Population divergence of genetic (co)variance matrices in a subdivided plant species,Brassica cretica

Abstract The present study of Brassica cretica had two objectives. First, we compared estimates of population structure (Q_st) for seven phenotypic characters with the corresponding measures for allozyme markers (F_st) to evaluate the supposition that genetic drift is a major determinant of the evolutionary history of this species. Secondly, we compared the genetic (co)variance ( G ) matrices of five populations to examine whether a long history of population isolation is associated with large, consistent differences in the genetic (co)variance structure. Differences between estimates of F_st and Q_st were too small to be declared significant, indicating that stochastic processes have played a major role in the structuring of quantitative variation in this species. Comparison of populations using the common principal component (CPC) method rejected the hypothesis that the G matrices differed by a simple constant of proportionality: most of the variation involved principal component structure rather than the eigenvalues. However, there was strong evidence for proportionality in comparisons using the method of percentage reduction in mean‐square error (MSE), at least when characters with unusually high (co)variance estimates were included in the analyses. Although the CPC and MSE methods provide different, but complementary, views of G matrix variation, we urge caution in the use of proportionality as an indicator of whether genetic drift is responsible for divergence in the G matrix.     

Comparison of genetic (co)variance matrices within and between Scabiosa canescens and S. columbaria

In the current study, we used bootstrap analyses and the common principal component (CPC) method of Flury (1988) to estimate and compare the G ‐matrix of Scabiosa columbaria and S. canescens populations. We found three major patterns in the G ‐matrices: (i) the magnitude of the (co)variances was more variable among characters than among populations, (ii) different populations showed high (co)variance for different characters, and (iii) there was a tendency for S. canescens to have higher genetic (co)variances than S. columbaria. The hypothesis of equal G ‐matrices was rejected in all comparisons and there was no evidence that the matrices differed by a proportional constant in any of the analyses. The two ‘species matrices’ were found to be unrelated, both for raw data and data standardized over populations, and there was significant between‐population variation in the G ‐matrix in both species. Populations of S. canescens showed conservation of structure (principal components) in their G ‐matrices, contrasting with the lack of common structure among the S. columbaria matrices. Given these observations and the results from previous studies, we propose that selection may be responsible for some of the variation between the G ‐matrices, at least in S. columbaria and at the between‐species level.     

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.     

Genetic evidence for the phylogenetic relationship between Na-Dene and Yeniseian speakers

Ruhlen's hypothesis, based on linguistic evidence, for a common phylogenetic origin of Na-Dene and Yeniseian speakers is tested using genetic data. Gene frequency data for the Kets, the only surviving Yeniseian speakers, were collected during a field study in 1993. Data for several Na-Dene groups, as well as other New World and Siberian populations, were compiled from the literature. These data were analyzed using R-matrix, principal components analysis, and Mantel tests. In a comparison of 10 New World and Siberian populations using eight alleles, 55.8% of the variation was accounted for by the first principal component, and 22.1% of the variation was subsumed by the second principal component. Contrary to Ruhlen's interpretation of the linguistic data, analysis of the genetic data shows that the Na-Dene cluster with other Native American populations, while the Kets genetically resemble the surrounding Siberian groups. This conclusion is further supported by correlations that are higher when the Kets are considered unrelated to Na-Dene speakers, and an insignificant partial correlation between genes and language when geography is held constant, indicating that spatial patterning accounts for most of the variation present in these populations.     

Quantitative Genetics of DROSOPHILA MELANOGASTER. I. Sexual Dimorphism in Genetic Parameters for Wing Traits

Sexual dimorphism in genetic parameters is examined for wing dimensions of Drosophila melanogaster. Data are fit to a quantitative genetic model where phenotypic variance is a linear function of additive genetic autosomal variance (common to both sexes), additive genetic X-linked variances distinct for each sex, variance due to common rearing environment of families, residual environmental variance, random error variance due to replication, and variance due to measurement error and developmental asymmetry (left vs. right sides). Polygenic dosage compensation and its effect on genetic variances and covariances between sexes is discussed. Variance estimates for wing length and other wing dimensions highly correlated with length support the hypothesis that the Drosophila system of dosage compensation will cause male X-linked genetic variance to be substantially larger than female X-linked variance. Results for various wing dimensions differ, suggesting that the level of dosage compensation may differ for different traits. Genetic correlations between sexes for the same trait are presented. Total additive genetic correlations are near unity for most wing traits; this indicates that selection in the same direction in both sexes would have a minor effect on changing the magnitude of difference between sexes. Additive X-linked correlations suggest some genotype x sex interactions for X-linked effects.     

