An analysis of G matrix variation in two closely related cricket species,Gryllus firmus and G. pennsylvanicus

An important issue in evolutionary biology is understanding the pattern of G matrix variation in natural populations. We estimated four G matrices based on the morphological traits of two cricket species, Gryllus firmus and G. pennsylvanicus, each reared in two environments. We used three matrix comparison approaches, including the Flury hierarchy, to improve our ability to perceive all aspects of matrix variation. Our results demonstrate that different methods perceive different aspects of the matrices, which suggests that, until more is known about these methods, future studies should use several different statistical approaches. We also found that the differences in G matrices within a species can be larger than the differences between species. We conclude that the expression of the genetic architecture can vary with the environment and that future studies should compare G matrices across several environments. We also conclude that G matrices can be conserved at the level of closely related species.     

The evolution of phenotypic integration: How directional selection reshapes covariation in mice

Variation is the basis for evolution, and understanding how variation can evolve is a central question in biology. In complex phenotypes, covariation plays an even more important role, as genetic associations between traits can bias and alter evolutionary change. Covariation can be shaped by complex interactions between loci, and this genetic architecture can also change during evolution. In this article, we analyzed mouse lines experimentally selected for changes in size to address the question of how multivariate covariation changes under directional selection, as well as to identify the consequences of these changes to evolution. Selected lines showed a clear restructuring of covariation in their cranium and, instead of depleting their size variation, these lines increased their magnitude of integration and the proportion of variation associated with the direction of selection. This result is compatible with recent theoretical works on the evolution of covariation that take the complexities of genetic architecture into account. This result also contradicts the traditional view of the effects of selection on available covariation and suggests a much more complex view of how populations respond to selection.     

Genotype–environment interaction and the ontogeny of diet-induced phenotypic plasticity in size and shape of Melanoplus femurrubrum (Orthoptera: Acrididae)

The developmental origin of phenotypic plasticity in morphological shape can be attributed to environment-specific changes in growth of overall body size, localized growth of a morphological structure or a combination of both. I monitored morphological development in the first four nymphal instars of grasshoppers (Melanoplus femurrubrum) raised on two different plant diets to determine the ontogenetic origins of diet-induced phenotypic plasticity and to quantify genetic variation for phenotypic plasticity. I measured diet-induced phenotypic plasticity in body size (tibia length), head size (articular width and mandible depth) and head shape (residual articular width and residual mandible depth) for grasshoppers from 37 full-sib families raised on either a hard plant diet (Lolium perenne) or a soft plant diet (Trifolium repens). By the second to third nymphal instar, grasshoppers raised on a hard plant diet had significantly smaller mean tibia length and greater mean residual articular width (distance between mandibles adjusted for body size) compared with full-sibs raised on a soft plant diet. However, there was no significant phenotypic plasticity in mean unadjusted articular width and mandible depth, and in mean residual mandible depth. At the population level, development of diet-induced phenotypic plasticity in grasshopper head shape is mediated by plastic changes in allocation to tissue growth that maintain growth of head size on hard, low-nutrient diets while reducing growth of body size. Within the population, there was substantial variation in the plasticity of growth trajectories since different full-sib families developed phenotypic plasticity of residual articular width through different combinations of head and body size growth. Genetic variation for diet-induced phenotypic plasticity of residual articular width, residual mandible depth and tibia length, as estimated by genotype–environment interaction, exhibited significant fluctuation through ontogeny (repeated measures MANOVA , family × plant × instar, P < 0.01). For example, there was significant genetic variation for phenotypic plasticity of residual articular width in the third nymphal instar, but not earlier or later in ontogeny. The observed patterns of genetic variation are discussed with reference to short-term constraints and the evolution of phenotypic plasticity.     

