A comparative method for both discrete and continuous characters using the threshold model

The threshold model developed by Sewall Wright in 1934 can be used to model the evolution of two-state discrete characters along a phylogeny. The model assumes that there is a quantitative character, called liability, that is unobserved and that determines the discrete character according to whether the liability exceeds a threshold value. A Markov chain Monte Carlo algorithm is used to infer the evolutionary covariances of the liabilities for discrete characters, sampling liability values consistent with the phylogeny and with the observed data. The same approach can also be used for continuous characters by assuming that the tip species have values that have been observed. In this way, one can make a comparative-methods analysis that combines both discrete and continuous characters. Simulations are presented showing that the covariances of the liabilities are successfully estimated, although precision can be achieved only by using a large number of species, and we must always worry whether the covariances and the model apply throughout the group. An advantage of the threshold model is that the model can be straightforwardly extended to accommodate within-species phenotypic variation and allows an interface with quantitative-genetics models.     

A test for the genetic basis of natural selection: an individual-based longitudinal study in a stream-dwelling fish

In addition to the well-studied evolutionary parameters of (1) phenotype-fitness covariance and (2) the genetic basis of phenotypic variation, adaptive evolution by natural selection requires that (3) fitness variation is effected by heritable genetic differences among individuals and (4) phenotype-fitness covariances must be, at least in part, underlain by genetic covariances. These latter two requirements for adaptive evolutionary change are relatively unstudied in natural populations. Absence of the latter requirements could explain stasis of apparently directionally selected heritable traits. We provide complementary analyses of selection and variation at phenotypic and genetic levels for juvenile growth rate in brook charr Salvelinus fontinalis in Freshwater River, Newfoundland, Canada. Contrary to the vast majority of reports in fish, we found very little viability selection of juvenile body size. Large body size appears nonetheless to be selectively advantageous via a relationship with early maturity. Genetic patterns in evolutionary parameters largely reflected phenotypic patterns. We have provided inference of selection based on longitudinal data, which are uncommon in high fecundity organisms. Furthermore we have provided a practicable framework for further studies of the genetic basis of natural selection.     

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

A modified minimum evolution approach is used to estimate covariance matrices for hypothetical ancestors. Branch lengths are calculated as the mean disparity in corresponding ancestor-descendent covariances. Branches are longest leading to terminal populations and subspecies, while interspecific branches are relatively short, indicating a general conservation of covariance structure among species despite a high degree of intraspecific variability. Absolute deviations in covariance structure are not correlated with phenotypic divergence. Interpreted in light of other studies, the analyses suggest that deviations in covariance structure are most strongly associated with the formation of diagnosably distinct taxa and stochastic sampling of genotypes at the population level. There is no evidence for restructuring of phenotypic covariance structure in association with reproductive isolation. The results suggest that phenotypic covariances are dynamic over short time scales and do not support attempts to extrapolate genetic covariance structure to explain or predict macroevolutionary change. This study further demonstrates that branch lengths, which are not usually analyzed in detail, contain valuable evolutionary information complementary to that residing in the branching pattern.     

PHYLOGENETIC ANALYSIS OF THE EVOLUTIONARY CORRELATION USING LIKELIHOOD

Many evolutionary processes can lead to a change in the correlation between continuous characters over time or on different branches of a phylogenetic tree. Shifts in genetic or functional constraint, in the selective regime, or in some combination thereof can influence both the evolution of continuous traits and their relation to each other. These changes can often be mapped on a phylogenetic tree to examine their influence on multivariate phenotypic diversification. We propose a new likelihood method to fit multiple evolutionary rate matrices (also called evolutionary variance–covariance matrices) to species data for two or more continuous characters and a phylogeny. The evolutionary rate matrix is a matrix containing the evolutionary rates for individual characters on its diagonal, and the covariances between characters (of which the evolutionary correlations are a function) elsewhere. To illustrate our approach, we apply the method to an empirical dataset consisting of two features of feeding morphology sampled from 28 centrarchid fish species, as well as to data generated via phylogenetic numerical simulations. We find that the method has appropriate type I error, power, and parameter estimation. The approach presented herein is the first to allow for the explicit testing of how and when the evolutionary covariances between characters have changed in the history of a group.     

