Measuring and comparing evolvability and constraint in multivariate characters

The Lande equation forms the basis for our understanding of the short-term evolution of quantitative traits in a multivariate context. It predicts the response to selection as the product of an additive genetic variance matrix and a selection gradient. The selection gradient approximates the force and direction of selection, and the genetic variance matrix quantifies the role of the genetic system in evolution. Attempts to understand the evolutionary significance of the genetic variance matrix are hampered by the fact that the majority of the methods used to characterize and compare variance matrices have not been derived in an explicit theoretical context. We use the Lande equation to derive new measures of the ability of a variance matrix to allow or constrain evolution in any direction in phenotype space. Evolvability captures the ability of a population to evolve in the direction of selection when stabilizing selection is absent. Conditional evolvability captures the ability of a population to respond to directional selection in the presence of stabilizing selection on other trait combinations. We then derive measures of character autonomy and integration from these evolvabilities. We study the properties of these measures and show how they can be used to interpret and compare variance matrices. As an illustration, we show that divergence of wing shape in the dipteran family Drosophilidae has proceeded in directions that have relatively high evolvabilities.     

The dimensionality of genetic variation for wing shape in Drosophila melanogaster

Absolute constraints are limitations on genetic variation that preclude evolutionary change in some aspect of the phenotype. Absolute constraints may reflect complete absence of variation, lack of genetic variation that extends the range of phenotypes beyond some limit, or lack of additive genetic variation. This last type of absolute constraint is bidirectional, because the mean cannot evolve to be larger or smaller. Most traits do possess genetic variation, so bidirectional absolute constraints are most likely to be detected in a multivariate context, where they would reflect combinations of traits, or dimensions in phenotype space that cannot evolve. A bidirectional absolute constraint will cause the additive genetic covariance matrix (G) to have a rank less than the number of traits studied. In this study, we estimate the rank of the G-matrix for 20 aspects of wing shape in Drosophila melanogaster. Our best estimates of matrix rank are 20 in both sexes. Lower 95% confidence intervals of rank are 17 for females and 18 for males. We therefore find little evidence of bidirectional absolute constraints. We discuss the importance of this result for resolving the relative roles of selection and drift processes versus constraints in the evolution of wing shape in Drosophila.     

Multivariate quantitative genetics and the lek paradox: genetic variance in male sexually selected traits of Drosophila serrata under field conditions

Single male sexually selected traits have been found to exhibit substantial genetic variance, even though natural and sexual selection are predicted to deplete genetic variance in these traits. We tested whether genetic variance in multiple male display traits of Drosophila serrata was maintained under field conditions. A breeding design involving 300 field-reared males and their laboratory-reared offspring allowed the estimation of the genetic variance-covariance matrix for six male cuticular hydrocarbons (CHCs) under field conditions. Despite individual CHCs displaying substantial genetic variance under field conditions, the vast majority of genetic variance in CHCs was not closely associated with the direction of sexual selection measured on field phenotypes. Relative concentrations of three CHCs correlated positively with body size in the field, but not under laboratory conditions, suggesting condition-dependent expression of CHCs under field conditions. Therefore condition dependence may not maintain genetic variance in preferred combinations of male CHCs under field conditions, suggesting that the large mutational target supplied by the evolution of condition dependence may not provide a solution to the lek paradox in this species. Sustained sexual selection may be adequate to deplete genetic variance in the direction of selection, perhaps as a consequence of the low rate of favorable mutations expected in multiple trait systems.     

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.     

Estimates of direct and indirect effects for early juvenile survival in captive populations maintained for conservation purposes: the case of Cuvier's gazelle

Together with the avoidance of any negative impact of inbreeding, preservation of genetic variability for life‐history traits that could undergo future selective pressure is a major issue in endangered species management programmes. However, most of these programmes ignore that, apart from the direct action of genes on such traits, parents, as contributors of offspring environment, can influence offspring performance through indirect parental effects (when parental genotype and phenotype exerts environmental influences on offspring phenotype independently of additive genetic effects). Using quantitative genetic models, we estimated the additive genetic variance for juvenile survival in a population of the endangered Cuvier's gazelle kept in captivity since 1975. The dataset analyzed included performance recording for 700 calves and a total pedigree of 740 individuals. Results indicated that in this population juvenile survival harbors significant additive genetic variance. The estimates of heritability obtained were in general moderate (0.115–0.457) and not affected by the inclusion of inbreeding in the models. Maternal genetic contribution to juvenile survival seems to be of major importance in this gazelle's population as well. Indirect genetic and indirect environmental effects assigned to mothers (i.e., maternal genetic and maternal permanent environmental effects) roughly explain a quarter of the total variance estimated for the trait analyzed. These findings have major evolutionary consequences for the species as show that offspring phenotypes can evolve strictly through changes in the environment provided by mothers. They are also relevant for the captive breeding programme of the species. To take into account, the contribution that mothers have on offspring phenotype through indirect genetic effects when designing pairing strategies might serve to identify those females with better ability to recruit, and, additionally, to predict reliable responses to selection in the captive population.     

