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

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

Evolution of the environmental component of the phenotypic variance: stabilizing selection in changing environments and the cost of homogeneity

Quantitative traits show abundant genetic, environmental, and phenotypic variance, yet if they are subject to stabilizing selection for an optimal phenotype, both the genetic and environmental components are expected to decline. The mechanisms that determine the level and maintenance of phenotypic variance are not yet fully understood. While there has been extensive study of mechanisms maintaining genetic variability, it has generally been assumed that environmental variance is not dependent on the genotype and therefore not subject to change. However, accumulating data suggest that the environmental variance is under some degree of genetic control. In this study, it is assumed accordingly that both the genotypic value (i.e., mean phenotypic value) and the variance of phenotypic value given genotypic value depend on the genotype. Two models are investigated as potentially able to explain the protected maintenance of environmental variance of quantitative traits under stabilizing selection. One is varying environment among generations, such that both the optimal phenotype and the strength of the stabilizing selection vary between generations. The other is the cost of homogeneity, which is based on an assumption of an engineering cost of minimizing variability in development. It is shown that a small homogeneity cost is enough to maintain the observed levels of environmental variance, whereas a large amount of temporal variation in the optimal phenotype and the strength of selection would be necessary.     

Competition can maintain genetic but not environmental variance in the presence of stabilizing selection

A population in which there is stabilizing selection acting on quantitative traits toward an intermediate optimum becomes monomorphic in the absence of mutation. Further, genotypes that show least environmental variation are also favored, such that selection is likely to reduce both genetic and environmental components of phenotypic variance. In contrast, intraspecific competition for resources is more severe between phenotypically similar individuals, such that those deviating from prevailing phenotypes have a selective advantage. It has been shown previously that polymorphism and phenotypic variance can be maintained if competition between individuals is "effectively" stronger than stabilizing selection. Environmental variance is generally observed in quantitative traits, so mechanisms to explain its maintenance are sought, but the impact of competition on its magnitude has not previously been studied. Here we assume that a quantitative trait is subject to selection for an optimal value and to selection due to competition. Further, we assume that both the mean and variance of the phenotypic value depend on genotype, such that both may be affected by selection. Theoretical analysis and numerical simulations reveal that environmental variance can be maintained only when the genetic variance (in mean phenotypic value) is constrained to a very low level. Environmental variance will be replaced entirely by genotypic variance if a range of genotypes that vary widely in mean phenotype are present or become so by mutation. The distribution of mean phenotypic values is discrete when competition is strong relative to stabilizing selection; but more genotypes segregate and the distribution can approach continuity as competition becomes extremely strong. If the magnitude of the environmental variance is not under genetic control, there is a complementary relationship between the levels of environmental and genetic variance such that the level of phenotypic variance is little affected.     

A QUANTITATIVE-GENETIC MODEL FOR SELECTION ON DEVELOPMENTAL NOISE

We propose a simple model for analyzing the effects of microenvironmental variation in quantitative genetics. Our model assumes that the sensitivity of the phenotype to fluctuations in microenvironment has a genetic basis and allows for genetic correlation between trait value and microenvironmental sensitivity. We analyze the effects of short-term stabilizing and directional selection on the genotypic and microenvironmental components of phenotypic variance. Our model predicts that stabilizing selection on a quantitative trait increases developmental canalization. We show that stabilizing selection can result in an increase in the heritability. Our findings may provide an explanation for the results of selection experiments in which artificial stabilizing selection did not change the heritability coefficient or increased it.     

IS INBREEDING DEPRESSION LOWER IN MALADAPTED POPULATIONS? A QUANTITATIVE GENETICS MODEL

Despite abundant empirical evidence that inbreeding depression varies with both the environment and the genotypic context, theoretical predictions about such effects are still rare. Using a quantitative genetics model, we predict amounts of inbreeding depression for fitness emerging from Gaussian stabilizing selection on some phenotypic trait, on which, for simplicity, genetic effects are strictly additive. Given the strength of stabilizing selection, inbreeding depression then varies simply with the genetic variance for the trait under selection and the distance between the mean breeding value and the optimal phenotype. This allows us to relate the expected inbreeding depression to the degree of maladaptation of the population to its environment. We confront analytical predictions with simulations, in well-adapted populations at equilibrium, as well as in maladapted populations undergoing either a transient environmental shift, or gene swamping in heterogeneous habitats. We predict minimal inbreeding depression in situations of extreme maladaptation. Our model provides a new basis for interpreting experiments that measure inbreeding depression for the same set of genotypes in different environments, by demonstrating that the history of adaptation, in addition to environmental harshness per se, may account for differences in inbreeding depression.     