A phylogenetic model for investigating correlated evolution of substitution rates and continuous phenotypic characters

The comparative approach is routinely used to test for possible correlations between phenotypic or life-history traits. To correct for phylogenetic inertia, the method of independent contrasts assumes that continuous characters evolve along the phylogeny according to a multivariate Brownian process. Brownian diffusion processes have also been used to describe time variations of the parameters of the substitution process, such as the rate of substitution or the ratio of synonymous to nonsynonymous substitutions. Here, we develop a probabilistic framework for testing the coupling between continuous characters and parameters of the molecular substitution process. Rates of substitution and continuous characters are jointly modeled as a multivariate Brownian diffusion process of unknown covariance matrix. The covariance matrix, the divergence times and the phylogenetic variations of substitution rates and continuous characters are all jointly estimated in a Bayesian Monte Carlo framework, imposing on the covariance matrix a prior conjugate to the Brownian process so as to achieve a greater computational efficiency. The coupling between rates and phenotypes is assessed by measuring the posterior probability of positive or negative covariances, whereas divergence dates and phenotypic variations are marginally reconstructed in the context of the joint analysis. As an illustration, we apply the model to a set of 410 mammalian cytochrome b sequences. We observe a negative correlation between the rate of substitution and mass and longevity, which was previously observed. We also find a positive correlation between ω = dN/dS and mass and longevity, which we interpret as an indirect effect of variations of effective population size, thus in partial agreement with the nearly neutral theory. The method can easily be extended to any parameter of the substitution process and to any continuous phenotypic or environmental character.     

Developmental interactions and the constituents of quantitative variation

Development is the process by which genotypes are transformed into phenotypes. Consequently, development determines the relationship between allelic and phenotypic variation in a population and, therefore, the patterns of quantitative genetic variation and covariation of traits. Understanding the developmental basis of quantitative traits may lead to insights into the origin and evolution of quantitative genetic variation, the evolutionary fate of populations, and, more generally, the relationship between development and evolution. Herein, we assume a hierarchical, modular structure of trait development and consider how epigenetic interactions among modules during ontogeny affect patterns of phenotypic and genetic variation. We explore two developmental models, one in which the epigenetic interactions between modules result in additive effects on character expression and a second model in which these epigenetic interactions produce nonadditive effects. Using a phenotype landscape approach, we show how changes in the developmental processes underlying phenotypic expression can alter the magnitude and pattern of quantitative genetic variation. Additive epigenetic effects influence genetic variances and covariances, but allow trait means to evolve independently of the genetic variances and covariances, so that phenotypic evolution can proceed without changing the genetic covariance structure that determines future evolutionary response. Nonadditive epigenetic effects, however, can lead to evolution of genetic variances and covariances as the mean phenotype evolves. Our model suggests that an understanding of multivariate evolution can be considerably enriched by knowledge of the mechanistic basis of character development.     

TRANSLATING BETWEEN MICROEVOLUTIONARY PROCESS AND MACROEVOLUTIONARY PATTERNS: THE CORRELATION STRUCTURE OF INTERSPECIFIC DATA

