Relationships among ontogenetic,static, and evolutionary allometry

The relationship between ontogenetic, static, and evolutionary levels of allometry is investigated. Extrapolation from relative size relationships in adults to relative growth in ontogeny depends on the variability of slopes and intercepts of ontogenetic vectors relative to variability in length of the vector. If variability in slopes and intercepts is low relative to variability in length, ontogenetic and static allometries will be similar. The similarity of ontogenetic and static allometries was tested by comparing the first principal component, or size vector, for correlations among 48 cranial traits in a cross-sectional ontogenetic sample of rhesus macaques from Cayo Santiago with a static sample from which all age- and sex-related variation had been removed. The vector correlation between the components is high but significantly less than one while two of three allometric patterns apparent in the ontogenetic component are not discernable in the static component. This indicates that there are important differences in size and shape relationships among adults and within ontogenies. Extrapolation from intra- or interspecific phenotypic allometry to evolutionary allometry is shown to depend on the similarity of genetic and phenotypic allometry patterns. Similarity of patterns was tested by comparing the first principal components of the phenotypic, genetic, and environmental correlation matrices calculated using standard quantitative genetic methods. The patterns of phenotypic, genetic, and environmental allometry are dissimilar; only the environmental allometries show ontogenetic allometric patterns. This indicates that phenotypic allometry may not be an accurate guide to patterns of evolutionary change in size and shape.     

Genetic covariance structure of growth in the salamander Ambystoma macrodactylum

The size of an organism at any point during ontogeny often has fitness consequences through either direct selection on size or through selection on size-related morphological, performance, or life history traits. However, the evolutionary response to selection on size across ontogeny (a growth trajectory) may be limited by genetic correlations across ages. Here we characterize the phenotypic and genetic covariance structure of length and mass growth trajectories in a natural population of larval Ambystoma macrodactylum using function-valued quantitative genetic analyses and principal component decomposition. Most of the phenotypic and genetic variation in both growth trajectories appears to be confined to a single principal component describing a pattern of positive covariation among sizes across all ages. Higher order principal components with no significant associated genetic variation were identified for both trajectories, suggesting that evolution towards certain patterns of negative covariation between sizes across ages is constrained. The well-characterized positive relationship between size at metamorphosis and fitness in pond-breeding amphibians predicts that the across-age covariance structure will strongly limit evolution only if there is negative selection on size prior to metamorphosis. The pattern of genetic covariation observed in this study is similar to that observed in other vertebrate taxa, indicating that size may often be highly genetically and phenotypically integrated across ontogeny. Additionally, we find that phenotypic and genetic analyses of growth trajectories can yield qualitatively similar patterns of covariance structure.     

Sets of complementary phenotypic relationships across five isolated populations: Traces of expression of different gene complexes?

The aim of this study is to search for certain repeating phenotypic patterns, i.e. sets of complementary relationships across five isolated populations, which may represent the traces of expression of different genes or gene complexes. The study was conducted among isolates of five island populations of eastern Adriatic, Croatia, and the data were collected between 1979 and 1990. Selected phenotypic characteristics included measures of biological distances (e.g. anthropometrical body and head distances, physiological, dermatoglyphic and radiogrammetric bone distances), while other examined traits included sociocultural (linguistic), bio-cultural (migrational kinship) and genetic distances. The sample consisted of 6,286 examinees from 43 villages of five isolate populations. Correlations between distance matrices based on examined traits were analyzed in each of five populations using Mantel's test of matrix correspondence, and factor analysis (rotated principal component) was then performed over obtained correlation matrices. The results showed that there were several consistent and significant correlations between some analyzed traits across all of the studied isolate populations, which might indicate their regulation by the shared gene complexes or genome regions. The analyses identified three main clusters of correlations in all five isolate populations: the first one containing anthropometric measures (body and head measures and physiological properties in both sexes), the second one containing geographic distance-related traits (migrational kinship, linguistic and genetic distances), and the third one containing dermatoglyphic properties and radiogrammetric bone measures in both sexes. The higher order varimax rotation over the matrix of factor correlations revealed that the primary source of variation within all five analyzed populations was not sex-related, but rather variable-specific.     

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.     

