gradient. The extensive empirical and theoretical literature on the evolutionary biology of plasticity has strongly focused on demonstrating the adaptive nature of cases of phenotypic plasticity (Gotthard & Nylin, 1995), and examining the quantitative genetic basis of reaction norms (Scheiner & Lyman, 1989; de Jong, 1995; Via et al., 1995; Pigliucci, 2005). The latter research has focused on the interaction of genotypes with their environment.

Plasticity allows an organism to ‘fit’ its phenotype to the changeable environment: when the optimal phenotype varies with environmental conditions experienced, the evolution of phenotypic plasticity is predicted (Van Tienderen, 1991; Houston & McNamara, 1992). However, it is important to note that interest within evolutionary ecology is not limited to incidences where plasticity is adaptive. Plasticity can be maladaptive, for example if a canalized phenotype is optimal (Eshel & Matessi, 1998), or can be neither strictly speaking adaptive or maladaptive, for example where environmental conditions impose physiological constraints that limit or alter trait expression (Gotthard & Nylin, 1995). It is also important to investigate these cases if we are to fully understand the evolutionary and ecological basis of phenotypic variation across environments (Miner et al., 2005; Pigliucci, 2005, Postma & van Noordwijk, 2005).

Changes in the environmental conditions experienced by naturally occurring populations are frequently accompanied by changes in morphological and life-history traits expressed by individuals within those populations (Stearns & Koella, 1986; Stenseth et al., 2002; Walther et al., 2002). In long-lived organisms such traits are often ‘labile’: they are expressed repeatedly across the lifetimes of individuals and can vary over the course of an organism's ontogeny (Gomulkiewicz & Kirkpatrick, 1992; Lynch & Walsh, 1998). This is in contrast to so-called ‘non-labile’ traits which are expressed once in an individual's lifetime (e.g. amphibian metamorphosis, Newman, 1994). When individuals are monitored throughout their life, repeated measures of the expression of labile traits are collected over a range of environmental conditions experienced by those individuals. Examples of labile traits that can be recorded in wild populations are reproductive traits (such as the timing of reproduction and the number or size of offspring produced), morphological characters that are regularly re-grown (such as moulted feathers or patches of feather colouration in birds and antlers or horns in ungulates), and measures of body size or condition. The ability of individual organisms to alter the expression of a labile trait in response to environmental conditions is a form of phenotypic plasticity that is widely assumed to underlie correlations between environment and phenotype observed at the population level in wild animals (e.g. Réale et al., 2003; Both et al., 2004). Until very recently, explicit empirical examination of individual plasticity in wild populations was lacking, despite its fundamental importance to any population's ability to deal with environmental change (Przybylo et al., 2000; Nussey et al., 2005b).

Despite the profound interest in phenotypic plasticity within the fields of evolutionary biology and ecology, we still know little about the causes and consequences of variation in life history plasticity in the wild, or how natural selection operates on plasticity (Pigliucci, 2005). Plasticity in labile traits is ubiquitous in natural populations of long-lived, iteroparous organisms. However, analysis of the between-individual variation in reaction norms that may underlie population-level responses to the environment in such systems requires the collection of individual based data on natural systems over long time series. Nevertheless, data sets that meet these demanding criteria are increasingly available, most notably for populations of hole-nesting passerines and ungulates (e.g. Coulson et al., 2000; Saether et al., 2005). Here we present a conceptual and analytical framework to assess patterns of individual plasticity and the evolutionary potential of this plasticity using data collected from wild populations. This framework utilizes a particular kind of mixed-effect statistical model, the random regression, to explore between-individual variation in reaction norms at the level of individual phenotype and at the underlying genetic level. This analytical approach is general, and can be used to model variation genetic and non-genetic variation in individual plasticity in any labile trait expressed across any environmental continuum. Here, we specifically discuss its application to date with respect to wild vertebrate populations. We present a review of analyses of individual plasticity in wild vertebrate populations to date, and then illustrate how this conceptual and analytical framework is likely to improve our ability predict changes in the way a population responds to the environment. Finally, we discuss challenges and future applications for this approach.

Variation in individual reaction norms

  1. Top of page
  2. Abstract
  3. Introduction
  4. Variation in individual reaction norms
  5. Ecological and evolutionary causes of reaction norm variation
  6. Using random regression to measure I × E and G × E
  7. Analyses of individual plasticity in wild vertebrate populations
  8. Predicting a population's response to the environment: a reaction norm perspective
  9. Future directions and applications
  10. Conclusions
  11. Acknowledgments
  12. References

Our approach to labile trait plasticity in natural systems hinges on the measurement of variation in phenotypic reaction norms. The simplest and most widely applied form of reaction norm is a simple linear relationship, where the reaction norm is described by the coefficients of a linear regression of the phenotype on the environmental variable of interest (Pigliucci, 2001). A phenotypic response to the environment using the linear reaction norm approach is characterized by two parameters: elevation and slope. Where the environmental covariate of interest is mean-centred, elevation equates to the expected trait value in the average environment. The slope parameter estimates the change in phenotype across an environmental gradient and is therefore a measure of phenotypic plasticity. These reaction norm parameters can themselves be treated as quantitatively varying traits. Here we consider only linear reaction norms, both by way of illustration and because the studies we review have examined systems showing linear trait–environment relationships. However, extension of the approach described below to nonlinear reaction norms, for example through polynomial regression, is straightforward (Gilbert et al., 1998; Pigliucci, 2001).

In this section, we specifically aim to detail a conceptual framework for the investigation of variation in reaction norms at the level of the individual as measured in natural settings. The reaction norm approach to phenotypic plasticity has a long and distinguished history (Via et al., 1995; Pigliucci, 2001). However, the approach taken in the analysis of longitudinal data collected on individuals necessarily, but subtly, differs from the vast majority of empirical research on phenotypic plasticity, which tends to focus on non-labile traits and to be experimental in nature. In non-labile traits, which are expressed only once in an individual's lifetime, individual phenotypic reaction norms cannot be measured. However, many traits are labile and variation at the level of the individual phenotype has been explored relatively infrequently in either experimental or natural settings. Empirical enquiry into plasticity in labile traits at the within-individual level has not been limited to vertebrates. There has been work of an experimental nature on plants (e.g. Cook & Johnson, 1968; Winn, 1996) comparing changes within individuals across discrete, experimentally manipulated environments. The approach discussed here models reactions norms against continuously varying environments, but it is general and can be applied to model variation in plasticity in any labile trait in any system.

