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

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

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

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

MEASURING THE PLASTICITY OF DEVELOPMENTAL RATE ACROSS INSECT POPULATIONS: COMMENT ON ROCHA AND KLACZKO (2012)

Rocha and Klaczko emphasize the general complexity of reaction norm shape and caution that ignoring such complexity can be misleading when forcing nonlinear reaction norms into linear shapes. They refer to our article on differences in plasticity of Drosophila serrata populations along a latitudinal gradient as an example of a misleading simplifying approach. However, their claim that an artifact is introduced into our analyses by calculating developmental rate as the reciprocal of development time (rate = time^?1) is based on a misunderstanding of the mathematical properties of the thermal developmental rate reaction norm. Here we discuss why developmental rate is a suitable measure for our study and under which circumstances it is appropriate to describe developmental rate by a linear model.     

The genetics of phenotypic plasticity. VI. Theoretical predictions for directional selection

We explore the effects of linear and quadratic reaction norms on heritability and directional selection. Genetic variation for reaction norm parameters can alter the heritability of traits; the magnitude of the heritability depends upon both the environment and the correlation among the parameters. Genetic variation for reaction norm parameters can alter the response to directional selection. Selection on a trait in one environment can shift both the mean of the trait measured across environments and the plasticity of the trait; the signs and magnitudes of these responses depend on the correlations among the parameters of the reaction norm. Our model is consistent with the results of ten experiments for selection on a trait in a single environment. In all experiments, selection towards the overall mean of the population always resulted in a relatively lower plasticity than selection away from the overall mean. Our model was able to predict the results of two experiments for selection on a trait index calculated over more than one environment. Predictions were good for the direct response to selection but poorer for the correlated response to selection. Our results indicate the need for more data on the effects of environment on genetic parameters, especially correlations among reaction norm parameters.     

Maintenance of genetic variation in phenotypic plasticity: the role of environmental variation

We study genetic variation in phenotypic plasticity maintained by a balance between mutation and weak stabilizing selection. We consider linear reaction norms allowing for spatial and/or temporal variation in the environments of development and selection. We show that the overall genetic variation maintained does not depend on whether the trait is plastic or not. The genetic variances in height and slope of a linear reaction norm, and their covariance, are predicted to decrease with the variation in the environment. Non-pleiotropic loci influencing either height or slope are expected to decrease the genetic variance in slope relative to that in height. Decrease in the ratio of genetic variance in slope to genetic variance in height with increasing variation in the environment presents a test for the presence of loci that only influence the slope, and not the height. We use data on Drosophila to test the theory. In seven of eight pair-wise comparisons genetic variation in reaction norm is higher in a less variable environment than in a more variable environment, which is in accord with the model's predictions.     

DENSITY DEPENDENCE AND UNPREDICTABLE SELECTION IN A HETEROGENEOUS ENVIRONMENT: COMPROMISE AND POLYMORPHISM IN THE ESS REACTION NORM

In quantitative genetic models of the evolution of reaction norms, an individual is selected in the habitat in which it develops; as a consequence, selection leads to the optimum phenotype in each habitat. Here, individuals are assumed to experience unpredictable habitat change between development and selection, so that the environment in which an individual is selected may differ from the environment in which it developed. The model reveals that unpredictability of the selection an individual actually faces leads to the evolutionarily stable bet-hedging reaction norm constituting a compromise between the phenotypic optima in the different patches. We also examine the effect of local density regulation before selection, in the patches in which the individuals develop, and after selection, in the patches in which they are selected. Density regulation before selection has a much lower influence on the evolution of the reaction norm than density regulation after selection. The source-sink structure of the environment caused by differential productivity of patches strongly affects how the compromise bet-hedging strategy weighs the different phenotypic optima and might compromise the local evolutionary stability of the evolved reaction norm. If the strength and variability among patches of density regulation after selection is sufficiently large, no single reaction norm is evolutionary stable: Polymorphic reaction norms constitute the evolutionarily stable population. We also show that a polymorphic reaction norm is more likely to be observed in a less productive habitat. The relations between the present model and the Dempster and the Levene models are discussed.     

