Quantitative trait loci for directional but not fluctuating asymmetry of mandible characters in mice

Non-directional variation in right minus left differences in bilateral characters, referred to as fluctuating asymmetry (FA), often has been assumed to be largely or entirely environmental in origin. FA increasingly has been used as a measure of developmental stability, and its presumed environmental origin has facilitated the comparisons of populations believed to differ in their levels of stability. Directional asymmetry (DA), in which one side is consistently larger than the other, has been assumed to be at least partially heritable. Both these assumptions were tested with interval mapping techniques designed to detect any quantitative trait loci (QTLs) affecting FA or DA in 15 bilateral mandible characters in house mice resulting from a cross of the F1 between CAST/Ei (wild strain) and M16i (selected for rapid growth rate) back to M16i. For purposes of the analysis, all mandibles were triply measured and 92 microsatellite markers were scored in a total of 350 mice. No significant QTLs were found for FA, but three QTLs significantly affected DA in several characters, confirming both assumptions. The QTLs for DA were similar in location to those affecting the size of several of the mandible characters, although they accounted for an average of only 1% of the total phenotypic variation in DA.     

A SEARCH FOR QUANTITATIVE TRAIT LOCI AFFECTING ASYMMETRY OF MANDIBULAR CHARACTERS IN MICE

An interval mapping procedure was used to search for and describe the effects of any quantitative trait loci (QTLs) for directional asymmetry (DA) and fluctuating asymmetry (FA) of 10 bilateral mandible characters in house mice. It was hypothesized that more QTLs would be found for DA than for FA, but that any discovered for FA should tend to exhibit dominance. All mandible characters were triply measured and 76 microsatellite markers were scored in an average of 471 mice from the F₂ intercross of the Large (LG/J) and Small (SM/J) inbred strains. A total of 16 QTLs significantly affected DA in nine of the 10 mandible characters, and this was more than the 9.5 expected by chance alone. These QTLs were found on seven of the 19 chromosomes, often at or near locations of QTLs affecting the mean of the two sides for various dimensions on the mandible. It was concluded that there is genetical variability for DA in these characters, although its level was low (4.4% of the total variation in this particular F₂ population). Eleven QTLs were detected for FA, suggesting that there is very little genetic variability for FA, at least as seen in the mandible characters in this particular F₂ population. As hypothesized, however, these QTLs did tend to exhibit dominance.     

A meta-analysis of the heritability of developmental stability

The existence of additive genetic variance in developmental stability has important implications for our understanding of morphological variation. The heritability of individual fluctuating asymmetry and other measures of developmental stability have frequently been estimated from parent-offspring regressions, sib analyses, or from selection experiments. Here we review by meta-analysis published estimates of the heritability of developmental stability, mainly the degree of individual fluctuating asymmetry in morphological characters. The overall mean effect size of heritabilities of individual fluctuating asymmetry was 0.19 from 34 studies of 17 species differing highly significantly from zero (P < 0.0001). The mean heritability for 14 species was 0.27. This indicates that there is a significant additive genetic component to developmental stability. Effect size was larger for selection experiments than for studies based on parent-offspring regression or sib analyses, implying that genetic estimates were unbiased by maternal or common environment effects. Additive genetic coefficients of variation for individual fluctuating asymmetry were considerably higher than those for character size per se. Developmental stability may be significantly heritable either because of strong directional selection, or fluctuating selection regimes which prevent populations from achieving a high degree of developmental stability to current environmental and genetic conditions.     