Our approach to modelling individual reaction norms considers variation at the level of the individual phenotype, and contributions to this from both genetic and non-genetic effects. This again differentiates it from much of the experimental literature. Experimental studies of non-labile trait plasticity typically expose inbred or clonal groups to different environmental conditions and can thus infer whether genetic variation in plasticity (a genotype by environment interaction, or G × E) is present by comparing the responses to environmental variation in the different groups. In contrast, for labile traits measured in natural systems, phenotypic variation at the between-individual level need not equate to additive genetic variation. This is because, in addition to genetic differences, individuals may also experience differing sets of non-genetic effects on their phenotypes. However, given appropriate data, the between-individual phenotypic variation can be decomposed into genetic and non-genetic (or so-called ‘permanent environmental’) components using quantitative genetic models (Lynch & Walsh, 1998; Meyer & Kirkpatrick, 2005).

Although a population-level response to the environment will depend on individual-level plasticity, the nature of individual reaction norms cannot necessarily be inferred from population-level analyses. We propose that a population-level phenotypic response to the environment can be broken down based first on whether or not there is variation in plasticity among individuals at a phenotypic level, and secondly, the relative contribution of genetic and non-genetic sources to variation to phenotypic variation in reaction norms (Fig. 1). As evolutionary biologists, we are especially interested in determining whether genetic variation in individual plasticity is present as this will determine its evolutionary potential (Scheiner & Lyman, 1989). We refer to the presence of between-individual variation in plasticity (i.e. differences in reaction norm slope across individuals) as an individual by environment interaction (‘I × E’; Fig. 1). The presence of additive genetic variation in phenotypic plasticity in labile traits is equivalent to a genotype by environment interaction (‘G × E’; Fig. 1), and means that observed plasticity may itself be thought of as a quantitative trait with the potential to evolve under selection (Scheiner, 2002).

image

Figure 1.  Three different levels of analysis are involved in understanding individual plasticity in labile life history traits. Cross-sectional studies examine population-level responses to the environment (left most graph), which can be underpinned by variation between individuals in their plastic response to the environment (I × E) or not. The presence or absence of I × E can itself be accompanied by underlying variation in plasticity at the additive genetic level (G × E) or not.

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Quantification of individual reaction norms and I × E in wild populations opens a largely unexplored level of phenotypic variation for enquiry. Empirical research to date has largely ignored variation in reaction norms at the individual level, focusing on the genetic architecture and potential for evolution of plasticity (i.e. G × E; Pigliucci, 2005). However, non-genetic sources of variation in labile trait plasticity are also expected to occur in nature. For example, differences in the ecological conditions experienced by individuals across their lifetimes or variation in non-genetic aspects of individual quality may lead to a pattern of I × E without underlying G × E (Fig. 1). Furthermore, consideration of I × E offers a notable advantage over experimental studies when it comes to assessing natural selection on plasticity. In non-labile traits the fitness consequences of differential trait expression must be somehow integrated across all possible environments, creating nonindependence between plasticity and fitness (Weis & Gorman, 1990). In contrast, by estimating selection on labile traits that occur repeatedly within individuals, the same entity expresses plasticity and is under selection. Thus, an individual's lifetime fitness and response to the environments it encountered during its life can be quantified directly.

As an illustrative example of these concepts, the average egg laying date in many bird species is known to advance in response to warm spring temperatures (e.g. Visser et al., 2002; Both et al., 2004). However, the pattern of individual reaction norms underlying these trends is rarely explored. If, for simplicity, we assume that individual reaction norms are linear, we can see that such patterns can be readily described through the measurement of between-individual variation and covariation in trait elevation and slope. Eight possible basic patterns of reaction norm variation (shown in Fig. 2) can be differentiated based on the presence or absence of: (1) an average plastic response to the environment amongst individuals in a population (‘E’: present in Fig. 2b, c, e & h); (2) the presence of variation between individuals in their reaction norm elevation (‘I’: Fig. 2a–f) and/or slope (‘I × E’: Fig. 2c–h) and (3) covariation between individuals’ reaction norm elevation and slope [‘Correl (I, I × E)’: Fig. 2e & f].

image

Figure 2.  Eight possible patterns of linear reaction norms, differentiated based on the presence of a response to the environment on average (‘E’: b, c, e, h) variation in elevation (‘I’: a–f), slope (‘I × E’: c–h), and covariance between the two [‘Correl (I, I × E)’: e & f]. This is illustrated using six hypothetical individual reaction norms. Inset in each panel is a graph showing the population average response to the environment (blue lines) and the change in phenotypic variance across the environment (red lines) expected given the pattern of reaction norms.

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The pattern of individual plasticity expressed also affects the observed population-level response to the environment and the levels of phenotypic variance observed under differing environmental conditions (inset panels of Fig. 2). Note that even in the absence of a significant population-level response to the environment, some individuals may still respond plastically to the environment (I × E present but mean slope of zero: Fig. 2d, f & g). Furthermore, where individual elevations and slopes both vary and also covary (Fig. 2e & f), or where elevations show no variation but slopes do vary (Fig. 2g & h) levels of phenotypic variance in the trait measured will change across the environmental gradient (Postma & van Noordwijk, 2005).

The importance of measuring phenotype against relevant values of the environmental parameter (E) is also apparent from the scenarios presented in Fig. 2. Although the patterns in Fig. 2a–d are robust to the range of environments they are measured in, if we were to shift the scenarios in Fig. 2g or h to the left along the environmental x-axis, we would observe the situation observed in Fig. 2f and e, respectively. Hence, examination of phenotypes in a laboratory setting, against a range of environments that is different to that experienced in nature could potentially result in a pattern of plasticity different to that seen in the wild. Studies of plasticity in natural populations therefore have the advantage that, by definition, reaction norms are considered over appropriate values of E. It is worth noting that under circumstances where each individual experiences only a narrow range of possible conditions along the environmental x-axis, the average slope of individual's reaction norms will not necessarily equate to the population level response to the environment. In the illustrative examples of Fig. 2, we have assumed that individuals experience a normally distributed (random) set of conditions along the environmental x-axis.

