Stability and Response of Polygenic Traits to Stabilizing Selection and Mutation

When polygenic traits are under stabilizing selection, many different combinations of alleles allow close adaptation to the optimum. If alleles have equal effects, all combinations that result in the same deviation from the optimum are equivalent. Furthermore, the genetic variance that is maintained by mutation–selection balance is 2μ/S per locus, where μ is the mutation rate and S the strength of stabilizing selection. In reality, alleles vary in their effects, making the fitness landscape asymmetric and complicating analysis of the equilibria. We show that that the resulting genetic variance depends on the fraction of alleles near fixation, which contribute by 2μ/S, and on the total mutational effects of alleles that are at intermediate frequency. The interplay between stabilizing selection and mutation leads to a sharp transition: alleles with effects smaller than a threshold value of 2μ/S remain polymorphic, whereas those with larger effects are fixed. The genetic load in equilibrium is less than for traits of equal effects, and the fitness equilibria are more similar. We find that if the optimum is displaced, alleles with effects close to the threshold value sweep first, and their rate of increase is bounded by μS. Long-term response leads in general to well-adapted traits, unlike the case of equal effects that often end up at a suboptimal fitness peak. However, the particular peaks to which the populations converge are extremely sensitive to the initial states and to the speed of the shift of the optimum trait value.     

The Relationship between Sexual Selection and Sexual Conflict

Evolutionary conflicts of interest arise whenever genetically different individuals interact and their routes to fitness maximization differ. Sexual selection favors traits that increase an individual’s competitiveness to acquire mates and fertilizations. Sexual conflict occurs if an individual of sex A’s relative fitness would increase if it had a “tool” that could alter what an individual of sex B does (including the parental genes transferred), at a cost to B’s fitness. This definition clarifies several issues: Conflict is very common and, although it extends outside traits under sexual selection, sexual selection is a ready source of sexual conflict. Sexual conflict and sexual selection should not be presented as alternative explanations for trait evolution. Conflict is closely linked to the concept of a lag load, which is context-dependent and sex-specific. This makes it possible to ask if one sex can “win.” We expect higher population fitness if females win.Many published studies ask if sexual selection or sexual conflict drives the evolution of key reproductive traits (e.g., mate choice). Here we argue that this is an inappropriate question. By analogy, G. Evelyn Hutchinson (1965) coined the phrase “the ecological theatre and the evolutionary play” to capture how factors that influence the birth, death, and reproduction of individuals (studied by ecologists) determine which individuals reproduce, and “sets the stage” for the selective forces that drive evolutionary trajectories (studied by evolutionary biologists). The more modern concept of “eco-evolutionary feedback” (Schoener 2011) emphasizes that selection changes the character of the actors over time, altering their ecological interactions. No one would sensibly ask whether one or the other shapes the natural world, when obviously both interact to determine the outcome.So why have sexual conflict and sexual selection sometimes been elevated to alternate explanations? This approach is often associated with an assumption that sexual conflict affects traits under direct selection, favoring traits that alter the likelihood of a potential mate agreeing or refusing to mate because it affects the bearer’s immediate reproductive output, whereas “traditional” sexual selection is assumed to favor traits that are under indirect selection because they increase offspring fitness. These “traditional” models are sometimes described as “mutualistic” (e.g., Pizzari and Snook 2003; Rice et al. 2006), although this term appears to be used only when contrasting them with sexual conflict models. The investigators of the original models never describe them as “mutualistic,” which is hardly surprising given that some males are rejected by females.In this review, we first define sexual conflict and sexual selection. We then describe how the notion of a “lag load” can reveal which sex currently has greater “power” in a sexual conflict over a specific resource. Next, we discuss why sexual conflict and sexual selection are sometimes implicitly (or explicitly) presented as alternative explanations for sexual traits (usually female mate choice/resistance). To illustrate the problems with the assumptions made to take this stance, we present a “toy model” of snake mating behavior based on a study by Shine et al. (2005). We show that empirical predictions about the mating behavior that will be observed if females seek to minimize direct cost of mating or to obtain indirect genetic benefits were overly simplistic. This allows us to make the wider point that whom a female is willing to mate with and how often she mates are often related questions. Finally, we discuss the effect of sexual conflict on population fitness.     