Mixture analysis of asymmetry: modelling directional asymmetry, antisymmetry and heterogeneity in fluctuating asymmetry

The occurrence of different forms of asymmetry complicates the analysis and interpretation of patterns in asymmetry. Furthermore, between-individual heterogeneity in developmental stability (DS) and thus fluctuating asymmetry (FA), is required to find relationships between DS and other factors. Separating directional asymmetry (DA) and antisymmetry (AS) from real FA and understanding between-individual heterogeneity in FA is therefore crucial in the analysis and interpretation of patterns in asymmetry. In this paper we introduce and explore mixture analysis to (i) identify FA, DA and AS from the distribution of the signed asymmetry, and (ii) to model and quantify between-individual heterogeneity in developmental stability and FA. In addition, we expand mixtures to the estimation of the proportion of variation in the unsigned FA that can be attributed to between-individual heterogeneity in the presumed underlying developmental stability (the so-called hypothetical repeatability). Finally, we construct weighted normal probability plots to investigate the assumption of underlying normality of the different components. We specifically show that (i) model selection based on the likelihood ratio test has the potential to yield models that incorporate nearly all heterogeneity in FA; (ii) mixtures appear to be a powerful and sensitive statistical technique to identify the different forms of asymmetry; (iii) restricted measurement accuracy and the occurrence of many zero observations results in an overestimation of the hypothetical repeatability on the basis of the model parameters; and (iv) as judged from the high correlation coefficients of the normal probability plots, the underlying normality assumption appears to hold for the empirical data we analysed. In conclusion, mixtures provide a useful statistical tool to study patterns in asymmetry.     

Morphological integration of fluctuating asymmetry in the mouse mandible

Morphological integration of fluctuating asymmetry (FA) was assessed for nine mandibular characters in random-bred house mice to test the hypothesis that there should be a significant integration or concordance of FAs at the population level, but not at the individual level. FA estimates for each of the nine characters were made for each of 16 subpopulations (two replicates each for mice varying in sex and age) and their correlations indicated a moderate level of integration (index of integration = 0.42). A matrix permutation test of the differences of the correlations within two (‘incisor’ and ‘muscle’) developmentally different character groups versus correlations between groups was significant, indicating the presence of morphological integration. Kendall's coefficient of concordance also indicated a significant population asymmetry parameter for FAs within the two character groups. Correlations among individual FA estimates were generally lower than those calculated from subpopulations, the index of integration being 0.21. The matrix permutation test failed to show significant morphological integration among individual FAs, but Kendall's coefficient of concordance was significant, indicating the presence of an ‘individual asymmetry parameter’ among the nine characters. Principal components analysis and canonical correlation analysis confirmed the overall higher level of integration of FAs among the subpopulations and within the two character groupings.     

Patterns of leaf asymmetry changes in Plantago major L. (ssp. major) natural populations exposed to different environmental conditions

In the present study, developmental stability of leaf traits was examined in three natural populations of Plantago major L. (ssp. major), representing two polluted environments (Karaburma and Zemun) and an unpolluted area (Crni Lug). Developmental stability was assessed as fluctuating asymmetry (FA). The magnitude of FA is believed to reflect differences in the ability of individuals to buffer their development in natural populations. We hypothesized that there are differences within characters and among characters in response to environmental conditions. Significant patterns of asymmetry correlations and asymmetry changes were detected both within characters and between characters. The manova results revealed a significant effect of individual and a significant individual × environment interaction on actual asymmetry (logL_i ? logR_i) and on the amount of asymmetry |(logL_i ? logR_i)| for leaf width and vein distances within a leaf. Over time, statistically significant and positive correlations of the FA values were detected for each trait separately per sample (population). For both leaf traits, there were differences for (logL_i ? logR_i) and |(logL_i ? logR_i)| asymmetry values among individuals within samples in response to yearly variations. Statistically significant and negative correlations for (logL_i ? logR_i) versus |(logL_i ? logR_i)| asymmetries were detected for both leaf traits. In summary, our results highlight the importance of differences in the ability of individuals to buffer their development under different environmental conditions and point to the concept that developmental stability is character specific.     