Ecological and evolutionary causes of reaction norm variation

  1. Top of page
  2. Abstract
  3. Introduction
  4. Variation in individual reaction norms
  5. Ecological and evolutionary causes of reaction norm variation
  6. Using random regression to measure I × E and G × E
  7. Analyses of individual plasticity in wild vertebrate populations
  8. Predicting a population's response to the environment: a reaction norm perspective
  9. Future directions and applications
  10. Conclusions
  11. Acknowledgments
  12. References

Having described how individual reaction norms might vary within a population, we must now consider the ecological and evolutionary forces driving that variation. Many examples of population-level plasticity in labile life history traits are thought to be the result of environmental effects on physiological condition (e.g. Albon et al., 1987; Stevenson & Bryant, 2000). Changes in another ecological parameter that also affects individual physiological condition, for example resource competition, could potentially alter the pattern of plasticity in the population (Nussey et al., 2005a,b). In a red deer population on the Isle of Rum in Scotland, females are known to respond to warm springs by producing heavier offspring (Albon et al., 1987). Population density has risen over the study period, and this increase in resource competition is associated with reduced maternal plasticity for offspring birth weight (Nussey et al., 2005a). Thus, in this system, the pattern of individual plasticity is itself determined by prevailing ecological conditions.

Natural selection may also act to change patterns of individual reaction norms where variation in those reaction norms has a heritable component (Scheiner & Lyman, 1991; Pigliucci, 2001). Our ability to understand and predict the micro-evolutionary dynamics of plasticity in nature hinge on our being able to assess both whether variance in individual phenotypic reaction norms is under natural selection and whether it has a genetic component. Quantitative genetic theory would lead us to expect a micro-evolutionary change in plasticity if there is directional selection on reaction norm slope as well as G × E (i.e. heritable variation in slope) (Lynch & Walsh, 1998, but see Meriläet al., 2001).

The possibility of G × E and the potential for a micro-evolutionary response to selection in plasticity must also be considered in systems where there is no evidence of I × E (Fig. 1). This may seem counterintuitive and may ultimately be unlikely, but as different factors can influence the genetic and non-genetic components of individual plasticity this could occur. Environmental forces could act to reduce variation among individual slopes (i.e. reduce I × E), although underlying genetic variation in plasticity is present. Conceivably, any reaction norm pattern described in Fig. 2 could be present at the genetic level so long as phenotypic variation at the individual level was present for the measured trait in question.

Using random regression to measure I × E and G × E

  1. Top of page
  2. Abstract
  3. Introduction
  4. Variation in individual reaction norms
  5. Ecological and evolutionary causes of reaction norm variation
  6. Using random regression to measure I × E and G × E
  7. Analyses of individual plasticity in wild vertebrate populations
  8. Predicting a population's response to the environment: a reaction norm perspective
  9. Future directions and applications
  10. Conclusions
  11. Acknowledgments
  12. References

When considering linear reaction norms of individuals, it is in principle possible to use a series of simple linear regressions to estimate reaction norm properties separately for each individual. However, adequately estimating an individual's elevation and slope in this way will require a substantial number of repeated measures per individual and will be highly sensitive to outliers (Pinheiro & Bates, 2000). An alternative and more powerful way to test for and describe individual plasticity is through the use of random regression models. This type of mixed effect model, in which individual functions of continuous covariates are fitted as random effects, was introduced by Henderson (1982), and has been widely applied within the animal breeding literature (Meyer, 1998; Schaeffer, 2004 for review). Within the field of evolutionary biology, Kirkpatrick & Heckman (1989) developed the same analytical framework which they termed ‘infinite dimensional models’.

Random regression (or infinite dimensional) models have been extensively applied to analyses of trait ontogeny, for example to understand the evolution of growth curves (e.g. Kirkpatrick & Heckman, 1989; Wilson et al., 2005) or milk yield in dairy cattle (e.g. Jamrozik & Schaeffer, 1997). Using an appropriate environmental parameter (E) in place of age, random regression models can also be used to the model reaction norms of labile traits more generally (Gomulkiewicz & Kirkpatrick, 1992), including specific testing of I × E and G × E. Random regression models are commonly fitted using higher order (Legendre) polynomials (Kirkpatrick & Heckman, 1989), or other nonlinear functions (e.g. splines; Schaeffer, 2004). Here, for simple illustration, we discuss these models in the context of a first order (i.e. linear) reaction norm characterized by an elevation and slope only.

Determining I × E

As an example, consider the relationship between the timing of a reproductive trait y (e.g. laying date) and an environmental variable E (e.g. spring temperature) both measured on occasion j. At the individual level, yij the phenotype of individual i on occasion j might be specified as:

  • image(1)

Here, the fixed part of the model describes the population average response of trait y to changing environment E. For simplicity this average response is assumed to be linear in Eqn 1, such that if the environmental variable is zero centred (i.e. mean E = 0 across all phenotypic records), μ is the population mean phenotype in the average environment. β is the population mean slope of y on E. More complex functions of E may be used if appropriate, and additional fixed effects included to account for known influences on phenotype (e.g. sex, age).

Individual phenotypic deviations from the population average elevation and slope are then modelled by the random effects structure. Thus pi represents a ‘permanent’ deviation from the population mean phenotype that is independent of E (i.e. the individual reaction norm elevation), whereas pEi represents the deviation from the population average slope (i.e. individual plasticity). It is assumed that pi and pEi are normally distributed with means of zero and variances of Vp and VpE, respectively. Vp is equal to the phenotypic variance in trait y when E = 0, whereas VpE is the variance in individual reaction norm slopes (i.e. the variance attributable to I × E).

