EFFECT OF AN EXPERIMENTAL BOTTLENECK ON MORPHOLOGICAL INTEGRATION IN THE HOUSEFLY

Three measures of multivariate integration were derived from both additive genetic covariance and correlation matrices estimated from parent-offspring covariances to investigate the effect of bottlenecks of different sizes on genetic integration of morphological traits in the housefly, Musca domestica L. Bottleneck lines were initiated with one, four, or 16 pairs of flies sampled from a natural outbred (control) population. Bottlenecks of intermediate size significantly increased the average genetic correlation among traits, resulting in nearly isomorphic variation among all traits in these lines. Single-pair bottlenecks significantly disrupted the trait interrelationships, and the suites of traits identified by principal components of the additive genetic correlation and covariance matrices for the control population were no longer evident in these bottleneck lines. The alteration of the genetic relationships among traits as a result of a bottleneck suggests that nonadditive components of genetic variation affecting these traits were present in the control line. We discuss the implications of nonadditive gene action, particularly epistasis, for speciation via bottlenecks.     

THE DETERMINATION OF GENETIC COVARIANCES AND PREDICTION OF EVOLUTIONARY TRAJECTORIES BASED ON A GENETIC CORRELATION MATRIX

There is much interest in measuring selection, quantifying evolutionary constraints, and predicting evolutionary trajectories in natural populations. For these studies, genetic (co)variances among fitness traits play a central role. We explore the conditions that determine the sign of genetic covariances and demonstrate a critical role of selection in shaping genetic covariances. In addition, we show that genetic covariance matrices rather than genetic correlation matrices should be characterized and studied in order to infer genetic basis of population differentiation and/or to predict evolutionary trajectories.     

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.     

Selection on Wing Allometry in Drosophila Melanogaster

Five bivariate distributions of wing dimensions of Drosophila melanogaster were measured, in flies 1) subjected to four defined environmental regimes during development, 2) taken directly from nature in seven U.S. states, 3) selected in ten populations for change in wing form, and 4) sampled from 21 long inbred wild-type lines. Environmental stresses during development altered both wing size and the ratios of wing dimensions, but regardless of treatment all wing dimensions fell near a common allometric baseline in each bivariate distribution. The wings of wild-caught flies from seven widely separated localities, and of their laboratory-reared offspring, also fell along the same baselines. However, when flies were selected divergently for lateral offset from these developmental baselines, response to selection was rapid in every case. The mean divergence in offset between oppositely selected lines was 14.68 SD of the base population offset, after only 15 generations of selection at 20%. Measurements of 21 isofemale lines, founded from wild-caught flies and maintained in small populations for at least 22 years, showed large reductions in phenotypic variance of offsets within lines, but a large increase in the variance among lines. The variance of means of isofemale lines within collection localities was ten times the variance of means among localities of newly established wild lines. These observations show that much additive genetic variance exists for individual dimensions within the wing, such that bivariate developmental patterns can be changed in any direction by selection or by drift. The relative invariance of the allometric baselines of wing morphology in nature is most easily explained as the result of continuous natural selection around a local optimum of functional design.     

Migration-induced phenotypic divergence: the migration-selection balance of correlated traits

Genetically correlated traits are known to respond to indirect selection pressures caused by directional selection on other traits. It is however unclear how local adaptation in populations diverging along some phenotypic traits but not others is affected by the joint action of gene flow and genetic correlations among traits. This simulation study shows that although gene flow is a potent constraining mechanism of population adaptive divergence, it may induce phenotypic divergence in traits under homogeneous selection among habitats if they are genetically correlated with traits under divergent selection. This correlated phenotypic divergence is a nonmonotonous function of migration and increases with mutational correlation among traits. It also increases with the number of divergently selected traits provided their genetic autonomy relative to the uniformly selected trait is reduced by specific patterns of genetic covariances: populations with lower effective trait dimensionality are more likely to generate very large correlated divergence. The correlated divergence is likely to be picked up by Q(ST)-F(ST) analysis of population genetic differentiation and be erroneously ascribed to adaptive divergence under divergent selection. This study emphasizes the necessity to understand the interaction between selection and the genetic basis of adaptation in a multivariate rather than univariate context.     

