Comparing G: multivariate analysis of genetic variation in multiple populations

The additive genetic variance–covariance matrix (G) summarizes themultivariate genetic relationships among a set of traits. The geometry of Gdescribes the distribution of multivariate genetic variance, and generates geneticconstraints that bias the direction of evolution. Determining if and how the multivariategenetic variance evolves has been limited by a number of analytical challenges incomparing G-matrices. Current methods for the comparison of G typically shareseveral drawbacks: metrics that lack a direct relationship to evolutionary theory, theinability to be applied in conjunction with complex experimental designs, difficultieswith determining statistical confidence in inferred differences and an inherentlypair-wise focus. Here, we present a cohesive and general analytical framework for thecomparative analysis of G that addresses these issues, and that incorporates andextends current methods with a strong geometrical basis. We describe the application ofrandom skewers, common subspace analysis, the 4th-order genetic covariance tensor and thedecomposition of the multivariate breeders equation, all within a Bayesian framework. Weillustrate these methods using data from an artificial selection experiment on eighttraits in Drosophila serrata, where a multi-generational pedigree was availableto estimate G in each of six populations. One method, the tensor, elegantlycaptures all of the variation in genetic variance among populations, and allows theidentification of the trait combinations that differ most in genetic variance. The tensorapproach is likely to be the most generally applicable method to the comparison ofG-matrices from any sampling or experimental design.     

Quantitative genetic analysis of skin reflectance: a multivariate approach.

Skin color is a polygenically determined quantitative trait. Although it has been used extensively in studies of between-population variation, there have been relatively few studies of the inheritance of skin color. In this article we use measurements on 359 members of the Jirel population of eastern Nepal to assess the heritabilities and additive genetic correlations of three skin reflectance measures. Skin color was measured at the upper inner arm site at three wavelengths. A maximum likelihood approach was used to estimate sex and age effects on skin reflectance, heritabilities, and phenotypic variances at each wavelength and both additive genetic and environmental correlations between wavelengths. This technique incorporated information from 36 pedigrees with 2-25 members and 173 independent individuals. Likelihood ratio tests were used to assess the significance of specific variance/covariance components. The results indicate that skin reflectances are moderately heritable at all three wavelengths. The pairwise phenotypic correlations ranged from 0.76 to 0.88. The observed additive genetic correlations were not significantly different from 1.00, suggesting that the same loci influence variation at each wavelength. This evidence for relatively complete pleiotropy implies that measurements at multiple wavelengths yield little additional genetic information, although they may be useful for reducing measurement error. Based on estimates of the genetic and phenotypic covariance matrices, we determined that skin reflectance measurements are expected to provide only as much information for assessing local between-population genetic variation as a single two-allele polymorphic marker. Therefore microevolutionary studies based on skin color variation should be viewed with caution.     

Correlated evolution of multivariate traits: detecting co-divergence across multiple dimensions

Tests of correlated evolution typically treat phenotypic characters as univariate variables, even though different trait attributes may contribute to their association with other traits. In this study, patterns of character covariation among species are analysed in a multivariate framework to test for both correlated rates and directions of evolutionary change in traits forming the genitalic complex of male grasshoppers. Although the covariation structure differs among traits, and among the constituent species of two grasshopper clades, significant co-divergence was detected among the most closely interacting genitalic traits (i.e. intromittent characters) in both clades. Co-divergence across shape space is not accompanied by similar rates of evolution among species, although the intromittent characters tend to show accelerated evolution (relative to nonintromittent characters). Differences in the evolutionary trajectories among traits may relate to their varied roles during mating. The study emphasizes the importance of a multivariate framework for detecting macroevolutionary patterns of correlated change.     

Patterns of quantitative genetic variation in multiple dimensions

A fundamental question for both evolutionary biologists and breeders is the extent to which genetic correlations limit the ability of populations to respond to selection. Here I view this topic from three perspectives. First, I propose several nondimensional statistics to quantify the genetic variation present in a suite of traits and to describe the extent to which correlations limit their selection response. A review of five data sets suggests that the total variation differs substantially between populations. In all cases analyzed, however, the “effective number of dimensions” is less than two: more than half of the total genetic variation is explained by a single combination of traits. Second, I consider how patterns of variation affect the average evolutionary response to selection in a random direction. When genetic variation lies in a small number of dimensions but there are a large number of traits under selection, then the average selection response will be reduced substantially from its potential maximum. Third, I discuss how a low genetic correlation between male fitness and female fitness limits the ability of populations to adapt. Data from two recent studies of natural populations suggest this correlation can diminish or even erase any genetic benefit to mate choice. Together these results suggest that adaptation (in natural populations) and genetic improvement (in domesticated populations) may often be as much constrained by patterns of genetic correlation as by the overall amount of genetic variation.     

