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.     

Fisher'S geometrical model of fitness landscape and variance in fitness within a changing environment

The fitness of an individual can be simply defined as the number of its offspring in the next generation. However, it is not well understood how selection on the phenotype determines fitness. In accordance with Fisher's fundamental theorem, fitness should have no or very little genetic variance, whereas empirical data suggest that is not the case. To bridge these knowledge gaps, we follow Fisher's geometrical model and assume that fitness is determined by multivariate stabilizing selection toward an optimum that may vary among generations. We assume random mating, free recombination, additive genes, and uncorrelated stabilizing selection and mutational effects on traits. In a constant environment, we find that genetic variance in fitness under mutation-selection balance is a U-shaped function of the number of traits (i.e., of the so-called "organismal complexity"). Because the variance can be high if the organism is of either low or high complexity, this suggests that complexity has little direct costs. Under a temporally varying optimum, genetic variance increases relative to a constant optimum and increasingly so when the mutation rate is small. Therefore, mutation and changing environment together can maintain high genetic variance. These results therefore lend support to Fisher's geometric model of a fitness landscape.     

The maintenance of phenotypic and genetic variation in threshold traits by frequency-dependent selection

Many traits are phenotypically dimorphic but determined by the action of many loci, the phenotype being a result of a threshold of sensitivity. Quantitative genetic analysis has shown that generally there is considerable additive genetic variation for the trait, the average heritability being 0.52. In numerous cases threshold traits have been shown, or are assumed, to be under frequency-dependent selection; examples include satellite-territorial behaviour, sex-determination, wing dimorphism and trophic dimorphism. In this paper I investigate the potential for frequency-dependent selection to maintain both phenotypic and additive genetic variation in threshold traits. The qualitative results are robust to the particular form of the frequency-dependent selection function. The equilibrium proportion is more or less independent of population size but the heritability increases with population size, typically approaching its maximal value at a population size of 5000, when the mutation rate is 10^?4. A tenfold decrease in the mutation rate requires an approximate doubling of the population size before an asymptotic value is approached. Thus frequency-dependent selection can account for both the existence of two morphs in a population and the observed levels of heritability. It is also shown, both via simulation and theory, that the quantitative genetic model and a simple phenotypic analysis predict the same equilibrium morph proportion.     

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.     

Genetic variance of sexually selected traits in waxmoths: maintenance by genotype x environment interaction

When traits experience directional selection, such as that imposed by sexual selection, their genetic variance is expected to diminish. Nonetheless, theory and findings from sexual selection predict and demonstrate that male traits favored by female choice retain substantial amounts of additive genetic variance. We explored this dilemma through an ecological genetic approach and focused on the potential contributions of genotype x environment interaction (GEI) to maintenance of additive genetic variance for male signal characters in the lesser waxmoth, Achroia grisella (Lepidoptera: Pyralidae). We artificially selected genetic variants for two male signal characters, signal rate (SR) and peak amplitude (PA), that influence female attraction and then examined the phenotypic plasticity of these variants (high- and low-SR and high- and low-PA lines) under a range of environmental conditions expected in natural populations. Our split-family breeding experiments indicated that two signal characters, SR and PA, and several developmental characters in both high- and low-SR and high- and low-PA lines displayed considerable phenotypic plasticity among the environments tested. Moreover, strong GEIs leading to crossover between high- and low-SR lines were found for SR and developmental period. Therefore, neither high- nor low-SR genetic variants would achieve maximum attractiveness and fitness in every environment, and those variants producing unattractive signals with low SRs under normal conditions may remain in populations provided that gene flow across environments or generation overlap are sufficiently high. We speculate that the phenotypic plasticity for SR and developmental period is adaptive in A. grisella populations experiencing a range of temperature and density conditions. Females mating with attractive (high-SR) males may be assured of obtaining good genes because these males sire offspring that develop more rapidly and a crossover for developmental period may parallel that for SR. Such parallel crossovers may be expected wherever good-genes sexual selection mechanisms operate.     