Relationship between parameters of early growth in Israeli infants

A sample of 1931 Israeli infants was measured for body weight (WT), length (HT) and head circumference (HC) for approximately 2 years. The Count model with 3 parameters was chosen as the best fitting and most parsimonious function to approximate growth of all 3 studied traits. In the model parameter a relates to birth indices, b--to velocity of growth, and c--to rapid early childhood growth, or acceleration. Assuming a difference in growth patterns in the periods of different length, the whole sample was divided into 3 groups: 1) infants with last measurement around the age of 12 months; 2) infants with last measurement around the age of 18 months, and 3) infants with last measurement around the age of 24 months. The individuals measured up to 12 months were presented in all three groups. 27 curve fitting parameters, corresponding to 3 different follow-up intervals for WT, HT and HC were computed for each individual. A high correlation was detected between the a parameters regardless of time interval for 3 measured traits. A negative correlation was found between b and c parameters within the same time interval. A consistent positive correlation was indicated between a and b parameters, especially for body length and head circumference. A principal component analysis extracted five independent factors explaining 88.1% of the total variance. Three first factors retained parameters b and c, describing growth rate and pattern of each trait separately, namely, F1 was responsible for head circumference, F2 was a body length factor, F3 was a body weight factor. F4 extracted all birth indices, observed (HC0, HT0 and WT0) and expected (parameters a). The composition of principal factors allowed us to assume that there might be a strong involvement of a pleiotropic genetic source in determination of birth size traits and an independent genetic source controlling the pattern of growth for each trait separately.     

Disentangling plastic and genetic changes in body mass of Siberian jays

Spatial and temporal phenotypic differentiation in mean body size is of commonplace occurrence, but the underlying causes remain often unclear: both genetic differentiation in response to selection (or drift) and environmentally induced plasticity can create similar phenotypic patterns. Studying changes in body mass in Siberian jays (Perisoreus infaustus) over three decades, we discovered that mean body mass declined drastically (ca. 10%) over the first two decades, but increased markedly thereafter back to almost the initial level. Quantitative genetic analyses revealed that although body mass was heritable (h² = 0.46), the pronounced temporal decrease in body mass was mainly a product of phenotypic plasticity. However, a concomitant and statistically significant decrease in predicted breeding values suggests a genetic component to this change. The subsequent increase in mean body mass was indicated to be entirely due to plasticity. Selection on body mass was estimated to be too weak to fully account for the observed genetic decline in body mass, but bias in selection differential estimates due to environmental covariance between body mass and fitness is possible. Hence, the observed body mass changes appear to be driven mainly by phenotypic plasticity. Although we were not able to identify the ecological driver of the observed plastic changes, the results highlight the utility of quantitative genetic approaches in disentangling genetic and phenotypic changes in natural populations.     

QUANTITATIVE GENETICS OF GEOMETRIC SHAPE IN THE MOUSE MANDIBLE

Abstract We combine the methods of geometric morphometrics and multivariate quantitative genetics to study the patterns of phenotypic and genetic variation of mandible shape in random‐bred mice. The data are the positions of 11 landmarks on the mandibles of 1241 mice from a parent‐offspring breeding design. We use Procrustes superimposition to extract shape variation and restricted maximum likelihood to estimate the additive genetic and environmental components of variance and covariance. Matrix permutation tests showed that the genetic and phenotypic as well as the genetic and environmental covariance matrices were similar, but not identical. Likewise, principal component analyses revealed correspondence in the patterns of phenotypic and genetic variation. Patterns revealed in these analyses also showed similarities to features previously found in the effects of quantitative trait loci and in the phenotypes generated in gene knockout experiments. We used the multivariate version of the breeder's equation to explore the potential for short‐term response to selection on shape. In general, the correlated response is substantial and regularly exceeds the direct response: Selection applied locally to one landmark usually produces a response in other parts of the mandible as well. Moreover, even selection for shifts of the same landmark in different directions can yield dramatically different responses. These results demonstrate the role of the geometry and anatomical structure of the mandible, which are key determinants of the patterns of the genetic and phenotypic covariance matrices, in molding the potential for adaptive evolution.     

Quantitative genetics of growth and cryptic evolution of body size in an island population