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.     

REDUCED GENETIC VARIANCE AMONG HIGH FITNESS INDIVIDUALS: INFERRING STABILIZING SELECTION ON MALE SEXUAL DISPLAYS IN DROSOPHILA SERRATA

Directional selection is prevalent in nature, yet phenotypes tend to remain relatively constant, suggesting a limit to trait evolution. However, the genetic basis of this limit is unresolved. Given widespread pleiotropy, opposing selection on a trait may arise from the effects of the underlying alleles on other traits under selection, generating net stabilizing selection on trait genetic variance. These pleiotropic costs of trait exaggeration may arise through any number of other traits, making them hard to detect in phenotypic analyses. Stabilizing selection can be inferred, however, if genetic variance is greater among low‐ compared to high‐fitness individuals. We extend a recently suggested approach to provide a direct test of a difference in genetic variance for a suite of cuticular hydrocarbons (CHCs) in Drosophila serrata. Despite strong directional sexual selection on these traits, genetic variance differed between high‐ and low‐fitness individuals and was greater among the low‐fitness males for seven of eight CHCs, significantly more than expected by chance. Univariate tests of a difference in genetic variance were nonsignificant but likely have low power. Our results suggest that further CHC exaggeration in D. serrata in response to sexual selection is limited by pleiotropic costs mediated through other traits.     

Characterizing the evolution of genetic variance using genetic covariance tensors

Determining how genetic variance changes under selection in natural populations has proved to be a very resilient problem in evolutionary genetics. In the same way that understanding the availability of genetic variance within populations requires the simultaneous consideration of genetic variance in sets of functionally related traits, determining how genetic variance changes under selection in natural populations will require ascertaining how genetic variance–covariance (G) matrices evolve. Here, we develop a geometric framework using higher-order tensors, which enables the empirical characterization of how G matrices have diverged among populations. We then show how divergence among populations in genetic covariance structure can then be associated with divergence in selection acting on those traits using key equations from evolutionary theory. Using estimates of G matrices of eight male sexually selected traits from nine geographical populations of Drosophila serrata, we show that much of the divergence in genetic variance occurred in a single trait combination, a conclusion that could not have been reached by examining variation among the individual elements of the nine G matrices. Divergence in G was primarily in the direction of the major axes of genetic variance within populations, suggesting that genetic drift may be a major cause of divergence in genetic variance among these populations.     

Quantitative Genetics of DROSOPHILA MELANOGASTER. I. Sexual Dimorphism in Genetic Parameters for Wing Traits

Sexual dimorphism in genetic parameters is examined for wing dimensions of Drosophila melanogaster. Data are fit to a quantitative genetic model where phenotypic variance is a linear function of additive genetic autosomal variance (common to both sexes), additive genetic X-linked variances distinct for each sex, variance due to common rearing environment of families, residual environmental variance, random error variance due to replication, and variance due to measurement error and developmental asymmetry (left vs. right sides). Polygenic dosage compensation and its effect on genetic variances and covariances between sexes is discussed. Variance estimates for wing length and other wing dimensions highly correlated with length support the hypothesis that the Drosophila system of dosage compensation will cause male X-linked genetic variance to be substantially larger than female X-linked variance. Results for various wing dimensions differ, suggesting that the level of dosage compensation may differ for different traits. Genetic correlations between sexes for the same trait are presented. Total additive genetic correlations are near unity for most wing traits; this indicates that selection in the same direction in both sexes would have a minor effect on changing the magnitude of difference between sexes. Additive X-linked correlations suggest some genotype x sex interactions for X-linked effects.     

The depletion of genetic variance by sexual selection

Sexually selected traits display substantial genetic variance [1, 2], in conflict with the expectation that sexual selection will deplete it [3-5]. Condition dependence is thought to resolve this paradox [5-7], but experimental tests that relate the direction of sexual selection to the availability of genetic variance are lacking. Here, we show that condition-dependent expression is not sufficient to maintain genetic variance available to sexual selection in multiple male sexually selected traits. We employed an experimental design that simultaneously determined the quantitative genetic basis of nine male cuticular hydrocarbons (CHCs) of Drosophila bunnanda, the extent of condition dependence of these traits, and the strength and direction of sexual selection acting upon them. The CHCs of D. bunnanda are condition dependent, with 18% of the genetic variance in male body size explained by genetic variance in CHCs. Despite the presence of genetic variance in individual male traits, 98% of the genetic variance in CHCs was found to be orientated more than 88 degrees away from the direction of sexual selection and therefore unavailable to selection. A lack of genetic variance in male traits in the direction of sexual selection may represent a general feature of sexually selected systems, even in the presence of condition-dependent trait expression.     

