An epistatic genetic basis for fluctuating asymmetry of mandible size in mice

The genetic basis of fluctuating asymmetry (FA), or nondirectional variation in the subtle differences between left and right sides of bilateral characters, continues to be of considerable theoretical interest. FA generally has been thought to arise from random noise during development and therefore to have a largely or entirely environmental origin. Whereas additive genetic variation for FA generally has been small and often insignificant, a number of investigators have hypothesized that interactions between loci, or epistasis, significantly influence FA. We tested this hypothesis by conducting a whole-genome scan to detect any epistasis in FA of centroid size in the mandibles of more than 400 mice from an F2 intercross population formed from crossing the Large (LG/J) and Small (SM/J) inbred strains. Genotypic deviations were imputed at each site 2 cM apart on all 19 autosomes, and these and centroid size asymmetry values were used in canonical correlation analyses for each of the 171 possible pairs of 19 autosomes to identify the most probable sites for epistasis. Epistasis for centroid size asymmetry was abundant, occurring far more often than was expected by chance alone (there were 30 separate instances of epistasis at the 0.001 significance level, when only two were expected by chance alone). The contributions of epistasis from 30 pairwise combinations of loci tended to suppress the additive and dominance genetic variance, but greatly increased the epistatic genetic variance for FA in centroid size given the intermediate allele frequencies of an F2 intercross population.     

Fluctuating asymmetry and allozymic heterozygosity among natural populations of pocket gophers (Thomomys bottae)

Fluctuating asymmetry, or random deviations from bilateral symmetry, has been widely used as a measure of developmental stability. The relationship between fluctuating asymmetry (FA) and allozymic heterozygosity was evaluated using 18 natural populations of pocket gophers ( Thomomys bottae ). Heterozygosity in local populations of pocket gophers ranges over more than an order of magnitude (1.5—18.4%), making this burrowing rodent particularly apt for such studies. Two measures of FA in mensural skull characters were examined: absolute deviations between left and right sides and the variance of signed differences. After log transformations, levels of FA among individuals and populations were not related to size. Repeated-measures analyses of variance showed that FA was significant relative to measurement error, both across populations and within them. Asymmetries of different characters were uncorrelated, despite positive significant correlations among the characters themselves. FA levels varied only slightly among populations of gophers, and this variation was not significant for most characters. FA levels of populations were not correlated with allozymic heterozygosity, and analyses of variance in FA employing heterozygosity were not significant. Heterozygosity levels in these rodents appear more strongly related to aspects of population history (especially effective size and gene flow) than to developmental stability. Because so many genomic and environmental factors can affect morphological variation, caution is needed in interpreting correlations between genetic and phenetic variation.     

Tarsal asymmetry, nutritional condition, and survival in water boatmen (Callicorixa Vulnerata)

Fluctuating asymmetry (FA) has been used as a measure of developmental stability and may indicate individual phenotypic or genotypic quality. Using water boatmen (Callicorixa vulnerata) from a natural population, we examined the relationship between tarsal FA (tarsal spine number, tarsal length) and indices of body condition in two habitats. We used body weight and residual body weight (controlling for body length) as indices of condition because experimental food deprivation in water boatmen led to a reduction in each. We detected a negative relationship between FA and both indices of condition in two ecologically distinct pond habitats. We predicted this association was due to a negative relationship between FA and competitive feeding ability. Consequently, we examined associations between survival time and tarsal FA in C. vulnerata under resource-limited laboratory conditions. Univariate analyses revealed a negative correlation between survival and tarsal FA in each trait. Inclusion of survival time, body length, gender, tarsal spine number, tarsal length, and measures of FA into multivariate analyses revealed a negative correlation between survival and FA. Individuals with the greatest survival had higher nutritional condition than individuals that succumbed early in the experiment. Asymmetric individuals may suffer a foraging handicap as a result of the use of tarsi in feeding or they may be of poor genetic quality. Our results suggest elevated FA may limit resource acquisition and are consistent with the use of FA as a measure of fitness.     