SIZE AND FLUCTUATING ASYMMETRY OF MORPHOMETRIC CHARACTERS IN MICE: THEIR ASSOCIATIONS WITH INBREEDING AND t-HAPLOTYPE

Abstract Fluctuating asymmetry (FA), a ubiquitous type of asymmetry of bilateral characters, often has been used as a measure of developmental instability in populations. FA is expected to increase in populations subjected to genetic stressors such as inbreeding or environmental stressors such as toxins or parasites, although results have not always been consistent. We tested whether FA in four skeletal size characters and mandible shape was greater in a population of wild‐derived mice reared in the laboratory and subjected to one generation of inbreeding (F = 0.25) versus that in an outbred group (F= 0.00). FA did not significantly differ between the inbred and outbred groups, despite the fact that these two groups differed dramatically in fitness under seminatural population conditions. As far as we know, this is the first study to evaluate the relationship between FA and inbreeding in wild house mice, and our general conclusion is opposite that of earlier work on laboratory inbred strains of mice and their hybrids. Size for two of the characters was significantly less in inbreds than in outbreds, however, and there was a significant difference between inbreds and outbreds in the signed differences of right and left sides in one character (humerus length). Some of the mice in both groups also were heterozygous or homozygous carriers of the t‐complex. Because mice carrying this chromosome 17 variant are known to have reduced fitness, we also tested whether they had greater FA than mice carrying non‐t‐haplotypes. The overall level of a composite FA index calculated from all four characters was in fact significantly higher in the t‐bearing mice. These combined results suggest that FA is not a generally sensitive proxy measure for fitness, but can be associated with fitness reductions for certain genetic stressors.     

THE ASSOCIATION BETWEEN FLUCTUATING ASYMMETRY,TRAIT VARIABILITY,TRAIT HERITABILITY,AND STRESS: A MULTIPLY REPLICATED EXPERIMENT ON COMBINED STRESSES IN DROSOPHILA MELANOGASTER

A number of hypotheses have been proposed about the association between developmental stability phenotypic variability, heritability, and environmental stress. Stress is often considered to increase both the asymmetry and phenotypic variability of bilateral traits, although this may depend on trait heritability. Empirical studies of such associations often yield inconsistent results. This may reflect the diversity of traits and conditions used or a low repeatability of any associations. To test for repeatable associations between these variables, multiply replicated experiments were undertaken on Drosophila melanogaster using a combination stress at the egg, larval and adult stages of reduced protein, ethanol in the medium, and a cold shock. Both metric and meristic traits were measured and levels of heritable variation for each trait estimated by maximum likelihood and parent-offspring regression over three generations. Trait means were reduced by stress, whereas among-individual variation increased Fluctuating asymmetry (FA) was increased by stress in some cases, but few comparisons were significant. Only one trait orbital bristle, showed consistent increases in FA. Changes in trait means, trait phenotypic variability, and developmental stability as a result of stress were not correlated. Extreme phenotypes tended to have higher levels of FA but only the results for orbital bristles were significant. All traits had low to intermediate heritabilities except orbital bristle, which showed no heritable variation. Only traits with low heritability and high levels of phenotypic variability may show consistent increases in FA under stress. Overall, the independence of phenotypic variability, plasticity, and the developmental stability of traits extend to changes in these measures under stressful conditions.     

Lopsided Fish in the Snake River Basin — Fluctuating Asymmetry as a way of Assessing Impact of Hatchery Supplementation in Chinook Salmon, Oncorhynchus tshawytscha