As species evolve along a phylogenetic tree, we expect closely related species to retain some phenotypic similarities due to their shared evolutionary histories. The amount of expected similarity depends both on the hierarchical phylogenetic structure, and on the specific magnitude and types of evolutionary changes that accumulate during each generation. In this study, we show how models of microevolutionary change can be translated into the resulting macroevolutionary patterns. We illustrate how the structure of phenotypic covariances expected in interspecific measurements can be derived, and how this structure depends on the microevolutionary forces guiding phenotypic change at each generation. We then explore the covariance structure expected from several simple microevolutionary models of phenotypic evolution, including various combinations of random genetic drift, directional selection, stabilizing selection, and environmental change, as well as models of punctuated or burst-like evolution. We find that stabilizing selection leads to patterns of exponential decrease of between species covariance with phylogenetic distance. This is different from the usual linear patterns of decrease assumed in most comparative and systematic methods. Nevertheless, linear patterns of decrease can result from many processes in addition to random genetic drift, such as directional and fluctuating selection as well as modes of punctuated change. Our framework can be used to develop methods for (1) phylogenetic reconstruction; (2) inference of the evolutionary process from comparative data; and (3) conducting or evaluating statistical analyses of comparative data while taking phylogenetic history into account.     

How to Explore Morphological Integration in Human Evolution and Development?

Most studies in evolutionary developmental biology focus on large-scale evolutionary processes using experimental or molecular approaches, whereas evolutionary quantitative genetics provides mathematical models of the influence of heritable phenotypic variation on the short-term response to natural selection. Studies of morphological integration typically are situated in-between these two styles of explanation. They are based on the consilience of observed phenotypic covariances with qualitative developmental, functional, or evolutionary models. Here we review different forms of integration along with multiple other sources of phenotypic covariances, such as geometric and spatial dependencies among measurements. We discuss one multivariate method [partial least squares analysis (PLS)] to model phenotypic covariances and demonstrate how it can be applied to study developmental integration using two empirical examples. In the first example we use PLS to study integration between the cranial base and the face in human postnatal development. Because the data are longitudinal, we can model both cross-sectional integration and integration of growth itself, i.e., how cross-sectional variance and covariance is actually generated in the course of ontogeny. We find one factor of developmental integration (connecting facial size and the length of the anterior cranial base) that is highly canalized during postnatal development, leading to decreasing cross-sectional variance and covariance. A second factor (overall cranial length to height ratio) is less canalized and leads to increasing (co)variance. In a second example, we examine the evolutionary significance of these patterns by comparing cranial integration in humans to that in chimpanzees.     

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.     

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

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

Evolutionary importance of parental care performance,food resources,and direct and indirect genetic effects in a burying beetle

Indirect genetic effects (IGE) of parental care performance and the direct–indirect covariance contribute substantially to total heritability in domesticated and laboratory mammals. For animals from natural populations empirical estimates of IGE are sparse. Thus, despite recent models relating IGE to evolution, evolutionary interpretations of IGE are limited. To address this deficit, we used a reciprocal cross‐fostering breeding design to estimate environmental influences, direct and indirect genetic effects, and direct–indirect genetic covariances in the burying beetle Nicrophorus pustulatus to determine the evolutionary importance of IGE arising from variation in parental care performance. Carrion size positively affected adult mass and time on carrion, but had no effect on total development time. Males were slightly larger than females. For both mass and development, independent of these environmental influences, direct and indirect genetic effects were of moderate magnitude. Total genetic effects explained 36–50% of the phenotypic variance in mass and size and 27–37% of phenotypic variance in development time. Direct–indirect genetic covariances were zero or close to zero. Thus, for both mass and development time, the response to natural selection arising from environmental variation may be accelerated by the presence of IGE in N. pustulatus. The generality of this pattern and the evolutionary significance of IGE arising from parental care awaits further study of natural populations.     

Genetic analysis of life-history constraint and evolution in a wild ungulate population