Excursions along the Interface between Disruptive and Stabilizing Selection

When a polygenic character is exposed to natural selection in which the curve giving fitness as a function of phenotype is a mixture of two Gaussian (normal) curves, the population may respond either by evolving to a specialized phenotype near one of the two optimum phenotypes, or by evolving to a generalized phenotype between them. Using approximate multivariate normal distribution methods, it is demonstrated that the condition for selection to result in a specialized phenotype is that the curve of fitness as a function of breeding value be bimodal. This implies that a specialized phenotype is more likely to result the higher is the heritability of the character. Numerical iterations of four-locus models and algebraic analysis of a symmetric two-locus model generally support the conclusions of the normal approximation.     

Selection for Increased Mutation Rates with Fertility Differences between Matings

Previous studies of mutation modification have considered models in which selection is a result of viability differences that are sex symmetric. The results of a numerical study of a model in which selection is a result of fertility differences between mated pairs demonstrate that the type of selection to which a population is subject can have a significant impact on the evolution of various parameters of the genetic system. When the fertility of matings between individuals with different genotypes exceeds the fertility of at least some of the matings between individuals with the same genotype, selection may favor increased rates of mutation, in contrast to the results from all existing constant viability models with random mating and infinite population size. Increased mutation rates are most frequently favored when forward and back mutation occur at approximately equal rates and when the modifying locus is loosely linked to the selected locus. We present one example in which selection favors increased rates of mutation even though the selection scheme is reducible to one of differential viability between the sexes.     