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.     

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 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.     

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.     

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.     

An application of common principal component analysis to cranial morphometry of Microtus californicus and M. ochrogaster(Mammalia, Rodentia)

Principal component analysis (PCA) is a one-group method. Its purpose is to transform correlated variables into uncorrelated ones and to find linear combinations accounting for a relatively large amount of the total variability, thus reducing the number of original variables to a few components only.
In the simultaneous analysis of different groups, similarities between the principal component structures can often be modelled by the methods of common principal components (CPCs) or partial CPCs. These methods assume that either all components or only some of them are common to all groups, the discrepancies being due mainly to sampling error.
Previous authors have dealt with the k-group situation either by pooling the data of all groups, or by pooling the within-group variance-covariance matrices before performing a PCA. The latter technique is known as multiple group principal component analysis or MGPCA (Thorpe, 1983a). We argue that CPC- or partial CPC-analysis is often more appropriate than these previous methods.
A morphometrical example using males and females of Microtus californicus and M. ochrogaster is presented, comparing PCA, CPC and partial CPC analyses. It is shown that the new methods yield estimated components having smaller standard errors than when groupwise analyses are performed. Formulas are given for estimating standard errors of the eigenvalues and eigenvectors, as well as for computing the likelihood ratio statistic used to test the appropriateness of the CPC- or partial CPC-model.     

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 covariation in the hominoid craniofacial skeleton: implications for paleoanthropological models

Living species are often used as analogues for fossil ones. When this is done, the implicit assumption is made that hominids and living hominoids vary in the same way. This paper addresses the validity of this assumption by comparing patterns of facial variation among humans and African apes. In particular, it addresses three major questions that underlie approaches to reconstructing hominid relationships. First, is phenotypic variation similar between closely related species? Second, if it is dissimilar, why? Third, is it feasible to use analogue species for modeling purposes? Measurements are obtained from 542 crania of adult apes and humans. Care is taken to choose homologous data, and account for differences in population size and structure. Variance/covariance and correlation matrices among the species are compared using common principal component (CPC) analysis, random skewers methods and matrix correlations. Morphological distances (D(2)) are calculated between population means, and between randomized pairs of individuals within each population, to evaluate intraspecific variation. Morphological distances are also calculated between randomized pairs of individuals using the variation patterns of analogue populations, in order to evaluate the efficacy of such substitutions. Results show that while the hominoids share a similar pattern of facial variation overall, the patterns do diverge. This difference generally corresponds to the phylogenetic relationships among these species, suggesting that patterns of variation may have diverged through time in the large bodied hominoids. Because interpretation of relationships in the fossil record is confounded by a lack of understanding of how variation changes through time, exploration of such patterns of divergence can provide important clues to understanding human evolution. Additionally, neglecting to account for this divergence when using living analogues as variation "yardsticks" can give rise to interpretations of the fossil record that are more speciose than is warranted.     

RESISTANCE OF GENETIC CORRELATION STRUCTURE TO DIRECTIONAL SELECTION IN DROSOPHILA MELANOGASTER

The genetic covariance and correlation matrices for five morphological traits were estimated from four populations of fruit flies, Drosophila melanogaster, to measure the extent of change in genetic covariances as a result of directional selection. Two of the populations were derived from lines that had undergone selection for large or small thorax length over the preceding 23 generations. A third population was constituted using flies from control lines that were maintained with equivalent population sizes as the selected lines. The fourth population contained flies from the original cage population from which the selected and control lines had been started. Tests of the homogeneity of covariance matrices using maximum likelihood techniques revealed significant changes in covariance structure among the selected lines. Prediction of base population trait means from selected line means under the assumption of constant genetic covariances indicated that genetic covariances for the small population differed more from the base population than did the covariances for the large population. The predicted small population means diverged farther from the expected means because the additive genetic variance associated with several traits increased in value and most of the genetic covariances associated with one trait changed in sign. These results illustrate that genetic covariances may remain nearly constant in some situations while changing markedly in others. Possible developmental reasons for the genetic changes are discussed.     