Selection on plasticity of seasonal life-history traits using random regression mixed model analysis

Theory considers the covariation of seasonal life-history traits as an optimal reaction norm, implying that deviating from this reaction norm reduces fitness. However, the estimation of reaction-norm properties (i.e., elevation, linear slope, and higher order slope terms) and the selection on these is statistically challenging. We here advocate the use of random regression mixed models to estimate reaction-norm properties and the use of bivariate random regression to estimate selection on these properties within a single model. We illustrate the approach by random regression mixed models on 1115 observations of clutch sizes and laying dates of 361 female Ural owl Strix uralensis collected over 31 years to show that (1) there is variation across individuals in the slope of their clutch size-laying date relationship, and that (2) there is selection on the slope of the reaction norm between these two traits. Hence, natural selection potentially drives the negative covariance in clutch size and laying date in this species. The random-regression approach is hampered by inability to estimate nonlinear selection, but avoids a number of disadvantages (stats-on-stats, connecting reaction-norm properties to fitness). The approach is of value in describing and studying selection on behavioral reaction norms (behavioral syndromes) or life-history reaction norms. The approach can also be extended to consider the genetic underpinning of reaction-norm properties.     

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

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

Measuring probabilistic reaction norms for age and size at maturation

We present a new probabilistic concept of reaction norms for age and size at maturation that is applicable when observations are carried out at discrete time intervals. This approach can also be used to estimate reaction norms for age and size at metamorphosis or at other ontogenetic transitions. Such estimations are critical for understanding phenotypic plasticity and life-history changes in variable environments, assessing genetic changes in the presence of phenotypic plasticity, and calibrating size- and age-structured population models. We show that previous approaches to this problem, based on regressing size against age at maturation, give results that are systematically biased when compared to the probabilistic reaction norms. The bias can be substantial and is likely to lead to qualitatively incorrect conclusions; it is caused by failing to account for the probabilistic nature of the maturation process. We explain why, instead, robust estimations of maturation reaction norms should be based on logistic regression or on other statistical models that treat the probability of maturing as a dependent variable. We demonstrate the utility of our approach with two examples. First, the analysis of data generated for a known reaction norm highlights some crucial limitations of previous approaches. Second, application to the northeast arctic cod (Gadus morhua) illustrates how our approach can be used to shed new light on existing real-world data.     

Adaptive and nonadaptive plasticity in changing environments: Implications for sexual species with different life history strategies

Populations adapt to novel environmental conditions by genetic changes or phenotypic plasticity. Plastic responses are generally faster and can buffer fitness losses under variable conditions. Plasticity is typically modeled as random noise and linear reaction norms that assume simple one‐to‐one genotype–phenotype maps and no limits to the phenotypic response. Most studies on plasticity have focused on its effect on population viability. However, it is not clear, whether the advantage of plasticity depends solely on environmental fluctuations or also on the genetic and demographic properties (life histories) of populations. Here we present an individual‐based model and study the relative importance of adaptive and nonadaptive plasticity for populations of sexual species with different life histories experiencing directional stochastic climate change. Environmental fluctuations were simulated using differentially autocorrelated climatic stochasticity or noise color, and scenarios of directional climate change. Nonadaptive plasticity was simulated as a random environmental effect on trait development, while adaptive plasticity as a linear, saturating, or sinusoidal reaction norm. The last two imposed limits to the plastic response and emphasized flexible interactions of the genotype with the environment. Interestingly, this assumption led to (a) smaller phenotypic than genotypic variance in the population (many‐to‐one genotype–phenotype map) and the coexistence of polymorphisms, and (b) the maintenance of higher genetic variation—compared to linear reaction norms and genetic determinism—even when the population was exposed to a constant environment for several generations. Limits to plasticity led to genetic accommodation, when costs were negligible, and to the appearance of cryptic variation when limits were exceeded. We found that adaptive plasticity promoted population persistence under red environmental noise and was particularly important for life histories with low fecundity. Populations producing more offspring could cope with environmental fluctuations solely by genetic changes or random plasticity, unless environmental change was too fast.     

