Evolution and maintenance of the environmental component of the phenotypic variance: benefit of plastic traits under changing environments

How environmental variances in quantitative traits are influenced by variable environments is an important problem in evolutionary biology. In this study, the evolution and maintenance of phenotypic variance in a plastic trait under stabilizing selection are investigated. The mapping from genotypic value to phenotypic value of the quantitative trait is approximated by a linear reaction norm, with genotypic effects on its phenotypic mean and sensitivity to environment. The environmental deviation is assumed to be decomposed into environmental quality, which interacts with genotypic value, and residual developmental noise, which is independent of genotype. Environmental quality and the optimal phenotype of stabilizing selection are allowed to randomly fluctuate in both space and time, and individuals migrate equally before development and reproduction among different niches. Analyses show that phenotypic plasticity is adaptive within variable environments if correlations have become established between the optimal phenotype and environmental quality in space and/or time. The evolved plasticity increases with variances in optimal phenotypes and correlations between optimal phenotype and environmental quality; this further induces increases in mean fitness and the environmental variance in the trait. Under certain circumstances, however, the environmental variance may decrease with increase in variation in environmental quality.     

Pleiotropic model of maintenance of quantitative genetic variation at mutation-selection balance

A pleiotropic model of maintenance of quantitative genetic variation at mutation-selection balance is investigated. Mutations have effects on a metric trait and deleterious effects on fitness, for which a bivariate gamma distribution is assumed. Equations for calculating the strength of apparent stabilizing selection (V(s)) and the genetic variance maintained in segregating populations (V(G)) were derived. A large population can hold a high genetic variance but the apparent stabilizing selection may or may not be relatively strong, depending on other properties such as the distribution of mutation effects. If the distribution of mutation effects on fitness is continuous such that there are few nearly neutral mutants, or a minimum fitness effect is assumed if most mutations are nearly neutral, V(G) increases to an asymptote as the population size increases. Both V(G) and V(s) are strongly affected by the shape of the distribution of mutation effects. Compared with mutants of equal effect, allowing their effects on fitness to vary across loci can produce a much higher V(G) but also a high V(s) (V(s) in phenotypic standard deviation units, which is always larger than the ratio V(P)/V(m)), implying weak apparent stabilizing selection. If the mutational variance V(m) is approximately 10(-3)V(e) (V(e), environmental variance), the model can explain typical values of heritability and also apparent stabilizing selection, provided the latter is quite weak as suggested by a recent review.     

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.     

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.     

QUANTITATIVE GENETIC VARIANCE MAINTAINED BY FLUCTUATING SELECTION WITH OVERLAPPING GENERATIONS: VARIANCE COMPONENTS AND COVARIANCES

The quantitative genetic variance-covariance that can be maintained in a random environment is studied, assuming overlapping generations and Gaussian stabilizing selection with a fluctuating optimum. The phenotype of an individual is assumed to be determined by additive contributions from each locus on paternal and maternal gametes (i.e., no epistasis and no dominance). Recurrent mutation is ignored, but linkage between loci is arbitrary. The genotype distribution in the evolutionarily stable population is generically discrete: only a finite number of polymorphic alleles with distinctly different effects are maintained, even though we allow a continuum of alleles with arbitrary phenotypic contributions to invade. Fluctuating selection maintains nonzero genetic variance in the evolutionarily stable population if the environmental heterogeneity is larger than a certain threshold. Explicit asymptotic expressions for the standing variance-covariance components are derived for the population near the threshold, or for large generational overlap, as a function of environmental variability and genetic parameters (i.e., number of loci, recombination rate, etc.), using the fact that the genotype distribution is discrete. Above the threshold, the population maintains considerable genetic variance in the form of positive linkage disequilibrium and positive gamete covariance (Hardy-Weinberg disequilibrium) as well as allelic variance. The relative proportion of these disequilibrium variances in the total genetic variance increases with the environmental variability.     