Trade-offs among life-history traits are central to evolutionary theory. In quantitative genetic terms, trade-offs may be manifested as negative genetic covariances relative to the direction of selection on phenotypic traits. Although the expression and selection of ecologically important phenotypic variation are fundamentally multivariate phenomena, the in situ quantification of genetic covariances is challenging. Even for life-history traits, where well-developed theory exists with which to relate phenotypic variation to fitness variation, little evidence exists from in situ studies that negative genetic covariances are an important aspect of the genetic architecture of life-history traits. In fact, the majority of reported estimates of genetic covariances among life-history traits are positive. Here we apply theory of the genetics and selection of life histories in organisms with complex life cycles to provide a framework for quantifying the contribution of multivariate genetically based relationships among traits to evolutionary constraint. We use a Bayesian framework to link pedigree-based inference of the genetic basis of variation in life-history traits to evolutionary demography theory regarding how life histories are selected. Our results suggest that genetic covariances may be acting to constrain the evolution of female life-history traits in a wild population of red deer Cervus elaphus: genetic covariances are estimated to reduce the rate of adaptation by about 40%, relative to predicted evolutionary change in the absence of genetic covariances. Furthermore, multivariate phenotypic (rather than genetic) relationships among female life-history traits do not reveal this constraint.     

Genetic variance and covariance patterns of larval development in the small white butterflyPieris rapae crucivora Boisduval

Quantitative genetic theory indicates that genetic covariance patterns among life history characters should have played an important role as genetic constraint in life history evolution. Highly positve (and negative) genetic correlations between larval development time (or larval growth rate) and adult size characters were detected by means of sib analysis for the small white butterfly Pieris rapae crucivora. The genetic associations suggested that evolution of developmental characteristics and adult phenotypic traits were constrained by pleiotropy. The positive genetic correlations between development time and adult body size may be compatible with the trade-off between them, but the negative genetic correlations between larval growth rate and adult body size are not predicted from theories of optimal energy allocation. That phenotypic correlations drastically differed from the genetic correlations indicates limitations of evolutionary inferences based only on phenotypic variation.     

Concordance between stabilizing sexual selection,intraspecific variation,and interspecific divergence in Phymata

Empirical studies show that lineages typically exhibit long periods of evolutionary stasis and that relative levels of within‐species trait covariance often correlate with the extent of between‐species trait divergence. These observations have been interpreted by some as evidence of genetic constraints persisting for long periods of time. However, an alternative explanation is that both intra‐ and interspecific variation are shaped by the features of the adaptive landscape (e.g., stabilizing selection). Employing a genus of insects that are diverse with respect to a suite of secondary sex traits, we related data describing nonlinear phenotypic (sexual) selection to intraspecific trait covariances and macroevolutionary divergence. We found support for two key predictions (1) that intraspecific trait covariation would be aligned with stabilizing selection and (2) that there would be restricted macroevolutionary divergence in the direction of stabilizing selection. The observed alignment of all three matrices offers a point of caution in interpreting standing variability as metrics of evolutionary constraint. Our results also illustrate the power of sexual selection for determining variation observed at both short and long timescales and account for the apparently slow evolution of some secondary sex characters in this lineage.     

The Genetic Covariance between Characters Maintained by Pleiotropic Mutations

A statistical genetic model of a multivariate phenotype is derived to investigate the covariation of pleiotropic mutations with additive effects under the combined action of phenotypic selection, linkage and the mating system. Equilibrium formulas for large, randomly mating populations demonstrate that, when selection on polygenic variation is much smaller than twice the harmonic mean recombination rate between loci with interacting fitnesses, linkage disequilibrium is negligible and pleiotropy is the main cause of genetic correlations between characters. Under these conditions, approximate expressions for the dynamics of the genetic covariances due to pleiotropic mutations are obtained. Patterns of genetic covariance between characters and their evolution are discussed with reference to data on polygenic mutation, chromosomal organization and morphological integration.     

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.     