Individual differences in estrogen receptor alpha in select brain nuclei are associated with individual differences in aggression

Steroid hormones play an important role in modulating social behavior in many species. Estrogens are thought to act on an interconnected network of hypothalamic and limbic brain areas to affect aggressive behavior, although the specific nuclei unknown remain unspecified. We show that individual variation in estrogen receptor alpha (ERalpha) immunoreactivity in the lateral septum (LS), ventral bed nucleus of the stria terminalis (vBNST), and anterior hypothalamus (AHA) of CD-1 mice is positively correlated with aggressive behavior. When males were treated with fadrozole (an aromatase inhibitor), aggressive behavior was reduced, although castration did not reduce aggression. These results suggest that estrogens modulate aggressive behavior by acting on a circuit that includes the LS, vBNST, and AHA and that the source of estrogens is non-gonadal. Fadrozole also decreased c-fos expression in the lateral septum following aggressive encounters. Although the effects of estrogen on aggression appear to involve regulation of neuronal activity in the LS, additional processes are likely involved. These results suggest that estrogen acts in a specific subset of a complex network of nuclei to affect aggressive behavior.     

A univariate and multivariate examination of measurement error in anthropometry

Replicate anthropometric measurements on 20 male and 22 female Eskimos were examined using analysis of variance, product-moment correlation coefficients, and canonical variates with Mahalanobis' D² distances. Analysis of variance indicated that 12 of the 16 variables could be measured comparably by two investigators. Those variables with readily defined endpoints yielded the highest correlations between the results of two anthropometrists. The multivariate analysis demonstrated a high level of discrimination between two sets of data taken on the same group of subjects. This suggests that population comparisons using data from two or more investigators could be significantly affected by measurement error.     

adegenet: a R package for the multivariate analysis of genetic markers

The package adegenet for the R software is dedicated to the multivariate analysis of genetic markers. It extends the ade4 package of multivariate methods by implementing formal classes and functions to manipulate and analyse genetic markers. Data can be imported from common population genetics software and exported to other software and R packages. adegenet also implements standard population genetics tools along with more original approaches for spatial genetics and hybridization. AVAILABILITY: Stable version is available from CRAN: http://cran.r-project.org/mirrors.html. Development version is available from adegenet website: http://adegenet.r-forge.r-project.org/. Both versions can be installed directly from R. adegenet is distributed under the GNU General Public Licence (v.2).     

Probability binning comparison: a metric for quantitating univariate distribution differences

BACKGROUND: Comparing distributions of data is an important goal in many applications. For example, determining whether two samples (e.g., a control and test sample) are statistically significantly different is useful to detect a response, or to provide feedback regarding instrument stability by detecting when collected data varies significantly over time. METHODS: We apply a variant of the chi-squared statistic to comparing univariate distributions. In this variant, a control distribution is divided such that an equal number of events fall into each of the divisions, or bins. This approach is thereby a mini-max algorithm, in that it minimizes the maximum expected variance for the control distribution. The control-derived bins are then applied to test sample distributions, and a normalized chi-squared value is computed. We term this algorithm Probability Binning. RESULTS: Using a Monte-Carlo simulation, we determined the distribution of chi-squared values obtained by comparing sets of events derived from the same distribution. Based on this distribution, we derive a conversion of any given chi-squared value into a metric that is analogous to a t-score, i.e., it can be used to estimate the probability that a test distribution is different from a control distribution. We demonstrate that this metric scales with the difference between two distributions, and can be used to rank samples according to similarity to a control. Finally, we demonstrate the applicability of this metric to ranking immunophenotyping distributions to suggest that it indeed can be used to objectively determine the relative distance of distributions compared to a single control. CONCLUSION: Probability Binning, as shown here, provides a useful metric for determining the probability that two or more flow cytometric data distributions are different. This metric can also be used to rank distributions to identify which are most similar or dissimilar. In addition, the algorithm can be used to quantitate contamination of even highly-overlapping populations. Finally, as demonstrated in an accompanying paper, Probability Binning can be used to gate on events that represent significantly different subsets from a control sample. Published 2001 Wiley-Liss, Inc.     