The final term in the Eqn 1 is ɛij, a residual error term. Where repeated records on individuals are analysed using mixed models (including random regressions), it is often assumed that residual errors are uncorrelated across measurements (j) within individuals (i). In this case ɛij is assumed normally distributed with zero mean and variance of V. However, this assumption will not always be valid and it may be more appropriate to model the (co)variance structure of residual errors across measurements using a j × j variance–covariance matrix (where j is the number of measurement occasions for each individual). Such multivariate error structures allow for correlation of residuals within individuals and are commonly applied in random regression models of trait ontogeny (e.g. Wilson et al., 2005). Although little used for analyses of reaction norms to date, this more general structure would seem appropriate in this context where within-individual phenotypic correlations might also arise from temporal structuring of repeated measures.

Equation 1 can be solved, typically using restricted maximum likelihood (REML), to estimate the fixed effects, the residual (co)variance structure, and a symmetrical 2 × 2 variance–covariance matrix containing the variances in elevation (pi) and slope (pEi), as well as the covariance between them. Although it should be noted that methods for making statistical inference from mixed models are still under development by statisticians, likelihood ratio tests can be used to assess the statistical significance of the (co)variance components estimated using REML (Self & Liang, 1987; Stram & Lee, 1994; Pinheiro & Bates, 2000). Significance of the Vp would indicate significant variation between individuals in their average trait value (Fig. 2a–f), whereas significance of VpE would mean that there was variation in individual plasticity and therefore that I × E was present (Fig. 2c–h).

If random effects are found to be statistically significant, then individual-specific predictor values of elevation (pi) and slope (or plasticity; pEi) can also be generated a posteriori (as Best Linear Unbiased Predictors, BLUPs; see Lynch & Walsh, 1998). These predictors can be treated as quantitative characters themselves and, assuming estimates of fitness are available, can be used to estimate natural selection on reaction norm components using standard regression techniques (e.g. Lande & Arnold, 1983). These predictors of elevation and slope can also be used to explore the sensitivity of the trait to ecological conditions. For example, changes in individual slope may occur as a response to increasing population density, or weather conditions (cf. Brommer et al., 2005, Nussey et al., 2005a). Even if further partitioning of the phenotypic variance in elevation and slope (see next section) is not feasible, gaining an understanding of the ecological factors underlying individual plasticity will be worthwhile.

Determining G × E

Where pedigree information is available, it is possible to statistically separate genetic and non-genetic effects on reaction norms, and hence to test explicitly for G × E. Individual deviations from the population mean elevation and slope (i.e., pi and pEi from equation 1), may be viewed as arising from both genetic and non-genetic effects. Thus the phenotype of individual i at measurement j may be rewritten as:

  • image(2)

The effects, denoted ai and ei, are independent of environment (E) and are equivalent to the ‘breeding value’ and ‘permanent environment effect’ of classical quantitative genetic models. These are therefore the genetic and non-genetic components of individual i’s reaction norm elevation. Similarly aEi and eEi represent genetic and nongenetic effects on i’s reaction norm slope. Other terms are as specified in Eqn 1.

In natural populations, genetic components of variance are most straightforwardly calculated by using a so-called ‘animal model’, a form of linear mixed model that incorporates a pedigree-derived matrix of relatedness across individuals (for more details on see e.g. Lynch & Walsh, 1998; Kruuk, 2004). The animal model framework can readily be extended to include interactions of individual genetic effects with environmental covariates (i.e. a random regression animal model; RRAM), thus allowing Eqn 2 to be solved where pedigree data are available. This will yield estimates of the variance in ai (denoted Va) and aEi (denoted VaE). These represent the genetic variance for reaction norm elevation (or for phenotype y in a mean environment) and for slope (or plasticity) respectively. Thus VaE corresponds to variance arising from G × E, the significance of which may again be tested using a likelihood ratio test.

Although it is perfectly possible to specify a model in which genetic effects on elevation and slope are independent, it might be expected that they will be correlated within individuals. Hence it will generally be appropriate to estimate a 2 × 2 variance–covariance matrix containing not only the variances in elevation (V) and slope (VαE), but also the covariance between them. Estimation of this genetic variance–covariance matrix is in many respects analogous to fitting a multivariate model and is therefore more demanding computationally than a single trait animal model (see Lynch & Walsh, 1998 for discussion of the matrix algebra involved).

Random Regression Animal Models have been used to scrutinize G × E in both domestic and natural ungulate systems (e.g. Ravagnolo & Misztal, 2000; Kolmodin et al., 2002; Wilson et al., 2006). However, to date, most studies of natural systems have focused on comparing additive genetic variances between discretely defined environments (e.g. ‘good’ vs. ‘bad’; Hoffman & Merilä, 1999; Charmantier & Garant, 2005). Random regression models offer two advantages over this approach. First, environmental parameters often vary continuously in nature, such that defining discrete environments may be somewhat arbitrary. Secondly, analysis of environment-specific sub-traits requires subdivision of data sets, and this imposes very real statistical constraints for quantitative genetic studies of natural populations which are inherently data limited by comparison to animal breeding studies (Wilson et al., 2005).

An additional approach employed in several studies of G × E, has been to first generate estimates of individual plasticity (e.g. as the BLUP's of pEi from Eqn 1) and then to treat these as the phenotypic trait of interest in a conventional animal model (as heritability of plasticity implies G × E; Brommer et al., 2005; Nussey et al., 2005c). However, this is a two-step process that is likely to be subject to error compounding, reducing precision of final parameter estimates. If pedigree data are available and the goal is explicitly to test for G × E (as opposed to I × E), directly formulating Eqn 2 as a RRAM will be more appropriate than going via an initial step of first solving Eqn 1. The latter approach generates predictions of reaction norm properties on the assumption that all individuals are fully independent of each other, which they are not in case these properties are heritable. The RRAM, on the other hand, explicitly uses the resemblance between relatives in order to estimate the additive genetic (co)variances directly.