PHENOTYPIC PLASTICITY OF ANNUAL PHLOX: TESTS OF SOME HYPOTHESES

Phenotypic plasticity is an important means by which individual plants respond to environmental heterogeneity. Relative plasticities were compared for three species of annual Phlox grown in a set of six environmental treatments. Two measures of plasticity were computed for 18 characters per species: the Coefficient of Variation to measure amounts of plasticity and a new measure, the correlation of responses between species, which compares patterns of plasticity. Three hypotheses concerning the species’ amounts and patterns of plasticity were examined. The heterozygosity hypothesis states that levels of heterozygosity and amounts of plasticity should be inversely related. The relatedness hypothesis states that more distantly related species should have less similar patterns and amounts of plasticity. The ecological hypothesis states that species from similar habitats should have more similar amounts and patterns of plasticity than species which evolved under differing conditions. The results suggest that heterozygosity, relatedness, and ecology may all affect patterns and amounts of plasticity, and that no single hypothesis is sufficient to explain the observed results. Some data from previous studies are examined in relation to the proposed hypotheses.     

Fluctuating asymmetry and morphometric variation of hand bones

The major aim of this study was to test three hypotheses: 1) more complex traits of the hand are less prone to developmental insults and therefore show lower fluctuating asymmetry (FA) as compared with simple traits; 2) the manifestation of FA correlates with the variability of the trait (i.e., CV); and 3) FA is an organ-wide property, and therefore a concordance exists between the FA measures of different traits in hand bones. Seventy-two bilateral measurements of hand bones, were made from plain-film radiographs of 365 cadavers. A complex trait was considered as the total length of the three phalanges of a finger and their contiguous metacarpals. Simple traits were considered to be the lengths of individual bone that made up the complex trait. The following results were obtained: 1) on the average simple traits, composing the complex trait, show much higher FA than the corresponding complex trait, but this result is expected if there is no correlation (or low correlation) between FA of simple traits within the complex trait, due to random direction of right-left differences; 2) strong and highly significant correlation was observed between FA and CV of studied traits, regardless of sex and age of individuals; and 3) the majority of FA measurements of hand bones showed no correlation. However, correlations between some sets of FA traits were highly significant. They were interpreted, although not specifically tested, as the result of a tight relationship between traits related not only developmentally but also by active performance of the same function. Am J Phys Anthropol 107:125–136, 1998. © 1998 Wiley-Liss, Inc.     

Fluctuating asymmetry as a possible measure of developmental homeostasis in humans: a review

We investigate three hypotheses related to fluctuating asymmetry (FA) of bilateral morphologic traits in humans: (1) the magnitude of FA in individual suffering from different levels of morbidity is significantly elevated compared with FA in healthy control subjects, (2) FA is negatively correlated with an individual's heterozygosity, and (3) phenotypic variance of FA may have a significant genetic component (or at least a family resemblance). Our experimental data and the literature support the first hypothesis and indicate that individuals who suffer from chromosomal or polygenic morbidity and from anomalies or conditions of development with still unknown genetic components demonstrate an elevated FA of various structures. The literature regarding the second hypothesis is sparse but is generally in agreement with it, although some exceptions exist. A study of correlations of phenotypic scores of FA between family members of nuclear families in two independent samples has shown that FA variance in individual traits probably does not have any significant genetic component. However, phenotypic variance of the mean estimate of FA over 8 traits showed significant additive and nonadditive (dominance) genetic components, each about 0.30.     

Variation in bilateral asymmetry of the Lusitanian toadfish along the Portuguese coast

Three types of bilateral asymmetry [antisymmetry (AS), directional asymmetry (DA) and fluctuating asymmetry (FA)] have long been recognized in the literature. It is often assumed that DA and AS have a larger genetic basis than FA, which therefore provides a measure of developmental stability. To examine changes in bilateral asymmetry of the Lusitanian toadfish, Halobatrachus didactylus (Bloch & Schneider, 1801), collected in 10 localities along the Portuguese coast, the distribution of left–right values of three external and two internal morphometric variables and one meristic variable were evaluated for normality and deviations of the mean to 0; kurtosis and skewness were also determined. AS was found for the majority of variables in all locations, although DA was also very frequent. FA was observed in only four locations for three variables. A general pattern of negative and low Spearman correlations between asymmetry levels and concentrations of heavy metals and pollutants and mean heterozygosity was found. However, exceptions to this pattern indicate that different asymmetry types can occur across the distribution range in a single trait and that the three types of asymmetry are dynamically interrelated, the shifts from FA to the other two types possibly being due to environmental stress.     

