Interaction of directional and stabilizing selection for wing characteristics in Drosophila melanogaster

The effects of interaction of artificial directional and stabilizing selection were studied using a recessive mutation of Drosophila melanogaster radius incompletus which causes interruption of the second longitudinal wing vein (L2). The character under directional selection was the length of the proximal segment of L2; stabilizing selection was conducted for a complex of morphometric wing characters. Three experimental designs in three replications were used: 1) directional and stabilizing selection; 2) directional selection; 3) unselected controls. The dynamics and variation of the character under directional selection was shown to be different in the stabilized and unstabilized lines. Coefficient of variation which increased in the unstabilized lines remained at the same level in the stabilized lines and in the controls. The results are in agreement with those of the previous experiment, where directional selection was conducted for a behavioral trait, which suggests general character of the relationships observed.     

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.     

The Selection Limit Due to the Conflict between Truncation and Stabilizing Selection with Mutation

Long-term selection response could slow down from a decline in genetic variance or in selection differential or both. A model of conflict between truncation and stabilizing selection in infinite population size is analysed in terms of the reduction in selection differential. Under the assumption of a normal phenotypic distribution, the limit to selection is found to be a function of kappa, the intensity of truncation selection, omega 2, a measure of the intensity of stabilizing selection, and sigma 2, the phenotypic variance of the character. The maintenance of genetic variation at this limit is also analyzed in terms of mutation-selection balance by the use of the "House-of-cards" approximation. It is found that truncation selection can substantially reduce the equilibrium genetic variance below that when only stabilizing selection is acting, and the proportional reduction in variance is greatest when the selection is very weak. When truncation selection is strong, any further increase in the strength of selection has little further influence on the variance. It appears that this mutation-selection balance is insufficient to account for the high levels of genetic variation observed in many long-term selection experiments.     

The effect of non-additive genetic interactions on selection in multi-locus genetic models

Additive genetic variance might usually be expected to decrease in a finite population because of genetic drift. However, both theoretical and empirical studies have shown that the additive genetic variance of a population could, in some cases, actually increase owing to the action of genetic drift in presence of non-additive effects. We used Monte-Carlo simulations to address a less-well-studied issue: the effects of directional truncation selection on a trait affected by non-additive genetic variation. We investigated the effects on genetic variance and the response to selection. We compared two different genetic models, representing various numbers of loci. We found that the additive genetic variance could also increase in the case of truncation selection, when dominance and epistasis was present. Additive-by-additive epistatic effects generally gave a higher increase in additive variance compared to dominance. However, the magnitude of the increase differed depending on the particular model and on the number of loci.     

Spatial processes and evolutionary models: a critical review

Evolution is a fundamentally population level process in which variation, drift and selection produce both temporal and spatial patterns of change. Statistical model fitting is now commonly used to estimate which kind of evolutionary process best explains patterns of change through time using models like Brownian motion, stabilizing selection (Ornstein–Uhlenbeck) and directional selection on traits measured from stratigraphic sequences or on phylogenetic trees. But these models assume that the traits possessed by a species are homogeneous. Spatial processes such as dispersal, gene flow and geographical range changes can produce patterns of trait evolution that do not fit the expectations of standard models, even when evolution at the local‐population level is governed by drift or a typical OU model of selection. The basic properties of population level processes (variation, drift, selection and population size) are reviewed and the relationship between their spatial and temporal dynamics is discussed. Typical evolutionary models used in palaeontology incorporate the temporal component of these dynamics, but not the spatial. Range expansions and contractions introduce rate variability into drift processes, range expansion under a drift model can drive directional change in trait evolution, and spatial selection gradients can create spatial variation in traits that can produce long‐term directional trends and punctuation events depending on the balance between selection strength, gene flow, extirpation probability and model of speciation. Using computational modelling that spatial processes can create evolutionary outcomes that depart from basic population‐level notions from these standard macroevolutionary models.     