Pleiotropic Mutations Are Subject to Strong Stabilizing Selection

The assumption that pleiotropic mutations are more deleterious than mutations with more restricted phenotypic effects is an important premise in models of evolution. However, empirical evidence supporting this assumption is limited. Here, we estimated the strength of stabilizing selection on mutations affecting gene expression in male Drosophila serrata. We estimated the mutational variance (V_M) and the standing genetic variance (V_G) from two well-matched panels of inbred lines: a panel of mutation accumulation (MA) lines derived from a single inbred ancestral line and a panel of inbred lines derived from an outbred population. For 855 gene-expression traits, we estimated the strength of stabilizing selection as s = V_M/V_G. Selection was observed to be relatively strong, with 17% of traits having s > 0.02, a magnitude typically associated with life-history traits. Randomly assigning expression traits to five-trait sets, we used factor analytic mixed modeling in the MA data set to identify covarying traits that shared pleiotropic mutations. By assigning traits to the same trait sets in the outbred line data set, we then estimated s for the combination of traits affected by pleiotropic mutation. For these pleiotropic combinations, the median s was three times greater than s acting on the individual component traits, and 46% of the pleiotropic trait combinations had s > 0.02. Although our analytical approach was biased toward detecting mutations with relatively large effects, likely overestimating the average strength of selection, our results provide widespread support for the prediction that stronger selection can act against mutations with pleiotropic effects.THE extent to which new mutations have pleiotropic effects on multiple traits, and ultimately on fitness is central to our understanding of the maintenance of genetic variation and the process of adaptation (Kondrashov and Turelli 1992; Otto 2004; Johnson and Barton 2005; Zhang and Hill 2005). Analyses of Fisher’s (1930) geometric model of adaptation have shown that a mutation with effects on many traits will have a reduced probability of contributing to adaptive evolution (Orr 2000; Welch and Waxman 2003; see also Haygood 2006). For a population close to its optimum under mutation–selection balance, a direct corollary of this is that selection must act more strongly against mutations with wider pleiotropic effects (Zhang 2012).Evidence for the strength of selection increasing with the number of traits that are pleiotropically affected by a mutation is limited. At a phenotypic level, nonlinear (stabilizing) selection is much stronger on combinations of metric traits than on each individual trait contributing to the combination (Blows and Brooks 2003; Walsh and Blows 2009). Given that genetic correlations among such traits are expected to be a consequence of pleiotropic alleles (Lande 1980), stronger selection on trait combinations is consistent with stronger selection on pleiotropic mutations that are likely to underlie the genetic covariance among such traits. There is some evidence that per-trait allelic effects might be greater for alleles with more widespread pleiotropic effects (Wagner et al. 2008; Wang et al. 2010); as mutations with larger phenotypic effects might be more effectively targeted by selection, this also suggests stronger selection against more pleiotropic mutation.Mutation accumulation (MA) breeding designs, in which the opportunity for selection is reduced, allowing new mutations to drift to fixation, provide an opportunity to characterize the strength of selection acting directly against new mutations. Rice and Townsend (2012) proposed an approach for determining the strength of selection acting against mutations at individual loci, combining information from QTL mapping and MA studies. This approach could conceivably be extended to associate the strength of selection with the number of traits a QTL affects. More typically, estimates of selection from MA designs are focused on traits, rather than alleles. Under the assumption that most mutations are deleterious, an assumption supported by MA studies (Halligan and Keightley 2009), the strength of selection acting on mutations affecting quantitative traits can be measured as the ratio of the mutational to the standing genetic variance, s = V_M/V_G, where s is the selection coefficient of the mutation in heterozygous form (Barton 1990; Houle et al. 1996). While estimating s in this way provides a framework for estimating selection on pleiotropic combinations of traits, we are not aware of any studies adopting this approach to directly estimate the strength of selection acting on mutations affecting multiple traits.Within an MA framework, Estes and Phillips (2006) manipulated the opportunity for selection, providing rare direct evidence of stronger selection against mutations with pleiotropic effects. In a DNA repair-deficient strain of Caenorhabditis elegans, Estes and Phillips (2006) observed lower mutational covariance among life-history components when selection was allowed (larger populations) than when the opportunity for selection was limited (small populations). Similarly, McGuigan et al. (2011) compared Drosophila serrata MA lines accumulating mutations in the presence or absence of sexual selection on males, reporting reduced covariance between two fitness components in the selection treatment. These studies reveal that selection can eliminate nonlethal alleles with pleiotropic effects, but whether traits other than life-history components exhibit similar evidence of selection against pleiotropic alleles remains unknown.In parallel to the quantitative genetic predictions that pleiotropic alleles will be under stronger selection, molecular genetic theory predicts that the rate of gene evolution will be negatively correlated with pleiotropy (Pal et al. 2006; Salathe et al. 2006). More highly pleiotropic genes, as identified through the extent of connectivity (the number of interactions) in protein–protein interaction networks (Jeong et al. 2001), or the number of gene ontology (GO) terms (Jovelin and Phillips 2009) are more likely to be essential (i.e., knockout mutations result in lethality), suggesting that selection is stronger against large-effect (knockout) mutations in more highly pleiotropic genes. However, the selection acting against small-effect, nonlethal mutations in pleiotropic genes is less clear (Pal et al. 2006). Several studies have found an association between gene pleiotropy indices, such GO annotation of the number of biological processes or tissue specificity of expression, and the rate of sequence evolution (e.g., Pal et al. 2001; Salathe et al. 2006; Jovelin and Phillips 2009; Su et al. 2010). These pleiotropy indices typically explain little of the variation in sequence evolutionary rates, and it remains unclear whether more highly pleiotropic mutations are typically under stronger selection (Pal et al. 2006; Salathe et al. 2006).Here, we estimate the selection coefficients acting against naturally occurring mutations affecting gene-expression traits in male D. serrata to quantitatively test if selection is stronger on mutations that affect multiple traits. Gene-expression phenotypes are uniquely positioned to enable detailed investigations of pleiotropy: there are many of them, they represent a broad coverage of biological function, they can be analyzed to quantify developmental pleiotropy in the same way as traits traditionally considered in quantitative genetics, and GO information can be used to index molecular genetic pleiotropy. We use multivariate mixed-model analyses of expression traits in a set of inbred lines from a mutation accumulation experiment to estimate the mutational variance in individual expression traits, and the pleiotropic mutational covariance among random sets of five expression traits. Using a second panel of inbred lines, derived from a natural, outbred, population, we estimate the standing genetic variance in the same individual traits and five-trait combinations. From these estimates of mutational and standing genetic variance, we calculate s for each of the individual traits and trait combinations to determine whether selection has typically been stronger on mutations with pleiotropic effects than on other mutations affecting each trait. We complement this quantitative genetic analysis of developmental pleiotropy with an analysis of molecular genetic pleiotropy (Paaby and Rockman 2013), determining whether the strength of selection acting on individual expression traits can be predicted from the number of biological functions that the gene annotates to in the GO database or to the range of tissues in which the gene is expressed.     