The use of developmental instability (an individual's failure to produce a consistent phenotype in a given environment) was evaluated to detect the effects of outplanting hatchery fish on wild salmon. Juvenile chinook salmon were collected in 1989, 1990, and 1991 from five drainages in the Snake River Basin. In each drainage we attempted to collect fish from streams with no hatchery supplementation (wild), naturally spawning fish from streams with hatchery supplementation (natural), and fish collected at a hatchery. Forty fish were collected per site and the number of elements in bilateral characters were counted on each side of the fish. Indices of fluctuating asymmetry (FA), a measure of minor, random deviations in perfect symmetry of bilateral counts, were calculated as an estimator of developmental instability. Analysis of character counts from seven paired characters revealed normal distributions. Only one of the characters displayed counts that were statistically larger on one side than the other, indicating that directional asymmetry (DA) or antisymmetry was not a major bias of FA. However, the means of all individual characters revealed a non-statistically significant left side bias. We analyzed our data using two indices of FA (FA1 and FA5) with different levels of sensitivity to DA. Differences in both FA indices were found among years, with collection sites in 1989 having significantly larger FA values than in 1991 (FA p < 0.01). Levels of FA among wild, natural, and hatchery fish were comparatively small (FA1 p = 0.17). This suggests developmental conditions were different in the first year of the study than in the last. The cause of these differences may be linked to either genetic or environmental variation or to gene—environment interactions, but the general population declines of salmon that occurred during this time obscures more specific conclusions.     

The quantitative genetics of fluctuating asymmetry: a comparison of two models

The genetic basis of fluctuating asymmetry (FA), a measure of random deviations from perfect bilateral symmetry, has been the subject of much recent work. In this paper we compare two perspectives on the quantitative genetic analysis of FA and directional asymmetry (DA). We call these two approaches the character-state model and the environmental responsiveness model. In the former approach, the right and left sides are viewed as separate traits whose genetic coupling is manifested by the genetic correlation. This model leads to the relationship, h2(DA) = h2[(1-rA)/(1-rp)), where h2 is the heritability of each component trait (assumed to be the same), rA and rp are the genetic and phenotypic correlations between traits, respectively. Simulation shows that, under this model, the heritability of FA is considerably less than that of DA, except when heritabilities are very close to zero. The environmental responsiveness model permits genetic variance in FA even when the genetic correlation between traits is + 1. Simulation shows that under this model the heritability of FA can be uncoupled from that of DA. The additive and nonadditive components of the component (right and left) traits, their DA and FA values are estimated using a diallel cross of seven inbred lines of the sand cricket, Gryllus firmus. Four leg measurements were made and both the individual DA and FA values and the compound measures DASUM and CFA estimated. The heritabilities of the compound measures are slightly larger than the individual estimates. Dominance variance is observed in the individual traits but predicted to be an even smaller component of the phenotypic variance than the additive genetic variance. The estimated values confirm this, although a previous study has demonstrated that dominance variance is present. Because the heritabilities of FA are generally larger than those of DA, which never exceed 0.02, the environmental responsiveness model is more consistent with the data than the character-state model. A review of other data suggests that both sources of variation might be found in some species.     

Fluctuating asymmetry and reproductive isolation between two sticklebacks

This paper describes patterns of developmental asymmetry in a limnetic-benthic stickleback species pair from Paxton Lake, British Columbia. Three gill raker characters and one armor character were compared among full-sib parental crosses and their hybrids (F₁, F₂ and backcrosses). All crosses displayed asymmetry, but no differences in mean or fluctuating asymmetry were detected among laboratory-reared crosses. When wild-caught limnetics and benthics were included in the analyses significant differences in FA among groups were detected in gill raker length and plate number. The effect appears to be solely due to wild-caught benthics, though the reasons for their greater asymmetry are unknown. The patterns in laboratory-reared crosses suggest that asymmetry is unlikely to promote reproductive isolation between the parental species.     

FLUCTUATING ASYMMETRY IS NONGENETICALLY RELATED TO MATING SUCCESS IN DROSOPHILA BUZZATII

Abstract To date, there is still no consensus on the real significance of fluctuating asymmetry (FA) in evolutionary biology. Some studies have established links between FA and Darwinian fitness, and in a number of cases intermediate heritabilities for FA have been reported. However, many claims have been raised against the generality of these findings. I therefore tested if FA of a sexually selected trait (wing length) is indeed related to male mating success in Drosophila buzzatii from field and laboratory samples and whether FA has detectable heritability. Single, unsuccessful males had greater asymmetry for wing length than their mating counterparts both in nature and under nonoptimal rearing environments, but the higher FA in single males is most likely due to a poorer average phenotypic condition because there was no evidence of a genetic basis for this trait. Further evidence of an increase in FA under larval food stress is suggested when comparing the magnitude of the FA levels between stressful and optimal environments. On methodological grounds, a linear model is suggested that allows directional asymmetry (DA) and any genetic variation of DA that may be present to be statistically eliminated from estimates of FA.     