Direct and indirect responses to selection on pollen size in Brassica rapa L.

Pollen size varies little within angiosperm species, but differs extensively between species, suggesting the action of strong selection. Nevertheless, the potential for genetic responses of pollen size to selection, as determined by additive genetic variance and genetic correlations with other floral traits, has received little attention. To assess this potential, we subjected Brassica rapa to artificial selection for large and small pollen during three generations. This selection caused significant divergence in pollen diameter, with additive genetic effects accounting for over 30% of the observed phenotypic variation in pollen size. Such heritable genetic variation suggests that natural selection could effect evolutionary change in this trait. Selection on pollen size also elicited correlated responses in pollen number (–), flower size (+), style length (+), and ovule number (+), suggesting that pollen size cannot evolve independently. The correlated responses of pollen number, flower size and ovule number probably reflect the genetically determined and physically constrained pattern of resource allocation in B. rapa. In contrast, the positive correlation between pollen size and style length may represent a widespread gametic‐phase disequilibrium in angiosperms that arises from nonrandom fertilization success of large pollen in pistils with long styles.     

Direct and indirect genetic effects on reproductive investment in a grasshopper

A fundamental part of the quantitative genetic theory deals with the partitioning of the phenotypic variance into additive genetic and environmental components. During interaction with conspecifics, the interaction partner becomes a part of the environment from the perspective of the focal individual. If the interaction effects have a genetic basis, they are called indirect genetic effects (IGEs) and can evolve along with direct genetic effects. Sexual reproduction is a classic context where potential conflict between males and females can arise from trade‐offs between current and future investments. We studied five female fecundity traits, egg length and number, egg pod length and number and latency to first egg pod, and estimated the direct and IGEs using a half‐sib breeding design in the grasshopper Chorthippus biguttulus. We found that the male IGEs were an order of magnitude lower than the direct genetic effects and were not significantly different from zero. However, there was some indication that IGEs were larger shortly after mating, consistent with the idea that IGEs fade with time after interaction. Female direct heritabilities were moderate to low. Simulation shows that the variance component estimates can appear larger with less data, calling for care when interpreting variance components estimated with low power. Our results illustrate that the contribution of male IGEs is overall low on the phenotypic variance of female fecundity traits. Thus, even in the relevant context of sexual conflict, the influence of male IGEs on the evolutionary trajectory of female reproductive traits is likely to be small.     

Concerted evolution and developmental integration in modular butterfly wing patterns

Developing organisms are thought to be modular in organization so that traits in different modules evolve independently whereas traits within a module change in a concerted manner. The eyespot pattern in Bicyclus anynana butterflies provides an ideal system where morphological modularity can be dissected and different levels of genetic integration analyzed. Several lines of evidence show that all eyespots in an individual butterfly are genetically integrated, suggesting that the whole pattern, rather than the separate eyespots, should be considered as a single character. However, despite the strong genetic correlations between the two eyespots on the dorsal forewing of B. anynana, there is great potential for independent changes. Here we use laboratory lines selected in different directions for the size of those eyespots to study correlated responses in the whole eyespot pattern. We show clear changes in eyespot size across all wing surfaces, which depend on eyespot position along the anterior-posterior axis. There are also changes in the number of extra eyespots and in eyespot color composition but no changes in eyespot position relative to wing margin. Our analysis of eyespot pattern modularity is discussed in the light of what is known about the cellular and genetic mechanisms of eyespot formation and the great potential for evolutionary diversification in butterfly wing patterns.     