POPULATION STRUCTURE OF MORPHOLOGICAL TRAITS IN CLARKIA DUDLEYANA. II. CONSTANCY OF WITHIN-POPULATION GENETIC VARIANCE

Recent quantitative genetic studies have attempted to infer long-term selection responsible for differences in observed phenotypes. These analyses are greatly simplified by the assumption that the within-population genetic variance remains constant through time and over space, or for the multivariate case, that the matrix of additive genetic variances and covariances (G matrix) is constant. We examined differences in G matrices and the association of these differences with differences in multivariate means (Mahalanobis D²) among 11 populations of the California endemic annual plant, Clarkia dudleyana. Based on nine continuous morphological traits, the relationship between Mahalanobis D² and a distance measure summarizing differences in G matrices reflected no concomitant change in (co)variances with changes in means. Based on both broad- and narrow-sense analyses, we found little evidence that G matrices differed between populations. These results suggest that both the additive and nonadditive (co)variances for traits have remained relatively constant despite changes in means.     

AN ANALYSIS OF SELECTIONAL RESPONSE IN RELATION TO A POPULATION BOTTLENECK

Selection for increased morphometric shape (ratio of wing length to thorax width) was compared between control (nonbottlenecked) populations and bottlenecked populations founded with two male–female pairs of flies. Contrary to neutral expectation, selectional response was not reduced in bottlenecked populations, and the mean realized heritabilities and additive genetic variances were higher for the bottlenecked lines than for the nonbottlenecked lines. Additive genetic variances based on these realized heritabilities were consistent with independent estimates of genetic variances based on parent–offspring covariances. Joint scaling tests applied to the crosses between selected lines and their controls revealed significant nonadditive components of genetic variance in the ancestor, which were not detected in the crosses involving bottlenecked lines. The nonbottlenecked lines responded principally by changes in one trait or the other (wing length or thorax width) but not in both, and regardless of which trait responded, larger trait size was dominant and epistatic to smaller size. Stabilizing selection for morphometric shape in the ancestor likely molded the genetic architecture to include nonadditive genetic effects.     

HOMOGENEITY OF THE GENETIC VARIANCE-COVARIANCE MATRIX FOR ANTIPREDATOR TRAITS IN TWO NATURAL POPULATIONS OF THE GARTER SNAKE THAMNOPHIS ORDINOIDES

Quantitative genetic models of evolution rely on the genetic variance-covariance matrix to predict the phenotypic response to selection. Both prospective and retrospective studies of phenotypic evolution across generations rely on assumptions about the constancy of patterns of genetic covariance through time. In the absence of robust theoretical predictions about the stability of genetic covariances, this assumption must be tested with empirical comparisons of genetic parameters among populations and species. Genetic variance-covariance matrices were estimated for a suite of antipredator traits in two populations of the northwestern garter snake, Thamnophis ordinoides. The characters studied include color pattern and antipredator behaviors that interact to facilitate escape from predators. Significant heritabilities for all traits were detected in both populations. Genetic correlations and covariances were found among behaviors in both populations and between color pattern and behavior in one of the populations. Phenotypic means differed among populations, but pairwise comparisons revealed no heterogeneity of genetic parameters between the populations. The structure of the genetic variance-covariance matrix has apparently not changed significantly during the divergence of these two populations.     

Patterns of phenotypic covariation and correlation in modern humans as viewed from morphological integration

Proportionality of phenotypic and genetic distance is of crucial importance to adequately focus on population history and structure, and it depends on the proportionality of genetic and phenotypic covariance. Constancy of phenotypic covariances is unlikely without constancy of genetic covariation if the latter is a substantial component of the former. If phenotypic patterns are found to be relatively stable, the most probable explanation is that genetic covariance matrices are also stable. Factors like morphological integration account for such stability. Morphological integration can be studied by analyzing the relationships among morphological traits. We present here a comparison of phenotypic correlation and covariance structure among worldwide human populations. Correlation and covariance matrices between 47 cranial traits were obtained for 28 populations, and compared with design matrices representing functional and developmental constraints. Among-population differences in patterns of correlation and covariation were tested for association with matrices of genetic distances (obtained after an examination of 10 Alu-insertions) and with Mahalanobis distances (computed after craniometrical traits). All matrix correlations were estimated by means of Mantel tests. Results indicate that correlation and covariance structure in our species is stable, and that among-group correlation/covariance similarity is not related to genetic or phenotypic distance. Conversely, genetic and morphological distance matrices were highly correlated. Correlation and covariation patterns were largely associated with functional and developmental factors, which probably account for the stability of covariance patterns.     

