PHYLOGENETIC ANALYSIS OF PHENOTYPIC COVARIANCE STRUCTURE. II. RECONSTRUCTING MATRIX EVOLUTION

HIERARCHICAL COMPARISON OF GENETIC VARIANCE-COVARIANCE MATRICES. II COASTAL-INLAND DIVERGENCE IN THE GARTER SNAKE, THAMNOPHIS ELEGANS

The time-scale for the evolution of additive genetic variance-covariance matrices (G-matrices) is a crucial issue in evolutionary biology. If the evolution of G-matrices is slow enough, we can use standard multivariate equations to model drift and selection response on evolutionary time scales. We compared the G-matrices for meristic traits in two populations of gaiter snakes (Thamnophis elegans) with an apparent separation time of 2 million years. Despite considerable divergence in the meristic traits, foraging habits, and diet, these populations show conservation of structure in their G-matrices. Using Flury's hierarchial approach to matrix comparisons, we found that the populations have retained the principal components (eigenvectors) of their G-matrices, but their eigenvalues have diverged. In contrast, we were unable to reject the hypothesis of equal environmental matrices (E-matrices) for these populations. We propose that a conserved pattern of multivariate stabilizing selection may have contributed to conservation of G- and E-matrix structure during the divergence of these populations.

Neopolyploidy and diversification in Heuchera grossulariifolia

Newly formed polyploid lineages must contend with several obstacles to avoid extinction, including minority cytotype exclusion, competition, and inbreeding depression. If polyploidization results in immediate divergence of phenotypic characters these hurdles may be reduced and establishment made more likely. In addition, if polyploidization alters the phenotypic and genotypic associations between traits, that is, the P and G matrices, polyploids may be able to explore novel evolutionary paths, facilitating their divergence and successful establishment. Here, we report results from a study of the perennial plant Heuchera grossulariifolia in which the phenotypic divergence and changes in phenotypic and genotypic covariance matrices caused by neopolyploidization have been estimated. Our results reveal that polyploidization causes immediate divergence for traits relevant to establishment and results in significant changes in the structure of the phenotypic covariance matrix. In contrast, our results do not provide evidence that polyploidization results in immediate and substantial shifts in the genetic covariance matrix.

Diversity trends and their ontogenetic basis: an exploration of allometric disparity in rodents

It has been hypothesized that most morphological evolution occurs by allometric differentiation. Because rodents encapsulate a phenomenal amount of taxonomic diversity and, among several clades, contrasting levels of morphological diversity, they represent an excellent subject to address the question: how variable are allometric patterns during evolution? We investigated the influence of phylogenetic relations and ecological factors on the results of the first quantification of allometric disparity among rodents by exploring allometric space, a multivariate morphospace here derived from, and encapsulating all, the ontogenetic trajectories of 34 rodent species from two parallel phylogenetic radiations. Disparity was quantified using angles between ontogenetic trajectories for different species and clades. We found an overlapping occupation of allometric space by muroid and hystricognath species, revealing both clades possess similar abilities to evolve in different directions of phenotypic space, and anatomical diversity does not act to constrain the labile nature of allometric patterning. Morphological features to enable efficient processing of food serve to group rodents in allometric space, reflecting the importance of convergent morphology, rather than shared evolutionary history, in the generation of allometric patterns. Our results indicate that the conserved level of morphological integration found among primates cannot simply be extended to all mammals.

Morphological diversity and the roles of contingency, chance and determinism in african cichlid radiations

Background

Deterministic evolution, phylogenetic contingency and evolutionary chance each can influence patterns of morphological diversification during adaptive radiation. In comparative studies of replicate radiations, convergence in a common morphospace implicates determinism, whereas non-convergence suggests the importance of contingency or chance.

Methodology/Principal Findings

The endemic cichlid fish assemblages of the three African great lakes have evolved similar sets of ecomorphs but show evidence of non-convergence when compared in a common morphospace, suggesting the importance of contingency and/or chance. We then analyzed the morphological diversity of each assemblage independently and compared their axes of diversification in the unconstrained global morphospace. We find that despite differences in phylogenetic composition, invasion history, and ecological setting, the three assemblages are diversifying along parallel axes through morphospace and have nearly identical variance-covariance structures among morphological elements.

Conclusions/Significance

By demonstrating that replicate adaptive radiations are diverging along parallel axes, we have shown that non-convergence in the common morphospace is associated with convergence in the global morphospace. Applying these complimentary analyses to future comparative studies will improve our understanding of the relationship between morphological convergence and non-convergence, and the roles of contingency, chance and determinism in driving morphological diversification.