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.     

Purifying Selection,Drift, and Reversible Mutation with Arbitrarily High Mutation Rates

Some species exhibit very high levels of DNA sequence variability; there is also evidence for the existence of heritable epigenetic variants that experience state changes at a much higher rate than sequence variants. In both cases, the resulting high diversity levels within a population (hyperdiversity) mean that standard population genetics methods are not trustworthy. We analyze a population genetics model that incorporates purifying selection, reversible mutations, and genetic drift, assuming a stationary population size. We derive analytical results for both population parameters and sample statistics and discuss their implications for studies of natural genetic and epigenetic variation. In particular, we find that (1) many more intermediate-frequency variants are expected than under standard models, even with moderately strong purifying selection, and (2) rates of evolution under purifying selection may be close to, or even exceed, neutral rates. These findings are related to empirical studies of sequence and epigenetic variation.     

Intra- and Interdomain Effects Due to Mutation of Calcium-binding Sites in Calmodulin

The IQ-motif protein PEP-19, binds to the C-domain of calmodulin (CaM) with significantly different k_on and k_off rates in the presence and absence of Ca²⁺, which could play a role in defining the levels of free CaM during Ca²⁺ transients. The initial goal of the current study was to determine whether Ca²⁺ binding to sites III or IV in the C-domain of CaM was responsible for affecting the kinetics of binding PEP-19. EF-hand Ca²⁺-binding sites were selectively inactivated by the common strategy of changing Asp to Ala at the X-coordination position. Although Ca²⁺ binding to both sites III and IV appeared necessary for native-like interactions with PEP-19, the data also indicated that the mutations caused undesirable structural alterations as evidenced by significant changes in amide chemical shifts for apoCaM. Mutations in the C-domain also affected chemical shifts in the unmodified N-domain, and altered the Ca²⁺ binding properties of the N-domain. Conversion of Asp⁹³ to Ala caused the greatest structural perturbations, possibly due to the loss of stabilizing hydrogen bonds between the side chain of Asp⁹³ and backbone amides in apo loop III. Thus, although these mutations inhibit binding of Ca²⁺, the mutated CaM may not be able to support potentially important native-like activity of the apoprotein. This should be taken into account when designing CaM mutants for expression in cell culture.     

Stabilizing Selection and the Structural Variability of Flowers within Species

Zoophilous flowers often appear to be precisely formed for pollentransfer and exhibit relatively little variability in structurewithin species. Functional optimization by the seemingly exactingrequirements of pollen transfer may account for these observations.I used the results of a literature survey to examine the levelsof intraspecific variation in flowers across a wide range oftaxa. The least variable attributes were those potentially affectingthe mechanical fit between flower and pollinator, which arepotentially constrained by selection for pollination performance.I discuss six mechanisms by which plant-pollinator interactionscould generate stabilizing selection on flowers. In addition,I consider the stabilizing roles of limiting resources and alsotwo functionally-neutral mechanisms. Further work is requiredto identify the actual mechanisms by which selection stabilizesthe evolution of flowers.Copyright 1998 Annals of Botany Company stabilizing selection, flowers, pollination, variation     

Stabilizing Selection,Purifying Selection,and Mutational Bias in Finite Populations

