Sexual Dimorphism Increases Evolvability in a Genetic Regulatory Network

The majority of work on genetic regulatory networks has focused on environmental and mutational robustness, and much less attention has been paid to the conditions under which a network may produce an evolvable phenotype. Sexually dimorphic characters often show rapid rates of change over short evolutionary time scales and while this is thought to be due to the strength of sexual selection acting on the trait, a dimorphic character with an underlying pleiotropic architecture may also influence the evolution of the regulatory network that controls the character and affect evolvability. As evolvability indicates a capacity for phenotypic change and mutational robustness refers to a capacity for phenotypic stasis, increases in evolvability may show a negative relationship with mutational robustness. I tested this with a computational model of a genetic regulatory network and found that, contrary to expectation, sexually dimorphic characters exhibited both higher mutational robustness and higher evolvability. Decomposition of the results revealed that linkage disequilibrium within sex and linkage disequilibrium between sexes, two of the three primary components of additive genetic variance and evolvability in quantitative genetics models, contributed to the differences in evolvability between sexually dimorphic and monomorphic populations. These results indicate that producing two pleiotropically linked characters did not constrain either the production of a robust phenotype or adaptive potential. Instead, the genetic system evolved to maximize both quantities.     

Homologues, Natural Kinds and the Evolution of Modularity

The fact that phenotypic evolution can be studied on a characterby character basis suggests that the body is composed of locallyintegrated units. These units can be considered as modular partsof the body which integrate functionally related charactersinto units of evolutionary transformation. These units may eitheremerge spontaneously by self-organization, or may be the productof natural selection. A selection scenario that could explainthe origin of modular units needs to explain the differentialsuppression of pleiotropic effects between different modulesand the augmentation of pleiotropic effects among the elementswithin the module. Four scenarios are discussed: selection foradaptation rate, constructional selection, stabilizing selectionand a combination of directional and stabilizing selection.It is concluded that a combination of directional and stabilizingselection is a prevalent mode of selection and a likely explanationfor the evolution of modularity.     

The genetics of adaptation: the roles of pleiotropy, stabilizing selection and drift in shaping the distribution of bidirectional fixed mutational effects

Pleiotropy allows for the deterministic fixation of bidirectional mutations: mutations with effects both in the direction of selection and opposite to selection for the same character. Mutations with deleterious effects on some characters can fix because of beneficial effects on other characters. This study analytically quantifies the expected frequency of mutations that fix with negative and positive effects on a character and the average size of a fixed effect on a character when a mutation pleiotropically affects from very few to many characters. The analysis allows for mutational distributions that vary in shape and provides a framework that would allow for varying the frequency at which mutations arise with deleterious and positive effects on characters. The results show that a large fraction of fixed mutations will have deleterious pleiotropic effects even when mutation affects as little as two characters and only directional selection is occurring, and, not surprisingly, as the degree of pleiotropy increases the frequency of fixed deleterious effects increases. As a point of comparison, we show how stabilizing selection and random genetic drift affect the bidirectional distribution of fixed mutational effects. The results are then applied to QTL studies that seek to find loci that contribute to phenotypic differences between populations or species. It is shown that QTL studies are biased against detecting chromosome regions that have deleterious pleiotropic effects on characters.     

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.     

A POPULATION GENETIC THEORY OF CANALIZATION

Canalization is the suppression of phenotypic variation. Depending on the causes of phenotypic variation, one speaks either of genetic or environmental canalization. Genetic canalization describes insensitivity of a character to mutations, and the insensitivity to environmental factors is called environmental canalization. Genetic canalization is of interest because it influences the availability of heritable phenotypic variation to natural selection, and is thus potentially important in determining the pattern of phenotypic evolution. In this paper a number of population genetic models are considered of a quantitative character under stabilizing selection. The main purpose of this study is to define the population genetic conditions and constraints for the evolution of canalization. Environmental canalization is modeled as genotype specific environmental variance. It is shown that stabilizing selection favors genes that decrease environmental variance of quantitative characters. However, the theoretical limit of zero environmental variance has never been observed. Of the many ways to explain this fact, two are addressed by our model. It is shown that a “canalization limit” is reached if canalizing effects of mutations are correlated with direct effects on the same character. This canalization limit is predicted to be independent of the strength of stabilizing selection, which is inconsistent with recent experimental data (Sterns et al. 1995). The second model assumes that the canalizing genes have deleterious pleiotropic effects. If these deleterious effects are of the same magnitude as all the other mutations affecting fitness very strong stabilizing selection is required to allow the evolution of environmental canalization. Genetic canalization is modeled as an influence on the average effect of mutations at a locus of other genes. It is found that the selection for genetic canalization critically depends on the amount of genetic variation present in the population. The more genetic variation, the stronger the selection for canalizing effects. All factors that increase genetic variation favor the evolution of genetic canalization (large population size, high mutation rate, large number of genes). If genetic variation is maintained by mutation-selection balance, strong stabilizing selection can inhibit the evolution of genetic canalization. Strong stabilizing selection eliminates genetic variation to a level where selection for canalization does not work anymore. It is predicted that the most important characters (in terms of fitness) are not necessarily the most canalized ones, if they are under very strong stabilizing selection (k > 0.2V_e). The rate of decrease of mutational variance V_m is found to be less than 10% of the initial V_m. From this result it is concluded that characters with typical mutational variances of about 10^–3 V_e are in a metastable state where further evolution of genetic canalization is too slow to be of importance at a microevolutionary time scale. The implications for the explanation of macroevolutionary patterns are discussed.     