Evolution of adaptive phenotypic traits without positive Darwinian selection

Recent evidence suggests the frequent occurrence of a simple non-Darwinian (but non-Lamarckian) model for the evolution of adaptive phenotypic traits, here entitled the plasticity-relaxation-mutation (PRM) mechanism. This mechanism involves ancestral phenotypic plasticity followed by specialization in one alternative environment and thus the permanent expression of one alternative phenotype. Once this specialization occurs, purifying selection on the molecular basis of other phenotypes is relaxed. Finally, mutations that permanently eliminate the pathways leading to alternative phenotypes can be fixed by genetic drift. Although the generality of the PRM mechanism is at present unknown, I discuss evidence for its widespread occurrence, including the prevalence of exaptations in evolution, evidence that phenotypic plasticity has preceded adaptation in a number of taxa and evidence that adaptive traits have resulted from loss of alternative developmental pathways. The PRM mechanism can easily explain cases of explosive adaptive radiation, as well as recently reported cases of apparent adaptive evolution over ecological time.     

Field and experimental evidence for competition's role in phenotypic divergence

Resource competition has long been viewed as a major cause of phenotypic divergence within and between species. Theory predicts that divergence arises because natural selection favors individuals that are phenotypically dissimilar from their competitors. Yet, there are few conclusive tests of this key prediction. Drawing on data from both natural populations and a controlled experiment, this paper presents such a test in tadpoles of two species of spadefoot toads (Spea bombifrons and S. multiplicata). These two species show exaggerated divergence in trophic morphology where they are found together (mixed-species ponds) but not where each is found alone (pure-species ponds), suggesting that they have undergone ecological character displacement. Moreover, in pure-species ponds, both species exhibit resource polymorphism. Using body size as a proxy for fitness, we found that in pure-species ponds disruptive selection favors extreme trophic phenotypes in both species, suggesting that intraspecific competition for food promotes resource polymorphism. In mixed-species ponds, by contrast, we found that trophic morphology was subject to stabilizing selection in S. multiplicata and directional selection in S. bombifrons. A controlled experiment revealed that the more similar an S. multiplicata was to its S. bombifrons tankmate in resource use, the worse was its performance. These results indicate that S. multiplicata individuals that differ from S. bombifrons would be selectively favored in competition. Our data therefore demonstrate how resource competition between phenotypically similar individuals can drive divergence between them. Moreover, our results indicate that how competition contributes to such divergence may be influenced not only by the degree to which competitors overlap in resource use, but also by the abundance and quality of resources. Finally, our finding that competitively mediated disruptive selection may promote resource polymorphism has potentially important implications for understanding how populations evolve in response to heterospecific competitors. In particular, once a population evolves resource polymorphism, it may be more prone to undergo ecological character displacement.     

Genetic heterogeneity of residual variance in broiler chickens

Aims were to estimate the extent of genetic heterogeneity in environmental variance. Data comprised 99 535 records of 35-day body weights from broiler chickens reared in a controlled environment. Residual variance within dam families was estimated using ASREML, after fitting fixed effects such as genetic groups and hatches, for each of 377 genetically contemporary sires with a large number of progeny (> 100 males or females each). Residual variance was computed separately for male and female offspring, and after correction for sampling, strong evidence for heterogeneity was found, the standard deviation between sires in within variance amounting to 15–18% of its mean. Reanalysis using log-transformed data gave similar results, and elimination of 2–3% of outlier data reduced the heterogeneity but it was still over 10%. The correlation between estimates for males and females was low, however. The correlation between sire effects on progeny mean and residual variance for body weight was small and negative (-0.1). Using a data set bigger than any yet presented and on a trait measurable in both sexes, this study has shown evidence for heterogeneity in the residual variance, which could not be explained by segregation of major genes unless very few determined the trait.     

A tale of two matrices: multivariate approaches in evolutionary biology

Two symmetric matrices underlie our understanding of microevolutionary change. The first is the matrix of nonlinear selection gradients (gamma) which describes the individual fitness surface. The second is the genetic variance-covariance matrix (G) that influences the multivariate response to selection. A common approach to the empirical analysis of these matrices is the element-by-element testing of significance, and subsequent biological interpretation of pattern based on these univariate and bivariate parameters. Here, I show why this approach is likely to misrepresent the genetic basis of quantitative traits, and the selection acting on them in many cases. Diagonalization of square matrices is a fundamental aspect of many of the multivariate statistical techniques used by biologists. Applying this, and other related approaches, to the analysis of the structure of gamma and G matrices, gives greater insight into the form and strength of nonlinear selection, and the availability of genetic variance for multiple traits.     

