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.     

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.     

TYPE I ERROR RATES FOR TESTING GENETIC DRIFT WITH PHENOTYPIC COVARIANCE MATRICES: A SIMULATION STUDY

Studies of evolutionary divergence using quantitative genetic methods are centered on the additive genetic variance–covariance matrix ( G ) of correlated traits. However, estimating G properly requires large samples and complicated experimental designs. Multivariate tests for neutral evolution commonly replace average G by the pooled phenotypic within‐group variance–covariance matrix ( W ) for evolutionary inferences, but this approach has been criticized due to the lack of exact proportionality between genetic and phenotypic matrices. In this study, we examined the consequence, in terms of type I error rates, of replacing average G by W in a test of neutral evolution that measures the regression slope between among‐population variances and within‐population eigenvalues (the Ackermann and Cheverud [AC] test) using a simulation approach to generate random observations under genetic drift. Our results indicate that the type I error rates for the genetic drift test are acceptable when using W instead of average G when the matrix correlation between the ancestral G and P is higher than 0.6, the average character heritability is above 0.7, and the matrices share principal components. For less‐similar G and P matrices, the type I error rates would still be acceptable if the ratio between the number of generations since divergence and the effective population size (t/N_e) is smaller than 0.01 (large populations that diverged recently). When G is not known in real data, a simulation approach to estimate expected slopes for the AC test under genetic drift is discussed.     

High Stressful Temperature and Genetic Variation of Five Quantitative Traits in Drosophila Melanogaster

Variation of five quantitative traits (thorax length, wing length, sternopleural bristle number, developmental time and larva-to-adult viability) was studied in Drosophila melanogaster reared at standard (25°C) and high stressful (32°C) temperatures using half-sib analysis. In all traits, both phenotypic and environmental variances increased at 32°C. For genetic variances, only two statistically significant differences between temperature treatments were found: the among-sire variance of viability and the among-dam variance of developmental time were higher under stress. Among-sire genetic variances and evolvabilities were generally higher at 32°C but narrow sense heritabilities were not. The results of the present work considered in the context of other studies in D. melanogaster indicate different patterns of genetic variation between stressful and nonstressful environments for the traits examined. Data on thorax length and viability agree with the hypothesis that genetic variance can be increased under extreme environmental conditions. This revised version was published online in July 2006 with corrections to the Cover Date.     

Genotypic variation in calling song and female preferences of the field cricket Teleogryllus oceanicus

Geographically isolated populations often show phenotypic divergence in traits important in reproduction. A large proportion of the phenotypic variation in temporal parameters of the calling song of the field cricket Teleogryllus oceanicus is related to geographical location. Similarity between the songs recorded in different populations reflects geographical proximity. I used a common-garden breeding experiment to determine whether differences between the songs of two populations from the extremes of the geographical and phenotypic distribution (Oahu, Hawaii and Cairns, Australia) have a genetic basis. Differences in the total song duration and the proportion of the long-chirp element in the song remained after five generations of common-garden breeding, indicating that the populations had diverged genetically for these traits. Differences in a third song trait, the intervals between sound pulses and chirps, disappeared after common-garden breeding, suggesting that either the difference between populations in these traits represents phenotypic plasticity or the populations converged as a result of adaptation to the laboratory environment. A prospective analysis of the patterns of genetic variation within populations is presented. Full-sib analyses suggested high levels of genetic variability in song traits. Family mean covariance matrices suggested that populations differ in the genetic architecture of their songs. Females from both populations preferred songs with a high proportion of the long-chirp element, and preferences appeared to have high genetic and residual variability, although the sampling variances on these parameters were high. There was little evidence of a correlation between female preference for the long-chirp element and the amount of the long-chirp element produced by their brothers.     

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.     

Phylogenetic analysis of correlation structure in stalk-eyed flies (Diasemopsis,Diopsidae)

Morphological divergence among species may be constrained by the pattern of genetic variances and covariances among traits within species. Assessing the existence of such a relationship in nature requires information on the stability of intraspecific correlation and covariance structure and the correspondence of this structure to the pattern of evolutionary divergence within a lineage. Here, we investigate these issues for nine morphological traits and 15 species of stalk-eyed flies in the genus Diasemopsis. Within-species matrices for these traits were generated from phenotypic data for all the Diasemopsis species and from genetic data for a single Diasemopsis species, D. dubia. The among-species pattern of divergence was assessed by calculating the evolutionary correlations for all pairwise combinations of the morphological traits along the phylogeny of these species. Comparisons of intraspecific matrices reveal significant similarity among all species in the phenotypic correlations matrices but not the covariance matrices. In addition, the differences in correlation structure that do exist among species are not related to their phylogenetic placement or change in the means of the traits. Comparisons of the phenotypic and phylogenetic matrices suggest a strong relationship between the pattern of evolutionary change among species and both the intraspecific correlation structure and the stability of this structure among species. The phenotypic and the phylogenetic matrices are significantly similar, and pairs of traits whose intraspecific correlations are more stable across taxa exhibit stronger coevolution on the phylogeny. These results suggest either the existence of strong constraints on the pattern of evolutionary change or a consistent pattern of correlated selection shaping both the phenotypic and phylogenetic matrices. The genetic correlation structure for D. dubia, however, does not correspond with patterns found in the phenotypic and phylogenetic data. Possible reasons for this disagreement are discussed.     