Are human preferences for facial symmetry focused on signals of developmental instability?

Humans find symmetrical faces more attractive than are asymmetricalfaces. Evolutionary psychologists claim that our preferencefor symmetry can be explained in the context of mate choicebecause symmetry is an honest indicator of the genetic qualityof potential mates. These arguments assume that asymmetry inhuman faces is fluctuating asymmetry (FA), because this formof asymmetry can be revealing of developmental instability.However, no study has yet examined the characteristics of facialasymmetry. Here we provide the first detailed study of the patternsof asymmetry in human faces. We measured asymmetry in 35 facialtraits. Although some traits had distributions characteristicof FA, many had distributions that characterize directionalasymmetry (DA); on average, both men and women had right hemi-facedominance. For DA traits we used deviations from the mean asymmetryas a measure of developmental instability. Our measures of asymmetryaccounted for a moderate proportion of the variance in perceivedsymmetry. Importantly, only FAs and random deviations from DAcontributed to people's perception of symmetry. DA was not importantin symmetry judgments. Faces rated as symmetrical were alsorated as attractive. Random deviations from DA were weakly relatedto women's attractiveness judgments of men's faces. DAs didnot influence attractiveness judgments. Our data suggest thatpeople focus on aspects of facial asymmetry that may be revealingof developmental instability. Further studies that isolate FAfrom other forms of asymmetry are required to accurately assessthe influence of developmental instability on the quality ofindividuals and its potential role in mate preferences.     

On hidden heterogeneity in directional asymmetry – can systematic bias be avoided?

Directional asymmetry (DA) biases the analysis of fluctuating asymmetry (FA) mainly because among-individual differences in the predisposition for DA are difficult to detect. However, we argue that systematic bias mainly results from predictable associations between signed right-left asymmetry and other factors, i.e. from systematic variation in DA. We here demonstrate methods to test and correct for this, by analysing bilateral asymmetry in size and shape of an irregular sea urchin. Notably, in this model system, DA depended significantly on body length and geographic origin, although mean signed asymmetry (mean DA) was not significant in the sample as a whole. In contrast to the systematic variation in DA, undetectable, random variability in the underlying DA mainly leads to reduced statistical power. Using computer simulations, we show that this loss of power is probably slight in most circumstances. We recommend future studies on FA to routinely test and correct for not only as yet for mean DA, but also for systematic variation in DA.     

Asymmetry of Early Paleozoic trilobites

Asymmetry in fossils can arise through a variety of biological and geological mechanisms. If geological sources of asymmetry can be minimized or factored out, it might be possible to assess biological sources of asymmetry. Fluctuating asymmetry (FA), a general measure of developmental precision, is documented for nine species of lower Paleozoic trilobites. Taphonomic analyses suggest that the populations studied for each taxon span relatively short time intervals that are approximately equal in duration. Tectonic deformation may have affected the specimens studied, since deviations from normal distributions are common. Several measures of FA were applied to 3–5 homologous measures in each taxon. Measurement error was assessed by the analysis of variance (ANOVA) for repeated measurements of individual specimens and by analysis of the statistical moments of the distributions of asymmetry measures. Measurement error was significantly smaller than the difference between measures taken on each side of a specimen. However, the distribution of differences between sides often deviated from a mean of zero, or was skewed or kurtosic. Regression of levels of FA against geologic age revealed no statistically significant changes in levels of asymmetry through time. Geological and taphonomic effects make it difficult to identify asymmetry due to biological factors. Although fluctuating asymmetry is a function of both intrinsic and extrinsic factors, the results suggest that early Cambrian trilobites possessed genetic or developmental mechanisms used to maintain developmental stability comparable to those of younger trilobites. Although the measures are biased by time averaging and deviations from the normal distribution, these data do not lend strong support to 'genomic' hypotheses that have been suggested to control the tempo of the Cambrian radiation.     