Correlation analysis of dissimilarity matrices

Distance-based methods have been a valuable tool for ecologists for decades. Indirectly, distance-based ordination and cluster analysis, in particular, have been widely practiced as they allow the visualization of a multivariate data set in a few dimensions. The explicitly distance-based Mantel test and multiple regression on distance matrices (MRM) add hypothesis testing to the toolbox. One concern for ecologists wishing to use these methods lies in deciding whether to combine data vectors into a compound multivariate dissimilarity to analyze them individually. For Euclidean distances on scaled data, the correlation of a pair of multivariate distance matrices can be calculated from the correlations between the two sets of individual distance matrices if one set is orthogonal, demonstrating a clear link between individual and compound distances. The choice between Mantel and MRM should be driven by ecological hypotheses rather than mathematical concerns. The relationship between individual and compound distance matrices also provides a means for calculating the maximum possible value of the Mantel statistic, which can be considerably less than 1 for a given analysis. These relationships are demonstrated with simulated data. Although these mathematical relationships are only strictly true for Euclidean distances when one set of variables is orthogonal, simulations show that they are approximately true for weakly correlated variables and Bray–Curtis dissimilarities.     

Variables affecting dental fluctuating asymmetry in human isolates

The aims of the present study are to 1) determine and describe levels of dental fluctuating asymmetry (FA) in a highly endogamous human group; 2) evaluate the effects of various FA measures on perceived FA levels and their interrelationships; 3) study the connections between dental variables (tooth size, class, position, type, location and dimension) and FA levels; and 4) estimate the interrelationships between dental FA measures. The study was carried out on 242 Bedouin boys aged 5 to 14 years. The results demonstrate that the main variables influencing dental FA levels within this population are tooth class (incisors, canine, premolars, molars) and position (mesial, distal) and that the interaction between the two is significant. When sample sizes are large enough and individual measures are needed for the statistical analysis, the use of a computational method based on absolute values is legitimate. Clear relationships between some FA dental traits are discerned though principal-components analysis. © 1993 Wiley-Liss, Inc.     

Fluctuating asymmetry and fitness correlations in two Engraulis encrasicolus populations

Correlations among several measures of fluctuating asymmetry (FA) and fitness‐related variables were assessed in two populations of the European anchovy Engraulis encrasicolus with fast growth (Aegean Sea) and slow growth (Ionian Sea), respectively. FA levels were borderline significantly higher in the Ionian than in the Aegean for some variables. Variation in otolith shape (deviation from population norm) was lower in the Ionian than the Aegean, contrary to expectation. Within the Aegean, there was no relation between any of the FA indexes and fitness estimators, while in the Ionian a composite otolith FA index was significantly negatively correlated to standard length at age only in 2 year‐old individuals. This difference between the Aegean and Ionian may have been related to the lower growth rate in the Ionian, as FA–fitness relations may be more apparent in less‐beneficial environments. The absence of significant correlations in the Aegean and the low correlation in one age group in the Ionian suggests that FA is not a sensitive indicator of individual fitness in adult E. encrasicolus.     