Isolation by Distance in a Quantitative Trait

Random genetic drift in a quantitative character is modeled for a population with a continuous spatial distribution in an infinite habitat of one or two dimensions. The analysis extends Wright's concept of neighborhood size to spatially autocorrelated sampling variation in the expected phenotype at different locations. Weak stabilizing selection is assumed to operate toward the same optimum phenotype in every locality, and the distribution of dispersal distances from parent to offspring is a (radially) symmetric function. The equilibrium pattern of geographic variation in the expected local phenotype depends on the neighborhood size, the genetic variance within neighborhoods, and the strength of selection, but is nearly independent of the form of the dispersal function. With all else equal, geographic variance is smaller in a two-dimensional habitat than in one dimension, and the covariance between expected local phenotypes decreases more rapidly with the distance separating them in two dimensions than in one. The equilibrium geographic variance is less than the phenotypic variance within localities, unless the neighborhood size is small and selection is extremely weak, especially in two dimensions. Nevertheless, dispersal of geographic variance created by random genetic drift is an important mechanism maintaining genetic variance within local populations. For a Gaussian dispersal function it is shown that, even with a small neighborhood size, a population in a two-dimensional habitat can maintain within neighborhoods most of the genetic variance that would occur in an infinite panmictic population.     

Variation in natural selection for growth and phlorotannins in the brown alga Fucus vesiculosus

Directional selection for plant traits associated with resistance to herbivory tends to eliminate genetic variation in such traits. On the other hand, balancing selection arising from trade-offs between resistance and growth or spatially variable selection acts against the elimination of genetic variation. We explore both the amount of genetic variation and variability of natural selection for growth and concentration of phenolic secondary compounds, phlorotannins, in the brown alga Fucus vesiculosus. We measured variation in selection at two growing depths and two levels of nutrient availability in algae that had faced two kinds of past growing environments. Genetic variation was low for growth but high for phlorotannins. The form and strength of selection for both focal traits depended on the past growing environment of the algae. We found strong directional selection for growth rate in algae previously subjected to higher ultraviolet radiation, but not in algae previously subjected to higher nutrient availability. Stabilizing selection for growth occurred especially in the deep growing environment. Selection for phlorotannins was generally weak, but in some past-environment-current-environment combinations we detected either directional selection against phlorotannins or stabilizing selection. Thus, phlorotannins are not selectively neutral but affect the fitness of F. vesiculosus. In particular, there may be a fitness cost of producing phlorotannins, but the realization of such a cost varies from one environment to another. Genetic correlations between selective environments were high for growth but nonexistent for phlorotannins, emphasizing the high phenotypic plasticity of phlorotannin production. The highly heterogeneous selection, including directional, stabilizing, and spatially variable selection as well as temporal change in selection due to responses to past environmental conditions, probably maintains a high amount of genetic variation in phlorotannins. Such variation provides the potential for rapid evolutionary response of phlorotannins under directional selection.     

EVOLUTION AND EXTINCTION IN A CHANGING ENVIRONMENT: A QUANTITATIVE-GENETIC ANALYSIS

Because of the ubiquity of genetic variation for quantitative traits, virtually all populations have some capacity to respond evolutionarily to selective challenges. However, natural selection imposes demographic costs on a population, and if these costs are sufficiently large, the likelihood of extinction will be high. We consider how the mean time to extinction depends on selective pressures (rate and stochasticity of environmental change, and strength of selection), population parameters (carrying capacity, and reproductive capacity), and genetics (rate of polygenic mutation). We assume that in a randomly mating, finite population subject to density-dependent population growth, individual fitness is determined by a single quantitative-genetic character under Gaussian stabilizing selection with the optimum phenotype exhibiting directional change, or random fluctuations, or both. The quantitative trait is determined by a finite number of freely recombining, mutationally equivalent, additive loci. The dynamics of evolution and extinction are investigated, assuming that the population is initially under mutation-selection-drift balance. Under this model, in a directionally changing environment, the mean phenotype lags behind the optimum, but on the average evolves parallel to it. The magnitude of the lag determines the vulnerability to extinction. In finite populations, stochastic variation in the genetic variance can be quite pronounced, and bottlenecks in the genetic variance temporarily can impair the population's adaptive capacity enough to cause extinction when it would otherwise be unlikely in an effectively infinite population. We find that maximum sustainable rates of evolution or, equivalently, critical rates of environmental change, may be considerably less than 10% of a phenotypic standard deviation per generation.     