Analyses of individual plasticity in wild vertebrate populations

  1. Top of page
  2. Abstract
  3. Introduction
  4. Variation in individual reaction norms
  5. Ecological and evolutionary causes of reaction norm variation
  6. Using random regression to measure I × E and G × E
  7. Analyses of individual plasticity in wild vertebrate populations
  8. Predicting a population's response to the environment: a reaction norm perspective
  9. Future directions and applications
  10. Conclusions
  11. Acknowledgments
  12. References

Analyses of individual phenotypic plasticity to date, using data from long-term individual based studies of wild vertebrate populations, are presented in Table 1. Timing of breeding (or phenology) in iteroparous species is a labile phenotypic trait that is expressed repeatedly by females across environments. Many of these studies have assessed maternal reaction norms for phenology on climate conditions prior to breeding. Several studies aimed to test whether observed population level correlations between phenology and the environment were driven by phenotypically plastic responses at the individual level (Przybylo et al., 2000; Réale et al., 2003). This research used linear mixed model analysis of long-term data sets to present the first clear demonstration of individual plasticity as a driver of trait–environment relationships (Przybylo et al., 2000) and as a contributing factor to population-level change in trait values over time (Réale et al., 2003). However, these studies did not use random regression models. These analyses implicitly assume that all individual reaction norms had equal slope (I × E not present) by only modelling variation in reaction norm elevations. Other research has used least-squares regression of repeated measures of individual phenotype on environment to demonstrate that individuals differ in their reaction norm slope (I × E present) in wild vertebrate populations (Brommer et al., 2003; Nussey et al., 2005a).

Table 1.   Published studies of maternal phenotypic plasticity in wild vertebrate populations. ‘√’ denotes a significant test, ‘X’ a non-significant test and blank cells indicate no test. The analyses of the latter four studies on the list were re-run using with the environmental covariate standardized to unit standard deviation in order to provide a similarly scaled comparison of the percentage of total variance accounted for by variance in individual elevations and slopes. We further provide the estimated correlation between elevation and slope.
Study speciesTraitCovariateIE I × ECorrel (I,E)Sel (I)Sel (I × E) G × EReference
  1. I, between-individual variation in elevation; E, overall population plasticity; I × E, variation in individual slope; Correl (I, E), phenotypic correlation between reaction norm elevations and slopes; Sel (I), phenotypic selection on elevation; Sel (I × E), phenotypic selection on slope; G × E, heritability of individual slope predictors.

  2. *Study used least squares regression methods rather than mixed-effects linear models.

Ficedula albicollisEgg laying dateNAO     Przybylo et al. (2000)
Picoides borealisEgg laying dateLocal temperature/rainfall     Scheigg et al. (2003)
Tamiasciurus hudsonicusParturition dateSpring temperature     Réale et al. (2003)
Cervus elaphus*Offspring birth weightSpring temperature    Nussey et al. (2005a)
Cervus elaphusParturition dateAutumn rainfall√ 9.6%√ 5.1%−0.23X Nussey et al. (2005b)
Ficedula albicollisEgg laying dateSpring temperature√ 13.8%√ 5.2%−0.07XBrommer et al. (2005)
Parus majorEgg laying dateSpring temperature√ 23.7%√ 4.2%0.40Nussey et al. (2005c)
Uria aalgeEgg laying dateNAO√ 21.8%X    Reed et al. (2006)

The use of simple random regression models (as in Eqn 1) has extended the modelling of maternal reaction norms to incorporate variation in maternal plasticity (slopes) as well as elevations, whilst also assessing covariation between these two reaction norm components (Brommer et al., 2005; Nussey et al., 2005b,c; Reed et al., 2006). Studies using this approach were able to differentiate between all eight patterns of plasticity shown in Fig. 2. The red deer (Cervus elaphus), great tit (Parus major), collared flycatcher (Ficedula albicollis) and common guillemot (Uria aalge) populations analysed in this way (Table 1) all showed a population level response of female phenology to climate variation (i.e. mean female plasticity was significantly different from zero). Females also varied in their reaction norm elevations (I; Table 1). Three of the populations showed evidence for significant variation between females in their plasticity (I × E), but there was no evidence of variation in plasticity in the guillemot population (Table 1).

In the red deer and flycatcher populations, elevation and slope of phenotypic reaction norms were not strongly correlated (Table 1). This observation renders some support for interpreting these coefficients as separate properties of the way in which organisms respond to their environment. The combination of significant variation in slope and a relatively low correlation between slope and elevation illustrates that the phenotypic reaction norms of these organisms cross within the range of the environmental covariate (as in Fig. 2c). There was evidence for a significantly positive covariance between elevation and slope in the great tit system, suggesting that individual reaction norms followed a fanning pattern, rather than a crossing one (as in Fig. 2e).

Scaling differences between elevation and slope parameters in random regression models mean that the random effect for slope is not a straightforward component of the total phenotypic variance. Re-analysis of data sets having standardized the environmental covariate to be dimensionless resolves this problem and allows the proportion of phenotypic variance accounted for by elevation and slope to be compared across studies. We re-ran the random regression analyses on the deer, flycatcher, great tit, and guillemot accordingly, and present the proportions in Table 1. Whilst variation in the elevations of individual reaction norms might be expected, variation in plasticity is rarely considered as a possible factor underlying trait–environment correlations at the population level (Nussey et al., 2005b). Although between-female variation in plasticity contributed less to overall variation in phenology than that attributable to differences in elevation, in three of the four systems examined it accounted for a significant proportion of around 5% of phenotypic variance (Table 1). Thus, variance in phenotypic plasticity among individuals appears to represent a hitherto ignored component of variation in this widely investigated life history trait.

These studies also presented evidence for natural selection on individual estimates of elevation [Sel (I); Table 1] and slope [Sel (I × E); Table 1]. In the Dutch great tit and Swedish collared flycatcher populations, there was evidence of directional selection favouring female birds that showed greater plasticity for laying date in response to spring temperatures. This is consistent with the fact that, in many passerines, ambient temperatures early in the breeding season will represent reliable cues to the timing of the emergence of caterpillar prey that are an important food source for parents provisioning their nestlings (Visser et al., 1998; Visser & Holleman, 2001). Plasticity in these populations can be considered adaptive as it will allow individuals to alter their reproductive phenology so as to maximize prey abundance when provisioning their offspring. In the guillemot population, the lack of variation in phenotypic plasticity between individuals was hypothesized to be the result of past stabilizing selection to synchronize phenology. Guillemots are a colonially breeding species and synchronizing breeding with neighbouring pairs may reduce predation risk and disturbance of the nest (Reed et al., 2006).