Pleiotropy and Multilocus Polymorphisms

It is demonstrated that systems of two pleiotropically related characters controlled by additive diallelic loci can maintain under Gaussian stabilizing selection a stable polymorphism in more than two loci. It is also shown that such systems may have multiple stable polymorphic equilibria. Stabilizing selection generates negative linkage disequilibrium, as a result of which the equilibrium phenotypic variances are quite low, even though the level of allelic polymorphisms can be very high. Consequently, large amounts of additive genetic variation can be hidden in populations at equilibrium under stabilizing selection on pleiotropically related characters.     

Apparent directional selection by biased pleiotropic mutation

Pleiotropic effects of deleterious mutations are considered to be among the factors responsible for genetic constraints on evolution by long-term directional selection acting on a quantitative trait. If pleiotropic phenotypic effects are biased in a particular direction, mutations generate apparent directional selection, which refers to the covariance between fitness and the trait owing to a linear association between the number of mutations possessed by individuals and the genotypic values of the trait. The present analysis has shown how the equilibrium mean value of the trait is determined by a balance between directional selection and biased pleiotropic mutations. Assuming that genes act additively both on the trait and on fitness, the total variance-standardized directional selection gradient was decomposed into apparent and true components. Experimental data on mutation bias from the bristle traits of Drosophila and life history traits of Daphnia suggest that apparent selection explains a small but significant fraction of directional selection pressure that is observed in nature; the data suggest that changes induced in a trait by biased pleiotropic mutation (i.e., by apparent directional selection) are easily compensated for by (true) directional selection.     

The Genetic Covariance between Characters Maintained by Pleiotropic Mutations

A statistical genetic model of a multivariate phenotype is derived to investigate the covariation of pleiotropic mutations with additive effects under the combined action of phenotypic selection, linkage and the mating system. Equilibrium formulas for large, randomly mating populations demonstrate that, when selection on polygenic variation is much smaller than twice the harmonic mean recombination rate between loci with interacting fitnesses, linkage disequilibrium is negligible and pleiotropy is the main cause of genetic correlations between characters. Under these conditions, approximate expressions for the dynamics of the genetic covariances due to pleiotropic mutations are obtained. Patterns of genetic covariance between characters and their evolution are discussed with reference to data on polygenic mutation, chromosomal organization and morphological integration.     

The Quantitative Genetic Consequences of Pleiotropy under Stabilizing and Directional Selection

The independence of two phenotypic characters affected by both pleiotropic and nonpleiotropic mutations is investigated using a generalization of M. Slatkin's stepwise mutation model of 1987. The model is used to determine whether predictions of either the multivariate normal model introduced in 1980 by R. Lande or the house-of-cards model introduced in 1985 by M. Turelli can be regarded as typical of models that are intermediate between them. We found that, under stabilizing selection, the variance of one character at equilibrium may depend on the strength of stabilizing selection on the other character (as in the house-of-cards model) or not (as in the multivariate normal model) depending on the types of mutations that can occur. Similarly, under directional selection, the genetic covariance between two characters may increase substantially (as in the house-of-cards model) or not (as in the multivariate normal model) depending on the kinds of mutations that are assumed to occur. Hence, even for the simple model we consider, neither the house-of-cards nor the multivariate normal model can be used to make predictions, making it unlikely that either could be used to draw general conclusions about more complex and realistic models.     