Common garden and natural selection experiments support ecotypic differentiation in the Dominican anole (Anolis oculatus)

The theory behind ecotypic differentiation and ecological speciation assumes a predominant role for natural selection working on characteristics with genetic variance, but experimental support for these assumptions is limited. Lesser Antillean anoles show marked ecotypic variation within islands and the potential for ecological speciation. Common garden rearing experiments on the Dominican anole (Anolis oculatus) suggest that the characters showing geographic variation have genetic variance and are not primarily determined by environmental plasticity. Replicated natural selection experiments using large-scale enclosures show that translocated montane samples experience significant (multivariate) directional selection in both wet and dry seasons in both males and females. The targets of selection appear to be spread among the various character systems. An experiment on 12 geographically segregated populations along a coastal xeric-montane rainforest gradient (four replicate enclosures) clearly showed that the magnitude of the directional selection intensity is positively related to the position along this gradient. The results of the common garden and natural selection experiments support the interpretation that the geographic differentiation is primarily driven by natural selection and are compatible with the potential for ecological speciation in this system.     

Multiplicative Genotype-Environment Interaction as a Cause of Reversed Response to Directional Selection

In experiments with directional selection on a quantitative character a "reversed response" to selection is occasionally observed, when selection of individuals for a higher (lower) value of the character results in a lower (higher) value of the character among their offspring. A sudden change in environments or random drift is often assumed to be responsible for this. It is demonstrated in this paper that these two causes cannot account for the reversed response at least in some of the experiments. Multiplicative genotype-environment interaction is discussed as a possible cause of a reversed response to directional selection. Such interaction entails either disruptive or stabilizing genotypic selection, even when the phenotypic selection is directional.     

A simple completion of Fisher’s fundamental theorem of natural selection

Fisher''s fundamental theorem of natural selection shows that the part of the rate of change of mean fitness that is due to natural selection equals the additive genetic variance in fitness. Fisher embedded this result in a model of total fitness, adding terms for deterioration of the environment and density dependence. Here, a quantitative genetic version of this neglected model is derived that relaxes its assumptions that the additive genetic variance in fitness and the rate of deterioration of the environment do not change over time, allows population size to vary, and includes an input of mutational variance. The resulting formula for total rate of change in mean fitness contains two terms more than Fisher''s original, representing the effects of stabilizing selection, on the one hand, and of mutational variance, on the other, making clear for the first time that the fundamental theorem deals only with natural selection that is directional (as opposed to stabilizing) on the underlying traits. In this model, the total (rather than just the additive) genetic variance increases mean fitness. The unstructured population allows an explanation of Fisher''s concept of fitness as simply birth rate minus mortality rate, and building up to the definition in structured populations.     

Non-linear selection response in Drosophila: a strategy for testing the rare-alleles model of quantitative genetic variability

Quantitative genetic theory predicts that variation due to rare alleles at many loci will generate a transient acceleration in the response to directional selection. We have tested this prediction by constructing experimental lines ofDrosophila melanogaster that carry positively selected ethanol resistance alleles at low frequencies, and then subjecting the lines to directional selection for ethanol resistance. Approximately 468,000 files were subjected to artificial selection over 30 generations. The predicted non-linear selection responses were observed in all experimental lines and replicates, on three genetic backgrounds. In contrast, un-selected controls and lines carrying random alleles at low frequencies on the same genetic backgrounds exhibited linear selection responses. These results demonstrate that non-linearities due to rare alleles are detectable and repeatable, provided that experiments are done on a sufficiently large scale. The results suggest that it may be possible to test for rare-alleles as a component of naturally occurring genetic variation by careful examination of selection response curves.     