In the great tit and collared flycatcher studies, the presence of G × E underlying observed I × E was tested using a two-step approach. This approach tests for additive genetic variation in elevation and slope by applying pedigree-based ‘animal model’ analyses to BLUPs of individual reaction norm components generated by simple random regression models (Eqn 1). Although additive genetic variation was found in both bird populations for laying date elevation, it was present for plasticity (i.e. reaction norm slope) only in the great tit population. This result implies that only in the great tit population would we expect to see a micro-evolutionary response to directional selection on individual plasticity (Nussey et al., 2005c). However, as described in the previous section, the use of RRAMs (Eqn 2) is likely to represent a more precise approach to assessing levels of genetic and non-genetic variation in individual reaction norm components. The RRAM approach to examining G × E has been successfully applied to explore how additive genetic variation in a labile trait varies with environmental quality and age (Wilson et al., 2005, 2006). RRAM can be used to assess patterns of reaction norms at the additive genetic level directly, whilst the covariance components of the genetic reaction norm obtained can also be used to recover environment-specific estimates of genetic variance for the measured trait (as well as genetic correlations between environments; Wilson et al., 2005, 2006).

We have here adhered to the typical convention of viewing phenotypic variation as the result of additive genetic and environmental components (and their interaction) only, thereby ignoring nonadditive genetic and epistatic components. Although the scope for estimating these latter components in the wild is highly restrictive, such effects may still exist. In particular, dominance effects on reaction norm properties may be apparent in inbred populations (e.g. Scheigg et al. 2003).

Predicting a population's response to the environment: a reaction norm perspective

  1. Top of page
  2. Abstract
  3. Introduction
  4. Variation in individual reaction norms
  5. Ecological and evolutionary causes of reaction norm variation
  6. Using random regression to measure I × E and G × E
  7. Analyses of individual plasticity in wild vertebrate populations
  8. Predicting a population's response to the environment: a reaction norm perspective
  9. Future directions and applications
  10. Conclusions
  11. Acknowledgments
  12. References

Life-history traits are typically correlated to fitness (Roff 1992), and plasticity in such traits is thought to represent the main mechanism by which populations can respond rapidly to either natural or anthropogenic changes in their environment (Stenseth et al., 2002; Walther et al., 2002; Parmesan & Yohe, 2003). Many studies have documented responses to recent climate change in natural systems, particularly in important life-history traits like phenology (Fochhammer et al., 1998; Fitter & Fitter, 2002; Both et al., 2004). The individual reaction norm perspective and random regression analytical techniques described in the last two sections provide a means of dissecting a population level response to the environment, of the kind frequently documented in the ecological literature, into its individual and genetic components. In the long term, climate change (or other changes in the average conditions experienced by individuals) could alter the mean population level response to environmental variation. In this section, and in Fig. 3, we refer to ‘ecological’ rather than ‘environmental’ change to distinguish general shifts in the conditions experienced by individuals in a population from changes in the distribution of the environmental variable to which the population is responding. The ecological change of interest may or may not involve a shift in either mean or variance of the environmental axis of individual reaction norms. Figure 3 illustrates three possible consequences of ecological change for an observed population level phenotypic response to the environment: (1) the average plastic response remains constant; (2) the response declines or disappears and (3) the response increases.

image

Figure 3.  The reaction norm perspective presented here reveals that a given population-level response to the environment will not necessarily be maintained in the face of ecological change. The graph on the left depicts a current population response, the graphs on the right show three possible scenarios for this response following a change in ecological conditions. Examples of when and why we might expect each scenario are discussed in the text.

Download figure to PowerPoint

Most ecological studies examine environment-dependent trait expression by correlating annual mean values of a labile trait with an environmental variable. By implicitly overlooking the possibility of ecological or evolutionary forces affecting individual plasticity within the population, such studies invariably predict Scenario 1 in Fig. 3. However, as discussed above, the average response across the population (Fig. 1), tells us nothing about the presence of I × E or G × E, and therefore does not allow us to determine the potential for change in the average plastic response of the population. By considering: (1) presence or absence of I × E and G × E; (2) selection on phenotypic plasticity and (3) how ecological conditions affect plasticity itself, we can obtain a more accurate and detailed insight into how ecological change may impact on trait expression.

Let us illustrate this by considering a recent study of North American red squirrels (Tamiasciurus hudsonicus). These squirrels have started to reproduce earlier in the season in an apparent response to increasing spring temperatures and concurrent increases in food availability (Réale et al., 2003; Berteaux et al., 2004). The study concluded that this response was due partly to micro-evolution towards earlier average breeding times, and partly to the fact that, on average, female squirrels are plastic and respond to improved conditions by breeding earlier within their lifetimes (Réale et al., 2003). However, because neither I × E nor G × E were tested for, the individual response to environment was implicitly assumed to remain constant as climate conditions improved (Scenario 1, Fig. 3). If conditions were to continue to improve, the prediction would be that breeding times would advance at the same rate in this population. In fact, if I × E and/or G × E were present then the population response might be predicted to increase (Scenario 3) or decrease, potentially to zero (Scenario 2).

Natural selection on heritable individual plasticity will be expected to generate micro-evolutionary changes in average response to the environment. Where selection favours increasingly plastic individuals, average plasticity should increase (Scenario 3, Fig. 3), but it should decrease where selection favours less plastic individuals (Scenario 2, Fig. 3). The strength and direction of natural selection on plasticity may itself be influenced by environmental change. In particular, the ability to adjust a reproductive trait to the environment may, in itself, become increasingly important when ecological conditions change.

The Dutch great tit population discussed earlier provides an excellent example. Warming spring temperatures in Holland over the last 15–20 years have resulted in an advance in the phenology of the birds’ ectothermic caterpillar prey. However the great tits have not, on average, advanced their phenology so as to match the timing of the peak in caterpillar availability with the peak in food required for provisioning nestlings (Visser et al., 1998, 2004). The observation that selection is increasingly favouring more plastic females appears to be a result of the emergence and widening of this phenological mismatch: individuals showing greater plasticity are better able to provision their offspring as climate conditions have changed (Nussey et al., 2005c). The presence of G × E and increasing natural selection favouring highly plastic individuals in this population leads to the expectation of a micro-evolutionary increase in individual plasticity (Fig. 3, Scenario 3).