While evolution occurs when selection acts on a heritable trait, empirical studies of natural systems have frequently reported phenotypic stasis under these conditions. We performed quantitative genetic analyses of weight and hindleg length in a free-living population of Soay sheep (Ovis aries) to test whether genetic constraints can explain previously reported stasis in body size despite evidence for strong positive directional selection. Genetic, maternal and environmental covariance structures were estimated across ontogeny using random regression animal models. Heritability increased with age for weight and hindleg length, though both measures of size were highly heritable across ontogeny. Genetic correlations among ages were generally strong and uniformly positive, and the covariance structures were also highly integrated across ontogeny. Consequently, we found no constraint to the evolution of larger size itself. Rather we expect size at all ages to increase in response to positive selection acting at any age. Consistent with expectation, predicted breeding values for age-specific size traits have increased over a twenty-year period, while maternal performance for offspring size has declined. Re-examination of the phenotypic data confirmed that sheep are not getting larger, but also showed that there are significant negative trends in size at all ages. The genetic evolution is therefore cryptic, with the response to selection presumably being masked at the phenotypic level by a plastic response to changing environmental conditions. Density-dependence, coupled with systematically increasing population size, may contribute to declining body size but is insufficient to completely explain it. Our results demonstrate that an increased understanding of the genetic basis of quantitative traits, and of how plasticity and microevolution can occur simultaneously, is necessary for developing predictive models of phenotypic change in nature.     

Individual variation in dispersal associated with phenotype influences fine-scale genetic structure in weasels

In general, landscape genetic studies have ignored the potential role that the phenotype of individuals plays in determining fine-scale genetic structure in species. This potential over-simplification ignores an important component that dispersal is both condition- and phenotype-dependent. In order to investigate the relationship between potential dispersal, habitat selection and phenotype, we examined the spatial ecology, body mass and fine-scale genetic structure of weasels (Mustela nivalis) in Bia?owie?a Forest in Poland. Our study population is characterized by an almost three-fold phenotypic variation in adult body mass and weasels were segregated in certain habitats according to size. We detected significant genetic structuring associated with habitat within the studied area and analyses of radio-tracking and re-capture data showed that the maximum extent of movement was achieved by weasels of medium body size, whereas the smallest and largest individuals exhibited higher site fidelity. With the unrestricted movement of the medium-sized individuals across optimal habitat, genetic admixture does occur. However, the presence of a barrier leads to unidirectional gene flow, with larger individuals outcompeting smaller individuals and therefore maintaining the genetic break in the study area. This highlights the importance of considering both intrinsic (phenotype) and extrinsic (environmental) factors in understanding dispersal patterns and ultimately, gene flow in complex landscapes.     

Host-related antennal variation in the polyphagous egg parasite Telenomus alsophilae (Hymenoptera: Scelionidae)

Abstract. The solitary egg parasite Telenomus alsophilae was reared from the eggs of six lepidopteran hosts of two families. One-way analyses of variance showed statistically significant differences among host classes for means of (a) lengths and widths of all female antennomeres; and (b) in twelve of twenty-three means of log-transformed ratios constructed from pairs of antennomere dimensions. Principal component analyses of dispersion matrices of both untransformed and log-transformed antennomere dimensions were conducted to examine patterns of variation among variables. In both analyses PCI was a general component and interpreted as a measure of overall size. One-way analyses of variance of projection scores of OTUs on each of the first five principal components showed significant differences among host classes for means of scores on (a) PCI (both analyses) and (b) PC4 for untransformed data and PC3 for log-transformed data. Differences among hosts classes for scores on the latter two components are interpreted to indicate that antennal variation results from factors in addition to simple size differences among host eggs and the allometric growth of body parts of parasites reared from them.     

Ecogeographic variation of body size in the spectacled salamanders (Salamandrina): influence of genetic structure and local factors

Aim The patterns and causes of ecogeographical body size variation in ectotherms remain controversial. In amphibians, recent genetic studies are leading to the discovery of many cryptic species. We analysed the relationships between body size and climate for a salamander (Salamandrina) that was recently separated into two sibling species, to evaluate how ignoring interspecific and intraspecific genetic structure may affect the conclusions of ecogeographical studies. We also considered the potential effects of factors acting at a local scale. Location Thirty‐four populations covering the whole range of Salamandrina, which is endemic to peninsular Italy. Methods We pooled original data and data from the literature to obtain information on the snout–vent length (SVL) of 3850 Salamandrina females; we obtained high‐resolution climatic data from the sampled localities. We used an information‐theoretic approach to evaluate the roles of climate, genetic features (mitochondrial haplogroup identity) and characteristics of aquatic oviposition sites. We repeated our analyses three times: in the first analysis we ignored genetic data on intraspecific and interspecific variation; in the second one we considered the recently discovered differences between the two sibling species; in the third one we included information on intraspecific genetic structure within Salamandrina perspicillata (for Salamandrina terdigitata the sample size was too small to perform intraspecific analyses). Results If genetic information was ignored, our analysis suggested the existence of a relationship between SVL and climatic variables, with populations of large body size in areas with high precipitation and high thermal range. If species identity was included in the analysis, the role of climatic features was much weaker. When intraspecific genetic differences were also considered, no climatic feature had an effect. In all analyses, local factors were important and explained a large proportion of the variation; populations spawning in still water had a larger body size. Main conclusions An imperfect knowledge of species boundaries, or overlooking the intraspecific genetic variation can strongly affect the results of analyses of body size variation. Furthermore, local factors can be more important than the large‐scale parameters traditionally considered, particularly in species with a small range.     