Effects of artificial stabilizing selection on Drosophila populations subjected to directional selection for another trait

Stabilizing selection for a set of morphometric wing traits was combined with directional selection for the increased expression of radius incompletus (ri) mutation of Drosophila melanogaster. Three experimental regimes were used: directional and stabilizing selection (stabilized lines); directional selection (unstabilized lines); no selection (controls). Response to selection for ri expression was similar in all selected lines but variation of this character was higher in the unstabilized lines compared to the stabilized ones. The competitive indices measured after termination of selection did not significantly differ under different treatments while fluctuating asymmetry was significantly lower in stabilized than in unstabilized lines. The possible causes of these differences are discussed.     

Environmental variance in male mating success modulates the positive versus negative impacts of sexual selection on genetic load

Sexual selection on males is predicted to increase population fitness, and delay population extinction, when mating success negatively covaries with genetic load across individuals. However, such benefits of sexual selection could be counteracted by simultaneous increases in genome-wide drift resulting from reduced effective population size caused by increased variance in fitness. Resulting fixation of deleterious mutations could be greatest in small populations, and when environmental variation in mating traits partially decouples sexual selection from underlying genetic variation. The net consequences of sexual selection for genetic load and population persistence are therefore likely to be context dependent, but such variation has not been examined. We use a genetically explicit individual-based model to show that weak sexual selection can increase population persistence time compared to random mating. However, for stronger sexual selection such positive effects can be overturned by the detrimental effects of increased genome-wide drift. Furthermore, the relative strengths of mutation-purging and drift critically depend on the environmental variance in the male mating trait. Specifically, increasing environmental variance caused stronger sexual selection to elevate deleterious mutation fixation rate and mean selection coefficient, driving rapid accumulation of drift load and decreasing population persistence times. These results highlight an intricate balance between conflicting positive and negative consequences of sexual selection on genetic load, even in the absence of sexually antagonistic selection. They imply that environmental variances in key mating traits, and intrinsic genetic drift, should be properly factored into future theoretical and empirical studies of the evolution of population fitness under sexual selection.     

A multilocus-multiallele analysis of frequency-dependent selection induced by intraspecific competition

The study of the mechanisms that maintain genetic variation has a long history in population genetics. We analyze a multilocus-multiallele model of frequency- and density-dependent selection in a large randomly mating population. The number of loci and the number of alleles per locus are arbitrary. The n loci are assumed to contribute additively to a quantitative character under stabilizing or directional selection as well as under frequency-dependent selection caused by intraspecific competition. We assume the strength of stabilizing selection to be weak, whereas the strength of frequency dependence may be arbitrary. Density-dependence is induced by population regulation. Our main result is a characterization of the equilibrium structure and its stability properties in terms of all parameters. It turns out that no equilibrium exists with more than two alleles segregating per locus. We give necessary and sufficient conditions on the strength of frequency dependence to ensure the maintenance of multilocus polymorphism. We also give explicit formulas on the number of polymorphic loci maintained at equilibrium. These results are based on the assumption that selection is sufficiently weak compared with recombination, so that linkage equilibrium can be assumed. If additionally the population size is assumed to be constant, we prove that the dynamics of the model form a generalized gradient system. For the model in its general form we are able to derive necessary and sufficient conditions for the stability of the monomorphic equilibria. Furthermore, we briefly analyze a special symmetric two-locus two-allele model for a constant population size but allowing for linkage disequilibrium. Finally, we analyze a single diallelic locus with dominance to illustrate the complications that can occur if the assumption of additivity is relaxed.     

