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.     

The evolution of sexual dimorphism in the house finch. I. Population divergence in morphological covariance structure

Abstract Patterns of genetic variation and covariation strongly affect the rate and direction of evolutionary change by limiting the amount and form of genetic variation available to natural selection. We studied evolution of morphological variance-covariance structure among seven populations of house finches (Carpodacus mexicanus) with a known phylogenetic history. We examined the relationship between within- and among-population covariance structure and, in particular, tested the concordance between hierarchical changes in morphological variance-covariance structure and phylogenetic history of this species. We found that among-population morphological divergence in either males or females did not follow the within-population covariance patterns. Hierarchical patterns of similarity in morphological covariance matrices were not congruent with a priori defined historical pattern of population divergence. Both of these results point to the lack of proportionality in morphological covariance structure of finch populations, suggesting that random drift alone is unlikely to account for observed divergence. Furthermore, drift alone cannot explain the sex differences in within- and among-population covariance patterns or sex-specific patterns of evolution of covariance structure. Our results suggest that extensive among-population variation in sexual dimorphism in morphological covariance structure was produced by population differences in local selection pressures acting on each sex.     

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.     

HOW SIMILAR ARE GENETIC CORRELATION STRUCTURES? DATA FROM MICE AND RATS

An integral assumption of many models of morphometric evolution is the equality of the genetic variance-covariance structure across evolutionary time. To examine this assumption, the quantitative-genetic aspects of morphometric form are examined for eight pelvic traits in laboratory rats (Rattus norvegicus) and random-bred ICR mice (Mus musculus). In both species, all traits are significantly heritable, and there are significant phenotypic and genetic correlations among traits, although environmental correlations among the eight traits are low. The size relations among the pelvic variables are isometric. Three matrix-permutation tests are used to examine similarity of phenotypic, genetic, and environmental covariance and correlation matrices within and between species. Independent patterns of morphometric covariation and correlation arise from genetic and environmental effects within each species and from environmental effects between species. The patterns of phenotypic and genetic covariation and correlation are similar within each species, and the phenotypic and genetic correlations are also similar between these species. However, genetic covariance matrices show no significant statistical association between species. It is suggested that the assumption of equality of genetic variance-covariance structures across divergent taxa should be approached with caution.     

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.     

Patterns of genotypic variation and phenotypic plasticity of light response in two tropical Piper (Piperaceae) species

Patterns of phenotypic plasticity and genotypic variation in light response of growth and photosynthesis were examined in two species of rain forest shrub that differ in ecological distribution within the forest. We further examined correlations among photosynthetic and growth traits. We hypothesized that the pioneer species, Piper sancti-felicis, would display greater phenotypic plasticity than the shade-tolerant species, Piper arieianum. We further proposed that, in both species, genotypic effects would be more apparent in growth-related traits than photosynthetic traits due to more concentrated selection pressure on gas-exchange traits. P. sancti-felicis did not demonstrate greater phenotypic plasticity of light response. Although many of the traits measured had significant genotype effects, neither species showed any significant effects of genotype on light response of photosynthesis, suggesting little genetic variation for this trait within populations. A principal components analysis clearly illustrated both species and light effects, with the treatments dividing neatly along the axis of the first principal component and the species separating along the second principal component axis. Results indicated general similarities between the species in their trait correlation structure and level of integration among traits, but characteristic differences were observed in the patterns of change between low and high light. Both species had more correlations than expected within groups of growth-related or photosynthetic traits; strong correlations of traits between these two groups were underrepresented. The similar pattern of genetic variation and phenotypic integration observed in these two congeners may be due more to their close phylogenetic relation than to their ecological distributions.     