Joint effects of pleiotropic selection and stabilizing selection on the maintenance of quantitative genetic variation at mutation-selection balance

In quantitative genetics, there are two basic "conflicting" observations: abundant polygenic variation and strong stabilizing selection that should rapidly deplete that variation. This conflict, although having attracted much theoretical attention, still stands open. Two classes of model have been proposed: real stabilizing selection directly on the metric trait under study and apparent stabilizing selection caused solely by the deleterious pleiotropic side effects of mutations on fitness. Here these models are combined and the total stabilizing selection observed is assumed to derive simultaneously through these two different mechanisms. Mutations have effects on a metric trait and on fitness, and both effects vary continuously. The genetic variance (V(G)) and the observed strength of total stabilizing selection (V(s,t)) are analyzed with a rare-alleles model. Both kinds of selection reduce V(G) but their roles in depleting it are not independent: The magnitude of pleiotropic selection depends on real stabilizing selection and such dependence is subject to the shape of the distributions of mutational effects. The genetic variation maintained thus depends on the kurtosis as well as the variance of mutational effects: All else being equal, V(G) increases with increasing leptokurtosis of mutational effects on fitness, while for a given distribution of mutational effects on fitness, V(G) decreases with increasing leptokurtosis of mutational effects on the trait. The V(G) and V(s,t) are determined primarily by real stabilizing selection while pleiotropic effects, which can be large, have only a limited impact. This finding provides some promise that a high heritability can be explained under strong total stabilizing selection for what are regarded as typical values of mutation and selection parameters.     

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.     

Pleiotropic Models of Polygenic Variation, Stabilizing Selection, and Epistasis

We show that in polymorphic populations many polygenic traits pleiotropically related to fitness are expected to be under apparent ``stabilizing selection' independently of the real selection acting on the population. This occurs, for example, if the genetic system is at a stable polymorphic equilibrium determined by selection and the nonadditive contributions of the loci to the trait value either are absent, or are random and independent of those to fitness. Stabilizing selection is also observed if the polygenic system is at an equilibrium determined by a balance between selection and mutation (or migration) when both additive and nonadditive contributions of the loci to the trait value are random and independent of those to fitness. We also compare different viability models that can maintain genetic variability at many loci with respect to their ability to account for the strong stabilizing selection on an additive trait. Let V(m) be the genetic variance supplied by mutation (or migration) each generation, V(g) be the genotypic variance maintained in the population, and n be the number of the loci influencing fitness. We demonstrate that in mutation (migration)-selection balance models the strength of apparent stabilizing selection is order V(m)/V(g). In the overdominant model and in the symmetric viability model the strength of apparent stabilizing selection is approximately 1/(2n) that of total selection on the whole phenotype. We show that a selection system that involves pairwise additive by additive epistasis in maintaining variability can lead to a lower genetic load and genetic variance in fitness (approximately 1/(2n) times) than an equivalent selection system that involves overdominance. We show that, in the epistatic model, the apparent stabilizing selection on an additive trait can be as strong as the total selection on the whole phenotype.     

Phenotypic, maximum genetic, and special environmental variability in prehistoric human populations

The phenotypic variance (V(P)) may be divided into the genetic variance (V(G)), the general environmental variance (V(Eg)), and the special environmental variance (V(Es)). The latter is estimated through repeatability calculation (b). This value is considered the upper limit of heritability and represents maximum genetic variance proportion (V(Gm) = V(G) + V(Eg)) in relation to V(P) (b = (V(G) + V(Eg))/V(P)). This process allows an improved determination of biological relationships among groups from estimators maximizing the genetic information of quantitative characters. Two hundred and thirty-seven individuals inhabiting the northern coast of Chile for 4,000 years were taken as a sample. Measurement was made of six metric characters at both sides of the cranium. Special environmental values (es) were obtained by regression. The difference between these values and the phenotypic values (p) consists in the genetic values plus the general environmental values (g + eg). A mean b value of 0.83 indicated that V(Es) represents 17% of V(P). The results showed: 1) high stability of the maximum genetic variance in time and space, 2) high correlation between the biological relationships model, the phenotypic model, and the maximum genetic model, and 3) random distribution of the nongenetic variation, as expected from the quantitative genetics theory. These results support the use of phenotypic data for the interpretation of the evolution history of prehistoric populations.     