Geography of fluctuating asymmetry in the greenfinch, Carduelis chloris

Levels of fluctuating asymmetry (FA) in 12 bilateral skeletal traits were estimated from 12 populations of greenfinches (Carduelis chloris) collected along a north‐south gradient across Europe. Average FA of measured traits was positively correlated with latitude indicating that the younger and genetically less diverse northern European populations are developmentally less stable than the older and genetically more diverse southern populations. Levels of FA differed significantly between different traits being lowest for functionally important traits (limb and wing bones) and highest for functionally less important traits such as foramina (apertures through bones)– a pattern that was highly concordant across different populations. Males tended to exhibit higher levels of FA than females, a finding consistent with the suggestions that males are more prone to developmental perturbations than females. Age differences in levels of FA were relatively clear, but inconsistent across traits with different degree of functionality. Individual heterozygosity – as enumerated from variation in allozyme loci – was unrelated to individual FA. No evidence for existence of individual asymmetry parameter (IAP) was found although traits related to locomotion indicated some degree of integration, which was expressed by correlations in the signed asymmetry. Nevertheless, an individual's overall asymmetry was poorly predicted by asymmetry of individual characters. Evidence for existence of population asymmetry parameter (PAP) was clear since all traits exhibited a similar degree of association with latitude. That the latitudinal cline of increasing FA towards north coincided with decreasing levels of genetic variability across the cline could be indicative of break down of developmental stability in the recently established and genetically impoverished populations. To what extent a reduced heterozygosity, the break up of co‐adapted gene complexes and/or environmental differences contributed to this process cannot be distinguished from our data.     

Genetic and environmental influence on the asymmetry of dermatoglyphic traits

Fluctuating asymmetry (FA) is defined as random deviations from bilateral symmetry of the body. Thus, its magnitude is often used to evaluate developmental homeostasis. In this study we evaluate the following hypotheses: 1) FA of dermatoglyphic traits has a significant genetic component; 2) prenatal maternal environment (PME) has a significant effect on the FA of dermatoglyphic traits in developmentally healthy individuals; and 3) genetic or environmental factors affect FA on organismal or systemic levels. Therefore, their effect is better seen in composite scores of FA rather than in FA indices for single traits. We analyzed 15 dermatoglyphic traits from 140 pairs of monozygous twins, 120 pairs of dizygous twins, and 106 pairs of mothers and daughters. All individuals were developmentally healthy. The influence of genetic and environmental factors on FA was evaluated by analysis of variance and regression analysis. For a majority of the traits in our study, FA showed significant but weak heritabilities, with values falling within the 0.20-0.35 range. None of the traits taken separately demonstrated the effect of PME on FA to be significantly greater than zero. The composite score of FA tended to have greater heritability values than individual traits. One of them, obtained in principal components analysis, showed a significant PME effect, supporting the hypothesis that FA is a systemic property.     

Is phenotypic canalization involved in the decline of the endemic Aquilegia thalictrifolia? Rethinking relationships between fluctuating asymmetry and species conservation status

Fluctuating asymmetry (FA), the deviation from the normal symmetrical condition of a morphological trait having specific morphological symmetry, increases in response to environmental and genetic stress, is related to phenotypic plasticity and is considered a tool for monitoring a species conservation status. However, FA–stress relations are dependent on measured traits or species‐specific characteristics such as mating system and habitat. This study investigates the relationships between FA, genetic diversity, population size, density and individual fitness traits (plant height, fruit and seed set), in the endemic Aquilegia thalictrifolia, a mixed breeder that is declining, but maintaining high levels of heterozygosity. Leaf and flower FA and other traits were investigated in 10 populations of A. thalictrifolia, the whole species range. As a result, we found similar patterns of FA in leaves and flowers between populations, indicating a homogenous level of stress between populations that differed for other traits. FA and the other traits were not related, including heterozygosity. Heterozygosity was not related to individual fitness traits with the exception of plant height. In accordance with other studies, we found that the role of FA as a tool for assessing the conservation status of a species or population should be reconsidered. However, we conclude that a low level of FA should not automatically be considered an indicator of good conservation status or low level of stress, because in species that evolved in highly stable environments it may indicate a scarce ability to plastically respond to environmental changes, as a consequence of environmental and genetic canalization. Further investigation of this point is needed.     

An epistatic genetic basis for fluctuating asymmetry of tooth size and shape in mice

Although there typically is little additive genetic variation for fluctuating asymmetry (FA), or variation in nondirectional differences between left and right sides of bilateral characters, several investigators have hypothesized that FA may have an epistatic genetic basis. We tested this hypothesis by conducting a whole genome scan of FA of size and shape of the mandibular molars in house mice from an F2 intercross population generated from crossing the Large (LG/J) and Small (SM/J) inbred strains. Although no individual genes (QTLs=quantitative trait loci) on any of the 19 autosomes significantly affected FA for centroid size, and only two affected shape FA, a number of pairwise combinations of QTLs exhibited significant epistasis for FA in both molar size and shape. The QTLs involved in these interactions differed for FA in molar size versus FA in molar shape, but their epistatic contributions to the total variance was nearly the same (about 20%) for FA in both molar characters. It was noted that the genetic architecture of FA in the molar characters, consisting of little or no additive genetic variance but an abundance of epistatic genetic variance, is consistent with that of other typical fitness components such as litter size.     

