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.     

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.     

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.     

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.     

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.     

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.     

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.     

Natural selection on the genetical component of variance in body condition in a wild bird population

Although there is substantial evidence that skeletal measures of body size are heritable in wild animal populations, it is frequently assumed that the nonskeletal component of body weight (or ‘condition’) is determined primarily by environmental factors, in particular nutritional state. We tested this assumption by quantifying the genetic and environmental components of variance in fledgling body condition index (=relative body weight) in a natural population of collared flycatchers (Ficedula albicollis), and compared the strength of natural selection on individual breeding values with that on phenotypic values. A mixed model analysis of the components of variance, based on an ‘animal model’ and using 18 years of data on 17 717 nestlings, revealed a significant additive genetic component of variance in body condition, which corresponded to a narrow sense heritability (h²) of 0.30 (SE=0.03). Nongenetic contributions to variation in body condition were large, but there was no evidence of dominance variance nor of contributions from early maternal or common environment effects (pre‐manipulation environment) in condition at fledging. Comparison of pre‐ and post‐selection samples revealed virtually identical h² of body condition index, despite the fact that there was a significant decrease (35%) in the levels of additive genetic variance from fledging to breeding. The similar h² in the two samples occurred because the environmental component of variance was also reduced by selection, suggesting that natural selection was acting on both genotypic and environmental variation. The effects of selection on genetic variance were confirmed by calculation of the selection differentials for both phenotypic values and best linear unbiased predictor (BLUP) estimates of breeding values: there was positive directional selection on condition index both at the phenotypic and the genotypic level. The significant h² of body condition index is consistent with data from human and rodent populations showing significant additive genetic variance in relative body mass and adiposity, but contrasts with the common assumption in ecology that body condition reflects an individual’s nongenetic nutritional state. Furthermore, the substantial reduction in the additive genetic component of variance in body condition index suggests that selection on environmental deviations cannot alone explain the maintenance of additive genetic variation in heritable traits, but that other mechanisms are needed to explain the moderate to high heritabilities of traits under consistent and strong directional selection.     

Quantifying the genetic component of phenotypic variation in unpedigreed wild plants: tailoring genomic scan for within-population use

The study of adaptive genetic variation in natural populations is central to evolutionary biology. Quantitative genetics methods, however, are hardly applicable to long-lived organisms, and current knowledge on adaptive genetic variation in wild plants mostly refers to annuals and short-lived perennials. Studies on long-lived species are essential to explore possible life-history correlates of genetic variation, selection, and trait heritability. In this paper, we propose a method based on molecular markers to quantify the genetic basis of individual phenotypic differences in wild plants under natural conditions. Rather than focusing on inferring individual relatedness to estimate the heritability of phenotypic traits, we directly estimate the proportion of observed phenotypic variance that is statistically accounted for by genotypic differences between individuals. This is achieved by (i) identifying loci that are correlated across individuals with the phenotypic trait of interest by means of an amplified fragment length polymorphism (AFLP)-based explorative genomic scan, and (ii) fitting multiple regression and linear random effect models to estimate the effects of genotype, environment and genotype × environment on phenotypes. We apply this method to estimate genotypic and environmental effects on cumulative maternal fecundity in a wild population of the long-lived Viola cazorlensis monitored for 20 years. Results show that between 56–63% (depending on estimation method) of phenotypic variance in fecundity is accounted for by genotypic differences in 11 AFLP loci that are significantly related to fecundity. Genotype × environment effects accounted for 38% of fecundity variance, which may help to explain the unexpectedly high levels of genetic variance for fecundity found.     

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.     

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.     

Stabilizing selection on sperm number revealed by artificial selection and experimental evolution

Sperm competition is taxonomically widespread in animals and is usually associated with large sperm production, being the number of sperm in the competing pool the prime predictor of fertilization success. Despite the strong postcopulatory selection acting directionally on sperm production, its genetic variance is often very high. This can be explained by trade‐offs between sperm production and traits associated with mate acquisition or survival, that may contribute to generate an overall stabilizing selection. To investigate this hypothesis, we first artificially selected male guppies (Poecilia reticulata) for high and low sperm production for three generations, while simultaneously removing sexual selection. Then, we interrupted artificial selection and restored sexual selection. Sperm production responded to divergent selection in one generation, and when we restored sexual selection, both high and low lines converged back to the mean sperm production of the original population within two generations, indicating that sperm number is subject to strong stabilizing total sexual selection (i.e., selection acting simultaneously on all traits associated with reproductive success). We discuss the possible mechanisms responsible for the maintenance of high genetic variability in sperm production despite strong selection acting on it.     