Phenotypic noise and the cost of complexity

Experimental studies demonstrate the existence of phenotypic diversity despite constant genotype and environment. Theoretical models based on a single phenotypic character predict that during an adaptation event, phenotypic noise should be positively selected far from the fitness optimum because it increases the fitness of the genotype, and then be selected against when the population reaches the optimum. It is suggested that because of this fitness gain, phenotypic noise should promote adaptive evolution. However, it is unclear how the selective advantage of phenotypic noise is linked to the rate of evolution, and whether any advantage would hold for more realistic, multidimensional phenotypes. Indeed, complex organisms suffer a cost of complexity, where beneficial mutations become rarer as the number of phenotypic characters increases. Using a quantitative genetics approach, we first show that for a one-dimensional phenotype, phenotypic noise promotes adaptive evolution on plateaus of positive fitness, independently from the direct selective advantage on fitness. Second, we show that for multidimensional phenotypes, phenotypic noise evolves to a low-dimensional configuration, with elevated noise in the direction of the fitness optimum. Such a dimensionality reduction of the phenotypic noise promotes adaptive evolution and numerical simulations show that it reduces the cost of complexity.     

Effects of Pleiotropy on Predictions concerning Mutation-Selection Balance for Polygenic Traits

Previous mathematical analyses of mutation-selection balance for metric traits assume that selection acts on the relevant loci only through the character(s) under study. Thus, they implicitly assume that all of the relevant mutation and selection parameters are estimable. A more realistic analysis must recognize that many of the pleiotropic effects of loci contributing variation to a given character are not known. To explore the consequences of these hidden effects, I analyze models of two pleiotropically connected polygenic traits, denoted P1 and P2. The actual equilibrium genetic variance for P1, based on complete knowledge of all mutation and selection parameters for both P1 and P2, can be compared to a prediction based solely on observations of P1. This extrapolation mimics empirically obtainable predictions because of the inevitability of unknown pleiotropic effects. The mutation parameters relevant to P1 are assumed to be known, but selection intensity is estimated from the within-generation reduction of phenotypic variance for P1. The extrapolated prediction is obtained by substituting these parameters into formulas based on single-character analyses. Approximate analytical and numerical results show that the level of agreement between these univariate extrapolations and the actual equilibrium variance depends critically on both the genetic model assumed and the relative magnitudes of the mutation and selection parameters. Unless per locus mutation rates are extremely high, i.e., generally greater than 10(-4), the widely used gaussian approximation for genetic effects at individual loci is not applicable. Nevertheless, the gaussian approximations predict that the true and extrapolated equilibria are in reasonable agreement, i.e., within a factor of two, over a wide range of parameter values. In contrast, an alternative approximation that applies for moderate and low per locus mutation rates predicts that the extrapolation will generally overestimate the true equilibrium variance unless there is little selection associated with hidden effects. The tendency to overestimate is understandable because selection acts on all of the pleiotropic manifestations of a new mutation, but equilibrium covariances among the characters affected may not reveal all of this selection. This casts doubt on the proposal that much of the additive polygenic variance observed in natural populations can be explained by mutation-selection balance. It also indicates the difficulty of critically evaluating this hypothesis.     

Generic scan using AFLP markers as a means to assess the role of directional selection in the divergence of sympatric whitefish ecotypes

Under the ecological theory of adaptive radiation, adaptation and reproductive isolation are thought to evolve as a result of divergent natural selection. Accordingly, elucidating the genetic basis of these processes is essential toward understanding the role of selection in shaping biological diversity. In this respect, the number of genes that evolved by selection remains contentious. To address this issue, the pattern of genetic differentiation obtained using 440 AFLP loci was compared with that expected under neutrality in four sympatric pairs of lake whitefish ecotypes that evolved adaptive phenotypic differences associated with the exploitation of distinct ecological niches. On average, 14 loci showed restricted gene flow relative to neutral expectation, suggesting a role of directional selection on their divergence. Among all loci that are most likely under directional selection, six exhibited parallel patterns of divergence, which provided further support for the role of selection in driving their divergence. Overall, these results indicate that only a small proportion of scored AFLP loci (between 1.4% and 3.2%) might be linked to genes implicated in the adaptive radiation of lake whitefish.     

Independent contrasts succeed where ancestor reconstruction fails in a known bacteriophage phylogeny

Abstract.— Methods of ancestor reconstruction are important tools for evolutionary inference that are difficult to test empirically because ancestral states are rarely known with certainty. We evaluated reconstruction methods for continuous phenotypic characters using taxa from an experimentally generated bacteriophage phylogeny. Except for one slowly evolving character, the estimated ancestral states of continuous phenotypic characters were highly inaccurate and biased, even when including a known ancestor at the root. This error was caused by a directional trend in character evolution and by rapid rates of character evolution. Computer simulations confirmed that such factors affect reconstruction of continuous characters in general. We also used phenotypic viral characters to evaluate two methods that attempt to estimate the correlation between characters during evolution. Whereas a nonphylogenetic regression was relatively inaccurate and biased, independent contrasts accurately estimated the correlation between characters with little bias.     

