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.     

Parasitism, developmental plasticity and bilateral asymmetry of wing feathers in alpine swift, Apus melba, nestlings

The hypothesis that developmental instability is a cost of developmental plasticity is explored using the alpine swift ( Apus melba ) as a model organism. In a previous study, experimentally parasitized nestlings showed a reduced wing growth rate in the first half of the rearing period when parasites were abundant (i.e. peak infestation) and an accelerated growth rate (i.e. compensatory growth) in the second half when parasites decreased in number. This suggests that alpine swifts are able to adjust growth rate in relation to variation in parasite loads. Because developmental plasticity may entail fitness costs, the energy required to sustain compensatory growth may be invested at the expense of developmental stability, potentially resulting in larger deviations from symmetry in paired, bilateral traits (i.e. fluctuating asymmetry, FA). This hypothesis predicts higher FA in parasitized than deparasitized nestlings because of compensatory growth, and hence individuals sustaining the highest level of compensatory growth rate should exhibit the highest FA levels. Another non-mutually exclusive hypothesis argues that parasites directly cause FA by diverting energy required by host for maintenance and growth, and predicts that individuals suffering the most from parasitism during peak infestation should exhibit the highest FA levels. The present study shows that wing feathers of experimentally parasitized nestlings were more asymmetrical than those of experimentally deparasitized ones 50 days after hatching. Furthermore, in parasitized individuals FA was negatively correlated with wing growth rate during the period of peak infestation but not during the period of compensatory growth. These findings suggest that developmental homeostasis is more sensitive to parasites than to compensatory growth.     

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.     

Morphological asymmetry of insular freshwater populations of threespine stickleback

Fluctuating asymmetry (FA), random deviations from perfect symmetry in a bilateral organism, has been widely used as a proxy for developmental instability in stressed populations. In order to test the utility of FA of resident freshwater threespine stickleback (Gasterosteus aculeatus) as a biomonitoring tool for contaminated sites, we compared levels of asymmetry of seven morphological traits of threespine stickleback collected from lakes at three islands with a history of military contamination and three islands with no military history, in the Aleutian Archipelago, Alaska. Traits examined include eye diameter, operculum width, pectoral fin ray number, pectoral fin width, lateral plate number, lateral plate length, and pelvic spine length. All morphometric traits demonstrated some degree of FA or directional asymmetry (DA), but the military history of a lake was not a predictor of the degree or type of asymmetry. Overall, the patterns of asymmetry were similar for all traits, irrespective of military contamination at a lake. Our results demonstrate that the suite of threespine stickleback traits measured are not suitable for examination of FA as a proxy for aquatic pollution in this region. DA also does not appear to be suitable as an indicator of aquatic pollution, but may instead be driven by local ecological factors such as predation.     

Zinc and cadmium accumulation in cabbage aphid (Brevicoryne brassicae) host plants and developmental instability

Developmental instability in morphological characters can occur during individual development due to various environmental stresses. Fluctuating asymmetry (FA) is often used as a measurement of developmental instability, but within-environment variation (CV_e) is also considered an indicator of developmental instability. Cabbage aphid ( Brevicoryne brassicae ) populations were reared on zinc- (Zn) or cadmium- (Cd) contaminated cabbage and radish plants. Developmental instability indicators were measured and their relations with fitness were explored. Results revealed that cabbage aphids exposed to Cd and Zn displayed considerable developmental instability, particularly fluctuating asymmetry. Differences in developmental instability between the two metals were also detected, as well as differences between the two developmental instability measurements. For almost all measured traits, FA was greater on Cd- and Zn-contaminated compared to non-contaminated host plants. In contrast, CV_e of some traits was greater on non-contaminated host plants, yet for other traits CV_e was greater on contaminated host plants. There were also non-significant inverse relationships between FA and fitness of cabbage aphid populations. Due to weak correlations between FA and different patterns of two developmental instability measurements, this study does not support the hypothesis that developmental instability is a useful bioindicator of environmental quality.     

Hand asymmetry does not relate to key life history traits in post-menopausal contemporary Finnish women

Associations between fluctuating asymmetry (FA, a putative marker of developmental instability, DI) and life history traits have received a great deal of attention in the non-human literature. However, the patterns found are very heterogeneous and generalizations are difficult to make. In humans, only a few studies have related FA to life histories and fitness. In this paper we study such relationships using hand FA and several key life history traits in 209 post-menopausal Finnish women born between 1946 and 1958. Asymmetry measurements were based on scans of the hands and the life histories of these women were collected using questionnaires. No significant associations were detected and trends were opposite to expectations. We did find evidence for directional asymmetry, as traits in the right hand were larger on average. This may be due to handedness, questioning the usefulness of hand FA as a measure of DI. We conclude that future studies in humans should carefully examine the usefulness of traits as measures of DI.     

Fluctuating asymmetry in certain morphological traits in laboratory populations of Drosophila ananassae.