Phenotypic evolution in stochastic environments: The contribution of frequency- and density-dependent selection

Understanding how environmental variation affects phenotypic evolution requires models based on ecologically realistic assumptions that include variation in population size and specific mechanisms by which environmental fluctuations affect selection. Here we generalize quantitative genetic theory for environmentally induced stochastic selection to include general forms of frequency- and density-dependent selection. We show how the relevant fitness measure under stochastic selection relates to Fisher's fundamental theorem of natural selection, and present a general class of models in which density regulation acts through total use of resources rather than just population size. In this model, there is a constant adaptive topography for expected evolution, and the function maximized in the long run is the expected factor restricting population growth. This allows us to generalize several previous results and to explain why apparently “-selected” species with slow life histories often have low carrying capacities. Our joint analysis of density- and frequency-dependent selection reveals more clearly the relationship between population dynamics and phenotypic evolution, enabling a broader range of eco-evolutionary analyses of some of the most interesting problems in evolution in the face of environmental variation.     

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.     

Transposable elements, mutational correlations, and population divergence in Caenorhabditis elegans

Transposable element activity is thought to be responsible for a large portion of all mutations, but its influence on the evolution of populations has not been well studied. Using mutation accumulation experiments with the nematode Caenorhabditis elegans, we investigated the impact of transposable element activity on the production of mutational variances and covariances. The experiments involved the use of two mutator strains (RNAi-deficient mutants) that are characterized by high levels of germline transposition, as well as the Bristol N2 strain, which lacks germline transposition. We found that transposition led to an increase in mutational heritabilities, as well as to the intensification of correlation patterns observed in the absence of transposition. No mutational trade-offs were detected and mutations generally had a deleterious effect on components of fitness. We also tested whether the pattern of mutational covariation could be used to predict observed patterns of population divergence in this species. Using 15 natural populations, we found that population divergence of C. elegans in multivariate phenotypic space occurred in directions only partially concordant with mutation, and thus other evolutionary factors, such as natural selection and genetic drift, must be acting to produce divergence within this species. Our results suggest that mutations induced by mobile elements in C. elegans are similar to other spontaneous mutations with respect to their contribution to the microevolution of quantitative traits.     

Estimating sampling error of evolutionary statistics based on genetic covariance matrices using maximum likelihood

We explore the estimation of uncertainty in evolutionary parameters using a recently devised approach for resampling entire additive genetic variance–covariance matrices ( G ). Large‐sample theory shows that maximum‐likelihood estimates (including restricted maximum likelihood, REML) asymptotically have a multivariate normal distribution, with covariance matrix derived from the inverse of the information matrix, and mean equal to the estimated G . This suggests that sampling estimates of G from this distribution can be used to assess the variability of estimates of G , and of functions of G . We refer to this as the REML‐MVN method. This has been implemented in the mixed‐model program WOMBAT. Estimates of sampling variances from REML‐MVN were compared to those from the parametric bootstrap and from a Bayesian Markov chain Monte Carlo (MCMC) approach (implemented in the R package MCMCglmm). We apply each approach to evolvability statistics previously estimated for a large, 20‐dimensional data set for Drosophila wings. REML‐MVN and MCMC sampling variances are close to those estimated with the parametric bootstrap. Both slightly underestimate the error in the best‐estimated aspects of the G matrix. REML analysis supports the previous conclusion that the G matrix for this population is full rank. REML‐MVN is computationally very efficient, making it an attractive alternative to both data resampling and MCMC approaches to assessing confidence in parameters of evolutionary interest.     

Evolutionary rates for multivariate traits: the role of selection and genetic variation

A fundamental question in evolutionary biology is the relative importance of selection and genetic architecture in determining evolutionary rates. Adaptive evolution can be described by the multivariate breeders'' equation (), which predicts evolutionary change for a suite of phenotypic traits () as a product of directional selection acting on them (β) and the genetic variance–covariance matrix for those traits (G). Despite being empirically challenging to estimate, there are enough published estimates of G and β to allow for synthesis of general patterns across species. We use published estimates to test the hypotheses that there are systematic differences in the rate of evolution among trait types, and that these differences are, in part, due to genetic architecture. We find some evidence that sexually selected traits exhibit faster rates of evolution compared with life-history or morphological traits. This difference does not appear to be related to stronger selection on sexually selected traits. Using numerous proposed approaches to quantifying the shape, size and structure of G, we examine how these parameters relate to one another, and how they vary among taxonomic and trait groupings. Despite considerable variation, they do not explain the observed differences in evolutionary rates.     