Lack of response to selection for lower fluctuating asymmetry of mutant eyespots in the butterfly Bicyclus anynana

Fluctuating asymmetry (FA) is claimed both to provide a means of evaluating developmental stability, and to reflect an individual's quality or the stress experienced during development. FA refers to the nondirectional variation between left and right sides, whereas directional asymmetry (DA) refers to a significant directional variation between the sides. We studied four eyespots on the dorsal forewing of the tropical butterfly, Bicyclus anynana. Two of the eyespots were specified by a mutant allele, Spotty, that was fixed in the stock. These eyespots showed higher FA than the two flanking, wild-type eyespots, although they are all formed by the same developmental pathway. We applied artificial selection for lower FA of the novel eyespots in an attempt to increase their developmental stability. There was significant variation present in individual FA in our study. However, this did not change as a result of the artificial selection. Most of the variation in FA can be accounted for by individual differences in developmental stability rather than by the applied selection or by environmental variation. Thus, it was not possible to produce any increased developmental stability of the novel eyespots by selecting for low FA. The estimates of realized heritability for both FA and DA of each eyespot were not significantly different from zero. The results suggest that FA provides little, if any, potential for exploring the mechanistic basis of developmental stability.     

精神分裂症患者皮纹a-b嵴线数波动性不对称的研究

本文分析了精神分裂症患者134例(男性70例,女性64例)和正常对照人群331例(男性170例,女性161例)皮纹a-b嵴线数波动性不对称的分布特征。结果表明:⑴精神分裂症患者双手皮纹a-b嵴线数明显低于正常对照组(P<0.01),表现出明显增高。     

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.     

How repeatable is the estimation of developmental stability by fluctuating asymmetry?

The estimation of individual fluctuating asymmetry (FA) is subject to large sampling variabilities. Heritability estimates, as well as correlations between developmental stability and any other individual character and/or between-trait correlations, are consequently biased downward if FA is used as an estimate of an individual''s ability to buffer its development against developmental noise. The estimation of the hypothetical repeatability, defined as the ratio of the between-individual component of variation in the unsigned FA divided by the total variance, allows correction for these biases such that patterns observed for FA can be translated to make inferences about the presumed underlying developmental stability. In this paper I show that previous estimates of this repeatability are incorrect. I provide a new method and show by means of simulations that the hypothetical repeatability is in most cases even lower than previously thought. This has important consequences for the analysis of FA with respect to statistical power and the interpretation of patterns in FA.     

Developmental stability in brown trout: are there any effects of heterozygosity or environmental stress?

We studied the developmental stability of brown trout, Salmo trutta L., in 10 populations (five acidified, five control) in Norway, measured as fluctuating asymmetry (FA) and departure from the morphological norm. We measured four meristic and four morphometric characters, and scored the level of biochemical heterozygosity at 49 loci (20 polymorphic). We reared eggs of a single population in a hatchery using four different water qualities (three replicates of each treatment) to test the effect of acidification stress on developmental instability. There were no significant differences in the level of FA, in departure from the morphological norm between brown trout sampled from lakes with acidified or control water qualities, or in brown trout hatched at different water qualities. There was no correlation between level of heterozygosity and FA or departure from the morphological norm, either when tested within populations or among populations. There were no single-locus effects on developmental stability tested for 11 loci. We conclude that measures of developmental stability or morphological variability are not useful for detecting acidification stress in brown trout. Furthermore, we conclude that developmental stability in our material varies independently of heterozygosity.