The Effects of Stabilizing and Directional Selection on Phenotypic and Genotypic Variation in a Population of RNA Enzymes

The distribution of variation in a quantitative trait and its underlying distribution of genotypic diversity can both be shaped by stabilizing and directional selection. Understanding either distribution is important, because it determines a population’s response to natural selection. Unfortunately, existing theory makes conflicting predictions about how selection shapes these distributions, and very little pertinent experimental evidence exists. Here we study a simple genetic system, an evolving RNA enzyme (ribozyme) in which a combination of high throughput genotyping and measurement of a biochemical phenotype allow us to address this question. We show that directional selection, compared to stabilizing selection, increases the genotypic diversity of an evolving ribozyme population. In contrast, it leaves the variance in the phenotypic trait unchanged.     

Genetic evolution,plasticity, and bet‐hedging as adaptive responses to temporally autocorrelated fluctuating selection: A quantitative genetic model

Adaptive responses to autocorrelated environmental fluctuations through evolution in mean reaction norm elevation and slope and an independent component of the phenotypic variance are analyzed using a quantitative genetic model. Analytic approximations expressing the mutual dependencies between all three response modes are derived and solved for the joint evolutionary outcome. Both genetic evolution in reaction norm elevation and plasticity are favored by slow temporal fluctuations, with plasticity, in the absence of microenvironmental variability, being the dominant evolutionary outcome for reasonable parameter values. For fast fluctuations, tracking of the optimal phenotype through genetic evolution and plasticity is limited. If residual fluctuations in the optimal phenotype are large and stabilizing selection is strong, selection then acts to increase the phenotypic variance (bet‐hedging adaptive). Otherwise, canalizing selection occurs. If the phenotypic variance increases with plasticity through the effect of microenvironmental variability, this shifts the joint evolutionary balance away from plasticity in favor of genetic evolution. If microenvironmental deviations experienced by each individual at the time of development and selection are correlated, however, more plasticity evolves. The adaptive significance of evolutionary fluctuations in plasticity and the phenotypic variance, transient evolution, and the validity of the analytic approximations are investigated using simulations.     

Mutation-selection balance for environmental variance

The role of mutation-selection balance in maintaining environmental variance (V(E)) of quantitative traits is investigated under the assumption that genotypes differ in the magnitude of phenotypic variance, given genotypic value. Thus, V(E) can be regarded as a quantitative trait. As stabilizing selection on phenotype favors genotypes contributing low V(E), mutations that decrease V(E) are more likely to become fixed than those that increase it, and therefore V(E) should decline. If, however, essentially all mutants increase V(E) and overall selection is sufficiently strong that no mutants become fixed, then V(E) can be maintained. The heritability of the trait is determined by the relative sizes of mutational effects on phenotypic mean and residual variance and is independent of mutation rate and pleiotropic effects. This conclusion is not robust for small populations because some mutants may become fixed, which indicates that other selective forces must be involved, such as an intrinsic cost of homogeneity.     

The Evolution of Continuous Variation. III. Joint Transmission of Genotype, Phenotype and Environment

Evolutionary models of continuous traits are developed. The models are based on the ideas that: (1) the phenotype is the result of the interaction between genotype and environment; (2) the phenotype is the object of natural selection; (3) not only the genotype but also environmental variables and even phenotypes can be directly transmitted. The phenotype of an offspring at birth is a linear combination of its genotypic value, the phenotypic values of its parents, and their environmental values, all measured on the phenotypic scale. The genetic effects are additive polygenic, and a mutation contribution to the within family variance is admitted.—The values of the offspring phenotype and environment before selection are each linear combinations of these values at birth, the coefficients defining what we call "development." Selection is mostly stabilizing of the Gaussian type, but directional selection is introduced using a Gaussian fitness function with a large variance and a mean far from the current population.—Assortative mating for both phenotype and environment are considered. The analysis in all cases is made by iteration of the means, variances and covariances of the trivariate random variable (genotype, phenotype, environment) whose changes over time completely specify the evolution. In most cases numerical methods are used. The problems of estimating the relative roles of each of the variates in the parents in determining the variates in the offspring are discussed. The major results concern the relative magnitudes of the variances and correlations of the three variates, genotype, phenotype and environment, in a variety of selective, developmental and assorting situations with complex transmission in which G-(genetic), F-(phenotypic), E-(environment) inheritance mechanisms operate jointly. The transmission rules and development patterns (i.e., interactions between phenotype and environment during development) are of major importance in determining qualitative features of the equilibrium distribution.     