Testing the phenotypic gambit: phenotypic, genetic and environmental correlations of colour

Evolutionary theory is primarily concerned with genetic processes, yet empirical testing of this theory often involves data collected on phenotypes. To make this tenable, the implicit assumption is often made that phenotypic patterns are good predictors of genetic patterns; an assumption that coined the phenotypic gambit. Although this assumption has been validated for traits with high heritability, such as morphology, its generality for traits with low heritabilities, such as life-history and behavioural traits, remains controversial. Using a large-scale cross-fostering experiment, we were able to measure genetic, common environmental and phenotypic correlations between four colour traits and two skeletal traits in a wild population of passerine birds, the blue tit (Parus caeruleus). Colour traits had little heritable variation but common environment effects were found to be important; skeletal traits showed the opposite pattern. Positive correlations because of a shared natal environment were found between all traits, obscuring negative genetic correlations between some colour and skeletal traits. Consequently, phenotypic patterns were poor surrogates for genetic patterns and we suggest that this may be common if trade-offs or substantial parental effects exist. For this group of traits, the phenotypic gambit cannot be made and we suggest caution when inferring genetic patterns from phenotypic data, especially for behavioural and life-history traits.     

The evolution of trade-offs: testing predictions on response to selection and environmental variation

The concept of phenotypic trade-offs is a central element in evolutionary theory. In general, phenotypic models assume a fixed trade-off function, whereas quantitative genetic theory predicts that the trade-off function will change as a result of selection. For a linear trade-off function selection will readily change the intercept but will have to be relatively stronger to change the slope. We test these predictions by examining the trade-off between fecundity and flight capability, as measured by dorso-longitudinal muscle mass, in four different populations of the sand cricket, Gryllus firmus. Three populations were recently derived from the wild, and the fourth had been in the laboratory for 19 years. We hypothesized that the laboratory population had most likely undergone more and different selection from the three wild populations and therefore should differ from these in respect to both slope and intercept. Because of geographic variation in selection, we predicted a general difference in intercept among the four populations. We further tested the hypothesis that this intercept will be correlated with proportion macropterous and that this relationship will itself vary with environmental conditions experienced during both the nymphal and adult period. Observed variation in the phenotypic trade-off was consistent with the predictions of the quantitative genetic model. These results point to the importance of modeling trade-offs as dynamic rather than static relationships. We discuss how phenotypic models can incorporate such variation. The phenotypic trade-off between fecundity and dorso-longitudinal muscle mass is determined in part by variation in body size, illustrating the necessity of considering trade-offs to be multi factorial rather than simply bivariate relationships.     

The effects of stress and sex on selection,genetic covariance,and the evolutionary response

The capacity of a population to adapt to selection (evolvability) depends on whether the structure of genetic variation permits the evolution of fitter trait combinations. Selection, genetic variance and genetic covariance can change under environmental stress, and males and females are not genetically independent, yet the combined effects of stress and dioecy on evolvability are not well understood. Here, we estimate selection, genetic (co)variance and evolvability in both sexes of Tribolium castaneum flour beetles under stressful and benign conditions, using a half‐sib breeding design. Although stress uncovered substantial latent heritability, stress also affected genetic covariance, such that evolvability remained low under stress. Sexual selection on males and natural selection on females favoured a similar phenotype, and there was positive intersex genetic covariance. Consequently, sexual selection on males augmented adaptation in females, and intralocus sexual conflict was weak or absent. This study highlights that increased heritability does not necessarily increase evolvability, suggests that selection can deplete genetic variance for multivariate trait combinations with strong effects on fitness, and tests the recent hypothesis that sexual conflict is weaker in stressful or novel 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.     