Phenotypic plasticity for life history traits in Drosophila melanogaster. I. Effect on phenotypic and environmental correlations

All 36 possible crosses among 6 homozygous lines of Drosophila melanogaster were tested for their phenotypic response in developmental time and dry weight at eclosion to variation in temperature and yeast concentration. This method was chosen because it allows one to produce the same heterozygous offspring repeatedly for testing under more conditions than could be handled at once. We estimated the effects of yeast concentration and temperature and their interaction on both the phenotypic and the environmental components of variation and covariation of the two traits. Development was slower at low temperatures and yeast concentrations, and dry weight and viability were lower at higher temperatures and lower yeast levels. Interactions of the two factors with the crosses and with each other indicated that there were genetic differences in plasticity and that the sensitivity of a trait to one factor depended on the level of the other. The covariation of the two traits was generally weak within an environment. Across environments, its sign depended on the factor that changed between the environments: positive for temperature, negative for yeast concentration. These findings can be explained in terms of an established growth model for Drosophila larvae. We conclude that for plastic traits with moderate or low heritability, the relationship between the phenotypic and genetic covariance matrices may be a complex function of the environmental factors that affect the traits. Some implications for the prediction of the evolution in fluctuating environments are outlined.     

Comparison of isogenic lines provides evidence that phenotypic plasticity is under genetic control in rainbow trout Oncorhynchus mykiss

Comparison of nine isogenic lines of rainbow trout Oncorhynchus mykiss kept in the same environment showed significant genetic determinism of phenotypic plasticity assessed through body mass measurements. Ranking of lines differed between two tested environments.     

Partitioning of population genetic variance under multiplicative-epistatic gene action

Determining the way in which different QTLs interact (epistasis) in their effects on the phenotype is crucial to many areas in population genetics and evolutionary biology. For example, in the founder event, a separated population readapts to a new environment through the release of cryptic gene-gene interactions. In hybrid zones, hybrid speciation must be subjected to natural selection for epistasis resulting from genomic recombinations between different species. However, there is a severe shortage of relevant methodologies to estimate epistatic genetic effects and variances. A statistical model has recently been proposed to estimate the number of QTLs, their genetic effects and allelic frequencies in segregating populations. This model is based on multiplicative gene action and derived from a two-level intra- and interspecific mating design. In this paper, we formulate a statistical procedure for partitioning the genetic variance into additive, dominant and various kinds of epistatic components in an intra- or mixed intra- and interspecific hybrid population. The procedure can be used to study the genetic architecture of fragmented populations and hybrid zones, thus allowing for a better recognition of the role of epistasis in evolution and hybrid speciation. A real example for two Populus species, P. tremuloides and P. tremula, is provided to illustrate the procedure. In this example, we found that considerable new genetic variation is formed through genomic recombination between two aspen species. Received: 1 May 1999 / Accepted: 27 July 1999     

The phenotypic variance gradient – a novel concept

Evolutionary ecologists commonly use reaction norms, which show the range of phenotypes produced by a set of genotypes exposed to different environments, to quantify the degree of phenotypic variance and the magnitude of plasticity of morphometric and life‐history traits. Significant differences among the values of the slopes of the reaction norms are interpreted as significant differences in phenotypic plasticity, whereas significant differences among phenotypic variances (variance or coefficient of variation) are interpreted as differences in the degree of developmental instability or canalization. We highlight some potential problems with this approach to quantifying phenotypic variance and suggest a novel and more informative way to plot reaction norms: namely “a plot of log (variance) on the y‐axis versus log (mean) on the x‐axis, with a reference line added”. This approach gives an immediate impression of how the degree of phenotypic variance varies across an environmental gradient, taking into account the consequences of the scaling effect of the variance with the mean. The evolutionary implications of the variation in the degree of phenotypic variance, which we call a “phenotypic variance gradient”, are discussed together with its potential interactions with variation in the degree of phenotypic plasticity and canalization.     