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.     

福寿螺表型性状的空间尺度变异

格局和尺度是生态学的核心概念。尺度的变化可能导致生态学格局的改变。入侵物种性状的变异会对种群的建立和扩散产生重要的影响。为了研究入侵物种福寿螺(Pomacea canaliculata)表型性状的尺度变异并推测可能的作用机制,在广东省开展了福寿螺的体质量、体高、体宽、壳口宽4个表型性状在城市、乡镇、生境、样方、个体5个空间尺度上变异的研究。通过拟合混合模型,进行方差分解,结果发现个体和样方差异解释了近80%的性状变异,生境的差异解释了除体重外其他性状的剩余变异;除体重外乡镇和城市尺度上性状的变异并不明显。结果进一步表明,区域尺度的过程如气候特征等对福寿螺表型性状变异不起主要作用;福寿螺种群特征的研究及防控的重点应考虑其遗传结构特征及局部尺度环境因素。通过不同尺度下性状的变异系数和频度分布曲线的分析,进一步验证了以上结果。     

Order-preserving principles underlying genotype-phenotype maps ensure high additive proportions of genetic variance

In quantitative genetics, the degree of resemblance between parents and offspring is described in terms of the additive variance (V(A)) relative to genetic (V(G)) and phenotypic (V(P)) variance. For populations with extreme allele frequencies, high V(A)/V(G) can be explained without considering properties of the genotype-phenotype (GP) map. We show that randomly generated GP maps in populations with intermediate allele frequencies generate far lower V(A)/V(G) values than empirically observed. The main reason is that order-breaking behaviour is ubiquitous in random GP maps. Rearrangement of genotypic values to introduce order-preservation for one or more loci causes a dramatic increase in V(A)/V(G). This suggests the existence of order-preserving design principles in the regulatory machinery underlying GP maps. We illustrate this feature by showing how the ubiquitously observed monotonicity of dose-response relationships gives much higher V(A)/V(G) values than a unimodal dose-response relationship in simple gene network models.     

Quantifying natural seasonal variation in mutation parameters with mutation accumulation lines

Mutations create novel genetic variants, but their contribution to variation in fitness and other phenotypes may depend on environmental conditions. Furthermore, natural environments may be highly heterogeneous. We assessed phenotypes associated with survival and reproductive success in over 30,000 plants representing 100 mutation accumulation lines of Arabidopsis thaliana across four temporal environments at a single field site. In each of the four assays, environmental variance was substantially larger than mutational variance. For some traits, whether mutational variance was significantly varied between seasons. The founder genotype had mean trait values near the mean of the distribution of the mutation accumulation lines in all field experiments. New mutations also contributed more phenotypic variation than would be predicted, given phenotypic and sequence‐level divergence among natural populations of A. thaliana. The combination of large environmental variance with a mean effect of mutation near zero suggests that mutations could contribute substantially to standing genetic variation.     