The effect of a population bottleneck on the evolution of genetic variance/covariance structure

It is well known that standard population genetic theory predicts decreased additive genetic variance (V(a) ) following a population bottleneck and that theoretical models including interallelic and intergenic interactions indicate such loss may be avoided. However, few empirical data from multicellular model systems are available, especially regarding variance/covariance (V/CV) relationships. Here, we compare the V/CV structure of seventeen traits related to body size and composition between control (60 mating pairs/generation) and bottlenecked (2 mating pairs/generation; average F = 0.39) strains of mice. Although results for individual traits vary considerably, multivariate analysis indicates that V(a) in the bottlenecked populations is greater than expected. Traits with patterns and amounts of epistasis predictive of enhanced V(a) also show the largest deviations from additive expectations. Finally, the correlation structure of weekly weights is not significantly different between control and experimental lines but correlations between necropsy traits do differ, especially those involving the heart, kidney and tail length.     

The G matrix under fluctuating correlational mutation and selection

Theoretical quantitative genetics provides a framework for reconstructing past selection and predicting future patterns of phenotypic differentiation. However, the usefulness of the equations of quantitative genetics for evolutionary inference relies on the evolutionary stability of the additive genetic variance-covariance matrix (G matrix). A fruitful new approach for exploring the evolutionary dynamics of G involves the use of individual-based computer simulations. Previous studies have focused on the evolution of the eigenstructure of G. An alternative approach employed in this paper uses the multivariate response-to-selection equation to evaluate the stability of G. In this approach, I measure similarity by the correlation between response-to-selection vectors due to random selection gradients. I analyze the dynamics of G under several conditions of correlational mutation and selection. As found in a previous study, the eigenstructure of G is stabilized by correlational mutation and selection. However, over broad conditions, instability of G did not result in a decreased consistency of the response to selection. I also analyze the stability of G when the correlation coefficients of correlational mutation and selection and the effective population size change through time. To my knowledge, no prior study has used computer simulations to investigate the stability of G when correlational mutation and selection fluctuate. Under these conditions, the eigenstructure of G is unstable under some simulation conditions. Different results are obtained if G matrix stability is assessed by eigenanalysis or by the response to random selection gradients. In this case, the response to selection is most consistent when certain aspects of the eigenstructure of G are least stable and vice versa.     

The genetics of phenotypic plasticity. VI. Theoretical predictions for directional selection

We explore the effects of linear and quadratic reaction norms on heritability and directional selection. Genetic variation for reaction norm parameters can alter the heritability of traits; the magnitude of the heritability depends upon both the environment and the correlation among the parameters. Genetic variation for reaction norm parameters can alter the response to directional selection. Selection on a trait in one environment can shift both the mean of the trait measured across environments and the plasticity of the trait; the signs and magnitudes of these responses depend on the correlations among the parameters of the reaction norm. Our model is consistent with the results of ten experiments for selection on a trait in a single environment. In all experiments, selection towards the overall mean of the population always resulted in a relatively lower plasticity than selection away from the overall mean. Our model was able to predict the results of two experiments for selection on a trait index calculated over more than one environment. Predictions were good for the direct response to selection but poorer for the correlated response to selection. Our results indicate the need for more data on the effects of environment on genetic parameters, especially correlations among reaction norm parameters.     

Understanding the evolution and stability of the G-matrix

The G-matrix summarizes the inheritance of multiple, phenotypic traits. The stability and evolution of this matrix are important issues because they affect our ability to predict how the phenotypic traits evolve by selection and drift. Despite the centrality of these issues, comparative, experimental, and analytical approaches to understanding the stability and evolution of the G-matrix have met with limited success. Nevertheless, empirical studies often find that certain structural features of the matrix are remarkably constant, suggesting that persistent selection regimes or other factors promote stability. On the theoretical side, no one has been able to derive equations that would relate stability of the G-matrix to selection regimes, population size, migration, or to the details of genetic architecture. Recent simulation studies of evolving G-matrices offer solutions to some of these problems, as well as a deeper, synthetic understanding of both the G-matrix and adaptive radiations.     