The effects of different farm environments on the performance of Texel sheep

In order to assess the extent of genotype by environment interactions (G×E) and environmental sensitivity in sheep farm systems, environmental factors must be identified and quantified, after which the relationship with the traits(s) of interest can be investigated. The objectives of this study were to develop a farm environment (FE) scale, using a canonical correlation analysis, which could then be used in linear reaction norm models. Fine-scale farm survey data, collected from a sample of 39 Texel flocks across the United Kingdom, was combined with information available at the national level. The farm survey data included information on flock size and concentrate feed use. National data included flock performance averages for 21-week-old weight (21WT), ultrasound back-fat (UFD) and muscle (UMD) depths, as well as regional climatic data. The FE scale developed was then combined with 181 555 (21WT), 175 399 (UMD) and 175 279 (UFD) records from lambs born between 1990 and 2011, on 494 different Texel flocks, to predict reaction norms for sires used within the population. A range of sire sensitivities estimated across the FE scale confirmed the presence of genetic variability as both ‘plastic’ and ‘robust’ genotypes were observed. Variations in heritability estimates were also observed indicating that the rate genetic progress was dependent on the environment. Overall, the techniques and approaches used in this study have proven to be useful in defining sheep FEs. The results observed for 21WT, UMD and UFD, using the reaction norm models, indicate that in order to improve genetic gain and flock efficiency, future genetic evaluations would benefit by accounting for the G×E observed.     

Adaptation and constraint in the evolution of environmental sex determination

When environments differentially influence male and female performance, environmental sex determination (ESD) might evolve. The conclusion from several previous theoretical models was that reaction norms for sex determination should have a single, sharp threshold, with only females being produced in some environments and only males in others. These reaction norms can be disadvantageous in fluctuating environments, however, because they lead to sex-ratio fluctuations. We analysed the evolution of ESD, looking for equilibrium strategies in unconstrained as well as constrained strategy spaces. We identified situations where a single-threshold reaction norm is not evolutionarily stable. In these cases, we found stable strategies in the form of complex reaction norms, showing an oscillatory pattern of sex determination with respect to variation in an environmental variable. Considering that constraints could prevent such phenotypes from being realized, we found that certain randomized reaction norms, with probabilistic sex determination for a range of environments, would achieve nearly the same fitness. We also investigated reaction norms constrained to have a single threshold and found that genetic polymorphism in the environmental threshold value could evolve, producing a similar effect as a randomized reaction norm. We argue that the appearance of genetic variation can be regarded as an alternative outcome when constraints prevent the evolution of a more complex or a randomized strategy.     

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

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

Variation in reaction norms: Statistical considerations and biological interpretation

Analysis of reaction norms, the functions by which the phenotype produced by a given genotype depends on the environment, is critical to studying many aspects of phenotypic evolution. Different techniques are available for quantifying different aspects of reaction norm variation. We examine what biological inferences can be drawn from some of the more readily applicable analyses for studying reaction norms. We adopt a strongly biologically motivated view, but draw on statistical theory to highlight strengths and drawbacks of different techniques. In particular, consideration of some formal statistical theory leads to revision of some recently, and forcefully, advocated opinions on reaction norm analysis. We clarify what simple analysis of the slope between mean phenotype in two environments can tell us about reaction norms, explore the conditions under which polynomial regression can provide robust inferences about reaction norm shape, and explore how different existing approaches may be used to draw inferences about variation in reaction norm shape. We show how mixed model‐based approaches can provide more robust inferences than more commonly used multistep statistical approaches, and derive new metrics of the relative importance of variation in reaction norm intercepts, slopes, and curvatures.     