Evolutionary aspects and sensitivity studies of some major gene models

Extensive biometrical and statistically oriented studies in segregation and pedigree analyses reflect current efforts to demonstrate major gene factors playing a significant role for a whole hierarchy of multifactorial diseases and related risk factors exhibiting continuous variation. The evolutionary aspects of the changes in gene frequencies of some major gene one locus models admitting a broad range of genotype-phenotype associations and different forms of selection functions are investigated. The flexibility of differences among the genotypic-phenotypic distribution can take account of variable penetrance expressivity, complex multifarious heterogeneous background effects, or partial dominance concepts. The phenotype distribution and selection function are assumed to be time invariant such that the environments with which the population interacts do not depend on either the phenotypes or the genotypes present in the population of any particular generation. Viability selection optimizing or directional acts on the phenotypic level. We consider random mating, and concentrate mostly on evaluating the nature of the equilibrium structure for the cases of “strong” and “weak” selection. For weak stabilizing selection the determinants of superior genotypic fitness in the class of phenotypic symmetric distributions reside in minimizing a combination of the phenotypic variance and the deviation of the phenotypic mean from the optimal phenotype. With equal means of central phenotype values, a canalizing selection effect signifying fitness superiority for the genotype with minimal variance is in force. For strong stabilizing selection the genotype-phenotype density at the optimal value determines the relative genotype fitness value. For directional selection the determinants of the selection realizations depend on a “standardized” deviation of the mean phenotype distributional value relative to its total variance. The effects of symmetry as against asymmetry in the genotype distributions with prescribed means and variances were investigated by numerical computations.     

The Evolution of Plasticity and Nonplastic Spatial and Temporal Adaptations in the Presence of Imperfect Environmental Cues

A model for the evolution of plasticity is considered in which the phenotype, undergoing stabilizing selection, is modeled as a linear function of an environmental cue correlated with the phenotypic optimum, with the coefficients z(0) and z(1) evolving according to standard quantitative genetic theory. In contrast to previous theoretical models, as the rate of migration between demes or the rate of cyclic fluctuations in the optimum increases, the amount of plasticity z&d1;1 at equilibrium is shown to increase gradually, in part accounting for the effect of reduced nonplastic adaptation and reaching a maximum equal to the squared correlation between the environmental cue and the phenotypic optimum. Given that information available to the organism is limited, this bias of the expressed phenotype toward the global optimum is still optimal, however, in a certain decision-theoretic sense. When genetic variation in the plastic component of the trait is small so that spatial or temporal differentiation in plasticity is small, the effect of plasticity on nonplastic adaptation is to reduce the effects of variation in the phenotypic optimum by a factor 1-z&d1;1 only. Information acquisition costs and joint evolution of sensory systems are discussed.     

The spatial scale of local adaptation in a stochastic environment

The distribution of phenotypes in space will be a compromise between adaptive plasticity and local adaptation increasing the fit of phenotypes to local conditions and gene flow reducing that fit. Theoretical models on the evolution of quantitative characters on spatially explicit landscapes have only considered scenarios where optimum trait values change as deterministic functions of space. Here, these models are extended to include stochastic spatially autocorrelated aspects to the environment, and consequently the optimal phenotype. Under these conditions, the regression of phenotype on the environmental variable becomes steeper as the spatial scale on which populations are sampled becomes larger. Under certain deterministic models – such as linear clines – the regression is constant. The way in which the regression changes with spatial scale is informative about the degree of phenotypic plasticity, the relative scale of effective gene flow and the environmental dependency of selection. Connections to temporal models are discussed.     

Plasticity and evolution in correlated suites of traits

When organisms are faced with new or changing environments, a central challenge is the coordination of adaptive shifts in many different phenotypic traits. Relationships among traits may facilitate or constrain evolutionary responses to selection, depending on whether the direction of selection is aligned or opposed to the pattern of trait correlations. Attempts to predict evolutionary potential in correlated traits generally assume that correlations are stable across time and space; however, increasing evidence suggests that this may not be the case, and flexibility in trait correlations could bias evolutionary trajectories. We examined genetic and environmental influences on variation and covariation in a suite of behavioural traits to understand if and how flexibility in trait correlations influences adaptation to novel environments. We tested the role of genetic and environmental influences on behavioural trait correlations by comparing Trinidadian guppies (Poecilia reticulata) historically adapted to high‐ and low‐predation environments that were reared under native and non‐native environmental conditions. Both high‐ and low‐predation fish exhibited increased behavioural variance when reared under non‐native vs. native environmental conditions, and rearing in the non‐native environment shifted the major axis of variation among behaviours. Our findings emphasize that trait correlations observed in one population or environment may not predict correlations in another and that environmentally induced plasticity in correlations may bias evolutionary divergence in novel environments.     