The adaptive value of phenotypic floral integration

Floral integration has been deemed an adaptation to increase the benefits of animal pollination, yet no attempts have been made to estimate its adaptive value under natural conditions. Here, the variation in the magnitude and pattern of phenotypic floral integration and the variance-covariance structure of floral traits in four species of Rosaceae were examined. The intensity of natural selection acting on floral phenotypic integration was also estimated and the available evidence regarding the magnitude of floral integration reviewed. The species studied had similar degrees of floral integration, although significant differences were observed in their variance-covariance structure. Selection acted on subsets of floral traits (i.e. selection on intrafloral integration) rather than on the integration of the whole flower. Average integration was 20% and similar to the estimated mean value of flowering plants. The review indicated that flowering plants present lower integration than expected by chance. Numerical simulations suggest that this pattern may result from selection favouring intrafloral integration. Phenotypic integration at the flower level seems to have a low adaptive value among the species surveyed. Moreover, it is proposed that pollinator-mediated selection promotes the evolution of intrafloral integration.     

Convergent evolution of phenotypic integration and its alignment with morphological diversification in Caribbean Anolis ecomorphs

The adaptive landscape and the G-matrix are keys concepts for understanding how quantitative characters evolve during adaptive radiation. In particular, whether the adaptive landscape can drive convergence of phenotypic integration (i.e., the pattern of phenotypic variation and covariation summarized in the P-matrix) is not well studied. We estimated and compared P for 19 morphological traits in eight species of Caribbean Anolis lizards, finding that similarity in P among species was not correlated with phylogenetic distance. However, greater similarity in P among ecologically similar Anolis species (i.e., the trunk-ground ecomorph) suggests the role of convergent natural selection. Despite this convergence and relatively deep phylogenetic divergence, a large portion of eigenstructure of P is retained among our eight focal species. We also analyzed P as an approximation of G to test for correspondence with the pattern of phenotypic divergence in 21 Caribbean Anolis species. These patterns of covariation were coincident, suggesting that either genetic constraint has influenced the pattern of among-species divergence or, alternatively, that the adaptive landscape has influenced both G and the pattern of phenotypic divergence among species. We provide evidence for convergent evolution of phenotypic integration for one class of Anolis ecomorph, revealing yet another important dimension of evolutionary convergence in this group.     

Variation in growth in the blue tit (Parus caeruleus)

The pattern and amount of phenotypic and genetic variation in growth was analysed using the infinite-dimensional model in natural populations of the blue tit (Parus caeruleus). A size-index was used to analyse patterns of variation and covariation across ages (2, 5, 8, 11 and 14 days). Genetic variation was analysed using mother-, father-, and midparent-offspring regressions in the blue tit. Phenotypic variation in growth was limited to a few dimensions only, while heritabilities were close to zero at all ages except at 2 days when a significant mother-offspring relation was found. The phenotypic variance-covariance matrix over ages was found to be singular, which suggests that there are trajectories for which there is no phenotypic variation, and which therefore they cannot evolve. The phenotypic growth trajectory associated with the largest amount of variation basically showed a high to moderately high covariation across ages. These results have macroevolutionary implications in terms of the outcome of selection which generally will be in terms of overall size changes but with a slow rate of change due to low heritabilities; an outcome consistent with macro-evolutionary patterns of morphological variation in birds. A simulation study supported the conclusion that high covariances among traits and ages can impose considerable constraint on a microevolutionary scale.     

Phenotypic integration and conserved covariance structure in calopterygid damselflies

By comparing the phenotypic (P) variance-covariance matrices between closely related taxa or conspecific populations, one can study the outcome of the interplay between selection and developmental constraints in phenotypic evolution. Shared patterns of phenotypic integration are also of interest and might result from similarities in either selection or developmental pathways. We compared P-matrices and phenotypic integration indices between populations and species of the damselfly genus Calopteryx. P(max)-comparisons between parapatric C. splendens populations revealed stronger conserved phenotypic covariance structure than P(max)-comparisons between species, suggesting that divergence in its early stages proceeds along phenotypic lines of least resistance. Within- and among-population correlations in C. splendens were highly concordant, in further support of initial divergence along P(max). Despite some similarities in overall phenotypic integration between C. splendens and C. virgo, these two species only had several P-matrix eigenvectors in common, indicating that after reproductive isolation, divergence has proceeded against P(max).     