QUANTITATIVE GENETICS AND THE EVOLUTION OF REACTION NORMS

We extend methods of quantitative genetics to studies of the evolution of reaction norms defined over continuous environments. Our models consider both spatial variation (hard and soft selection) and temporal variation (within a generation and between generations). These different forms of environmental variation can produce different evolutionary trajectories even when they favor the same optimal reaction norm. When genetic constraints limit the types of evolutionary changes available to a reaction norm, different forms of environmental variation can also produce different evolutionary equilibria. The methods and models presented here provide a framework in which empiricists may determine whether a reaction norm is optimal and, if it is not, to evaluate hypotheses for why it is not.     

MEASURING SELECTION ON REACTION NORMS: AN EXPLORATION OF THE EUROSTA-SOLIDAGO SYSTEM

The sensitivity of genotypic expression to the environment can be depicted as the reaction norm, which is defined as the array of phenotypes produced by a single genotype over a range of environments. We studied selection on reaction norms of the gall-inducing insect Eurosta solidaginis (Diptera; Tephritidae), which attacks tall goldenrod Solidago altissima (Compositae). Gall size was treated as a component of insect phenotype and attributes of the host plant as environmental influences on gall development. Genetic differences in the response of gall size to plant lag time (the number of days before a plant responds to the gall maker) were examined. Reaction norms for full-sib families of flies were quantified as linear functions; the elevation of the function denoted gall size produced by the family averaged across all plants, and the function's slope denoted family sensitivity to lag time. Expected fitness of each family was regressed over reaction norm elevation and slope to yield selection gradients on these reaction norm parameters. Directional selection on gall size averaged across environments is four times stronger than selection on sensitivity. Yet, genetic variation for sensitivity contributes more than twice as much to gall phenotypic variance as family mean gall size. Our results suggest that selection on environmental sensitivity will be weak for populations restricted to a narrow segment of an environmental gradient, but strong for broadly distributed species.     

Symbolic modeling of epistasis

The workhorse of modern genetic analysis is the parametric linear model. The advantages of the linear modeling framework are many and include a mathematical understanding of the model fitting process and ease of interpretation. However, an important limitation is that linear models make assumptions about the nature of the data being modeled. This assumption may not be realistic for complex biological systems such as disease susceptibility where nonlinearities in the genotype to phenotype mapping relationship that result from epistasis, plastic reaction norms, locus heterogeneity, and phenocopy, for example, are the norm rather than the exception. We have previously developed a flexible modeling approach called symbolic discriminant analysis (SDA) that makes no assumptions about the patterns in the data. Rather, SDA lets the data dictate the size, shape, and complexity of a symbolic discriminant function that could include any set of mathematical functions from a list of candidates supplied by the user. Here, we outline a new five step process for symbolic model discovery that uses genetic programming (GP) for coarse-grained stochastic searching, experimental design for parameter optimization, graphical modeling for generating expert knowledge, and estimation of distribution algorithms for fine-grained stochastic searching. Finally, we introduce function mapping as a new method for interpreting symbolic discriminant functions. We show that function mapping when combined with measures of interaction information facilitates statistical interpretation by providing a graphical approach to decomposing complex models to highlight synergistic, redundant, and independent effects of polymorphisms and their composite functions. We illustrate this five step SDA modeling process with a real case-control dataset.     

The reaction norm for abdominal pigmentation and its curve in Drosophila mediopunctata depend on the mean phenotypic value

The idea of a general independence between the phenotypic plasticity and the mean value of a trait is, presently, a consensus. Here, we use the reaction norm of abdominal pigmentation (number of dark spots) of Drosophila mediopunctata in response to temperature, to test this idea. We raised eight strains, bearing two different chromosomal inversions and with varying mean phenotypic values, under 11 temperatures in a thermal gradient to test for predictions concerning mean phenotypic values, chromosomal inversions, and reaction norms. Our results revealed a strong effect of different phenotypic groups and no effect of different karyotypes on reaction norms. Moreover, we found a significant negative correlation between mean phenotypic value and the curvature of the reaction norms, revealing a high dependency of the reaction norm shape on mean phenotypic value. These results clearly reject the idea of genetic independence between mean value and phenotypic plasticity, and may indicate a pattern of correlation, which may include results from other traits and species, with an importance that has not been fully appreciated.     

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

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