Comparing Evolvability and Variability of Quantitative Traits

There are two distinct reasons for making comparisons of genetic variation for quantitative characters. The first is to compare evolvabilities, or ability to respond to selection, and the second is to make inferences about the forces that maintain genetic variability. Measures of variation that are standardized by the trait mean, such as the additive genetic coefficient of variation, are appropriate for both purposes. Variation has usually been compared as narrow sense heritabilities, but this is almost always an inappropriate comparative measure of evolvability and variability. Coefficients of variation were calculated from 842 estimates of trait means, variances and heritabilities in the literature. Traits closely related to fitness have higher additive genetic and nongenetic variability by the coefficient of variation criterion than characters under weak selection. This is the reverse of the accepted conclusion based on comparisons of heritability. The low heritability of fitness components is best explained by their high residual variation. The high additive genetic and residual variability of fitness traits might be explained by the great number of genetic and environmental events they are affected by, or by a lack of stabilizing selection to reduce their phenotypic variance. Over one-third of the quantitative genetics papers reviewed did not report trait means or variances. Researchers should always report these statistics, so that measures of variation appropriate to a variety of situations may be calculated.     

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.     

Basal metabolic rate can evolve independently of morphological and behavioural traits

Quantitative genetic analyses of basal metabolic rate (BMR) can inform us about the evolvability of the trait by providing estimates of heritability, and also of genetic correlations with other traits that may constrain the ability of BMR to respond to selection. Here, we studied a captive population of zebra finches (Taeniopygia guttata) in which selection lines for male courtship rate have been established. We measure BMR in these lines to see whether selection on male sexual activity would change BMR as a potentially correlated trait. We find that the genetic correlation between courtship rate and BMR is practically zero, indicating that the two traits can evolve independently of each other. Interestingly, we find that the heritability of BMR in our population (h²=0.45) is markedly higher than was previously reported for a captive zebra finch population from Norway. A comparison of the two studies shows that additive genetic variance in BMR has been largely depleted in the Norwegian population, especially the genetic variance in BMR that is independent of body mass. In our population, the slope of BMR increase with body mass differs not only between the sexes but also between the six selection lines, which we tentatively attribute to genetic drift and/or founder effects being strong in small populations. Our study therefore highlights two things. First, the evolvability of BMR may be less constrained by genetic correlations and lack of independent genetic variation than previously described. Second, genetic drift in small populations can rapidly lead to different evolvabilities across populations.     

The evolvability of herkogamy: Quantifying the evolutionary potential of a composite trait

Accurate estimates of trait evolvabilities are central to predicting the short‐term evolutionary potential of populations, and hence their ability to adapt to changing environments. We quantify and evaluate the evolvability of herkogamy, the spatial separation of male and female structures in flowers, a key floral trait associated with variation in mating systems. We compiled genetic‐variance estimates for herkogamy and related floral traits, computed evolvabilities, and compared these among trait groups and among species differing in their mating systems. When measured in percentage of its own size, the median evolvability of herkogamy was an order of magnitude greater than the evolvability of other floral size measurements, and was generally not strongly constrained by genetic covariance between its components (pistil and stamen lengths). Median evolvabilities were similar across mating systems, with only a tendency toward reduction in highly selfing taxa. We conclude that herkogamy has the potential to evolve rapidly in response to changing environments. This suggests that the extensive variation in herkogamy commonly observed among closely related populations and species may result from rapid adaptive tracking of fitness optima determined by variation in pollinator communities or other selective factors.     

Genetic constraints predict evolutionary divergence in Dalechampia blossoms

If genetic constraints are important, then rates and direction of evolution should be related to trait evolvability. Here we use recently developed measures of evolvability to test the genetic constraint hypothesis with quantitative genetic data on floral morphology from the Neotropical vine Dalechampia scandens (Euphorbiaceae). These measures were compared against rates of evolution and patterns of divergence among 24 populations in two species in the D. scandens species complex. We found clear evidence for genetic constraints, particularly among traits that were tightly phenotypically integrated. This relationship between evolvability and evolutionary divergence is puzzling, because the estimated evolvabilities seem too large to constitute real constraints. We suggest that this paradox can be explained by a combination of weak stabilizing selection around moving adaptive optima and small realized evolvabilities relative to the observed additive genetic variance.     