VARIATION IN GENETIC ARCHITECTURE OF CALLING SONG AMONG POPULATIONS OF ALLONEMOBIUS SOCIUS,A. FASCIATUS,AND A HYBRID POPULATION: DRIFT OR SELECTION?

Predictions using quantitative genetic models generally assume that the variance-covariance matrices remain constant over time. This assumption is based on the supposition that selection is generally weak and hence variation lost through selection can be replaced by new mutations. Whether this is generally true can only be ascertained from empirical studies. Ideally for such a study we should be able to make a prediction concerning the relative strength of selection versus genetic drift. If the latter force is prevalent then the variance-covariances matrices should be proportional to each other. Previous studies have indicated that females in the two sibling cricket species Allonemobius socius and A. fasciatus do not discriminate between males of the two species by their calling song. Therefore, differences between the calling song of the two males most likely result from drift rather than sexual selection. We test this hypothesis by comparing the genetic architecture of calling song of three populations of A. fasciatus with two populations of A. socius. We found no differences among populations within species, but significant differences in the G (genetic) and P (phenotypic) matrices between species, with the matrices being proportional as predicted under the hypothesis of genetic drift. Because of the proportional change in the (co)variances no differences between species are evident in the heritabilities or genetic correlations. Comparison of the two species with a hybrid population from a zone of overlap showed highly significant nonproportional variation in genetic architecture. This variation is consistent with a general mixture of two separate genomes or selection. Qualitative conclusions reached using the phenotypic matrices are the same as those reached using the genetic matrices supporting the hypothesis that the former may be used as surrogate measures of the latter.     

Evolutionary transition between bee pollination and hummingbird pollination in Salvia: Comparing means,variances and covariances of corolla traits

Covariation among traits can modify the evolutionary trajectory of complex structures. This process is thought to operate at a microevolutionary scale, but its long‐term effects remain controversial because trait covariation can itself evolve. Flower morphology, and particularly floral trait (co)variation, has been envisioned as the product of pollinator‐mediated selection. Available evidence suggests that major changes in pollinator assemblages may affect the joint expression of floral traits and their phenotypic integration. We expect species within a monophyletic lineage sharing the same pollinator type will show not only similarity in trait means but also similar phenotypic variance‐covariance structures. Here, we tested this expectation using eighteen Salvia species pollinated either by bees or by hummingbirds. Our findings indicated a nonsignificant multivariate phylogenetic signal and a decoupling between means and variance‐covariance phenotypic matrices of floral traits during the evolution to hummingbird pollination. Mean trait value analyses revealed significant differences between bee‐ and hummingbird‐pollinated Salvia species although fewer differences were detected in the covariance structure between groups. Variance‐covariance matrices were much more similar among bee‐ than hummingbird‐pollinated species. This pattern is consistent with the expectation that, unlike hummingbirds, bees physically manipulate the flower, presumably exerting stronger selection pressures favouring morphological convergence among species. Overall, we conclude that the evolution of hummingbird pollination proceeded through different independent transitions. Thus, although the evolution of hummingbird pollination led to a new phenotypic optimum, the process involved the diversification of the covariance structure.     

Phenotypic selection and covariation in the life‐history traits of elephant seals: heavier offspring gain a double selective advantage