Assessment of yield stability in sorghum using univariate and multivariate statistical approaches

The experiment was carried out to estimate GEI in sorghum for grain yield using univariate and multivariate statistical approaches based on two sets of performance trials (T1 and T2). While T1 consisted of 15 genotypes and tested in 8 environments, T2 that consisted of 13 genotypes was carried out in 13 environments. Because the combined ANOVA of each trial revealed significant differences among the genotypes, among the environments and GEI, the five univariate stability estimates: CV(i), S(i)(2), W(i)(2), sigma(i)(2), b(i) and Sd(i)(2) were evaluated for ranking the genotypes. There was positive rank-correlation between CVi and S(i)(2) and among W(i)(2), sigma(i)(2), b(i). Sd(i)(2) had significant positive rank-correlation with sigma(i)(2) and bi in T1 but weak rank-correlation with the remaining parameters in both trials. The three types of univariate stability estimates and the only multivariate stability estimate, the AMMI analysis declared genotypes 2 and 5 to be the most stable in T1, but they gave quite unrelated ranking in T2. Because of the lack of correspondence among the tested stability estimates in the two trials, it was difficult to reach a conclusion on producing genotype recommendation based on the univariate statistical approach. However, as GEI has multivariate nature, the multivariate approach is believed to give more robust inference. Hence, some stable genotypes were suggested using the AMMI model for sorghum growing dry lowlands of the country.     

Digital dermatoglyphics in the Basque population: univariate and multivariate comparison with other Spanish populations

We have analyzed dermatoglyphic finger patterns in a Spanish Basque population (841 males and 911 females). Bimanual and sexual comparisons have been carried out by means of contingency analysis. The results in the Basque population are compared with those of other Spanish populations, based on univariate (chi 2 contingency test and Student's t-test) and multivariate (principal components analyses) statistical methods. Bilateral distribution asymmetry and sexual dimorphism were observed in the Basque sample. The results of the chi 2 test for pattern types in males and females show statistically significant differences between the Basques and other Spanish populations, with the exception of the males from El Bierzo. Comparing populations with regard to the Pattern Intensity Index, the differences observed are much lower; therefore, this confirms what other authors have suggested regarding the limited usefulness of indexes in populational comparisons. In the Caucasian variation range of pattern types, Basques are located in the high part with regard to arches, in the low part with regard to whorls and radial loops, and in an intermediate part in relation to ulnar loops and overall pattern intensity. Results of the multivariate comparisons show which populations are more or less distant from the Basque population and which variables are significant in contributing to these population relationships.     

Opiate receptors in mice: genetic differences.

The concentration of opiate receptors in the brains of mice was determined by means of a naloxone-binding assay. The strains of mice used in these experiments were C57BL/6By, BALB/cBy, their reciprocal F₁ hybrids, and 7 recombinant-inbred strains derived by inbreeding from the F₂ generation. These strains could be divided into 3 groups on the basis of the number of opiate receptors: high (CXBH); low (CXBK); and intermediate (all the other strains). The difference in stereospecific binding of naloxone reflects a difference in the total number of receptor sites rather than in the affinity for the drug. The recombinantinbred strains also differ in their analgesic response to morphine, as previously determined by the tail-flick assay. The differences in the number of opiate receptors are not enough to account for the genetic difference in analgesic responsiveness. Both these parameters appear to be under different genetic control, and at least 2 genetic determinants may be involved in regulating the level of opiate receptors.     

Individual variation in social aggression and the probability of inheritance: theory and a field test

Recent theory suggests that much of the wide variation in individual behavior that exists within cooperative animal societies can be explained by variation in the future direct component of fitness, or the probability of inheritance. Here we develop two models to explore the effect of variation in future fitness on social aggression. The models predict that rates of aggression will be highest toward the front of the queue to inherit and will be higher in larger, more productive groups. A third prediction is that, in seasonal animals, aggression will increase as the time available to inherit the breeding position runs out. We tested these predictions using a model social species, the paper wasp Polistes dominulus. We found that rates of both aggressive "displays" (aimed at individuals of lower rank) and aggressive "tests" (aimed at individuals of higher rank) decreased down the hierarchy, as predicted by our models. The only other significant factor affecting aggression rates was date, with more aggression observed later in the season, also as predicted. Variation in future fitness due to inheritance rank is the hidden factor accounting for much of the variation in aggressiveness among apparently equivalent individuals in this species.     