A comparison of covariance structure in wild and laboratory muroid crania

Mutations have the ability to produce dramatic changes to covariance structure by altering the variance of covariance-generating developmental processes. Several evolutionary mechanisms exist that may be acting interdependently to stabilize covariance structure, despite this developmental potential for variation within species. We explore covariance structure in the crania of laboratory mouse mutants exhibiting mild-to-significant developmental perturbations of the cranium, and contrast it with covariance structure in related wild muroid taxa. Phenotypic covariance structure is conserved among wild muroidea, but highly variable and mutation-dependent within the laboratory group. We show that covariance structures in natural populations of related species occupy a more restricted portion of covariance structure space than do the covariance structures resulting from single mutations of significant effect or the almost nonexistent genetic differences that separate inbred mouse strains. Our results suggest that developmental constraint is not the primary mechanism acting to stabilize covariance structure, and imply a more important role for other mechanisms.

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.

Phylogeny, diet, and cranial integration in australodelphian marsupials

Studies of morphological integration provide valuable information on the correlated evolution of traits and its relationship to long-term patterns of morphological evolution. Thus far, studies of morphological integration in mammals have focused on placentals and have demonstrated that similarity in integration is broadly correlated with phylogenetic distance and dietary similarity. Detailed studies have also demonstrated a significant correlation between developmental relationships among structures and adult morphological integration. However, these studies have not yet been applied to marsupial taxa, which differ greatly from placentals in reproductive strategy and cranial development and could provide the diversity necessary to assess the relationships among phylogeny, ecology, development, and cranial integration. This study presents analyses of morphological integration in 20 species of australodelphian marsupials, and shows that phylogeny is significantly correlated with similarity of morphological integration in most clades. Size-related correlations have a significant affect on results, particularly in Peramelia, which shows a striking decrease in similarity of integration among species when size is removed. Diet is not significantly correlated with similarity of integration in any marsupial clade. These results show that marsupials differ markedly from placental mammals in the relationships of cranial integration, phylogeny, and diet, which may be related to the accelerated development of the masticatory apparatus in marsupials.

Shared quantitative trait loci underlying the genetic correlation between continuous traits

We review genetic correlations among quantitative traits in light of their underlying quantitative trait loci (QTL). We derive an expectation of genetic correlation from the effects of underlying loci and test whether published genetic correlations can be explained by the QTL underlying the traits. While genetically correlated traits shared more QTL (33%) on average than uncorrelated traits (11%), the actual number of shared QTL shared was small. QTL usually predicted the sign of the correlation with good accuracy, but the quantitative prediction was poor. Approximately 25% of trait pairs in the data set had at least one QTL with antagonistic effects. Yet a significant minority (20%) of such trait pairs have net positive genetic correlations due to such antagonistic QTL 'hidden' within positive genetic correlations. We review the evidence on whether shared QTL represent single pleiotropic loci or closely linked monotropic genes, and argue that strict pleiotropy can be viewed as one end of a continuum of recombination rates where r=0. QTL studies of genetic correlation will likely be insufficient to predict evolutionary trajectories over long time spans in large panmictic populations, but will provide important insights into the trade-offs involved in population and species divergence.

Conspecific density determines the magnitude and character of predator-induced phenotype

The benefits in survival gained from predator-induced phenotypes often come at a cost to other components of fitness. Therefore, the level of expression of an induced phenotype should mirror the level of risk in the environment. When a predator exhibits a saturating functional response the risk of mortality to a given prey decreases as prey density increases. Therefore, for a given predator threat, investment in defense should be lower in prey at high density relative to those at low density. In this study, I test whether the magnitude of predator-induced morphological plasticity decreases with increasing conspecific density by exposing pine woods tree frog (Hyla femoralis) tadpoles at three different densities to predators (present or absent) in a factorial experiment. Tadpole morphology was not affected by changes in density in the absence of predators. However, predators had a significant, density-dependent effect on tadpole morphology. Specifically, the magnitude of morphological response was graded and larger for animals in the low density (high risk) environment. This study demonstrates that tadpoles can modulate phenotypic plasticity in response to mortality risk as a function of both the density of conspecifics and chemical cues from predators, which suggests that they are able to detect and respond to fine-scale changes in the threat environment. In addition, this study highlights the need for analytical approaches that allow morphological plasticity studies to elucidate allometric relationships in addition to simply quantifying size-corrected traits.

Cranial Modularity Shifts during Mammalian Evolution

The mammalian skull has been studied as several separate functional components for decades, but the study of modularity is a more recent, integrative approach toward quantitative examination of independent subsets of highly correlated traits, or modules. Although most studies of modularity focus on developmental and genetic systems, phenotypic modules have been noted in many diverse morphological structures. However, few studies have provided empirical data for comparing modules across higher taxonomic levels, limiting the ability to assess the broader evolutionary significance of modularity. This study uses 18-32 three-dimensional cranial landmarks to analyze phenotypic modularity in 106 mammalian species and demonstrates that cranial modularity is generally conserved in the evolution of therian mammals (marsupials and placentals) but differs between therians and monotremes, the two extant subclasses of Mammalia. Within therians, cluster analyses identify six distinct modules, but only three modules display significant integration in all species. Monotremes display only two highly integrated modules. Specific hypotheses of functional and developmental influences on cranial bones were tested. Theoretical correlation matrices for bones were constructed on the basis of shared function, tissue origin, or mode of ossification, and all three of these models are significantly correlated with observed correlation matrices for the mammalian cranium.