Early developmental conditions contribute to individual heterogeneity of both phenotypic traits and fitness components, ultimately affecting population dynamics. Although the demographic consequences of ontogenic growth are best quantified using an integrated measure of fitness, most analyses to date have instead studied individual fitness components in isolation. Here, we estimated phenotypic selection on weaning mass in female southern elephant seals Mirounga leonina by analyzing individual‐based data collected between 1986 and 2016 with capture–recapture and matrix projection models. In support of a hypothesis predicting a gradual decrease of weaning mass effects with time since weaning (the replacement hypothesis), we found that the estimated effects of weaning mass on future survival and recruitment probability was of intermediate duration (rather than transient or permanent). Heavier female offspring had improved odds of survival in early life and a higher probability to recruit at an early age. The positive link between weaning mass and recruitment age is noteworthy, considering that pre‐recruitment mortality already imposed a strong selective filter on the population, leaving only the most ‘robust’ individuals to reproduce. The selection gradient on asymptotic population growth rate, a measure of mean absolute fitness, was weaker than selection on first‐year survival and recruitment probabilities. Weaker selection on mean fitness occurs because weaning mass has little impact on adult survival, the fitness component to which the population growth of long‐lived species is most sensitive. These results highlight the need to interpret individual variation in phenotypic traits in a context that considers the demographic pathways between the trait and an inclusive proxy of individual fitness. Although variation in weaning mass do not translate to permanent survival differences among individuals in adulthood, it explains heterogeneity and positive covariation between survival and breeding in early life, which contribute to between‐individual variation in fitness.     

Phenotypic covariance structure in tamarins (genus Saguinus): a comparison of variation patterns using matrix correlation and common principal component analysis

Constancy of variation/covariation structure among populations is frequently assumed in order to measure the differential selective forces which have caused population differentiation through evolutionary time. Following Steppan ([1997] Evolution 51:571-594), this assumption is examined among closely related tamarin species (genus Saguinus), using two distinct approaches applied to the task of evaluating similarity in patterns of morphological variation: common principal component analysis and matrix correlations. While the results of these analyses may appear contradictory, closer examination reveals them as complementary, highlighting the wisdom of combined methodologies. Overall, the results reveal a close relationship among the morphologically based variance structures of the tamarin species a relationship whose pattern is consistent with the pattern of phylogenetic relatedness as found via a molecular genetic study. More specifically, both methodological approaches provide some support for divergence of S. geoffroyi and S. oedipus (with regards to their patterns of morphological variation) from other tamarin species. This suggests that variance/covariance structure may have diverged through evolutionary time in the tamarin lineage, placing assumptions of constancy in doubt.     

Genetic and phenotypic correlations in a natural population of song sparrows

We estimated heritabilities, and genetic and phenotypic correlations between beak and body traits in the song sparrow ( Melospiza melodia ). We compared these estimates to values for the same traits in the Galápagos finches, Geospiza (Boag, 1983; Grant, 1983). Morphological variance is low in the song sparrow, and our results show that genetic and phenotypic correlations are considerably lower than correlations in the morphologically more variable Geospiza. Comparison using a larger sample of Galapagos populations confirms the existence of an association between variance and correlation for phenotypic values. We suggest two possible explanations for this association. First, most traits studied are functionally related, and the joint evolution of variance and correlation may have resulted from stabilizing selection about a line of optimal allometry between traits. Alternatively, introgression between populations and species could have caused correlation and variance to evolve jointly. Both selection and introgression were probably influential in producing the observed pattern, but it is not possible to estimate their relative importance with current data. Genetic and phenotypic correlations were correlated in the song sparrow, but heritabilities of traits varied greatly. As a result, the genetic variance-covariance matrix for traits is not simply a constant multiple of the phenotypic matrix. Evolutionary response to natural selection cannot, therefore, be predicted from the measurement of phenotypic characteristics alone.     