Constraints on evolution and postcopulatory sexual selection: trade-offs among ejaculate characteristics

Ejaculates function as an integrated unit to ensure male fertility and paternity, can have a complex structure, and can experience multiple episodes of selection. Current studies on the evolution of ejaculates typically focus on phenotypic variation in sperm number, size, or related traits such as testes size as adaptations to postcopulatory male-male competition. However, the evolution of the integrated nature of ejaculate structure and function depends on genetic variation in and covariation between the component parts. Here we report a quantitative genetic study of the components of the ejaculate of the cockroach Nauphoeta cinerea, including those we know to experience postcopulatory sexual selection, in the context of functional integration of ejaculate characters. We use the patterns of genetic variation and covariation to infer how the integration of the functions of the ejaculate constrain and shape its evolution. Ejaculate components were highly variable, showed significant additive genetic variance, and moderate to high evolvability. The level of genetic variation in these characters, despite strong directional or truncating selection, may reflect the integration of multiple episodes of selection that occur in N. cinerea. There were few significant phenotypic correlations, but all the genetic correlations among ejaculate characters were significantly different from zero. The patterns of genetic variation and covariation suggest that there are important trade-offs among individual traits of the ejaculate and that evolution of ejaculate characteristics will not proceed unconstrained. Fully describing the genetic relationships among traits that perform as an integrated unit helps us understand how functional relationships constrain or facilitate the evolution of the complex structure that is the ejaculate.     

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.     

The effect of trait type and strength of selection on heritability and evolvability in an island bird population

The heritability (h²) of fitness traits is often low. Although this has been attributed to directional selection having eroded genetic variation in direct proportion to the strength of selection, heritability does not necessarily reflect a trait's additive genetic variance and evolutionary potential (“evolvability”). Recent studies suggest that the low h² of fitness traits in wild populations is caused not by a paucity of additive genetic variance (V_A) but by greater environmental or nonadditive genetic variance (V_R). We examined the relationship between h² and variance‐standardized selection intensities (i or β_σ), and between evolvability (I_A:V_A divided by squared phenotypic trait mean) and mean‐standardized selection gradients (β_μ). Using 24 years of data from an island population of Savannah sparrows, we show that, across diverse traits, h² declines with the strength of selection, whereas I_A and I_R (V_R divided by squared trait mean) are independent of the strength of selection. Within trait types (morphological, reproductive, life‐history), h², I_A, and I_R are all independent of the strength of selection. This indicates that certain traits have low heritability because of increased residual variance due to the age at which they are expressed or the multiple factors influencing their expression, rather than their association with fitness.     

Phenotypic variation and covariation indicate high evolvability of acoustic communication in crickets

Studying the genetic architecture of sexual traits provides insight into the rate and direction at which traits can respond to selection. Traits associated with few loci and limited genetic and phenotypic constraints tend to evolve at high rates typically observed for secondary sexual characters. Here, we examined the genetic architecture of song traits and female song preferences in the field crickets Gryllus rubens and Gryllus texensis. Song and preference data were collected from both species and interspecific F1 and F2 hybrids. We first analysed phenotypic variation to examine interspecific differentiation and trait distributions in parental and hybrid generations. Then, the relative contribution of additive and additive‐dominance variation was estimated. Finally, phenotypic variance–covariance ( P ) matrices were estimated to evaluate the multivariate phenotype available for selection. Song traits and preferences had unimodal trait distributions, and hybrid offspring were intermediate with respect to the parents. We uncovered additive and dominance variation in song traits and preferences. For two song traits, we found evidence for X‐linked inheritance. On the one hand, the observed genetic architecture does not suggest rapid divergence, although sex linkage may have allowed for somewhat higher evolutionary rates. On the other hand, P matrices revealed that multivariate variation in song traits aligned with major dimensions in song preferences, suggesting a strong selection response. We also found strong covariance between the main traits that are sexually selected and traits that are not directly selected by females, providing an explanation for the striking multivariate divergence in male calling songs despite limited divergence in female preferences.     