Size correction: comparing morphological traits among populations and environments

Morphological relationships change with overall body size and body size often varies among populations. Therefore, quantitative analyses of individual traits from organisms in different populations or environments (e.g., in studies of phenotypic plasticity) often adjust for differences in body size to isolate changes in allometry. Most studies of among population variation in morphology either (1) use analysis of covariance (ANCOVA) with a univariate measure of body size as the covariate, or (2) compare residuals from ordinary least squares regression of each trait against body size or the first principal component of the pooled data (shearing). However, both approaches are problematic. ANCOVA depends on assumptions (small variance in the covariate) that are frequently violated in this context. Residuals analysis assumes that scaling relationships within groups are equal, but this assumption is rarely tested. Furthermore, scaling relationships obtained from pooled data typically mischaracterize within-group scaling relationships. We discuss potential biases imposed by the application of ANCOVA and residuals analysis for quantifying morphological differences, and elaborate and demonstrate a more effective alternative: common principal components analysis combined with Burnaby's back-projection method.

Developmental regulation of skull morphology II: ontogenetic dynamics of covariance

Canalization may play a critical role in molding patterns of integration when variability is regulated by the balance between processes that generate and remove variation. Under these conditions, the interaction among those processes may produce a dynamic structure of integration even when the level of variability is constant. To determine whether the constancy of variance in skull shape throughout most of postnatal growth results from a balance between processes generating and removing variation, we compare covariance structures from age to age in two rodent species, cotton rats (Sigmodon fulviventer) and house mice (Mus musculus domesticus). We assess the overall similarity of covariance matrices by the matrix correlation, and compare the structures of covariance matrices using common subspace analysis, a method related to common principal components (PCs) analysis but suited to cases in which variation is so nearly spherical that PCs are ambiguous. We find significant differences from age to age in covariance structure and the more effectively canalized ones tend to be least stable in covariance structure. We find no evidence that canalization gradually and preferentially removes deviations arising early in development as we might expect if canalization results from compensatory differential growth. Our results suggest that (co)variation patterns are continually restructured by processes that equilibrate variance, and thus that canalization plays a critical role in molding patterns of integration.

Interspecific analysis of covariance structure in the masticatory apparatus of galagos

The primate masticatory apparatus (MA) is a functionally integrated set of features, each of which performs important functions in biting, ingestive, and chewing behaviors. A comparison of morphological covariance structure among species for these MA features will help us to further understand the evolutionary history of this region. In this exploratory analysis, the covariance structure of the MA is compared across seven galago species to investigate 1) whether there are differences in covariance structure in this region, and 2) if so, how has this covariation changed with respect to size, MA form, diet, and/or phylogeny? Ten measurements of the MA functionally related to bite force production and load resistance were obtained from 218 adults of seven galago species. Correlation matrices were generated for these 10 dimensions and compared among species via matrix correlations and Mantel tests. Subsequently, pairwise covariance disparity in the MA was estimated as a measure of difference in covariance structure between species. Covariance disparity estimates were correlated with pairwise distances related to differences in body size, MA size and shape, genetic distance (based on cytochrome-b sequences) and percentage of dietary foods to determine whether one or more of these factors is linked to differences in covariance structure. Galagos differ in MA covariance structure. Body size appears to be a major factor correlated with differences in covariance structure among galagos. The largest galago species, Otolemur crassicaudatus, exhibits large differences in body mass and covariance structure relative to other galagos, and thus plays a primary role in creating this association. MA size and shape do not correlate with covariance structure when body mass is held constant. Diet also shows no association. Genetic distance is significantly negatively correlated with covariance disparity when body mass is held constant, but this correlation appears to be a function of the small body size and large genetic distance for Galagoides demidoff. These exploratory results indicate that changing body size may have been a key factor in the evolution of the galago MA.

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.

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.

Comparing G Matrices: Are Common Principal Components Informative?