Any study considering the effects of natural selection on heritable variation for individual elevation or plasticity should also consider genetic correlations between these reaction norm components. Strong positive or negative genetic covariance between parameters relating environment to a trait may constrain the response of the reaction norm to natural selection (Gomulkiewicz & Kirkpatrick, 1992). In the Dutch great tit population, heritable variation in slope (individual plasticity) was present, but so was a strong genetic correlation between individual elevation and slope (Nussey et al., 2005c). Consequently, a response to natural selection favouring increased plasticity in this population would also result in a positive correlated response in individual elevations, potentially constraining micro-evolution towards an optimal reaction norm shape.

A variety of ecological factors may also constrain individual plasticity, resulting in rapid changes in population level responses to the environment that will occur regardless of the presence of G × E and selection on plasticity. For example, female collared flycatchers in Gotland, Sweden that lived during a period with warmer than average temperatures were less likely to advance their laying dates in response to warm springs (i.e. they were less plastic; Brommer et al., 2005). In this migratory species, there is likely to be some minimum period between arrival at the breeding grounds and earliest possible laying date. As migratory birds cannot use local environmental cues in their breeding ground to determine their arrival, there may be some upper temperature threshold beyond which females cannot advance their laying dates (Both & Visser, 2001). Thus a female's plasticity in laying date may be limited in generally warm conditions. Although natural selection favours increasing plasticity in the Swedish flycatcher population, plasticity is not genetically determined (i.e. there is I × E but no G × E; Brommer et al., 2005) and so we expect no micro-evolutionary increase in responses to temperature. Hence, individual plasticity will be reduced if temperatures in this region get warmer and the individual capacity for a plastic response becomes increasingly constrained (Scenario 2 in Fig. 3). In the closely related pied flycatcher, the inability to respond to a changing environment has caused dramatic reductions in population growth rate (Both et al., 2006).

Similar predictions follow from analyses of maternal plasticity in the red deer population on the Isle of Rum, where environmental deterioration has constrained female plasticity in both timing of breeding and offspring birth weight (Nussey et al., 2005a,b). In this case, the reduction in a female's tendency to respond to warm spring temperatures by increasing offspring birth weight is linked to an ecological variable (population density) that is unrelated to spring temperature (although both are likely to influence individual physiological condition). In both examples, an understanding of the environmental determination of I × E leads us to expect that the mean response to climate under novel conditions will decline (Scenario 2 of Fig. 3), rather than remaining constant (Scenario 1). Conversely, the release of an environmental constraint on individual plasticity (e.g. by reduced resource competition in the red deer) would be expected to increase individual plasticity (Scenario 3).

Although three of the four studies of individual plasticity for life history traits reviewed here found evidence of I × E, there is no reason to expect this to be a general finding. The study of Reed et al. (2006) illustrates that some populations may show individual plasticity but no variation for it (i.e. a population level response to the environment but no I × E; Fig. 2b). It suggests that the particularities of the species’ life history, in this case the colonial breeding system, may be important in determining the pattern of selection on plasticity present in wild populations. Further scrutiny of such cases should hopefully allow us to build an understanding of when and why I × E should be present. Wherever possible, and specifically where pedigree data are available, RRAM should also be used in such cases to test the possibility that G × E might exist even in the absence of detectable I × E because, as our discussion has illustrated, the patterns of phenotypic and genetic reaction norms are not necessarily similar.

Future directions and applications

  1. Top of page
  2. Abstract
  3. Introduction
  4. Variation in individual reaction norms
  5. Ecological and evolutionary causes of reaction norm variation
  6. Using random regression to measure I × E and G × E
  7. Analyses of individual plasticity in wild vertebrate populations
  8. Predicting a population's response to the environment: a reaction norm perspective
  9. Future directions and applications
  10. Conclusions
  11. Acknowledgments
  12. References

Analyses of individual plasticity in the wild, where organisms experience naturally occurring ranges of environmental conditions (rather than those imposed in the lab), are still extremely rare (Table 1). A key challenge is to generate more information on the patterns of I × E and G × E from a variety of natural systems, in order to improve our understanding of when and why individual plasticity varies at both phenotypic and genetic levels. Our ability to do this for labile life history traits rests crucially on the collection of individual-based data over extended time series from wild populations. Despite the demanding data requirements for the analyses proposed here, study systems meeting them are surprisingly abundant. For example, decades of bird ringing has produced many individual-based time series data sets (Saether et al., 2005). Such data sets are vital for our understanding of the phenotypic consequences of environmental change and their scientific value will increase exponentially with the length of the time-series.

Quantifying environmental heterogeneity

A major challenge for the analysis of plasticity lies in determining the appropriate environmental variable against which to measure an individual's phenotypic response (Visser & Both, 2005). Work to date has typically selected a single climate variable measured over a set time period (e.g. average daily regional temperature between April and May). However, the use of set time periods in this way may actually be problematic as variation in individual phenology will mean that a given time period will not influence all individuals in the same way. Recently, bird laying dates have been successfully modelled using proportional hazard techniques where only the daily temperatures up to the actual laying date are considered (Gienapp et al., 2005). This approach may help determine what the relevant time windows for reaction norms really are.

It is also true that although studies to date have focused on single environmental parameters, multiple environmental factors might determine an individual's reaction norm. Although reaction norms could in principle be modelled as functions of multiple environmental parameters, the use of principal component analyses (or similar techniques) to reduce the dimensionality of environmental variation may represent a more practical way forward in this regard. However, there is no guarantee that the major axis of environmental variation (which assumes additive environmental effects) will be the proper cue for determining plastic responses. Furthermore, additional difficulties may arise if plasticity occurs in response to environmental heterogeneity on a fine scale which is particularly difficult to quantify. This may be problematic because fine-scale environmental effects (e.g. variation in microclimate across bird nests or mammalian home ranges) can potentially affect individual phenotypes more than large-scale effects. Despite being potentially large, such effects will tend to be relatively unique, with few relatives experiencing the same environment. However, a certain amount of replication is necessary in order to estimate G × E.