THE COVARIANCE STRUCTURE OF LIFE-HISTORY CHARACTERS IN DAPHNIA PULEX

The genetic covariance structure for life-history characters in two populations of cyclically parthenogenetic Daphnia pulex indicates considerable positive correlation among important fitness components, apparently at odds with the expectation if antagonistic pleiotropy is the dominant cause of the maintanence of genetic variation. Although there is no genetic correlation between offspring size and offspring number, present growth and present reproduction are both strongly positively correlated genetically with future reproduction, and early maturity is genetically correlated with larger clutch size. Although the ubiquity of antagonistic pleiotropy has been recently questioned, there are peculiarities of cyclical parthenogenesis that could lead to positive life-history covariance even when negative covariance would be expected in a similar sexual species. These include the influence of nonadditive gene action on evolution in clonally reproducing organisms, and the periodic release of hidden genetic variance within populations of cyclical parthenogens. Examination of matrix similarity, using the bootstrap for distribution-free hypothesis testing, reveals no evidence to suggest that the genetic covariance matrices differ between the populations. However, there is considerable evidence that the phenotypic and environmental covariance matrices differ between populations. These results indicate approximate stability of the genetic covariance matrix within species, an important assumption of many phenotypic evolution models, but should caution against the use of phenotypic in place of genetic covariance matrices.     

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.     

QUANTITATIVE GENETICS OF THE WING COLOR PATTERN IN THE BUCKEYE BUTTERFLY (PRECIS COENIA AND PRECIS EVARETE): EVIDENCE AGAINST THE CONSTANCY OF G

Models for the evolution of continuously varying traits use heritabilities, genetic correlations, and the G -matrix to quantify the genetic variation upon which selection acts. Given estimates of these parameters, it is possible to predict the long-term effects of selection, infer past selective forces responsible for observed differences between populations or species, and distinguish the effects of drift from selection. Application of these methods, however, requires the unproven assumption that the G -matrix remains constant from one generation to the next. This study examines the assumption of constancy for the wing pattern characteristics of two sibling species of butterflies, Precis coenia and P. evarete (Lepidoptera: Nymphalidae). Quantitative genetic parameters were estimated from parent-offspring regression. Two approaches were taken to test the null hypothesis of equality between species. First, pairwise tests between corresponding elements of G and between heritabilities and genetic correlations for the two species were constructed. Second, a modification of Bartlett's modified likelihood-ratio test was used to test for equality between the G -matrices. The matrix test failed to detect any between species differences. In contrast, pairwise comparision revealed significant differences. Thus, it appears that constancy cannot be assumed at the species level in quantitative genetic studies. In particular, the assumption of constancy was violated for the trait with the greatest difference in mean phenotype.     

Environmental variation and quantitative genetic prameters in the feral pigeon, Columba livia

The estimation of quantitative genetic parameters and modes of selection in natural populations can provide critical information concerning both past and current evolution of mean phenotypes. We examine the influence of environmental variation on the genetic variance-covariance matrix ( G ) of external morphological traits in feral pigeons, and the degree of correspondence between phenotypic (r_p) and genetic correlations (r_g) of these characters. Our results suggest that adverse environmental conditions affect heritability, and that the correspondence between seasonal estimates of G based on midparent scores is low. There is, however, a strong correspondence between r_p and r_g. We suggest that, if environmental variation is relatively common, estimates of quantitative genetic parameters for prospective selection studies must be undertaken at each selection episode.     

Phenotypic variability and heritability of the cephalic region of Caiman latirostris

The study of the cephalic shape of crocodilian is relevant in the fields of ecology, systematics, evolution, and conservation. Therefore, the integration of geometric analysis within quantitative genetics allows the evaluation of the inheritable shape components. In this study, the dorsal cephalic region of 210 Caiman latirostris hatchlings was analyzed from seven populations in Santa Fe, Argentina, to detect intra‐, and inter‐population phenotypic variability, and to determine the heritability of biological shape and size, using newly available geometric morphometric tools. The principal component analysis showed two configurations of cephalic shape that could be related to sexual dimorphism. In the canonical variate analysis, Procrustes distances between groups indicated that there are differences in shape among populations. Furthermore, the method of partial least squares indicated a covariation between cephalic shape and environmental variables. Regarding to CS of the skull we found significant differences among populations, moreover the partial least squares was also significant. Estimates of the heritability of shape and size were high, indicating that the components of these features are susceptible to the selection. J. Morphol. 277:370–378, 2016. © 2015 Wiley Periodicals, Inc.