Limited plasticity in the phenotypic variance‐covariance matrix for male advertisement calls in the black field cricket,Teleogryllus commodus

Phenotypic integration and plasticity are central to our understanding of how complex phenotypic traits evolve. Evolutionary change in complex quantitative traits can be predicted using the multivariate breeders’ equation, but such predictions are only accurate if the matrices involved are stable over evolutionary time. Recent study, however, suggests that these matrices are temporally plastic, spatially variable and themselves evolvable. The data available on phenotypic variance‐covariance matrix ( P ) stability are sparse, and largely focused on morphological traits. Here, we compared P for the structure of the complex sexual advertisement call of six divergent allopatric populations of the Australian black field cricket, Teleogryllus commodus. We measured a subset of calls from wild‐caught crickets from each of the populations and then a second subset after rearing crickets under common‐garden conditions for three generations. In a second experiment, crickets from each population were reared in the laboratory on high‐ and low‐nutrient diets and their calls recorded. In both experiments, we estimated P for call traits and used multiple methods to compare them statistically (Flury hierarchy, geometric subspace comparisons and random skewers). Despite considerable variation in means and variances of individual call traits, the structure of P was largely conserved among populations, across generations and between our rearing diets. Our finding that P remains largely stable, among populations and between environmental conditions, suggests that selection has preserved the structure of call traits in order that they can function as an integrated unit.     

CONNECTING QTLS TO THE G-MATRIX OF EVOLUTIONARY QUANTITATIVE GENETICS

Evolutionary quantitative genetics has recently advanced in two distinct streams. Many biologists address evolutionary questions by estimating phenotypic selection and genetic (co)variances ( G matrices). Simultaneously, an increasing number of studies have applied quantitative trait locus (QTL) mapping methods to dissect variation. Both conceptual and practical difficulties have isolated these two foci of quantitative genetics. A conceptual integration follows from the recognition that QTL allele frequencies are the essential variables relating the G -matrix to marker-based mapping experiments. Breeding designs initiated from randomly selected parental genotypes can be used to estimate QTL-specific genetic (co)variances. These statistics appropriately distill allelic variation and provide an explicit population context for QTL mapping estimates. Within this framework, one can parse the G -matrix into a set of mutually exclusive genomic components and ask whether these parts are similar or dissimilar in their respective features, for example the magnitude of phenotypic effects and the extent and nature of pleiotropy. As these features are critical determinants of sustained response to selection, the integration of QTL mapping methods into G -matrix estimation can provide a concrete, genetically based experimental program to investigate the evolutionary potential of natural populations.     

Ontogenetic patterns in heritable variation for body size: using random regression models in a wild ungulate population

Body size is an important determinant of fitness in many organisms. While size will typically change over the lifetime of an individual, heritable components of phenotypic variance may also show ontogenetic variation. We estimated genetic (additive and maternal) and environmental covariance structures for a size trait (June weight) measured over the first 5 years of life in a natural population of bighorn sheep Ovis canadensis. We also assessed the utility of random regression models for estimating these structures. Additive genetic variance was found for June weight, with heritability increasing over ontogeny because of declining environmental variance. This pattern, mirrored at the phenotypic level, likely reflects viability selection acting on early size traits. Maternal genetic effects were significant at ages 0 and 1, having important evolutionary implications for early weight, but declined with age being negligible by age 2. Strong positive genetic correlations between age-specific traits suggest that selection on June weight at any age will likely induce positively correlated responses across ontogeny. Random regression modeling yielded similar results to traditional methods. However, by facilitating more efficient data use where phenotypic sampling is incomplete, random regression should allow better estimation of genetic (co)variances for size and growth traits in natural 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.     

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.     