The genetic structure of female life history in D. melanogaster: comparisons among populations

Two questions were addressed: (1) What is the genetic variance-covariance structure of a suite of four female life history traits in D. melanogaster? and (2) Does the genetic architecture of these traits differ among populations? Three populations of D. melanogaster were studied. Genetic variances and covariances were estimated by sib analysis three times for each population: immediately upon establishment of populations in the laboratory, and subsequently after approximately 6 months and 2 years of laboratory culture. Entire genetic variance-covariance matrices, as well as their individual components, were compared between populations by means of likelihood ratio tests. All traits studied were significantly heritable in at least one-half of estimates. Despite large sample sizes, additive genetic covariances were for the most part not statistically significant, and only two significant negative covariance estimates were obtained throughout the experiments. Therefore, these experiments provide little support for evolutionary life history theories that are based on negative genetic correlations among life history components. Neither do they support the idea that genetic variance for fitness components is maintained by trade-offs. Evidence suggests that the G matrix of one population was initially different from those of the other two populations. Those differences disappeared after 2 years of laboratory culture. At the level of individual (co)variance components, there were relatively few differences among populations, and the overall impression was that the three populations had generally similar genetic architectures for the traits studied.     

Epistatic pleiotropy and the genetic architecture of covariation within early and late-developing skull trait complexes in mice

The role of epistasis as a source of trait variation is well established, but its role as a source of covariation among traits (i.e., as a source of "epistatic pleiotropy") is rarely considered. In this study we examine the relative importance of epistatic pleiotropy in producing covariation within early and late-developing skull trait complexes in a population of mice derived from an intercross of the Large and Small inbred strains. Significant epistasis was found for several pairwise combinations of the 21 quantitative trait loci (QTL) affecting early developing traits and among the 20 QTL affecting late-developing traits. The majority of the epistatic effects were restricted to single traits but epistatic pleiotropy still contributed significantly to covariances. Because of their proportionally larger effects on variances than on covariances, epistatic effects tended to reduce within-group correlations of traits and reduce their overall degree of integration. The expected contributions of single-locus and two-locus epistatic pleiotropic QTL effects to the genetic covariance between traits were analyzed using a two-locus population genetic model. The model demonstrates that, for single-locus or epistatic pleiotropy to contribute to trait covariances in the study population, both traits must show the same pattern of single-locus or epistatic effects. As a result, a large number of the cases where loci show pleiotropic effects do not contribute to the covariance between traits in this population because the loci show a different pattern of effect on the different traits. In general, covariance patterns produced by single-locus and epistatic pleiotropy predicted by the model agreed well with actual values calculated from the QTL analysis. Nearly all single-locus and epistatic pleiotropic effects contributed positive components to covariances between traits, suggesting that genetic integration in the skull is achieved by a complex combination of pleiotropic effects.     

Up hill, down dale: quantitative genetics of curvaceous traits

'Repeated' measurements for a trait and individual, taken along some continuous scale such as time, can be thought of as representing points on a curve, where both means and covariances along the trajectory can change, gradually and continually. Such traits are commonly referred to as 'function-valued' (FV) traits. This review shows that standard quantitative genetic concepts extend readily to FV traits, with individual statistics, such as estimated breeding values and selection response, replaced by corresponding curves, modelled by respective functions. Covariance functions are introduced as the FV equivalent to matrices of covariances. Considering the class of functions represented by a regression on the continuous covariable, FV traits can be analysed within the linear mixed model framework commonly employed in quantitative genetics, giving rise to the so-called random regression model. Estimation of covariance functions, either indirectly from estimated covariances or directly from the data using restricted maximum likelihood or Bayesian analysis, is considered. It is shown that direct estimation of the leading principal components of covariance functions is feasible and advantageous. Extensions to multi-dimensional analyses are discussed.     