The beak of the other finch: coevolution of genetic covariance structure and developmental modularity during adaptive evolution

The link between adaptation and evolutionary change remains the most central and least understood evolutionary problem. Rapid evolution and diversification of avian beaks is a textbook example of such a link, yet the mechanisms that enable beak''s precise adaptation and extensive adaptability are poorly understood. Often observed rapid evolutionary change in beaks is particularly puzzling in light of the neo-Darwinian model that necessitates coordinated changes in developmentally distinct precursors and correspondence between functional and genetic modularity, which should preclude evolutionary diversification. I show that during first 19 generations after colonization of a novel environment, house finches (Carpodacus mexicanus) express an array of distinct, but adaptively equivalent beak morphologies—a result of compensatory developmental interactions between beak length and width in accommodating microevolutionary change in beak depth. Directional selection was largely confined to the elimination of extremes formed by these developmental interactions, while long-term stabilizing selection along a single axis—beak depth—was mirrored in the structure of beak''s additive genetic covariance. These results emphasize three principal points. First, additive genetic covariance structure may represent a historical record of the most recurrent developmental and functional interactions. Second, adaptive equivalence of beak configurations shields genetic and developmental variation in individual components from depletion by natural selection. Third, compensatory developmental interactions among beak components can generate rapid reorganization of beak morphology under novel conditions and thus greatly facilitate both the evolution of precise adaptation and extensive diversification, thereby linking adaptation and adaptability in this classic example of Darwinian evolution.     

Nonlinear selection and the evolution of variances and covariances for continuous characters in an anole

The pattern of genetic variances and covariances among characters, summarized in the additive genetic variance‐covariance matrix, G , determines how a population will respond to linear natural selection. However, G itself also evolves in response to selection. In particular, we expect that, over time, G will evolve correspondence with the pattern of multivariate nonlinear natural selection. In this study, we substitute the phenotypic variance‐covariance matrix ( P ) for G to determine if the pattern of multivariate nonlinear selection in a natural population of Anolis cristatellus, an arboreal lizard from Puerto Rico, has influenced the evolution of genetic variances and covariances in this species. Although results varied among our estimates of P and fitness, and among our analytic techniques, we find significant evidence for congruence between nonlinear selection and P , suggesting that natural selection may have influenced the evolution of genetic constraint in this species.     

The search for Pleiades in trait constellations: functional integration and phenotypic selection in the complex flowers of Morrenia brachystephana (Apocynaceae)

Pollinator‐mediated natural selection on single traits, such as corolla tube or spur length, has been well documented. However, flower phenotypes are usually complex, and selection is expected to act on several traits that functionally interact rather than on a single isolated trait. Despite the fact that selection on complex phenotypes is expectedly widespread, multivariate selection modelling on such phenotypes still remains under‐explored in plants. Species of the subfamily Asclepiadoideae (Apocynaceae) provide an opportunity to study such complex flower contrivances integrated by fine‐scaled organs from disparate developmental origin. We studied the correlation structure among linear floral traits (i) by testing a priori morphological, functional or developmental hypotheses among traits and (ii) by exploring the organization of flower covariation, considering alternative expectations of modular organization or whole flower integration through conditional dependence analysis (CDA) and integration matrices. The phenotypic selection approach was applied to determine whether floral traits involved in the functioning of the pollination mechanism were affected by natural selection. Floral integration was low, suggesting that flowers are organized in more than just one correlation pleiad; our hypothetical functional correlation matrix was significantly correlated with the empirical matrix, and the CDA revealed three putative modules. Analyses of phenotypic selection showed significant linear and correlational gradients, lending support to expectations of functional interactions between floral traits. Significant correlational selection gradients found involved traits of different floral whorls, providing evidence for the existence of functional integration across developmental domains.