Nonlinear reaction norms

A further challenge lies in moving beyond the assumption of linearity in individual reaction norms that has characterized most studies of I × E to date (e.g. Przybylo et al., 2000; Brommer et al., 2005; Nussey et al., 2005b). Although linear reaction norms allow the intuitive separation of measured phenotype into the distinct characters of average trait (i.e. elevation) and phenotypic plasticity (i.e. slope), there is no reason to believe that they will always be an adequate description of an individual's response to environment (e.g. Wilson et al., 2006). Higher order polynomial functions, for example, can be used in random regression models, with different functional forms of the reaction norm (e.g. linear vs. quadratic) fitted and statistically compared within a maximum likelihood framework (Wilson et al., 2005). These techniques have yet to be widely applied to analyses of individual plasticity for labile traits in the wild. However, it seems likely that by relaxing the assumption of reaction norm linearity, they may shed further light on the patterns and mechanisms of individual responses to environmental variation.

Non-normally distributed response variables

The reproductive traits that have been investigated thus far are reasonable proxies of fitness, but one future challenge is to extend these analyses to actual fitness components such as survival and reproduction. Such analyses will be important, because G × E in fitness components is fundamental for the maintenance of evolutionary potential (Roff 1997). However, in contrast to many of its proxies, fitness components themselves are rarely normally distributed. Likewise, other interesting response variables, such as count data on behavioural interactions, need not be distributed normally.

Non-normal error distributions lead to difficulties in reliably estimating variance components in mixed models (e.g. Jang & Lim, 2006). In particular, accuracy in the estimation of variance components in such models breaks down when the number of levels within a random effect (e.g. individual identity) starts to approach the number of observations (Breslow & Lin, 1995, Breslow, 2003). Unfortunately, this is precisely the type of analyses required, as we are interested in deriving individual-specific properties such as elevation and slope and their additive genetic merit from data with often relatively few repeated records per individual. There is, furthermore, little known about the accuracy of statistical tests in such models. Additional options for modelling such data involve Bayesian methods (Breslow, 2003). For survival data, proportional hazard models can accommodate random effects, and have been also used for genetic analyses (Ducrocq & Sölkner, 1998). Future studies on these currently largely unexplored issues seem likely to generate valuable insights in the evolutionary biology of wild populations.

Other applications of random regression in the wild

Finally, the random regression techniques considered within a reaction norm framework have potential applications beyond the analysis of plasticity in labile life history traits. Studies investigating variation in behavioural reaction norms are certainly lacking at present. It seems likely that behaviour is subject to both I × E and G × E, and that the ability for an individual to adjust behaviour to environmental conditions will have fitness consequences (Sih, 2004; Dingemanse & Realé, 2005). This approach could also be readily applied to better understand the evolutionary ecology of ageing patterns and senescence, using age as a sort of intrinsic environmental parameter. RRAMs have already been used to estimate genotype-by-age interactions in one wild vertebrate population (e.g. Wilson et al., 2005). Quantitative genetic analyses may also provide a useful way of testing competing evolutionary theories of senescence (Charmantier et al., 2005) and assessing between-individual variation in ageing patterns (van de Pol & Verhulst, 2006) in wild populations.

Conclusions

  1. Top of page
  2. Abstract
  3. Introduction
  4. Variation in individual reaction norms
  5. Ecological and evolutionary causes of reaction norm variation
  6. Using random regression to measure I × E and G × E
  7. Analyses of individual plasticity in wild vertebrate populations
  8. Predicting a population's response to the environment: a reaction norm perspective
  9. Future directions and applications
  10. Conclusions
  11. Acknowledgments
  12. References

Given the prevalence of phenotypic plasticity in nature, and the growing concern over the long-term consequences of anthropogenic effects on both habitats and climate for wild populations of animals, it seems clear we need to build on our understanding of how and why populations respond to the environment. A population consists of individuals, each of which may respond to its environment in its own particular way. Individual reaction norms therefore represent an important component of life history variation in nature, and there is potential for both environmental quality and natural selection to shape observed patterns of plasticity. The evolutionary ecology of plasticity in any system is likely to prove vital to our understanding of the ability of natural systems to cope with environmental change.

We have presented a conceptual and statistical approach to modelling I × E and G × E for labile traits and illustrated their application with examples from wild vertebrate populations. Random regression analyses conducted at the level of individual phenotypic reaction norms (as in Eqn 1) are likely to be of great interest in evolutionary and population ecology. Further application of these models should help reveal both the prevalence of and the ecological factors influencing variation between individuals in their responses to the environment. Where pedigree information is available for a population, the use of RRAMs will allow researchers to assess the contributions of genetic and non-genetic forces to between-individual variation in reaction norms and thereby gauge the micro-evolutionary potential of plasticity. Future applications of this statistical approach are likely be diverse within the field of evolutionary biology, and we believe their potential for increasing our understanding of the causes and consequences of phenotypic variation in nature to be significant.

Acknowledgments

  1. Top of page
  2. Abstract
  3. Introduction
  4. Variation in individual reaction norms
  5. Ecological and evolutionary causes of reaction norm variation
  6. Using random regression to measure I × E and G × E
  7. Analyses of individual plasticity in wild vertebrate populations
  8. Predicting a population's response to the environment: a reaction norm perspective
  9. Future directions and applications
  10. Conclusions
  11. Acknowledgments
  12. References

The work presented here owes a great debt to comments, ideas and support provided by Loeske Kruuk and Ben Sheldon. We are also very grateful to Hannu Pietiäinen, Anne Charmantier, Sarah Reece, Bruce Walsh and two anonymous referees for their constructive comments on earlier drafts of the manuscript. This work was supported by a NERC fellowship (to AJW) and the Academy of Finland (to JEB).

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  1. Top of page
  2. Abstract
  3. Introduction
  4. Variation in individual reaction norms
  5. Ecological and evolutionary causes of reaction norm variation
  6. Using random regression to measure I × E and G × E
  7. Analyses of individual plasticity in wild vertebrate populations
  8. Predicting a population's response to the environment: a reaction norm perspective
  9. Future directions and applications
  10. Conclusions
  11. Acknowledgments
  12. References
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