The relationship between parental genetic or phenotypic divergence and progeny variation in the maize nested association mapping population

Appropriate selection of parents for the development of mapping populations is pivotal to maximizing the power of quantitative trait loci detection. Trait genotypic variation within a family is indicative of the family's informativeness for genetic studies. Accurate prediction of the most useful parental combinations within a species would help guide quantitative genetics studies. We tested the reliability of genotypic and phenotypic distance estimators between pairs of maize inbred lines to predict genotypic variation for quantitative traits within families derived from biparental crosses. We developed 25 families composed of ~200 random recombinant inbred lines each from crosses between a common reference parent inbred, B73, and 25 diverse maize inbreds. Parents and families were evaluated for 19 quantitative traits across up to 11 environments. Genetic distances (GDs) among parents were estimated with 44 simple sequence repeat and 2303 single-nucleotide polymorphism markers. GDs among parents had no predictive value for progeny variation, which is most likely due to the choice of neutral markers. In contrast, we observed for about half of the traits measured a positive correlation between phenotypic parental distances and within-family genetic variance estimates. Consequently, the choice of promising segregating populations can be based on selecting phenotypically diverse parents. These results are congruent with models of genetic architecture that posit numerous genes affecting quantitative traits, each segregating for allelic series, with dispersal of allelic effects across diverse genetic material. This architecture, common to many quantitative traits in maize, limits the predictive value of parental genotypic or phenotypic values on progeny variance.     

Stabilizing Selection for Pupa Weight in TRIBOLIUM CASTANEUM

Ninety-five generations of stabilizing selection for pupa weight in Tribolium castaneum resulted in a significant decrease in phenotypic variance, moderate reductions in additive genetic variance, but only slight changes in heritability for the trait. Sterility was significantly lower and the average number of live progeny per fertile mating was significantly higher in populations where stabilizing selection was practiced as compared with random selected populations. The results indicate that more genetic variability is being maintained than would be expected unless a fraction of the genes have a heterozygote advantage on the fitness scale. The reduction in phenotypic variance indicated that the populations with stablizing selection became somewhat more buffered against environmental sources of variation over the course of the experiment.     

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.     

Study of Natural Genetic Variation in Early Fitness Traits Reveals Decoupling Between Larval and Pupal Developmental Time in <Emphasis Type="Italic">Drosophila melanogaster</Emphasis>

Characterizing the relationships between genotype and phenotype for developmental adaptive traits is essential to understand the evolutionary dynamics underlying biodiversity. In holometabolous insects, the time to reach the reproductive stage and pupation site preference are two such traits. Here we characterize aspects of the genetic architecture for Developmental Time (decomposed in Larval and Pupal components) and Pupation Height using lines derived from three natural populations of Drosophila melanogaster raised at two temperatures. For all traits, phenotypic differences and variation in plasticity between populations suggest adaptation to the original thermal regimes. However, high variability within populations shows that selection does not exhaust genetic variance for these traits. This could be partly explained by local adaptation, environmental heterogeneity and modifications in the genetic architecture of traits according to environment and ontogenetic stage. Indeed, our results show that the genetic factors affecting Developmental Time and Pupation Height are temperature-specific. Varying relationships between Larval and Pupal Developmental Time between and within populations also suggest stage-specific modifications of genetic architecture for this trait. This flexibility would allow for a somewhat independent evolution of adaptive traits at different environments and life stages, favoring the maintenance of genetic variability and thus sustaining the traits’ evolvabilities.     

Phenotypic plasticity for life history traits in Drosophila melanogaster. II. Epigenetic mechanisms and the scaling of variances

Abstract We manipulated developmental time and dry weight at eclosion in 15 genotypes of Drosophila melanogaster by growing the larvae in 9 environments defined by 3 yeast concentrations at 3 temperatures. We observed how the genetic and various environmental components of phenotypic variation scaled with the mean values of the traits. Temperature, yeast, within-environmental factors and genotype influenced the genotypic and environmental standard deviations of the two traits in patterns that point to very different modes of physiological and developmental action of these factors. Since different factors affected the environmental and genetic components of the phenotypic variation either in parallel or inversely, we conclude that environmental heterogeneity may have small or large effects on evolutionary rates depending on which factors cause the heterogeneity. The analysis also suggests that the scaling of variances with the mean is not as trivial as is often assumed when coefficients of variation are computed to “standardize” variation.     

Evolution of ejaculates: patterns of phenotypic and genotypic variation and condition dependence in sperm competition traits

Sperm competition is widely recognized as a potent force in evolution, influencing male behavior, morphology, and physiology. Recent game theory analyses have examined how sperm competition can influence the evolution of ejaculate expenditure by males and the morphology of sperm contained within ejaculates. Theoretical analyses rest on the assumption that there is sufficient genetic variance in traits important in sperm competition to allow evolving populations to move to the evolutionarily stable equilibrium. Moreover, patterns of genotypic variation can provide valuable insight into the nature of selection currently acting on traits. However, our knowledge of genetic variance underlying traits important in sperm competition is limited. Here we examine patterns of phenotypic and genotypic variation in four sperm competition traits in the dung beetle Onthophagus taurus. Testis weight, ejaculate volume, and copula duration were found to have high coefficients of additive genetic variation (CV(A)S), which is characteristic of fitness traits and traits subject to sexual selection. Heritabilities were high, and there was some evidence for Y-linked inheritance in testis weight. In contrast, sperm length had a low CV(A), which is characteristic of traits subject to stabilizing selection. Nevertheless, there was little residual variance so that the heritability of sperm length exceeded 1.0. Such a pattern is consistent with Y-linked inheritance in sperm length. Interestingly, we found that testis weight and sperm length were genetically correlated with heritable male condition. This finding holds important implications for potential indirect benefits associated with the evolution of polyandry.     

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.