Similarity in G matrix structure among natural populations of Arabidopsis lyrata

Understanding the stability of the G matrix in natural populations is fundamental for predicting evolutionary trajectories; yet, the extent of its spatial variation and how this impacts responses to selection remain open questions. With a nested paternal half‐sib crossing design and plants grown in a field experiment, we examined differences in the genetic architecture of flowering time, floral display, and plant size among four Scandinavian populations of Arabidopsis lyrata. Using a multivariate Bayesian framework, we compared the size, shape, and orientation of G matrices and assessed their potential to facilitate or constrain trait evolution. Flowering time, floral display and rosette size varied among populations and significant additive genetic variation within populations indicated potential to evolve in response to selection. Yet, some characters, including flowering start and number of flowers, may not evolve independently because of genetic correlations. Using a multivariate framework, we found few differences in the genetic architecture of traits among populations. G matrices varied mostly in size rather than shape or orientation. Differences in multivariate responses to selection predicted from differences in G were small, suggesting overall matrix similarity and shared constraints to trait evolution among populations.     

Selection for character displacement is constrained by the genetic architecture of floral traits in the ivyleaf morning glory

Evolutionary theory predicts that interactions between species such as resource competition or reproductive interference will generate selection for character displacement where similar species co-occur. However, the rate and direction of character displacement will depend not only on the strength of selection for trait divergence, but also on the amount of genetic variation for selected traits and the nature of genetic correlations between them. To assess the importance of genetic constraints for the evolution of character displacement, we examined the genetic architecture of a suite of floral traits previously shown to be under selection in the annual plant Ipomoea hederacea when this species co-occurs with Ipomoea purpurea. We found that the six floral traits we measured are all positively genetically correlated. We also demonstrate, using new statistical approaches, that the predicted response to selection for four of these six traits is substantially constrained by their genetic correlation structure. Most notably, the response to selection for reduced separation of the tallest and shortest anthers, which reduces the degree of detrimental heterospecific pollen flow, is substantially constrained. Our results suggest that the rate of evolution of reproductive character displacement in I. hederacea is limited by the genetic architecture of floral traits.     

Heritability is not Evolvability

Short-term evolutionary potential depends on the additive genetic variance in the population. The additive variance is often measured as heritability, the fraction of the total phenotypic variance that is additive. Heritability is thus a common measure of evolutionary potential. An alternative is to measure evolutionary potential as expected proportional change under a unit strength of selection. This yields the mean-scaled additive variance as a measure of evolvability. Houle in Genetics 130:195–204, (1992) showed that these two ways of scaling additive variance are often inconsistent and can lead to different conclusions as to what traits are more evolvable. Here, we explore this relation in more detail through a literature review, and through theoretical arguments. We show that the correlation between heritability and evolvability is essentially zero, and we argue that this is likely due to inherent positive correlations between the additive variance and other components of phenotypic variance. This means that heritabilities are unsuitable as measures of evolutionary potential in natural populations. More generally we argue that scaling always involves non-trivial assumptions, and that a lack of awareness of these assumptions constitutes a systemic error in the field of evolutionary biology.     

Genetic variation maintained in multilocus models of additive quantitative traits under stabilizing selection.

Stabilizing selection for an intermediate optimum is generally considered to deplete genetic variation in quantitative traits. However, conflicting results from various types of models have been obtained. While classical analyses assuming a large number of independent additive loci with individually small effects indicated that no genetic variation is preserved under stabilizing selection, several analyses of two-locus models showed the contrary. We perform a complete analysis of a generalization of Wright's two-locus quadratic-optimum model and investigate numerically the ability of quadratic stabilizing selection to maintain genetic variation in additive quantitative traits controlled by up to five loci. A statistical approach is employed by choosing randomly 4000 parameter sets (allelic effects, recombination rates, and strength of selection) for a given number of loci. For each parameter set we iterate the recursion equations that describe the dynamics of gamete frequencies starting from 20 randomly chosen initial conditions until an equilibrium is reached, record the quantities of interest, and calculate their corresponding mean values. As the number of loci increases from two to five, the fraction of the genome expected to be polymorphic declines surprisingly rapidly, and the loci that are polymorphic increasingly are those with small effects on the trait. As a result, the genetic variance expected to be maintained under stabilizing selection decreases very rapidly with increased number of loci. The equilibrium structure expected under stabilizing selection on an additive trait differs markedly from that expected under selection with no constraints on genotypic fitness values. The expected genetic variance, the expected polymorphic fraction of the genome, as well as other quantities of interest, are only weakly dependent on the selection intensity and the level of recombination.     