Microsatellites reveal heterosis in red deer.

The fitness consequences of inbreeding and outbreeding are poorly understood in natural populations. We explore two microsatellite-based variables, individual heterozygosity (likely to correlate with recent inbreeding) and a new individual-specific internal distance measure, mean d2 (focusing on events deeper in the pedigree), in relation to two measures of fitness expressed early in life, birth weight and neonatal survival, in 670 red deer calves (Cervus elaphus) born on the Isle of Rum between 1982 and 1996. For comparison, we also analyse inbreeding coefficients derived from pedigrees in which paternity was inferred by molecular methods. Only 14 out of 231 calves (6.1%) had non-zero inbreeding coefficients, and neither inbreeding coefficient nor individual heterozygosity was consistently related to birth weight or neonatal survival. However, mean d2 was consistently related to both fitness measures. Low mean d2 was associated with low birth weight, especially following cold Aprils, in which foetal growth is reduced. Low mean d2 was also associated with low neonatal survival, but this effect was probably mediated by birth weight because fitting birth weight to the neonatal survival model displaced mean d2 as an explanatory variable. We conclude that in the deer population fitness measures expressed early in life do not show evidence of inbreeding depression, but they do show evidence of heterosis, possibly as a result of population mixing. We also demonstrate the practical problems of estimating inbreeding via pedigrees compared with a direct marker-based estimate of individual heterozygosity. We suggest that, together, individual heterozygosity and mean d2, estimated using microsatellites, are useful tools for exploring inbreeding and outbreeding in natural population.     

Distance-based tests for homogeneity of multivariate dispersions

Summary The traditional likelihood‐based test for differences in multivariate dispersions is known to be sensitive to nonnormality. It is also impossible to use when the number of variables exceeds the number of observations. Many biological and ecological data sets have many variables, are highly skewed, and are zero‐inflated. The traditional test and even some more robust alternatives are also unreasonable in many contexts where measures of dispersion based on a non‐Euclidean dissimilarity would be more appropriate. Distance‐based tests of homogeneity of multivariate dispersions, which can be based on any dissimilarity measure of choice, are proposed here. They rely on the rotational invariance of either the multivariate centroid or the spatial median to obtain measures of spread using principal coordinate axes. The tests are straightforward multivariate extensions of Levene's test, with P‐values obtained either using the traditional F‐distribution or using permutation of either least‐squares or LAD residuals. Examples illustrate the utility of the approach, including the analysis of stabilizing selection in sparrows, biodiversity of New Zealand fish assemblages, and the response of Indonesian reef corals to an El Niño. Monte Carlo simulations from the real data sets show that the distance‐based tests are robust and powerful for relevant alternative hypotheses of real differences in spread.     

Genetic analysis of bilateral dermatoglyphic asymmetry in twins and their parents

The data for this study were collected on 64 twin pairs (30 MZ and 34 DZ) and their 128 parents. Two following hypotheses were evaluated: 1. Bilateral asymmetry is significantly genetically controlled; 2. The twinning phenomenon would affect the magnitude of bilateral asymmetry. The results revealed no statistically significant differences between mean values of MZ and DZ twins and their parents for the majority of the traits. Significant differences were recorded for only 6 of 96 comparisons (6%). Analysis of variance revealed separated sources of MZ, DZ and singleton variance. F-ratios, contrasting variances between different groups were significant for 26 of 96 comparisons (27%) showing heterogeneity of variance between zygosities and between twins and their parents. In addition, environmental covariance appeared to be larger for MZ than DZ with respect to directional asymmetry (DA) for all 16 traits and fluctuating asymmetry (FA) for 14 traits. These observations showed complex environmental determinism for bilateral asymmetry for the majority of dermatoglyphic traits. Significant genetic variance ratios (GVRs) were observed for four variables (25%) with respect to DA and three variables (18.75%) with respect to FA. All these significant GVRs were rendered insignificant because of evidence of greater environmental covariance for MZ twins, except possibly for DA for URC4.     