The evolution of the phenotypic covariance matrix: evidence for selection and drift in Melanoplus

Phenotypic variation in trait means is a common observation for geographically separated populations. Such variation is typically retained under common garden conditions, indicating that there has been evolutionary change in the populations, as a result of selection and/or drift. Much less frequently studied is variation in the phenotypic covariance matrix (hereafter, P matrix), although this is an important component of evolutionary change. In this paper, we examine variation in the phenotypic means and P matrices in two species of grasshopper, Melanoplus sanguinipes and M. devastator. Using the P matrices estimated for 14 populations of M. sanguinipes and three populations of M. devastator we find that (1) significant differences between the sexes can be attributed to scaling effects; (2) there is no significant difference between the two species; (3) there are highly significant differences among populations that cannot be accounted for by scaling effects; (4) these differences are a consequence of statistically significant patterns of covariation with geographic and environmental factors, phenotypic variances and covariances increasing with increased temperature but decreasing with increased latitude and altitude. This covariation suggests that selection has been important in the evolution of the P matrix in these populations Finally, we find a significant positive correlation between the average difference between matrices and the genetic distance between the populations, indicating that drift has caused some of the variation in the P matrices.     

Adaptive phenotypic plasticity and genetics of larval life histories in two Rana temporaria populations

Phenotypic plasticity provides means for adapting to environmental unpredictability. In terms of accelerated development in the face of pond-drying risk, phenotypic plasticity has been demonstrated in many amphibian species, but two issues of evolutionary interest remain unexplored. First, the heritable basis of plastic responses is poorly established. Second, it is not known whether interpopulational differences in capacity to respond to pond-drying risk exist, although such differences, when matched with differences in desiccation risk would provide strong evidence for local adaptation. We investigated sources of within- and among-population variation in plastic responses to simulated pond-drying risk (three desiccation treatments) in two Rana temporaria populations originating from contrasting environments: (1) high desiccation risk with weak seasonal time constraint (southern population); and (2) low desiccation risk with severe seasonal time constraint (northern population). The larvae originating from the environment with high desiccation risk responded adaptively to the fast decreasing water treatment by accelerating their development and metamorphosing earlier, but this was not the case in the larvae originating from the environment with low desiccation risk. In both populations, metamorphic size was smaller in the high-desiccation-risk treatment, but the effect was larger in the southern population. Significant additive genetic variation in development rate was found in the northern and was nearly significant in the southern population, but there was no evidence for genetic variation in plasticity for development rates in either of the populations. No genetic variation for plasticity was found either in size at metamorphosis or growth rate. All metamorphic traits were heritable, and additive genetic variances were generally somewhat higher in the southern population, although significantly so in only one trait. Dominance variances were also significant in three of four traits, but the populations did not differ. Maternal effects in metamorphic traits were generally weak in both populations. Within-environment phenotypic correlations between larval period and metamorphic size were positive and genetic correlations negative in both populations. These results suggest that adaptive phenotypic plasticity is not a species-specific fixed trait, but evolution of interpopulational differences in plastic responses are possible, although heritability of plasticity appears to be low. The lack of adaptive response to desiccation risk in northern larvae is consistent with the interpretation that selection imposed by shorter growing season has favored rapid development in north (approximately 8% faster development in north as compared to south) or a minimum metamorphic size at the expense of phenotypic plasticity.     

DIVERGENCE AND GENETIC STRUCTURE IN ADJACENT GRASS POPULATIONS. I. QUANTITATIVE GENETICS

Additive genetic variances and covariances were estimated for life history and morphological traits in two adjacent populations of the grass, Holcus lanatus L. Significant phenotypic differentiation was found between the two populations for four of the 15 morphological attributes measured. Significant differences in genetic architecture were found between the two populations for 11 of the 13 traits for which genetic variance components could be calculated. Estimates of genetic correlations also showed considerable divergence between the populations. The genetic divergence was much larger than would have been anticipated from simple measures of phenotypic differentiation. These results show that, even in plant species with relatively large population sizes, differences in genetic variance-covariance patterns can occur between adjacent populations.     

Evolutionary responses of Drosophila melanogaster to selection at different larval densities: changes in genetic variation,specialization and phenotypic plasticity

Abstract We studied the evolutionary response to novel environments by applying artificial selection for total progeny biomass in populations of Drosophila melanogaster maintained at three different larval population densities. We found the relative amount of genetic variability for characters related with biomass to be lower and the correlation between them more negative at the intermediate density, and that selection resulted in changes in phenotypic plasticity and in patterns of resource allocation between traits. We found some evidence for tradeoffs between densities, which suggests that populations living at heterogeneous densities might be subject to disruptive selection. Our results show that adaptation to new environments may be a complex process, involving not only changes in trait means, but also in correlations between traits and between environments.     