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.     

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.     

Evolution of phenotypic fluctuation under host-parasite interactions

Robustness and plasticity are essential features that allow biological systems to cope with complex and variable environments. In a constant environment, robustness, i.e., insensitivity of phenotypes, is expected to increase, whereas plasticity, i.e., the changeability of phenotypes, tends to diminish. Under a variable environment, existence of plasticity will be relevant. The robustness and plasticity, on the other hand, are related to phenotypic variances. As phenotypic variances decrease with the increase in robustness to perturbations, they are expected to decrease through the evolution. However, in nature, phenotypic fluctuation is preserved to a certain degree. One possible cause for this is environmental variation, where one of the most important “environmental” factors will be inter-species interactions. As a first step toward investigating phenotypic fluctuation in response to an inter-species interaction, we present the study of a simple two-species system that comprises hosts and parasites. Hosts are expected to evolve to achieve a phenotype that optimizes fitness. Then, the robustness of the corresponding phenotype will be increased by reducing phenotypic fluctuations. Conversely, plasticity tends to evolve to avoid certain phenotypes that are attacked by parasites. By using a dynamic model of gene expression for the host, we investigate the evolution of the genotype-phenotype map and of phenotypic variances. If the host–parasite interaction is weak, the fittest phenotype of the host evolves to reduce phenotypic variances. In contrast, if there exists a sufficient degree of interaction, the phenotypic variances of hosts increase to escape parasite attacks. For the latter case, we found two strategies: if the noise in the stochastic gene expression is below a certain threshold, the phenotypic variance increases via genetic diversification, whereas above this threshold, it is increased mediated by noise-induced phenotypic fluctuation. We examine how the increase in the phenotypic variances caused by parasite interactions influences the growth rate of a single host, and observed a trade-off between the two. Our results help elucidate the roles played by noise and genetic mutations in the evolution of phenotypic fluctuation and robustness in response to host–parasite interactions.     

The genetic variance but not the genetic covariance of life‐history traits changes towards the north in a time‐constrained insect

Seasonal time constraints are usually stronger at higher than lower latitudes and can exert strong selection on life‐history traits and the correlations among these traits. To predict the response of life‐history traits to environmental change along a latitudinal gradient, information must be obtained about genetic variance in traits and also genetic correlation between traits, that is the genetic variance‐covariance matrix, G . Here, we estimated G for key life‐history traits in an obligate univoltine damselfly that faces seasonal time constraints. We exposed populations to simulated native temperatures and photoperiods and common garden environmental conditions in a laboratory set‐up. Despite differences in genetic variance in these traits between populations (lower variance at northern latitudes), there was no evidence for latitude‐specific covariance of the life‐history traits. At simulated native conditions, all populations showed strong genetic and phenotypic correlations between traits that shaped growth and development. The variance–covariance matrix changed considerably when populations were exposed to common garden conditions compared with the simulated natural conditions, showing the importance of environmentally induced changes in multivariate genetic structure. Our results highlight the importance of estimating variance–covariance matrixes in environments that mimic selection pressures and not only trait variances or mean trait values in common garden conditions for understanding the trait evolution across populations and environments.     

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.     

QUANTITATIVE GENETICS OF BRYOZOAN PHENOTYPIC EVOLUTION. III. PHENOTYPIC PLASTICITY AND THE MAINTENANCE OF GENETIC VARIATION

Cheilostome bryozoan species show long-term morphologic stasis, implying stabilizing selection sustained for millions of years, but nevertheless retain significant heritable variation in traits of skeletal morphology. The possible role of within-genotype (within-colony) phenotypic variability in preserving genetic diversity was analyzed using breeding data for two species of Stylopoma from sites along 110 km of the Caribbean coast of Panama. Variation among zooids within colonies accounts for nearly two-thirds of the phenotypic variance on average, increases with environmental heterogeneity, and includes significant genotype-environment interaction. Thus, within-colony variability apparently represents phenotypic plasticity, at least some of which is heritable, rather than random “developmental noise.” Almost all of the among-colonies component of phenotypic variance is accounted for by additive genetic differences in trait means, suggesting that within-colony plasticity includes virtually all of the environmental component of phenotypic variance in these populations of Stylopoma. Thus, heritable within-colony plasticity could play a significant part in maintaining genetic diversity in cheilostomes, but it is also possible that rates of polygenic mutation alone are sufficient to balance the effects of selection.