Inheritance of finger pattern types in MZ and DZ twins

Digital patterns of a sample on twins were analyzed to estimate the resemblance between monozygotic (MZ) and dizygotic (DZ) twins and to evaluate the mode of inheritance by the use of maximum likelihood based variance decomposition analysis. MZ twin resemblance of finger pattern types appears to be more pronounced than in DZ twins, which suggests the presence of genetic factors in the forming of fingertip patterns. The most parsimonious model shows twin resemblance in count of all three basic finger patterns on 10 fingers. It has significant dominant genetic variance component across all fingers. In the general model, the dominant genetic variance component proportion is similar for all fingertips (about 60%) and the sibling environmental variance is significantly nonzero, but the proportion between additive and dominant variance components was different. Application of genetic model fitting technique of segregation analyses clearly shows mode of inheritance. A dominant genetic variance component or a specific genetic system modifies the phenotypic expression of the fingertip patterns. The present study provided evidence of strong genetic component in finger pattern types and seems more informative compared to the earlier traditional method of correlation analysis.     

Ontogenetic patterns in heritable variation for body size: using random regression models in a wild ungulate population

Body size is an important determinant of fitness in many organisms. While size will typically change over the lifetime of an individual, heritable components of phenotypic variance may also show ontogenetic variation. We estimated genetic (additive and maternal) and environmental covariance structures for a size trait (June weight) measured over the first 5 years of life in a natural population of bighorn sheep Ovis canadensis. We also assessed the utility of random regression models for estimating these structures. Additive genetic variance was found for June weight, with heritability increasing over ontogeny because of declining environmental variance. This pattern, mirrored at the phenotypic level, likely reflects viability selection acting on early size traits. Maternal genetic effects were significant at ages 0 and 1, having important evolutionary implications for early weight, but declined with age being negligible by age 2. Strong positive genetic correlations between age-specific traits suggest that selection on June weight at any age will likely induce positively correlated responses across ontogeny. Random regression modeling yielded similar results to traditional methods. However, by facilitating more efficient data use where phenotypic sampling is incomplete, random regression should allow better estimation of genetic (co)variances for size and growth traits in natural populations.     

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.     

Mapping major quantitative trait loci for postnatal growth in an intersubspecific backcross between C57BL/6J and Philippine wild mice by using principal component analysis

A number of quantitative trait loci (QTLs) for postnatal growth have previously been reported in mice. As effects of the QTLs are usually small and similar to one another in magnitude, it is generally difficult to know which loci are major contributors to postnatal growth. We applied principal component analysis to a genome-wide search for QTLs affecting postnatal growth in body weight weekly recorded from 3 to 10 weeks of age in an intersubspecific backcross population of C57BL/6J inbred mice (Mus musculus domesticus) and wild mice (M. m. castaneus) captured in the Philippines, in order to discover new QTLs from a gene pool of the wild mice and uncover major loci underlying variation in postnatal growth. Principal component analysis classified phenotypic variation in body weights at different ages into two independent principal components: the first principal component (PC1) extracted information on the entire growth process and the second principal component (PC2) contrasted middle (3-6 weeks of age) with late (6-10 weeks) growth phases. Simple interval mapping and composite interval mapping revealed 10 significant QTLs with main effects on PC1 or PC2 on eight chromosomes. Of these, the six main-effect QTLs interacted epistatically with one another or three new additional QTLs on different chromosomal regions without main effects. Several of the identified QTLs with main effects and/or epistatic interaction effects appeared to be sex specific. These results suggest that the identified 13 QTLs, most of which affected the entire growth process, are very important contributors to complex genetic networks of postnatal growth.     

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

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

Substantial changes in the genetic basis of tadpole morphology of Rana lessonae in the presence of predators

Predator-induced morphological plasticity is a model system for investigating phenotypic plasticity in an ecological context. We investigated the genetic basis of the predator-induced plasticity in Rana lessonae by determining the pattern of genetic covariation of three morphological traits that were found to be induced in a predatory environment. Body size decreased and tail dimensions increased when reared in the presence of preying dragonfly larvae. Genetic variance in body size increased by almost an order of magnitude in the predator environment, and the first genetic principal component was found to be highly significantly different between the two environments. The across environment genetic correlation for body size was significantly below 1 indicating that different genes contributed to this trait in the two environments. Body size may therefore be able to respond to selection independently in the two environments to some extent.     