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.     

Change of Genetic Architecture in Response to Sex

A traditional view is that sexual reproduction increases the potential for phenotypic evolution by expanding the range of genetic variation upon which natural selection can act. However, when nonadditive genetic effects and genetic disequilibria underlie a genetic system, genetic slippage (a change in the mean genotypic value contrary to that promoted by selection) in response to sex may occur. Additionally, depending on whether natural selection is predominantly stabilizing or disruptive, recombination may either enhance or reduce the level of expressed genetic variance. Thus, the role of sexual reproduction in the dynamics of phenotypic evolution depends heavily upon the nature of natural selection and the genetic system of the study population. In the present study, on a permanent lake Daphnia pulicaria population, sexual reproduction resulted in significant genetic slippage and a significant increase in expressed genetic variance for several traits. These observations provide evidence for substantial genetic disequilibria and nonadditive genetic effects underlying the genetic system of the study population. From these results, the fitness function of the previous clonal selection phase is inferred to be directional and/or stabilizing. The data are also used to infer the effects of natural selection on the mean and the genetic variance of the population.     

Multivariate stabilizing selection and pleiotropy in the maintenance of quantitative genetic variation

Abstract. We investigate maintenance of quantitative genetic variation at mutation-selection balance for multiple traits. The intrinsic strength of real stabilizing selection on one of these traits denoted the "target trait" and the observed strength of apparent stabilizing selection on the target trait can be quite different: the latter, which is estimable, is much smaller (i.e., implying stronger selection) than the former. Distinguishing them may enable the mutation load to be relaxed when considering multivariate stabilizing selection. It is shown that both correlations among mutational effects and among strengths of real stabilizing selection on the traits are not important unless they are high. The analysis for independent situations thus provides a good approximation to the case where mutant and stabilizing selection effects are correlated. Multivariate stabilizing selection can be regarded as a combination of stabilizing selection on the target trait and the pleiotropic direct selection on fitness that is solely due to the effects of real stabilizing selection on the hidden traits. As the overall fitness approaches a constant value as the number of traits increases, multivariate stabilizing selection can maintain abundant genetic variance only under quite weak selection. The common observations of high polygenic variance and strong stabilizing selection thus imply that if the mutation-selection balance is the true mechanism of maintenance of genetic variation, the apparent stabilizing selection cannot arise solely by real stabilizing selection simultaneously on many metric traits.     

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.     

A general population genetic framework for antagonistic selection that accounts for demography and recurrent mutation

Antagonistic selection--where alleles at a locus have opposing effects on male and female fitness ("sexual antagonism") or between components of fitness ("antagonistic pleiotropy")--might play an important role in maintaining population genetic variation and in driving phylogenetic and genomic patterns of sexual dimorphism and life-history evolution. While prior theory has thoroughly characterized the conditions necessary for antagonistic balancing selection to operate, we currently know little about the evolutionary interactions between antagonistic selection, recurrent mutation, and genetic drift, which should collectively shape empirical patterns of genetic variation. To fill this void, we developed and analyzed a series of population genetic models that simultaneously incorporate these processes. Our models identify two general properties of antagonistically selected loci. First, antagonistic selection inflates heterozygosity and fitness variance across a broad parameter range--a result that applies to alleles maintained by balancing selection and by recurrent mutation. Second, effective population size and genetic drift profoundly affect the statistical frequency distributions of antagonistically selected alleles. The "efficacy" of antagonistic selection (i.e., its tendency to dominate over genetic drift) is extremely weak relative to classical models, such as directional selection and overdominance. Alleles meeting traditional criteria for strong selection (N(e)s > 1, where N(e) is the effective population size, and s is a selection coefficient for a given sex or fitness component) may nevertheless evolve as if neutral. The effects of mutation and demography may generate population differences in overall levels of antagonistic fitness variation, as well as molecular population genetic signatures of balancing selection.