The mutation matrix and the evolution of evolvability

Evolvability is a key characteristic of any evolving system, and the concept of evolvability serves as a unifying theme in a wide range of disciplines related to evolutionary theory. The field of quantitative genetics provides a framework for the exploration of evolvability with the promise to produce insights of global importance. With respect to the quantitative genetics of biological systems, the parameters most relevant to evolvability are the G-matrix, which describes the standing additive genetic variances and covariances for a suite of traits, and the M-matrix, which describes the effects of new mutations on genetic variances and covariances. A population's immediate response to selection is governed by the G-matrix. However, evolvability is also concerned with the ability of mutational processes to produce adaptive variants, and consequently the M-matrix is a crucial quantitative genetic parameter. Here, we explore the evolution of evolvability by using analytical theory and simulation-based models to examine the evolution of the mutational correlation, r(mu), the key parameter determining the nature of genetic constraints imposed by M. The model uses a diploid, sexually reproducing population of finite size experiencing stabilizing selection on a two-trait phenotype. We assume that the mutational correlation is a third quantitative trait determined by multiple additive loci. An individual's value of the mutational correlation trait determines the correlation between pleiotropic effects of new alleles when they arise in that individual. Our results show that the mutational correlation, despite the fact that it is not involved directly in the specification of an individual's fitness, does evolve in response to selection on the bivariate phenotype. The mutational variance exhibits a weak tendency to evolve to produce alignment of the M-matrix with the adaptive landscape, but is prone to erratic fluctuations as a consequence of genetic drift. The interpretation of this result is that the evolvability of the population is capable of a response to selection, and whether this response results in an increase or decrease in evolvability depends on the way in which the bivariate phenotypic optimum is expected to move. Interestingly, both analytical and simulation results show that the mutational correlation experiences disruptive selection, with local fitness maxima at -1 and +1. Genetic drift counteracts the tendency for the mutational correlation to persist at these extreme values, however. Our results also show that an evolving M-matrix tends to increase stability of the G-matrix under most circumstances. Previous studies of G-matrix stability, which assume nonevolving M-matrices, consequently may overestimate the level of instability of G relative to what might be expected in natural systems. Overall, our results indicate that evolvability can evolve in natural systems in a way that tends to result in alignment of the G-matrix, the M-matrix, and the adaptive landscape, and that such evolution tends to stabilize the G-matrix over evolutionary time.     

Genetic constraints and sexual dimorphism in immune defense

The absence of continued evolutionary change despite the presence of genetic variation and directional selection is very common. Genetic correlations between traits can reduce the evolvability of traits. One intriguing example might be found in a sexual conflict over sexually dimorphic traits: a common genetic architecture constrains the response to selection on a trait subjected to sexually asymmetric selection pressures. Here we show that males and females of the mealworm beetle Tenebrio molitor differ in the quantitative genetic architecture of four traits related to immune defense and condition. Moreover, high genetic correlations between the sexes constitute a genetic constraint to the evolution of sexual dimorphism in immune defense. Our results suggest a general mechanism by which sexual conflict can promote evolutionary stasis. We furthermore show negative genetic correlations, strong indications of trade-offs, between immune traits for two pairs of traits in females.     

The role of genetic constraints on the diversification of Iberian taxa of the genus Aquilegia (Ranunculaceae)

The microevolutionary process of adaptive phenotypic differentiation of quantitative traits between populations or closely‐related taxa depends on the response of populations to the action of natural selection. However, this response can be constrained by the structure of the matrix of additive genetic variance and covariance between traits in each population ( G matrix). In the present study, we obtained additive genetic variance and narrow sense heritability for 25 floral and vegetative traits of three subspecies of Aquilegia vulgaris, and one subspecies of Aquilegia pyrenaica through a common garden crossing experiment. For two vegetative and one floral trait, we also obtained the G matrix and genetic correlations between traits in each subspecies. The amount of genetic variation available in wild populations is not responsible for the larger differentiation of vegetative than floral traits found in this group of columbines. However, the low heritability of some traits constrained their evolution because phenotypic variability among taxa was larger for traits with larger heritability. We confirmed that the process of diversification of the studied taxa involved shifts in the G matrix, mainly determined by changes in the genetic covariance between floral and vegetative traits, probably caused by linkage disequilibrium in narrow endemic taxa. © 2013 The Linnean Society of London, Biological Journal of the Linnean Society, 2014, 111 , 252–261.     