Male-limited evolution suggests no extant intralocus sexual conflict over the sexually dimorphic cuticular hydrocarbons of <Emphasis Type="Italic">Drosophila melanogaster</Emphasis>

Sexually dimorphic traits are likely to have evolved through sexually antagonistic selection. However, recent empirical data suggest that intralocus sexual conflict often persists, even when traits have diverged between males and females. This implies that evolved dimorphism is often incomplete in resolving intralocus conflict, providing a mechanism for the maintenance of genetic variance in fitness-related traits. We used experimental evolution in Drosophila melanogaster to directly test for ongoing conflict over a suite of sexually dimorphic cuticular hydrocarbons (CHCs) that are likely targets of sex-specific selection. Using a set of experimental populations in which the transmission of genetic material had been restricted to males for 82 generations, we show that CHCs did not evolve, providing experimental evidence for the absence of current intralocus sexual conflict over these traits. The absence of ongoing conflict could indicate that CHCs have never been the target of sexually antagonistic selection, although this would require the existing dimorphism to have evolved via completely sexlinked mutations or as a result of former, but now absent, pleiotropic effects of the underlying loci on another trait under sexually antagonistic selection. An alternative interpretation, and which we believe to be more likely, is that the extensive CHC sexual dimorphism is the result of past intralocus sexual conflict that has been fully resolved, implying that these traits have evolved genetic independence between the sexes and that genetic variation in them is therefore maintained by alternative mechanisms. This latter interpretation is consistent with the known roles of CHCs in sexual communication in this species and with previous studies suggesting the genetic independence of CHCs between males and females. Nevertheless, direct estimates of sexually antagonistic selection will be important to fully resolve these alternatives.     

Testing the correlated response hypothesis for the evolution and maintenance of male mating preferences in Drosophila serrata

Mate preferences are abundant throughout the animal kingdom with female preferences receiving the most empirical and theoretical attention. Although recent work has acknowledged the existence of male mate preferences, whether they have evolved and are maintained as a direct result of selection on males or indirectly as a genetically correlated response to selection for female choice remains an open question. Using the native Australian species Drosophila serrata in which mutual mate choice occurs for a suite of contact pheromones (cuticular hydrocarbons or CHCs), we empirically test key predictions of the correlated response hypothesis. First, within the context of a quantitative genetic breeding design, we estimated the degree to which the trait values favoured by male and female choice are similar both phenotypically and genetically. The direction of sexual selection on male and female CHCs differed statistically, and the trait combinations that maximized male and female mating success were not genetically correlated, suggesting that male and female preferences target genetically different signals. Second, despite detecting significant genetic variance in female preferences, we found no evidence for genetic variance in male preferences and, as a consequence, no detectable correlation between male and female mating preferences. Combined, these findings are inconsistent with the idea that male mate choice in D. serrata is simply a correlated response to female choice. Our results suggest that male and female preferences are genetically distinct traits in this species and may therefore have arisen via different evolutionary processes.     

The phenotypic and genetic covariance structure of drosphilid wings

Evolutionary constraint results from the interaction between the distribution of available genetic variation and the position of selective optima. The availability of genetic variance in multitrait systems, as described by the additive genetic variance-covariance matrix (G), has been the subject of recent attempts to assess the prevalence of genetic constraints. However, evolutionary constraints have not yet been considered from the perspective of the phenotypes available to multivariate selection, and whether genetic variance is present in all phenotypes potentially under selection. Determining the rank of the phenotypic variance-covariance matrix (P) to characterize the phenotypes available to selection, and contrasting it with the rank of G, may provide a general approach to determining the prevalence of genetic constraints. In a study of a laboratory population of Drosophila bunnanda from northern Australia we applied factor-analytic modeling to repeated measures of individual wing phenotypes to determine the dimensionality of the phenotypic space described by P. The phenotypic space spanned by the 10 wing traits had 10 statistically supported dimensions. In contrast, factor-analytic modeling of G estimated for the same 10 traits from a paternal half-sibling breeding design suggested G had fewer dimensions than traits. Statistical support was found for only five and two genetic dimensions, describing a total of 99% and 72% of genetic variance in wing morphology in females and males, respectively. The observed mismatch in dimensionality between P and G suggests that although selection might act to shift the intragenerational population mean toward any trait combination, evolution may be restricted to fewer dimensions.     

Developmental interactions and the constituents of quantitative variation

Development is the process by which genotypes are transformed into phenotypes. Consequently, development determines the relationship between allelic and phenotypic variation in a population and, therefore, the patterns of quantitative genetic variation and covariation of traits. Understanding the developmental basis of quantitative traits may lead to insights into the origin and evolution of quantitative genetic variation, the evolutionary fate of populations, and, more generally, the relationship between development and evolution. Herein, we assume a hierarchical, modular structure of trait development and consider how epigenetic interactions among modules during ontogeny affect patterns of phenotypic and genetic variation. We explore two developmental models, one in which the epigenetic interactions between modules result in additive effects on character expression and a second model in which these epigenetic interactions produce nonadditive effects. Using a phenotype landscape approach, we show how changes in the developmental processes underlying phenotypic expression can alter the magnitude and pattern of quantitative genetic variation. Additive epigenetic effects influence genetic variances and covariances, but allow trait means to evolve independently of the genetic variances and covariances, so that phenotypic evolution can proceed without changing the genetic covariance structure that determines future evolutionary response. Nonadditive epigenetic effects, however, can lead to evolution of genetic variances and covariances as the mean phenotype evolves. Our model suggests that an understanding of multivariate evolution can be considerably enriched by knowledge of the mechanistic basis of character development.     