The Hindlimb Elements of the Maas (Aves,Dinornithidae): A Multivariate Assessment of Size and Shape

A multivariate morphometric analysis of size and shape was performed on the hindlimb skeletal elements of the extinct New Zealand moas (Dinornithidae). Investigations were undertaken of size-shape patterns within species and among moas as a group using principal components analysis; between species investigations used canonical analysis. In addition, standard allometric curve-fitting of six femur, seven tibiotarsus, and nine tarsometatarsus variables against body size was performed. Size was the major discriminator along the first principal component for all three bones in the intraspecific and whole-group analyses. Shape was the important discriminator along the second component: in the whole-group analysis of all three bones, separation was based on relative robustness of the shaft, whereas in the intraspecific analyses shaft robustness was only expressed in the analysis of the femur, there being little correspondence in the results between the intraspeci fic and whole-group analyses of the tibiotarsus and tarsometatarsus. Size was the major discriminator along the first canonical axis for the between-group investigations of the femur and tibiotarsus, but in the analysis of the tarsometatarsus shape influences were equally as important as those of size. The second canonical axis separated groups on the basis of shape differences in all three hindlimb elements. The genus Dinornis, which contains the largest species of moas, has evolved sizeshape patterns very different from those of other moas. The species of Dinornis did not follow size-dependent allometric trends and evolved proportionately thinner legs than might be expected for their body size. All other moas exhibit allometric increase in all hindlimb variables except bone lengths. Dinornis may have evolved a cursorial mode of locomotion as an adaptation for certain intraspecific behavioral interactions.     

TYPE I ERROR RATES FOR TESTING GENETIC DRIFT WITH PHENOTYPIC COVARIANCE MATRICES: A SIMULATION STUDY

Studies of evolutionary divergence using quantitative genetic methods are centered on the additive genetic variance–covariance matrix ( G ) of correlated traits. However, estimating G properly requires large samples and complicated experimental designs. Multivariate tests for neutral evolution commonly replace average G by the pooled phenotypic within‐group variance–covariance matrix ( W ) for evolutionary inferences, but this approach has been criticized due to the lack of exact proportionality between genetic and phenotypic matrices. In this study, we examined the consequence, in terms of type I error rates, of replacing average G by W in a test of neutral evolution that measures the regression slope between among‐population variances and within‐population eigenvalues (the Ackermann and Cheverud [AC] test) using a simulation approach to generate random observations under genetic drift. Our results indicate that the type I error rates for the genetic drift test are acceptable when using W instead of average G when the matrix correlation between the ancestral G and P is higher than 0.6, the average character heritability is above 0.7, and the matrices share principal components. For less‐similar G and P matrices, the type I error rates would still be acceptable if the ratio between the number of generations since divergence and the effective population size (t/N_e) is smaller than 0.01 (large populations that diverged recently). When G is not known in real data, a simulation approach to estimate expected slopes for the AC test under genetic drift is discussed.     

PHYLOGENETIC ANALYSIS OF PHENOTYPIC COVARIANCE STRUCTURE. I. CONTRASTING RESULTS FROM MATRIX CORRELATION AND COMMON PRINCIPAL COMPONENT ANALYSES

Applications of quantitative techniques to understanding macroevolutionary patterns typically assume that genetic variances and covariances remain constant. That assumption is tested among 28 populations of the Phyllotis darwini species group (leaf-eared mice). Phenotypic covariances are used as a surrogate for genetic covariances to allow much greater phylogenetic sampling. Two new approaches are applied that extend the comparative method to multivariate data. The efficacy of these techniques are compared, and their sensitivity to sampling error examined. Pairwise matrix correlations of correlation matrices are consistently very high (> 0.90) and show no significant association between matrix similarity and phylogenetic relatedness. Hierarchical decomposition of common principal component (CPC) analyses applied to each clade in the phylogeny rejects the hypothesis that common principal component structure is shared in clades more inclusive than subspecies. Most subspecies also lack a common covariance structure as described by the CPC model. The hypothesis of constant covariances must be rejected, but the magnitudes of divergence in covariance structure appear to be small. Matrix correlations are very sensitive to sampling error, while CPC is not. CPC is a powerful statistical tool that allows detailed testing of underlying patterns of covariation.