Fecundity selection does not vary along a large geographical cline of trait means in a passerine bird

Local environmental and ecological conditions are commonly expected to result in local adaptation, although there are few examples of variation in phenotypic selection across continent‐wide spatial scales. We collected standardized data on selection with respect to the highly variable plumage coloration of pied flycatcher (Ficedula hypoleuca Pall.) males from 17 populations across the species' breeding range. The observed selection on multiple male coloration traits via the annual number of fledged young was generally relatively weak. The main aim of the present study, however, was to examine whether the current directional selection estimates are associated with distance to the sympatric area with the collared flycatcher (Ficedula albicollis Temminck), a sister species with which the pied flycatcher is showing character displacement. This pattern was expected because plumage traits in male pied flycatchers are changing with the distance to these areas of sympatry. However, we did not find such a pattern in current selection on coloration. There were no associations between current directional selection on ornamentation and latitude or longitude either. Interestingly, current selection on coloration traits was not associated with the observed mean plumage traits of the populations. Thus, there do not appear to be geographical gradients in current directional fecundity selection on male plumage ornamentation. The results of the present study do not support the idea that constant patterns in directional fecundity selection would play a major role in the maintenance of coloration among populations in this species. By contrast, the tendency for relatively weak mosaic‐like variation in selection among populations could reflect just a snapshot of temporally variable, potentially environment‐dependent, selection, as suggested by other studies in this system. Such fine‐grained variable selection coupled with gene flow could maintain extensive phenotypic variation across populations. © 2015 The Linnean Society of London, Biological Journal of the Linnean Society, 2015, 114 , 808–827.     

GENOTYPE-ENVIRONMENT INTERACTION AND THE EVOLUTION OF PHENOTYPIC PLASTICITY

Studies of spatial variation in the environment have primarily focused on how genetic variation can be maintained. Many one-locus genetic models have addressed this issue, but, for several reasons, these models are not directly applicable to quantitative (polygenic) traits. One reason is that for continuously varying characters, the evolution of the mean phenotype expressed in different environments (the norm of reaction) is also of interest. Our quantitative genetic models describe the evolution of phenotypic response to the environment, also known as phenotypic plasticity (Gause, 1947), and illustrate how the norm of reaction (Schmalhausen, 1949) can be shaped by selection. These models utilize the statistical relationship which exists between genotype-environment interaction and genetic correlation to describe evolution of the mean phenotype under soft and hard selection in coarse-grained environments. Just as genetic correlations among characters within a single environment can constrain the response to simultaneous selection, so can a genetic correlation between states of a character which are expressed in two environments. Unless the genetic correlation across environments is ± 1, polygenic variation is exhausted, or there is a cost to plasticity, panmictic populations under a bivariate fitness function will eventually attain the optimum mean phenotype for a given character in each environment. However, very high positive or negative correlations can substantially slow the rate of evolution and may produce temporary maladaptation in one environment before the optimum joint phenotype is finally attained. Evolutionary trajectories under hard and soft selection can differ: in hard selection, the environments with the highest initial mean fitness contribute most individuals to the mating pool. In both hard and soft selection, evolution toward the optimum in a rare environment is much slower than it is in a common one. A subdivided population model reveals that migration restriction can facilitate local adaptation. However, unless there is no migration or one of the special cases discussed for panmictic populations holds, no geographical variation in the norm of reaction will be maintained at equilibrium. Implications of these results for the interpretation of spatial patterns of phenotypic variation in natural populations are discussed.     

Evolution of branched regulatory genetic pathways: directional selection on pleiotropic loci accelerates developmental system drift

Developmental systems are regulated by a web of interacting loci. One common and useful approach in studying the evolution of development is to focus on classes of interacting elements within these systems. Here, we use individual-based simulations to study the evolution of traits controlled by branched developmental pathways involving three loci, where one locus regulates two different traits. We examined the system under a variety of selective regimes. In the case where one branch was under stabilizing selection and the other under directional selection, we observed "developmental system drift": the trait under stabilizing selection showed little phenotypic change even though the loci underlying that trait showed considerable evolutionary divergence. This occurs because the pleiotropic locus responds to directional selection and compensatory mutants are then favored in the pathway under stabilizing selection. Though developmental system drift may be caused by other mechanisms, it seems likely that it is accelerated by the same underlying genetic mechanism as that producing the Dobzhansky-Muller incompatibilities that lead to speciation in both linear and branched pathways. We also discuss predictions of our model for developmental system drift and how different selective regimes affect probabilities of speciation in the branched pathway system.     