The Evolution of Canalization and Evolvability in Stable and Fluctuating Environments

Using a multilinear model of epistasis we explore the evolution of canalization (reduced mutational effects) and evolvability (levels of additive genetic variance) under different forms of stabilizing and fluctuating selection. We show that the total selection acting on an allele can be divided into a component deriving from adaptation of the trait mean, a component of canalizing selection favoring alleles that epistatically reduce the effects of other allele substitutions, and a component of conservative selection disfavoring rare alleles. While canalizing selection operates in both stable and fluctuating environments, it may not typically maximize canalization, because it gets less efficient with increasing canalization, and reaches a balance with drift, mutation and indirect selection. Fluctuating selection leads to less canalized equilibria than stabilizing selection of comparable strength, because canalization then becomes influenced by erratic correlated responses to shifting trait adaptation. We conclude that epistatic systems under bounded fluctuating selection will become less canalized than under stabilizing selection and may support moderately increased evolvability if the amplitude of fluctuations is large, but canalization is still stronger and evolvability lower than expected under neutral evolution or under patterns of selection that shift the trait in directions of positive (reinforcing) epistasis.     

QTL analysis of floral traits in Louisiana iris hybrids

The formation of hybrid zones between nascent species is a widespread phenomenon. The evolutionary consequences of hybridization are influenced by numerous factors, including the action of natural selection on quantitative trait variation. Here we examine how the genetic basis of floral traits of two species of Louisiana Irises affects the extent of quantitative trait variation in their hybrids. Quantitative trait locus (QTL) mapping was used to assess the size (magnitude) of phenotypic effects of individual QTL, the degree to which QTL for different floral traits are colocalized, and the occurrence of mixed QTL effects. These aspects of quantitative genetic variation would be expected to influence (1) the number of genetic steps (in terms of QTL substitutions) separating the parental species phenotypes; (2) trait correlations; and (3) the potential for transgressive segregation in hybrid populations. Results indicate that some Louisiana Iris floral trait QTL have large effects and QTL for different traits tend to colocalize. Transgressive variation was observed for six of nine traits, despite the fact that mixed QTL effects influence few traits. Overall, our QTL results imply that the genetic basis of floral morphology and color traits might facilitate the maintenance of phenotypic divergence between Iris fulva and Iris brevicaulis, although a great deal of phenotypic variation was observed among hybrids.     

Natural selection on floral traits of female Silene dioica by a sexually transmitted disease

Floral traits endowing high reproductive fitness can also affect the probability of plants contracting sexually transmitted diseases. We explore how variations in floral traits influence the fitness of Silene dioica females in their interactions with pollinators carrying pollen or spores of the sterilizing anther-smut fungus Microbotryum violaceum. We collected healthy and infected plants in a highly diseased population and grew them under conditions that 'cure' infected individuals, and used standard regression methods to detect natural selection on floral traits. Narrow-sense heritabilities, coefficients of additive genetic variation (CV(A)) and genetic correlations among traits were estimated from paternal half-sib groups. Pollinator preferences imposed strong direct and directional selection on traits affecting female attractiveness and pollen-/spore-capturing abilities. Levels of additive genetic variance were high in these traits, suggesting that rapid responses to selection are possible. By considering our results in the light of spatial and temporal heterogeneity resulting from the colonization dynamics typical for this species, we suggest that the conflicting selective effects of pollen/spore loads lead to the maintenance of genetic variation in these traits.     

Genetic variation in pleiotropy: differential epistasis as a source of variation in the allometric relationship between long bone lengths and body weight

Pleiotropy is an aspect of genetic architecture underlying the phenotypic covariance structure. The presence of genetic variation in pleiotropy is necessary for natural selection to shape patterns of covariation between traits. We examined the contribution of differential epistasis to variation in the intertrait relationship and the nature of this variation. Genetic variation in pleiotropy was revealed by mapping quantitative trait loci (QTLs) affecting the allometry of mouse limb and tail length relative to body weight in the mouse-inbred strain LG/J by SM/J intercross. These relationship QTLs (rQTLs) modify relationships between the traits affected by a common pleiotropic locus. We detected 11 rQTLs, mostly affecting allometry of multiple bones. We further identified epistatic interactions responsible for the observed allometric variation. Forty loci that interact epistatically with the detected rQTLs were identified. We demonstrate how these epistatic interactions differentially affect the body size variance and the covariance of traits with body size. We conclude that epistasis, by differentially affecting both the canalization and mean values of the traits of a pleiotropic domain, causes variation in the covariance structure. Variation in pleiotropy maintains evolvability of the genetic architecture, in particular the evolvability of its modular organization.