Genetic basis of between‐individual and within‐individual variance of docility

Between‐individual variation in phenotypes within a population is the basis of evolution. However, evolutionary and behavioural ecologists have mainly focused on estimating between‐individual variance in mean trait and neglected variation in within‐individual variance, or predictability of a trait. In fact, an important assumption of mixed‐effects models used to estimate between‐individual variance in mean traits is that within‐individual residual variance (predictability) is identical across individuals. Individual heterogeneity in the predictability of behaviours is a potentially important effect but rarely estimated and accounted for. We used 11 389 measures of docility behaviour from 1576 yellow‐bellied marmots (Marmota flaviventris) to estimate between‐individual variation in both mean docility and its predictability. We then implemented a double hierarchical animal model to decompose the variances of both mean trait and predictability into their environmental and genetic components. We found that individuals differed both in their docility and in their predictability of docility with a negative phenotypic covariance. We also found significant genetic variance for both mean docility and its predictability but no genetic covariance between the two. This analysis is one of the first to estimate the genetic basis of both mean trait and within‐individual variance in a wild population. Our results indicate that equal within‐individual variance should not be assumed. We demonstrate the evolutionary importance of the variation in the predictability of docility and illustrate potential bias in models ignoring variation in predictability. We conclude that the variability in the predictability of a trait should not be ignored, and present a coherent approach for its quantification.     

Quantifying the decanalizing effects of spontaneous mutations in rhabditid nematodes

The evolution of canalization, the robustness of the phenotype to environmental or genetic perturbation, has attracted considerable recent interest. A key step toward understanding the evolution of any phenotype is characterizing the rate at which mutation introduces genetic variation for the trait (the mutational variance, V(M)) and the average directional effects of mutations on the trait mean (DeltaM). In this study, the mutational parameters for canalization of productivity and body volume are quantified in two sets of mutation accumulation lines of nematodes in the genus Caenorhabditis and are compared with the mutational parameters for the traits themselves. Four results emerge: (1) spontaneous mutations consistently decanalize the phenotype; (2) the mutational parameters for decanalization, V(M) (quantified as mutational heritability) and DeltaM, are of the same order of magnitude as the same parameters for the traits themselves; (3) the mutational parameters for canalization are roughly correlated with the parameters for the traits themselves across taxa; and (4) there is no evidence that residual segregating overdominant loci contribute to the decay of canalization. These results suggest that canalization is readily evolvable and that any evolutionary factor that causes mutations to accumulate will, on average, decanalize the phenotype.     

Mutational variance for pupa weight in Tribolium castaneum

Summary Directional selection for heavier pupa weight in Tribolium castaneum was practiced for 18 generations in two replicates of an inbred line, each separately maintained in small population cages for more than 90 generations. Mutational variance was estimated in two ways, based on Hill's (1982a) prediction equation for response to directional selection where an equilibrium state between effective population size and variation created by new mutation is assumed. Estimates of mutational variance based on response to selection in a selected population and from a sire-offspring regression analysis in an unselected control population were in strong agreement within each replicate population. Significant differences between the two replicates were observed. Estimates of the ratio of mutational variance to environmental variance ranged from 0.0002 to 0.0012, depending upon the assumptions made about effective population sizes maintained in the two replicate lines. Estimates of realized heritability from the 18 generations of selection were 0.23±0.02 and 0.12±0.02 in the two replicates. The results support the hypothesis that mutation may have played a significant role in supplying useful genetic variation for long-continuing response to selection for this trait in experiments reported earlier.     

Genetic basis of human female pelvic morphology: a twin study

To examine the relative role of genetic and environmental factors on pelvic morphology, data on 60 pairs of female twins (30 monozygotic (MZ) and 30 dizygotic (DZ)) were analyzed. Fourteen pelvic measurements were normally distributed, and two were not. Association of twin type with the mean value of a trait was found in only 1 out of 8 traits. Heterogeneity of variance between zygosities was observed in 4 pelvic traits (50%), invalidating within-pair estimates of genetic variance for these traits. Evidence of stronger environmental covariance for MZ than DZ twins was observed for only one trait (sitting height iliocristale). A significant genetic component of variation was observed for age at menarche and in the pelvic area. In instances where inequality of variances between zygosities was demonstrated, total among-pair and within-pair mean squares were larger for dizygotic than for monozygotic twins. This is interpreted as evidence of greater environmental influence between zygosities. Environmental modification was not of the same magnitude in various pelvic traits. Bitrochanteric breadth had the highest magnitude of cultural heritability, indicating that cultural factors played an important role in determining hip breadth.     