Rapid reversal of a potentially constraining genetic covariance between leaf and flower traits in Silene latifolia

Genetic covariance between two traits generates correlated responses to selection, and may either enhance or constrain adaptation. Silene latifolia exhibits potentially constraining genetic covariance between specific leaf area (SLA) and flower number in males. Flower number is likely to increase via fecundity selection but the correlated increase in SLA increases mortality, and SLA is under selection to decrease in dry habitats. We selected on trait combinations in two selection lines for four generations to test whether genetic covariance could be reduced without significantly altering trait means. In one selection line, the genetic covariance changed sign and eigenstructure changed significantly, while in the other selection line eigenstructure remained similar to the control line. Changes in genetic variance–covariance structure are therefore possible without the introduction of new alleles, and the responses we observed suggest that founder effects and changes in frequency of alleles of major effect may be acting to produce the changes.     

Evolutionary quantitative genetics of nonlinear developmental systems

In quantitative genetics, the effects of developmental relationships among traits on microevolution are generally represented by the contribution of pleiotropy to additive genetic covariances. Pleiotropic additive genetic covariances arise only from the average effects of alleles on multiple traits, and therefore the evolutionary importance of nonlinearities in development is generally neglected in quantitative genetic views on evolution. However, nonlinearities in relationships among traits at the level of whole organisms are undeniably important to biology in general, and therefore critical to understanding evolution. I outline a system for characterizing key quantitative parameters in nonlinear developmental systems, which yields expressions for quantities such as trait means and phenotypic and genetic covariance matrices. I then develop a system for quantitative prediction of evolution in nonlinear developmental systems. I apply the system to generating a new hypothesis for why direct stabilizing selection is rarely observed. Other uses will include separation of purely correlative from direct and indirect causal effects in studying mechanisms of selection, generation of predictions of medium‐term evolutionary trajectories rather than immediate predictions of evolutionary change over single generation time‐steps, and the development of efficient and biologically motivated models for separating additive from epistatic genetic variances and covariances.     

Genetics of body shape and armour variation in threespine sticklebacks

Patterns of genetic variation and covariation can influence the rate and direction of phenotypic evolution. We explored the possibility that the parallel morphological evolution seen in threespine stickleback (Gasterosteus aculeatus) populations colonizing freshwater environments is facilitated by patterns of genetic variation and covariation in the ancestral (marine) population. We estimated the genetic (G) and phenotypic (P) covariance matrices and directions of maximum additive genetic (g(max) ) and phenotypic (p(max) ) covariances of body shape and armour traits. Our results suggest a role for the ancestral G in explaining parallel morphological evolution in freshwater populations. We also found evidence of genetic constraints owing to the lack of variance in the ancestral G. Furthermore, strong genetic covariances and correlations among traits revealed that selective factors responsible for threespine stickleback body shape and armour divergence may be difficult to disentangle. The directions of g(max) and p(max) were correlated, but the correlations were not high enough to imply that phenotypic patterns of trait variation and covariation within populations are very informative of underlying genetic patterns.     

Adaptation in a spider mite population after long-term evolution on a single host plant

Evolution in a single environment is expected to erode genetic variability, thereby precluding adaptation to novel environments. To test this, a large population of spider mites kept on cucumber for approximately 300 generations was used to establish populations on novel host plants (tomato or pepper), and changes in traits associated to adaptation were measured after 15 generations. Using a half-sib design, we investigated whether trait changes were related to genetic variation in the base population. Juvenile survival and fecundity exhibited genetic variation and increased in experimental populations on novel hosts. Conversely, no variation was detected for host choice and developmental time and these traits did not evolve. Longevity remained unchanged on novel hosts despite the presence of genetic variation, suggesting weak selection for this trait. Hence, patterns of evolutionary changes generally matched those of genetic variation, and changes in some traits were not hindered by long-term evolution in a constant environment.     