Genomic traits such as codon usage and the lengths of noncoding sequences may be subject to stabilizing selection rather than purifying selection. Mutations affecting these traits are often biased in one direction. To investigate the potential role of stabilizing selection on genomic traits, the effects of mutational bias on the equilibrium value of a trait under stabilizing selection in a finite population were investigated, using two different mutational models. Numerical results were generated using a matrix method for calculating the probability distribution of variant frequencies at sites affecting the trait, as well as by Monte Carlo simulations. Analytical approximations were also derived, which provided useful insights into the numerical results. A novel conclusion is that the scaled intensity of selection acting on individual variants is nearly independent of the effective population size over a wide range of parameter space and is strongly determined by the logarithm of the mutational bias parameter. This is true even when there is a very small departure of the mean from the optimum, as is usually the case. This implies that studies of the frequency spectra of DNA sequence variants may be unable to distinguish between stabilizing and purifying selection. A similar investigation of purifying selection against deleterious mutations was also carried out. Contrary to previous suggestions, the scaled intensity of purifying selection with synergistic fitness effects is sensitive to population size, which is inconsistent with the general lack of sensitivity of codon usage to effective population size.     

The Maintenance of Genetic Variability in Two-Locus Models of Stabilizing Selection

The maintenance of genetic variability at two diallelic loci under stabilizing selection is investigated. Generations are discrete and nonoverlapping; mating is random; mutation and random genetic drift are absent; selection operates only through viability differences. The determination of the genotypic values is purely additive. The fitness function has its optimum at the value of the double heterozygote and decreases monotonically and symmetrically from its optimum, but is otherwise arbitrary. The resulting fitness scheme is identical to the symmetric viability model. Linkage disequilibrium is neglected, but the results are otherwise exact. Explicit formulas are found for all the equilibria, and explicit conditions are derived fro their existence and stability. A complete classification of the six possible global convergence patterns is presented. In addition to the symmetric equilibrium (with gene frequency 1/2 at both loci), a pair of unsymmetric equilibria may exist; the latter are usually, but not always, unstable. If the ratio of the effect of the major locus to that of the minor one exceeds a critical value, both loci will be stably polymorphic. If selection is weak at the minor locus, the more rapidly the fitness function decreases near the optimum, the lower is this critical value; for rapidly decreasing fitness functions, the critical value is close to one. If the fitness function is smooth at the optimum, then a stable polymorphism exists at both loci only if selection is strong at the major locus.     

Genetic Diversity in the Interference Selection Limit

Pervasive natural selection can strongly influence observed patterns of genetic variation, but these effects remain poorly understood when multiple selected variants segregate in nearby regions of the genome. Classical population genetics fails to account for interference between linked mutations, which grows increasingly severe as the density of selected polymorphisms increases. Here, we describe a simple limit that emerges when interference is common, in which the fitness effects of individual mutations play a relatively minor role. Instead, similar to models of quantitative genetics, molecular evolution is determined by the variance in fitness within the population, defined over an effectively asexual segment of the genome (a “linkage block”). We exploit this insensitivity in a new “coarse-grained” coalescent framework, which approximates the effects of many weakly selected mutations with a smaller number of strongly selected mutations that create the same variance in fitness. This approximation generates accurate and efficient predictions for silent site variability when interference is common. However, these results suggest that there is reduced power to resolve individual selection pressures when interference is sufficiently widespread, since a broad range of parameters possess nearly identical patterns of silent site variability.     

Stabilizing and Disruptive Selection on a Mutant Character in Drosophila. IV. Selection on Sensitivity to Temperature

Individual selection on temperature sensitivity was applied to the relative length of the 4th vein of the mutant ci^D-G in four selection lines according to different selection schemes indicated in Figure 1. These selection systems include, besides the selection on temperature, disruptive selection. In all lines the disruptive component causes an increase of the phenotypic variance, but there are large differences in its composition. The selection changed temperature sensitivity in the expected direction in all lines. In one line (C-D^-) however, the change in temperature sensitivity and the increase in variance were only small because the disruptive component and the canalizing component of the selection scheme restricted each others' effect. The results are discussed in relation to earlier results obtained by disruptive selection at one temperature.