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 variation in an endemic salamander, Salamandra atra, using amplified fragment length polymorphism

The pattern of genetic differentiation of the endemic alpine salamander, Salamandra atra, has been studied using amplified fragment length polymorphism (AFLP) from 11 populations throughout the range of the two currently recognized subspecies, atra and aurorae. Five different primer combinations produced 706 bands and were analyzed by constructing a phylogenetic tree using NJ and principal component analysis. Significant genetic variation was revealed by AFLP between and within populations but, our results show a lack of genetic structure. AFLP markers seems to be unsuitable to investigate complex and recent diversification.     

A TEST OF THE GLACIAL REFUGIUM HYPOTHESIS USING PATTERNS OF MITOCHONDRIAL AND NUCLEAR DNA SEQUENCE VARIATION IN ROCK PTARMIGAN (LAGOPUS MUTUS)

The glacial refugium hypothesis (GRH) proposes that glaciers promoted differentiation and generation of intraspecific diversity by isolating populations in ice-free refugia. We tested three predictions of this hypothesis for the evolutionary divergence of rock ptarmigan (Lagopus mutus) during the Wisconsin glaciation of the late Pleistocene. To do this, we examined subspecies distributions, population genetic structure, and phylogenetic relationships in 26 populations across North America and the Bering Sea region. First, we analyzed sequence variation in the mitochondrial control region, in a nuclear intron (Gapdh), and in an internal transcribed spacer (ITS1). Control region sequences of 154 rock ptarmigan revealed strong population and phylogeographic structure. Variation in intron sequences of 114 rock ptarmigan also revealed significant population structure compatible with results for the control region. Rock ptarmigan were invariant for ITS1. Second, we show that five known Nearctic refugia and an Icelandic refugium are concordant with the current distribution of morphologically distinct subspecies; five of these six refugia are geographically concordant with the distribution of closely related control region haplotypes. Third, our estimates of the time since phylogenetic lineages diverged predated the last glacial maximum for all but two lineages. In addition, all lines of evidence suggest that two unknown refugia in the Bering Sea region supported rock ptarmigan during the Wisconsin glaciation. Overall, our results are most consistent with the hypothesis that isolated populations of rock ptarmigan diverged in multiple refugia during the Wisconsin and that geographic variation reflects patterns of recolonization of the Nearctic after the ice receded. The GRH may therefore offer the most plausible explanation for similar biogeographic patterns in a variety of Nearctic vertebrates.     

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.     

MORPHOLOGICAL EVOLUTION IN MUROID RODENTS I. CONSERVATIVE PATTERNS OF CRANIOMETRIC COVARIANCE AND THEIR ONTOGENETIC BASIS IN THE NEOTROPICAL GENUS ZYGODONTOMYS

Analyses of craniodental measurement data from 15 wild-collected population samples of the Neotropical muroid rodent genus Zygodontomys reveal consistent patterns of relative variability and correlation that suggest a common latent structure. Eigenanalysis of each sample covariance matrix of logarithms yields a first principal component that accounts for a large fraction of the total variance. Variances of subsequent sample principal components are much smaller, and the results of bootstrap resampling together with asymptotic statistics suggest that characteristic roots of the covariance matrix after the first are seldom distinct. The coefficients of normalized first principal components are strikingly similar from sample to sample: inner products of these vectors reveal an average between-sample correlation of 0.989, and the mean angle of divergence is only about eight degrees. Since first principal component coefficients identify the same contrasts among variables as comparisons of relative variability and correlation, we conclude that a single factor accounts for most of the common latent determination of these sample dispersions. Analyses of variance based on toothwear (a coarse index of age) and sex in the wild-collected samples, and on known age and sex in a captive-bred population, reveal that specimen scores on sample first principal components are age- and sex-dependent; residual sample dispersion, however, is essentially unaffected by age, sex, or age × sex interaction. The sample first principal component therefore reflects the covariance among measured dimensions induced by general growth, and its coefficients are interpretable as exponents of postnatal growth allometry. Path-analytic models that incorporate prior knowledge of the equivalent allometric effects of general growth within these samples can be used to decompose the between-sample variance by factors corresponding to other ontogenetic mechanisms of form change. The genetic or environmental determinants of differences in sample mean phenotypes induced by such mechanisms, however, can be demonstrated only by experiment.