Persistence of changes in the genetic covariance matrix after a bottleneck

Abstract.— Genetic variance, phenotypic variance, and the genetic covariance matrix ( G ) can change as a result of genetic drift. These changes will persist over time to some extent and will continue if population size remains relatively small. Nine populations founded by a single pair of Drosophila melanogaster were measured for a series of six morphological characteristics for a large number of parent-offspring families at both the third generation after the bottlenecks and after 20 generations. From these data, the phenotypic variance, additive genetic variance, and G were estimated for each line at each generation. Phenotypic and genetic variances were highly correlated over time, so that the measurements made at the third generation were predictive of the state of the population 17 generations later. Genetic covariances were also somewhat stable over time; however, the G matrices of some lines changed significantly over the intervening generations. This change did not return the populations toward their original state before the population bottlenecks. We conclude that the genetic covariance matrix can change as a result of mild genetic drift over a short span of time.     

Genetic correlation and response to selection in simulated populations

Summary Effects of truncation selection of a primary trait upon genetic correlation with a secondary trait were examined over 30 generations in genetic populations simulated by computer. Populations were 24 males and 24 females mated randomly with replacement; number of offspring was determined by intensity of selection. Each trait was controlled by 48 loci segregating independently, effects were equal at every locus, and gene frequency was arbitrarily set at 0.5 at each locus in the initial generation. All combinations of three genetic correlations, three intensities of selection, and three environmental variances were simulated. Gene action was additive. Genetic correlation was set by number of loci which affected both traits and was measured each generation as the product-moment correlation of genotypic values and estimated by two methods of combining phenotypic covariances between parent and offspring.Genetic correlations in each offspring generation remained consistently near initial correlations for all environmental variances when fraction of offspring saved as parents was as large as one-half. When the fraction of offspring saved was as small as one-fifth, genetic correlations decreased but most rapidly with heritability high and after the 15th generation of selection. Truncation selection caused genetic correlation to decrease in those offspring selected to become parents of the next generation. Amount of reduction depended on heritability of the selected trait rather than on degree of truncation selection. Estimates of genetic correlation from phenotypic covariances between parent and offspring fluctuated markedly from real correlations in the small populations simulated.Michigan Agricultural Experiment Station Journal Article 4836. Part of North Central Regional Project NC-2.     

Genetic architecture of a selection response in Arabidopsis thaliana

Quantitative trait locus (QTL) mapping has become an established and effective method for studying the genetic architecture of complex traits. In this report, we use a QTL mapping approach in combination with data from a large selection experiment in Arabidopsis thaliana to explore a response to selection of experimental populations with differentiated genetic backgrounds. Experimental populations with genetic backgrounds derived from ecotypes Landsberg and Niederzenz were exposed to multiple generations of fertility and viability selection. This selection resulted in phenotypic shifts in a number of life-history and fitness-related characters including early development time, flowering time, dry biomass, longevity, and fruit production. Quantitative trait loci were mapped for these traits and their positions were compared to previously characterized allele frequency changes in the experimental populations (Ungerer et al. 2003). Quantitative trait locus positions largely colocalized with genomic regions under strong and consistent selection in populations with differentiated genetic backgrounds, suggesting that alleles for these traits were selected similarly in differentiated genetic backgrounds. However, one QTL region exhibited a more variable response; being positively selected on one genetic background but apparently neutral in another. This study demonstrates how QTL mapping approaches can be combined with map-based population genetic data to study how selection acts on standing genetic variation in populations.     

Genetic covariances promote climatic adaptation in Australian Drosophila*

Evolutionary potential for adaptation hinges upon the orientation of genetic variation for traits under selection, captured by the additive genetic variance-covariance matrix (G), as well as the evolutionary stability of G. Yet studies that assess both the stability of G and its alignment with selection are extraordinarily rare. We evaluated the stability of G in three Drosophila melanogaster populations that have adapted to local climatic conditions along a latitudinal cline. We estimated population- and sex-specific G matrices for wing size and three climatic stress-resistance traits that diverge adaptively along the cline. To determine how G affects evolutionary potential within these populations, we used simulations to quantify how well G aligns with the direction of trait divergence along the cline (as a proxy for the direction of local selection) and how genetic covariances between traits and sexes influence this alignment. We found that G was stable across the cline, showing no significant divergence overall, or in sex-specific subcomponents, among populations. G also aligned well with the direction of clinal divergence, with genetic covariances strongly elevating evolutionary potential for adaptation to climatic extremes. These results suggest that genetic covariances between both traits and sexes should significantly boost evolutionary responses to environmental change.