Migration-induced phenotypic divergence: the migration-selection balance of correlated traits

Genetically correlated traits are known to respond to indirect selection pressures caused by directional selection on other traits. It is however unclear how local adaptation in populations diverging along some phenotypic traits but not others is affected by the joint action of gene flow and genetic correlations among traits. This simulation study shows that although gene flow is a potent constraining mechanism of population adaptive divergence, it may induce phenotypic divergence in traits under homogeneous selection among habitats if they are genetically correlated with traits under divergent selection. This correlated phenotypic divergence is a nonmonotonous function of migration and increases with mutational correlation among traits. It also increases with the number of divergently selected traits provided their genetic autonomy relative to the uniformly selected trait is reduced by specific patterns of genetic covariances: populations with lower effective trait dimensionality are more likely to generate very large correlated divergence. The correlated divergence is likely to be picked up by Q(ST)-F(ST) analysis of population genetic differentiation and be erroneously ascribed to adaptive divergence under divergent selection. This study emphasizes the necessity to understand the interaction between selection and the genetic basis of adaptation in a multivariate rather than univariate context.     

Heritability and evolvability of fitness and nonfitness traits: Lessons from livestock

Data from natural populations have suggested a disconnection between trait heritability (variance standardized additive genetic variance, V_A) and evolvability (mean standardized V_A) and emphasized the importance of environmental variation as a determinant of trait heritability but not evolvability. However, these inferences are based on heterogeneous and often small datasets across species from different environments. We surveyed the relationship between evolvability and heritability in >100 traits in farmed cattle, taking advantage of large sample sizes and consistent genetic approaches. Heritability and evolvability estimates were positively correlated (r = 0.37/0.54 on untransformed/log scales) reflecting a substantial impact of V_A on both measures. Furthermore, heritabilities and residual variances were uncorrelated. The differences between this and previously described patterns may reflect lower environmental variation experienced in farmed systems, but also low and heterogeneous quality of data from natural populations. Similar to studies on wild populations, heritabilities for life‐history and behavioral traits were lower than for other traits. Traits having extremely low heritabilities and evolvabilities (17% of the studied traits) were almost exclusively life‐history or behavioral traits, suggesting that evolutionary constraints stemming from lack of genetic variability are likely to be most common for classical “fitness” (cf. life‐history) rather than for “nonfitness” (cf. morphological) traits.     

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.     

Studying phenotypic evolution using multivariate quantitative genetics

Quantitative genetics provides a powerful framework for studying phenotypic evolution and the evolution of adaptive genetic variation. Central to the approach is G, the matrix of additive genetic variances and covariances. G summarizes the genetic basis of the traits and can be used to predict the phenotypic response to multivariate selection or to drift. Recent analytical and computational advances have improved both the power and the accessibility of the necessary multivariate statistics. It is now possible to study the relationships between G and other evolutionary parameters, such as those describing the mutational input, the shape and orientation of the adaptive landscape, and the phenotypic divergence among populations. At the same time, we are moving towards a greater understanding of how the genetic variation summarized by G evolves. Computer simulations of the evolution of G, innovations in matrix comparison methods, and rapid development of powerful molecular genetic tools have all opened the way for dissecting the interaction between allelic variation and evolutionary process. Here I discuss some current uses of G, problems with the application of these approaches, and identify avenues for future research.     

Effects of stress and phenotypic variation on inbreeding depression in Brassica rapa

Stressful environments are often said to increase the expression of inbreeding depression. Alternatively, Crow's "opportunity for selection" (the squared phenotypic coefficient of variation) sets a limit to how much selection can occur, constraining the magnitude of inbreeding depression. To test these hypotheses, we planted self- and cross-fertilized seeds of Brassica rapa into a factorial experiment that varied plant density and saline watering stresses. We then repeated the experiment, reducing the salt concentration. We observed considerable inbreeding depression, particularly for survival in the first experiment and growth in the second. Both stresses independently depressed plant performance. Families differed in their amounts of inbreeding depression and reaction norms across environments. Outcrossed progeny were sometimes more variable. Stresses had small and inconsistent effects on inbreeding depression and, when significant, tended to diminish it. Levels of phenotypic variability often predicted whether inbreeding depression would increase or decrease across environments and were particularly effective in predicting which traits display the most inbreeding depression. Thus, we find little support for the stress hypothesis and mixed support for the phenotypic variability hypothesis. Variable levels of phenotypic variation provide a parsimonious explanation for shifts in inbreeding depression that should be tested before invoking more complex hypotheses.     

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

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