Population divergence along lines of genetic variance and covariance in the invasive plant Lythrum salicaria in eastern North America

Evolution during biological invasion may occur over contemporary timescales, but the rate of evolutionary change may be inhibited by a lack of standing genetic variation for ecologically relevant traits and by fitness trade-offs among them. The extent to which these genetic constraints limit the evolution of local adaptation during biological invasion has rarely been examined. To investigate genetic constraints on life-history traits, we measured standing genetic variance and covariance in 20 populations of the invasive plant purple loosestrife (Lythrum salicaria) sampled along a latitudinal climatic gradient in eastern North America and grown under uniform conditions in a glasshouse. Genetic variances within and among populations were significant for all traits; however, strong intercorrelations among measurements of seedling growth rate, time to reproductive maturity and adult size suggested that fitness trade-offs have constrained population divergence. Evidence to support this hypothesis was obtained from the genetic variance-covariance matrix (G) and the matrix of (co)variance among population means (D), which were 79.8% (95% C.I. 77.7-82.9%) similar. These results suggest that population divergence during invasive spread of L. salicaria in eastern North America has been constrained by strong genetic correlations among life-history traits, despite large amounts of standing genetic variation for individual traits.     

Study of Natural Genetic Variation in Early Fitness Traits Reveals Decoupling Between Larval and Pupal Developmental Time in <Emphasis Type="Italic">Drosophila melanogaster</Emphasis>

Characterizing the relationships between genotype and phenotype for developmental adaptive traits is essential to understand the evolutionary dynamics underlying biodiversity. In holometabolous insects, the time to reach the reproductive stage and pupation site preference are two such traits. Here we characterize aspects of the genetic architecture for Developmental Time (decomposed in Larval and Pupal components) and Pupation Height using lines derived from three natural populations of Drosophila melanogaster raised at two temperatures. For all traits, phenotypic differences and variation in plasticity between populations suggest adaptation to the original thermal regimes. However, high variability within populations shows that selection does not exhaust genetic variance for these traits. This could be partly explained by local adaptation, environmental heterogeneity and modifications in the genetic architecture of traits according to environment and ontogenetic stage. Indeed, our results show that the genetic factors affecting Developmental Time and Pupation Height are temperature-specific. Varying relationships between Larval and Pupal Developmental Time between and within populations also suggest stage-specific modifications of genetic architecture for this trait. This flexibility would allow for a somewhat independent evolution of adaptive traits at different environments and life stages, favoring the maintenance of genetic variability and thus sustaining the traits’ evolvabilities.     

Exploring the impact of neutral evolution on intrapopulation genetic differentiation in functional traits in a long-lived plant

Most plant species, particularly long-lived plants, harbor a large amount of genetic variation within populations. A central issue in evolutionary ecology is to explore levels of genetic variation and understand the mechanisms that influence them. In this study, our goals were to examine the impact of neutral evolutionary processes on the genetic variance and functional diversity within three populations of a long-lived plant (Quercus suber L.). For this purpose, we genotyped the progeny of 45 open-pollinated mother trees from three populations originating from Spain, Portugal, and Morocco using six microsatellite markers. Seedlings were planted in a common garden trial and were phenotypically characterized by seven leaf functional traits. Molecular analyses revealed weak genetic differences between Iberian and Moroccan populations. Nevertheless, high genetic differentiation was observed among maternal families within populations. Differentiation between particular maternal families from the same population reached values of 29.2 %, which far exceeds the values reported between the most genetically distant populations for this species (11.7 %). Maternal families differed also in phenology, leaf size, and shape traits. In the Moroccan population, there were correlations among matrices of distances for molecular markers, leaf shape traits (e.g., leaf circularity index), and phenology, indicating that maternal families with contrasting phenologies were genetically and functionally distinct. This, together with the moderate heritability for phenology in Moroccan population, suggests that besides selective forces, neutral evolutionary processes have promoted intrapopulation genetic divergence and contribute to maintain high levels of genetic variation within this population. Overall, our results reinforce the importance of intrapopulation studies in long-lived plants under an evolutionary context.     

The effect of temperature and wing morphology on quantitative genetic variation in the cricket Gryllus firmus, with an appendix examining the statistical properties of the Jackknife-MANOVA method of matrix comparison

We investigated the effect of temperature and wing morphology on the quantitative genetic variances and covariances of five size-related traits in the sand cricket, Gryllus firmus. Micropterous and macropterous crickets were reared in the laboratory at 24, 28 and 32 degrees C. Quantitative genetic parameters were estimated using a nested full-sib family design, and (co)variance matrices were compared using the T method, Flury hierarchy and Jackknife-manova method. The results revealed that the mean phenotypic value of each trait varied significantly among temperatures and wing morphs, but temperature reaction norms were not similar across all traits. Micropterous individuals were always smaller than macropterous individuals while expressing more phenotypic variation, a finding discussed in terms of canalization and life-history trade-offs. We observed little variation between the matrices of among-family (co)variation corresponding to each combination of temperature and wing morphology, with only one matrix of six differing in structure from the others. The implications of this result are discussed with respect to the prediction of evolutionary trajectories.