Fluctuating asymmetry (FA, subtle random deviations from perfect bilateral symmetry) is often used as a measure of developmental instability (DI), which results from perturbations in developmental pathways caused by genetic or environmental stressors. During the present study, we estimated FA in 5 morphological traits, viz. wing length (WL), wing to thorax ratio (W:T), sternopleural bristle number (SBN), sex-comb tooth number (SCTN), and ovariole number (ON) in 18 laboratory populations of Drosophila ananassae. FA levels of measured traits differed significantly among populations except for SBN (in males and females) and W:T ratio (in females). Positional fluctuating asymmetry (PFA), a sensitive measure of DI, also varied significantly among the populations for SBN in females and SCTN in males. Interestingly, both males and females were similar for nonsexual traits. However, when FA across all traits (sexual and nonsexual) was combined into a single composite index (CFA), significant differences were found for both populations and sexes. Males showed higher CFA values than females, suggesting that males are more prone to developmental perturbations. The magnitude of FA differed significantly among traits, being lowest for nonsexual traits (SBN, WL, W:T ratio) and highest for sexual traits (SCTN and ON). The trait size of sexual traits (SCTN and ON) was positively correlated with their asymmetry. The possible reasons for variation in FA both among traits and among populations, and the usefulness of FA as an indicator of developmental stress and phenotypic quality in D. ananassae are discussed.     

Fluctuating asymmetry in leaves and flowers of sympatric species in a tropical montane environment

Fluctuating asymmetry (FA) represents small, random variations in traits, presumably with bilateral symmetry, and is widely used as a tool to measure developmental instability in plants and animals. Because FA is a quick, simple and reliable measure, it has been frequently used for monitoring levels of environmental stress. This study investigated whether FA can be used as a predictor of individual developmental instability for four sympatric Melastomataceae species. To achieve that aim, 20 individuals of Trembleya laniflora, T. parviflora, Lavoisiera campos‐portoana and Tibouchina heteromalla were marked in southeastern Brazil and monitored before and during the flowering season. The FA index was calculated as the mean of the difference in the width or length between the left and right sides measured for each leaf or flower. All studied species exhibited asymmetry in the leaves and flowers, but the leaves of L. campos‐portoana and the petal width of T. heteromalla exhibited directional asymmetry, also an indicator of developmental instability. The highest level of leaf asymmetry was found in T. heteromalla and on flowers of L. campos‐portoana. None of the studied species exhibited a significant relationship between the FA level of the leaves and flowers on an individual basis, indicating that environmental and/or genetic sources of stress might act differently on different plant traits. For the studied species, measurements of FA can be suggested as useful tools to biomonitor levels of stress experienced by both leaves and flowers within the Melastomataceae family.     

Genetics of wing size asymmetry in Drosophila buzzatii

Contemporary approaches that use fluctuating asymmetry (FA) as a possible target for natural and sexual selection are based on the premise that FA is a quantifiable expression of developmental instability (DI) that is inherited. Previous work with Drosophila buzzatii found that male mating success was correlated positively to body size (wing length) and negatively to FA, but these relationships seem to be environmentally induced. Heritability of FA was low and not significantly different from zero, but statistical power was also estimated to be very low and, hence, no conclusive evidence could be obtained. A large half‐sib mating design is used here to examine the relationships of different aspects of development for wing size. Consistently with previous findings, I found high heritabilities for wing length (WL) and wing width (WW), and positive correlations between both traits. Heritabilities of FA (FA_WL, FA_WW) were low (0.037) but significantly different from zero, and the genetic correlation between FA_WL and FA_WW was estimated as ?1 because the absolute value for the genetic covariance was similar in magnitude or even larger than the estimated genetic variances of both traits. This suggests that these two traits should be considered to be the same character. The between‐trait phenotypic correlation in FA, which reduces to the repeatability in this situation, was positive and statistically significant thus rendering an estimate of heritability for DI in D. buzzatii of . Nevertheless, the fact that left/right wing sizes were found to be determined by the same set of genes is difficult to reconcile with the presence of special genetic mechanisms that stabilize left/right development in this species. A qualitatively different pattern for asymmetry was observed when the nonlinear composite character wing area (WA ≈ WL × WW) was used, and . Although the results could be made compatible with the existence of a diallelic locus with antagonistic pleiotropic effects on FA_WL and FA_WW that combine multiplicatively to produce overdominance for FA_WA, the available evidence is extremely weak at best. Finally, a test to the null hypothesis of a nongenetic basis of FA, particularly relevant to those situations when directional asymmetry may be heritable, is suggested.     