QUANTITATIVE GENETICS OF MORPHOLOGICAL DIFFERENTIATION IN PEROMYSCUS. I. TESTS OF THE HOMOGENEITY OF GENETIC COVARIANCE STRUCTURE AMONG SPECIES AND SUBSPECIES

Phenotypic and additive genetic covariance matrices were estimated for 15 morphometric characters in three species and subspecies of Peromyscus. Univariate and multivariate ANOVAs indicate these groups are highly diverged in all characters, P. leucopus having the largest body size, P. maniculatus bairdii the smallest, and P. maniculatus nebrascensis being intermediate. Comparing the structure of P and G within each taxon revealed significant similarities in all three cases. This proportionality was strong enough to justify using P in the place of G to analyze evolutionary processes using quantitative genetic models when G can not be estimated, as in fossil material. However, the similarity between genetic and phenotypic covariance structures is sufficiently low that estimates of the genetic parameters should be used when possible. The additive genetic covariance matrices were compared to examine the assumption that they remain constant during evolution, an assumption which underlies many applications of quantitative-genetic models. While matrix permutation tests indicated statistically significant proportionality between the genetic covariance structures of the two P. maniculatus subspecies, there is no evidence of significant genetic structural similarity between species. This result suggests that the assumption of constant genetic covariance structure may be valid only within species. (It does not, however, necessarily imply a causal relationship between speciation and heterogeneity of genetic covariance structures.) The low matrix correlation for the two P. maniculatus subspecies' genetic covariance matrices indicates G may not be functionally constant, even within species. The lack of similarity observed here may be due partly to sampling variation.     

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.     

Quantitative Genetics and Modularity in Cranial and Mandibular Morphology of Calomys expulsus

Patterns of genetic covariance between characters (represented by the covariance matrix \({\varvec{G}}\) ) play an important role in morphological evolution, since they interact with the evolutionary forces acting over populations. They are also expected to influence the patterns expressed in their phenotypic counterparts \(({\varvec{P}})\) , because of limits imposed by multiple developmental and functional restrictions on the genotype/phenotype map. We have investigated genetic covariances in the skull and mandible of the vesper mouse (Calomys expulsus) in order to estimate the degree of similarity between genetic and phenotypic covariances and its potential roots on developmental and functional factors shaping those integration patterns. We use a classic ad hoc analysis of morphological integration based on current state of art of developmental/functional factors during mammalian ontogeny and also applied a novel methodology that makes use of simulated evolutionary responses. We have obtained \({\varvec{P}}\) and \({\varvec{G}}\) that are strongly similar, for both skull and mandible; their similarity is achieved through the spatial and temporal organization of developmental and functional interactions, which are consistently recognized as hypothesis of trait associations in both matrices.     

Bottleneck Effects on Genetic Variance for Courtship Repertoire

Bottleneck effects on evolutionary potential in mating behavior were addressed through assays of additive genetic variances and resulting phenotypic responses to drift in the courtship repertoires of six two-pair founder-flush lines and two control populations of the housefly. A simulation addressed the complication that an estimate of the genetic variance for a courtship trait (e.g., male performance vigor or the female requirement for copulation) must involve assays against the background behavior of the mating partners. The additive ``environmental' effect of the mating partner's phenotype simply dilutes the net parent-offspring covariance for a trait. However, if there is an interaction with this ``environmental' component, negative parent-offspring covariances can result under conditions of high incompatibility between the population's distributions for male performance and female choice requirements, despite high levels of genetic variance. All six bottlenecked lines exhibited significant differentiation from the controls in at least one measure of the parent-offspring covariance for male performance or female choice (estimated by 50 parent-son and 50 parent-daughter covariances for 10 courtship traits per line) which translated to significant phenotypic drift. However, the average effect across traits or across lines did not yield a significant net increase in genetic variance due to bottlenecks. Concerted phenotypic differentiation due to the founder-flush event provided indirect evidence of directional dominance in a subset of traits. Furthermore, indirect evidence of genotype-environment interactions (potentially producing genotype-genotype effects) was found in the negative parent-offspring covariances predicted by the male-female interaction simulation and by the association of the magnitude of phenotypic drift with the absolute value of the parent-offspring covariance. Hence, nonadditive genetic effects on mating behavior may be important in structuring genetic variance for courtship, although most of the increases in genetic variance would be expected to reflect inbreeding depression with relatively rare situations representing the facilitation of speciation by bottlenecks.