Common principal components (CPC) analysis is a technique for assessing whether variance-covariance matrices from different populations have similar structure. One potential application is to compare additive genetic variance-covariance matrices, G. In this article, the conditions under which G matrices are expected to have common PCs are derived for a two-locus, two-allele model and the model of constrained pleiotropy. The theory demonstrates that whether G matrices are expected to have common PCs is largely determined by whether pleiotropic effects have a modular organization. If two (or more) populations have modules and these modules have the same direction, the G matrices have a common PC, regardless of allele frequencies. In the absence of modules, common PCs exist only for very restricted combinations of allele frequencies. Together, these two results imply that, when populations are evolving, common PCs are expected only when the populations have modules in common. These results have two implications: (1) In general, G matrices will not have common PCs, and (2) when they do, these PCs indicate common modular organization. The interpretation of common PCs identified for estimates of G matrices is discussed in light of these results.

Interpretation of the results of common principal components analyses

Common principal components (CPC) analysis is a new tool for the comparison of phenotypic and genetic variance-covariance matrices. CPC was developed as a method of data summarization, but frequently biologists would like to use the method to detect analogous patterns of trait correlation in multiple populations or species. To investigate the properties of CPC, we simulated data that reflect a set of causal factors. The CPC method performs as expected from a statistical point of view, but often gives results that are contrary to biological intuition. In general, CPC tends to underestimate the degree of structure that matrices share. Differences of trait variances and covariances due to a difference in a single causal factor in two otherwise identically structured datasets often cause CPC to declare the two datasets unrelated. Conversely, CPC could identify datasets as having the same structure when causal factors are different. Reordering of vectors before analysis can aid in the detection of patterns. We urge caution in the biological interpretation of CPC analysis results.

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.

Phenotypic plasticity is the major determinant of changes in phenotypic integration in Arabidopsis

•  The way in which novel genetic variation affects the patterns of phenotypic integration in natural populations is addressed here. •  An experimental study is presented of the variability in integration caused by interpopulation hybridization and consequent genetic reshuffling, as well as by changes in the physical environment in the model system Arabidopsis thaliana (Brassicaceae). •  Our results show a basic invariance of sets of covarying traits in A. thaliana, with changes in nutrient availability as the principal factor accounting for major departures from the general pattern and where differences in the genetic background of the recombinant lines are less important. In A. thaliana, the relationships among vegetative and reproductive traits form distinct clusters in multivariate space. A high degree of congruence was found between differences in the multivariate mean phenotype and the pattern of phenotypic integration, as expected on the basis of recent theoretical models. •  This relationship might indicate strong selective constraints acting on the specialized life history of these populations, which are spring ephemerals inhabiting ruderal habitats and prone to competition avoidance.

Density dependence and population differentiation of genetic architecture in Impatiens capensis in natural environments

We identified environment-dependent constraints on the evolution of plasticity to density under natural conditions in two natural populations of Impatiens capensis. We also examined the expression of population divergence in genetic variance-covariance matrices in these natural environments. Inbred lines, originally collected from a sunny site with high seedling densities and a woodland site with low seedling densities, were planted in both original sites at natural high densities and at low density. Morphological and life-history characters were measured. More genetic variation for plastic responses to density was expressed in the sun site than in the woodland site, so the evolutionary potential of plasticity was greater in the sun site. Strong genetic correlations between the same character expressed at different densities and correlations among different characters could constrain the evolution of plasticity in both sites. Genetically based trade-offs in meristem allocation to vegetative growth and reproduction were apparent only in the high-resource environment with no overhead canopy and no intraspecific competition. Therefore, genetic constraints on the evolution of plasticity depended on the site and density in which plants were grown, and correlated responses to selection on plastic characters are also expected to differ between sites and densities. Population differentiation in genetic variance-covariance matrices was detected, but matrix structural differences, as opposed to proportional differences, were detected between populations only in the sun site at natural high density. Thus, population divergence in genetic architecture can occur rapidly and on a fine spatial scale, but the expression of such divergence may depend on the environment.

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.

Habitat islands, genetic diversity, and gene flow in a Patagonian rodent

The effects of terrestrial habitat islands on gene flow and genetic diversity in animal populations have been predicted and discussed in theoretical terms, but empirical data are needed to test these predictions and provide an understanding of the relationships of life-history characteristics to genetics of insular species. We studied saxicolous mice (Phyllotis xanthopygus) in Patagonia to explore genetic structure, phylogeography, and gene flow in a species inhabiting natural habitat islands. Phylogeographic analyses based on mtDNA sequences revealed two haplotype clades, which presumably reflect early Pleistocene factors that temporarily separated the mice into two geographically isolated groups. The Río Chubut, which lies within a glacial drainage basin bisecting northern Patagonia, might have affected gene flow in the species. Although we anticipated isolation by distance and founder phenomena associated with habitat islands, in some habitat patches we found evidence of high local genetic diversity. The amount of divergence in the mitochondrial cytochrome b gene (approximately 3.4%) in animals at a single locality could best be explained through a combination of historical factors and metapopulation source-sink theory. Demographic shifts, dispersal, and episodic recolonization are important in the life history and genetic population structure of P. xanthopygus.