Effects of genetic drift on variance components under a general model of epistasis

We analyze the changes in the mean and variance components of a quantitative trait caused by changes in allele frequencies, concentrating on the effects of genetic drift. We use a general representation of epistasis and dominance that allows an arbitrary relation between genotype and phenotype for any number of diallelic loci. We assume initial and final Hardy-Weinberg and linkage equilibrium in our analyses of drift-induced changes. Random drift generates transient linkage disequilibria that cause correlations between allele frequency fluctuations at different loci. However, we show that these have negligible effects, at least for interactions among small numbers of loci. Our analyses are based on diffusion approximations that summarize the effects of drift in terms of F, the inbreeding coefficient, interpreted as the expected proportional decrease in heterozygosity at each locus. For haploids, the variance of the trait mean after a population bottleneck is var(delta(z)) = sigma(n)k=1 FkV(A(k)), where n is the number of loci contributing to the trait variance, V(A(1)) = V(A) is the additive genetic variance, and V(A(k)) is the kth-order additive epistatic variance. The expected additive genetic variance after the bottleneck, denoted (V*(A)), is closely related to var(delta(z)); (V*(A)) = (1 - F) sigma(n)k=1 kFk-1V(A(k)). Thus, epistasis inflates the expected additive variance above V(A)(1 - F), the expectation under additivity. For haploids (and diploids without dominance), the expected value of every variance component is inflated by the existence of higher order interactions (e.g., third-order epistasis inflates (V*(AA. This is not true in general with diploidy, because dominance alone can reduce (V*(A)) below V(A)(1 - F) (e.g., when dominant alleles are rare). Without dominance, diploidy produces simple expressions: var(delta(z)) = sigma(n)k=1 (2F)kV(A(k)) and (V(A)) = (1 - F) sigma(n)k=1 k(2F)k-1V(A(k)). With dominance (and even without epistasis), var(delta(z)) and (V*(A)) no longer depend solely on the variance components in the base population. For small F, the expected additive variance simplifies to (V*(A)) approximately equal to (1 - F)V(A) + 4FV(AA) + 2FV(D) + 2FC(AD), where C(AD) is a sum of two terms describing covariances between additive effects and dominance and additive X dominance interactions. Whether population bottlenecks lead to expected increases in additive variance depends primarily on the ratio of nonadditive to additive genetic variance in the base population, but dominance precludes simple predictions based solely on variance components. We illustrate these results using a model in which genotypic values are drawn at random, allowing extreme and erratic epistatic interactions. Although our analyses clarify the conditions under which drift is expected to increase V(A), we question the evolutionary importance of such increases.     

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.     

Fly wing evolution explained by a neutral model with mutational pleiotropy

To what extent the speed of mutational production of phenotypic variation determines the rate of long-term phenotypic evolution is a central question. Houle et al. recently addressed this question by studying the mutational variances, additive genetic variances, and macroevolution of locations of vein intersections on fly wings, reporting very slow phenotypic evolution relative to the rates of mutational input, high phylogenetic signals, and a strong, linear relationship between the mutational variance of a trait and its rate of evolution. Houle et al. found no existing model of phenotypic evolution to be consistent with all these observations, and proposed the improbable scenario of equal influence of mutational pleiotropy on all traits. Here, we demonstrate that the purported linear relationship between mutational variance and evolutionary divergence is artifactual. We further show that the data are explainable by a simple model in which the wing traits are effectively neutral at least within a range of phenotypic values but their evolutionary rates are differentially reduced because mutations affecting these traits are purged owing to their different pleiotropic effects on other traits that are under stabilizing selection. Thus, the evolutionary patterns of fly wing morphologies are explainable under the existing theoretical framework of phenotypic evolution.