Deleterious Mutations, Apparent Stabilizing Selection and the Maintenance of Quantitative Variation

Apparent stabilizing selection on a quantitative trait that is not causally connected to fitness can result from the pleiotropic effects of unconditionally deleterious mutations, because as N. Barton noted, "...individuals with extreme values of the trait will tend to carry more deleterious alleles...." We use a simple model to investigate the dependence of this apparent selection on the genomic deleterious mutation rate, U; the equilibrium distribution of K, the number of deleterious mutations per genome; and the parameters describing directional selection against deleterious mutations. Unlike previous analyses, we allow for epistatic selection against deleterious alleles. For various selection functions and realistic parameter values, the distribution of K, the distribution of breeding values for a pleiotropically affected trait, and the apparent stabilizing selection function are all nearly Gaussian. The additive genetic variance for the quantitative trait is kQa2, where k is the average number of deleterious mutations per genome, Q is the proportion of deleterious mutations that affect the trait, and a2 is the variance of pleiotropic effects for individual mutations that do affect the trait. In contrast, when the trait is measured in units of its additive standard deviation, the apparent fitness function is essentially independent of Q and a2; and beta, the intensity of selection, measured as the ratio of additive genetic variance to the "variance" of the fitness curve, is very close to s = U/k, the selection coefficient against individual deleterious mutations at equilibrium. Therefore, this model predicts appreciable apparent stabilizing selection if s exceeds about 0.03, which is consistent with various data. However, the model also predicts that beta must equal Vm/VG, the ratio of new additive variance for the trait introduced each generation by mutation to the standing additive variance. Most, although not all, estimates of this ratio imply apparent stabilizing selection weaker than generally observed. A qualitative argument suggests that even when direct selection is responsible for most of the selection observed on a character, it may be essentially irrelevant to the maintenance of variation for the character by mutation-selection balance. Simple experiments can indicate the fraction of observed stabilizing selection attributable to the pleiotropic effects of deleterious mutations.     

Evolvability and genetic constraint in Dalechampia blossoms: genetic correlations and conditional evolvability

The short-term evolvability of a character is closely related to its level of additive genetic variation. However, a large component of the variation in any one character may be pleiotropically linked to other characters under the influence of different selective factors. Therefore, the organization of the organism into quasi-independent modules may be an important prerequisite for evolvability. In this paper we propose to study character evolvability in terms of conditional genetic variation. By estimating the amount of genetic variation in a character, y, that is independent of other characters, x, we can assess the evolvability of y when there is stabilizing selection on x. We suggest that systematic use of conditioning may help build a picture of modular organization and quasi-independent evolvability. As an illustration, we use this approach to assess the evolvability of floral characters in Dalechampia scandens (Euphorbiaceae). Although our study population had relatively low levels of genetic variation at the outset, we find evidence that conditioning may lead to substantial further reduction in the genetic variation available for independent adaptation. This provides additional evidence that the D. scandens blossom is constrained in its short-term evolvability.     

Spatial variation in phenotypic selection on floral characteristics in an epiphytic orchid

Spatial variation in twelve floral characters was examined in an epiphytic orchidLepanthes rupestris to evaluate the strength and direction of phenotypic selection in seven riparian populations along two river basins in the Caribbean National Forest “El Yunque” for a range of 18–34 months. We evaluated selection on floral characters based on male (pollinaria removal) and female fitness (fruit set). Simple linear and quadratic regressions were used to evaluate the strength of directional, disruptive and stabilizing selections. Univariate and multivariate analyses were used to estimate the total strength of the selection acting on a character. Phenotypic selection was inconsistent among characters and populations. Few of the characters appeared to be under selection and none of them was found to be consistent throughout all populations. Inconsistency in selection coefficients among populations could suggest that selection is spatially variable. We only noted one character (column length) which had some consistency in differential selection coefficients among populations. Previous studies have shown that effective population sizes inL. rupestris are small and the observed “fitness differences” among populations could as easily be explained as stochastic events at play. We argue that the observed “fitness differences” in most characters and inconsistency among populations are likely from stochastic noise and not phenotypic selection. Consequently, we propose that random selection on character state support the hypothesis of genetic drift in small orchid populations.