A latent variable model of developmental instability in relation to men's sexual behaviour

A single trait's fluctuating asymmetry (FA) is expected to be a poor measure of developmental instability. Hence, studies that examine associations between FA and outcomes expected to covary with developmental instability often have little power in detecting meaningful relationships. One way of increasing the power of detecting relationships between developmental instability and outcomes is through the use of multiple traits' FA. The way multiple traits have typically been used is in trait aggregates. Here, we illustrate another way of examining relationships with developmental instability using multiple traits' FA: through structural equation modelling. Covariances between measures of FA and an outcome variable are interpreted within the context of an explicit model of associations between variables, which is tested for fit and the parameters specified within the model are estimated. We used nine traits' FA as markers of a latent variable of men's developmental instability, which was associated with the number of sexual partners. The results indicate a sizeable correlation between developmental instability and men's sexual history, despite small correlations between individual traits' FA and sexual history.     

Macro-alga population shows low but significant heterogeneity in developmental instability with no detectable association with individual fitness

We studied among-individual variation in developmental instability (DI) and fitness-related parameters in 80 individual plants of Fucus vesiculosus (Phaeophyta). To minimize differential environmental effects, plants were sampled from one environmentally homogenous population. DI was measured as fluctuating asymmetry (FA) of four bilaterally symmetric traits (branch length, receptacle length and width, and bladder width) for an average total of 30 structures per individual. FA levels varied significantly among individual plants, consistent with a coefficient of variation of 0.12 for organism-wide DI or 0.13–0.21 for trait-specific DI. These values are lower than estimates for other organisms, suggesting that the genetic heterogeneity in DI was low. The data provide some evidence for organism-wide DI, but simulations show that organism-wide and trait-specific variation cannot be conclusively separated. Growth rate of branch tips was determined experimentally, demonstrating significant variation among individuals. FA was not significantly correlated with growth rate or with morphological variables associated with fecundity, age, size, and health. At the same time, the signs of all the correlation coefficients were consistent with the expectation of a negative relationship between DI and fitness. The simulations indicated that the correlation between FA and the underlying DI was comparatively strong (high hypothetical repeatability), implying that the lack of significant associations between FA and fitness variables reflected a weak relationship between DI and these fitness parameters. This weak relationship may be related to the low amount of DI variation in the study population.  © 2007 The Linnean Society of London, Biological Journal of the Linnean Society , 2007, 92 , 277–286.     

Detection of differential gene flow from patterns of quantitative variation

A major goal in anthropological genetics is the assessment of the effects of different microevolutionary forces. Harpending and Ward (1982) developed a model that aids in this effort by comparing observed and expected heterozygosity within populations in a local region. The expected heterozygosity within a population is a function of the total heterozygosity of the entire region and the distance of the population from the regional mean centroid of allele frequencies. Greater than average gene flow from an external source will result in a population having greater heterozygosity than expected. Less than average gene flow from an external source will result in a population having less heterozygosity than expected. We extend the Harpending-Ward model to quantitative traits using an equal and additive effects model of inheritance. Here the additive genetic variance within a population is directly proportional to heterozygosity, and its expectation is directly proportional to the genetic distance from the centroid. Under certain assumptions the expectations for phenotypic variances are similar. Observed and expected genetic or phenotypic variance can then be compared to assess the effects of differential external gene flow. When the additive genetic covariance matrix or heritabilities are not known, the phenotypic covariance matrix can be used to provide a conservative application of the model. In addition, we develop new methods for estimation of the genetic relationship matrix (R) from quantitative traits. We apply these models to two data sets: (1) six principal components derived from twenty dermatoglyphic ridge count measures for nine villages in Nepal and (2) ten anthropometric measurements for seven isolated populations in western Ireland. In both cases both the univariate and multivariate analyses provide results that can be directly interpreted in terms of historically known patterns of gene flow.