Pleiotropic Models of Polygenic Variation, Stabilizing Selection, and Epistasis

We show that in polymorphic populations many polygenic traits pleiotropically related to fitness are expected to be under apparent ``stabilizing selection' independently of the real selection acting on the population. This occurs, for example, if the genetic system is at a stable polymorphic equilibrium determined by selection and the nonadditive contributions of the loci to the trait value either are absent, or are random and independent of those to fitness. Stabilizing selection is also observed if the polygenic system is at an equilibrium determined by a balance between selection and mutation (or migration) when both additive and nonadditive contributions of the loci to the trait value are random and independent of those to fitness. We also compare different viability models that can maintain genetic variability at many loci with respect to their ability to account for the strong stabilizing selection on an additive trait. Let V(m) be the genetic variance supplied by mutation (or migration) each generation, V(g) be the genotypic variance maintained in the population, and n be the number of the loci influencing fitness. We demonstrate that in mutation (migration)-selection balance models the strength of apparent stabilizing selection is order V(m)/V(g). In the overdominant model and in the symmetric viability model the strength of apparent stabilizing selection is approximately 1/(2n) that of total selection on the whole phenotype. We show that a selection system that involves pairwise additive by additive epistasis in maintaining variability can lead to a lower genetic load and genetic variance in fitness (approximately 1/(2n) times) than an equivalent selection system that involves overdominance. We show that, in the epistatic model, the apparent stabilizing selection on an additive trait can be as strong as the total selection on the whole phenotype.     

Evolution of tolerance: the genetic basis of a host's resistance against parasite manipulation

Despite considerable theoretical advances in the evolutionary biology of host–parasite systems, our knowledge of host–parasite coevolution in natural systems is often limited. Among the reasons for the lag of experimental insight behind theory is that the parasite's virulence is not a simple trait that is controlled by the parasite's genes. Rather, virulence can be expressed in several traits due to the subtle interactions between the host and the parasite. Furthermore, the host might evolve tolerance to the parasite if there is sufficient genetic variance to reduce the detrimental effect of the parasite on these traits. We studied the traits underlying virulence and the genetic potential to evolve tolerance to infection in the host–parasite system Aedes aegypti – Brachiola algerae . We reared the mosquitoes in a half-sib design, exposed half of the individuals in each full-sib family to the parasite and measured several life history traits – juvenile mortality, age at pupation and adult size – of infected and uninfected individuals. Virulence was due in large part to a delay of the mosquito's age at pupation by about 10%. Although this imposes strong selection pressure on the mosquito to resist the parasite, all of the mosquitoes were infected, implying a lack of resistance. Furthermore, although additive genetic variance was present for other traits, we found no indication of additive genetic variation for the age at pupation, nor for the delay of pupation due to infection, implying no potential for the evolution of tolerance. Overall, the results suggest that in this host–parasite system, the host has little evolutionary control over the expression of the parasite's virulence.     

Smaller, scale-free gene networks increase quantitative trait heritability and result in faster population recovery

One of the goals of biology is to bridge levels of organization. Recent technological advances are enabling us to span from genetic sequence to traits, and then from traits to ecological dynamics. The quantitative genetics parameter heritability describes how quickly a trait can evolve, and in turn describes how quickly a population can recover from an environmental change. Here I propose that we can link the details of the genetic architecture of a quantitative trait--i.e., the number of underlying genes and their relationships in a network--to population recovery rates by way of heritability. I test this hypothesis using a set of agent-based models in which individuals possess one of two network topologies or a linear genotype-phenotype map, 16-256 genes underlying the trait, and a variety of mutation and recombination rates and degrees of environmental change. I find that the network architectures introduce extensive directional epistasis that systematically hides and reveals additive genetic variance and affects heritability: network size, topology, and recombination explain 81% of the variance in average heritability in a stable environment. Network size and topology, the width of the fitness function, pre-change additive variance, and certain interactions account for ～75% of the variance in population recovery times after a sudden environmental change. These results suggest that not only the amount of additive variance, but importantly the number of loci across which it is distributed, is important in regulating the rate at which a trait can evolve and populations can recover. Taken in conjunction with previous research focused on differences in degree of network connectivity, these results provide a set of theoretical expectations and testable hypotheses for biologists working to span levels of organization from the genotype to the phenotype, and from the phenotype to the environment.