Phenotypic plasticity of introduced versus native purple loosestrife: univariate and multivariate reaction norm approaches

The plastic responses to environmental change by Lythrum salicaria (purple loosestrife) were compared between native plants derived from seeds collected in Europe and those introduced into North America. Plants from nine populations each were grown under two levels of water and nutrient conditions. At the end of the growing season, samples were evaluated for eight traits related to their life history, plant size/architecture, and reproduction. Genetic (G), environmental (E), and G × E interactions were assessed by restricted maximum likelihood (REML) analysis of covariance (ANCOVA) and multivariate analysis of covariance (MANCOVA). Both univariate and multivariate reaction norm analyses were used to test for differences in the magnitude and direction of phenotypic plasticity between introduced and native plants. Under high-nutrient conditions, introduced plants were taller and had more branches and greater aboveground biomass. They also exhibited significantly greater amounts of phenotypic plasticity for aboveground biomass than did the natives in response to changing nutrient levels in standing water. This difference in univariate plasticity contributed to the general contrast in multivariate plasticity between introduced and native plants. These results support the idea that introduced plants may successfully invade a habitat and grow better than native plants in response to increased resources.     

Individual differences affect honest signalling in a songbird

Research in the past decade has established the existence of consistent individual differences or ‘personality’ in animals and their important role in many aspects of animal behaviour. At the same time, research on honest signalling of aggression has revealed that while some of the putative aggression signals are reliable, they are only imperfectly so. This study asks whether a significant portion of the variance in the aggression-signal regression may be explained by individual differences in signalling strategies. Using the well-studied aggressive signalling system of song sparrows (Melospiza melodia), we carried out repeated assays to measure both aggressive behaviours and aggressive signalling of territorial males. Through these assays, we found that aggressive behaviours and aggressive signalling were both highly repeatable, and moreover that aggressive behaviours in 2009–2010 predicted whether the birds would attack a taxidermic mount over a year later. Most significantly, we found that residual variation in signalling behaviours, after controlling for aggressive behaviour, was individually consistent, suggesting there may be a second personality trait determining the level of aggressive signalling. We term this potential personality trait ‘communicativeness’ and discuss these results in the context of honest signalling theories and recent findings reporting prevalence of ‘under-signalling’.     

Otitis media: genetic factors and sex differences.

Although genetic factors are recognised as major contributors to otitis media, the presence of sex differences in heritability needs clarification. The aim of this study was to estimate the relative contribution of genetic and environmental effects in otitis media liability with particular focus on sex differences. Data from a cohort of Norwegian twins born between 1967 and 1979 with repeated measures on recurrent childhood otitis media were analysed. Altogether the sample included 4247 twin pairs. The tetrachoric correlations for monozygotic twins were .71 and .65 for males and females respectively. In dizygotic twins the correlations were .35 and .25 for males and females, respectively, and was.34 in opposite sexed pairs. The contribution of genetic and environmental effects was analyzed using structural equation modeling. The best fitting model showed that additive genetic effects explained 72% and 61% of the variance in males and females, respectively. The remaining variance was attributed to individual environmental effects. A model specifying equal heritability estimates for males and females yielded an almost equivalent fit. We found substantial genetic effects for liability to otitis media. There is no evidence that different sets of genes influence liability in males and females, but there may be sex differences in the relative importance of genetic effects.     

Morphological clues to genetic species: multivariate analysis of greater Galago sibling species

Several studies conducted in diverse fields indicate the presence of a genetic discontinuity within the taxon Galago crassicaudatus E. Geoffroy--the thick-tailed bushbaby. One of these areas is morphology. This contribution details a statistical analysis of skull material classified under this taxon in order 1) to confirm the objective existence of two morphotypes, and 2) to investigate the characters that allow the skull types to be distinguished. Emphasis is placed on multivariate techniques, although univariate and bivariate techniques are included where they are felt to be appropriate. All statistical analyses point to the reality of the morphological discontinuity between the groups. This is true even when size considerations have been reduced by rescaling the data. The results support separation of the populations at a specific level: G. crassicaudatus and G. garnettii. In addition, the structural changes observed in the two taxa--including an increase in overall size in G. crassicaudatus--are indicative of a divergence in preferred habitats: G. garnettii is adapted to more mesic environmental conditions, and to a softer, less fibrous diet than is its more robust sibling.