Trade‐offs between growth and reproduction: an analysis of the quantitative genetic evidence

The assumption of a trade‐off between development time and fecundity, resulting from a positive correlation between body size and fecundity and between body size and development time, is a common feature of life history models. The present paper examines the evidence for such a trade‐off as indicated by genetic correlations between traits. The genetic covariances between traits are derived using a model in which maturation occurs when the organism achieves a genetically variable size threshold, and fecundity is an allometric function of body size with one genetically variable parameter (excluding body size itself). This model predicts that the heritabilities of the life history traits (growth rate, development time, fecundity) will not necessarily be less than the heritability of adult size (i.e. morphological traits). It is shown that if growth rate is genetically correlated with adult size then it is not possible, in general, to predict the sign of the genetic correlation between development time and fecundity. For particular cases the signs of the covariances between traits can be predicted. These predictions are tested using data drawn from the literature.     

The Developmental Instability—Sexual Selection Hypothesis: A General Evaluation and Case Study

Developmental instability results from small, random perturbations to developmental processes of individual traits. Phenotypic outcomes of developmental instability include fluctuating asymmetry (FA, subtle deviations from perfect bilateral symmetry) and phenodeviance (minor morphological abnormalities). A great deal of research over the past 18 years has focused on the role of developmental instability in sexual selection. A driving force behind this research has been the developmental instability-sexual selection hypothesis, which posits that symmetry and lack of phenodeviance in secondary sexual traits are assessed by mates and rivals because they provide a reliable cue of individual genetic quality. The present article tests this hypothesis by evaluating its five main predictions using published results: expressions of developmental instability in secondary sexual traits should be (1) negatively correlated with mating success; (2) directly assessed by mates and sexual rivals; (3) heritable; (4) condition-dependent; and (5) negatively correlated with ornament size. The first two predictions receive considerable, though not ubiquitous, support from a range of animal species. However, FA in secondary sexual traits is generally not significantly heritable, indicating that FA is unlikely to reveal genetic quality that can be transmitted to offspring. Similarly, there is little evidence to support the predictions that FA is condition dependent, and that it is negatively phenotypically or genetically correlated with sexual trait size. Based on an evaluation of the evidence overall, it is concluded that this hypothesis is unlikely to be viable; it appears unlikely that mate choice for symmetry evolves by “good genes” sexual selection. Hypotheses that do not require asymmetry and phenodeviance to reveal heritable genetic quality may explain observed links between FA/phenodeviance and mating success. Results of a case study of Drosophila bipectinata are summarized, which reinforce this general conclusion. It is suggested that nonadditive genetic variation arising from an interaction between trait-specific developmental genes and genetic background may drive sexual selection for reducing developmental instability in some cases. Levels of developmental instability variation in a population may need to surpass a critical threshold for sexual selection to operate, possibly explaining some of the pronounced heterogeneity in the effect of developmental instability on sexual selection reported in the literature.     

Developmental instability in cabbage aphid (Brevicoryne brassicae) populations exposed to heavy metal accumulated host plants

Random deviations from the perfect symmetry of normally bilaterally symmetrical characters exist during individual development as a result of various environmental conditions. Fluctuating asymmetry (FA) is often used as a measurement of developmental instability, and within-environmental variation (CV_e) is also considered as an indicator of developmental deviations. These two parameters may indicate the quality of the environmental habitat of organisms. For herbivore insects, such as aphids, any change in their host plants conditions is important and directly affects their development. The presented investigation revealed that both Lead (Pb) and Copper (Cu) accumulation in different host plants resulted in a significant amount of deviations from bilateral symmetry in cabbage aphid (Brevicoryne brassicae). Cabbage aphid populations showed higher FA and CV_e on heavy metal accumulated cabbage and radish than on non-contaminated cabbage and radish plants. However, the pattern between developmental instability and fitness measurements was inconsistent. Thus, this study does not support the hypothesis that asymmetry is a valuable bioindicator of developmental instability.     

Hybridization, developmental stability, and functionality of morphological traits in the ground beetle Carabus solieri (Coleoptera, Carabidae)

The assessment of developmental stability in hybrids can provide valuable information in the study of species formation because it allows an evaluation of the degree of incompatibility of genetic systems that control developmental processes. The present study assessed the impact of two hybridization events, assumed to have occurred at different times, on developmental instability in the ground beetle Carabus solieri . Developmental instability was estimated in 678 individuals from 27 populations from the fluctuating asymmetry (FA) levels of four morphological traits: the tibia length of middle and hind legs, which are functional structures, and the length and the proximal width of the hind wings, which are vestigial and thus nonfunctional structures. Significant variations of FA levels between populations were shown only for the wing width. For this trait, FA levels in hybrids were higher than in their parental entities for both hybridization events, indicating a significant divergence of the gene systems controlling development between the parental entities in the two hybridization cases. As expected, wing traits exhibited FA levels at least three times higher than leg trait. Finally, the potential interest of vestigial traits in the particular context of hybridization is discussed.  © 2006 The Linnean Society of London, Biological Journal of the Linnean Society , 2006, 89 , 151–158.     

Estimation of fitness from energetics and life‐history data: An example using mussels

Changing environments have the potential to alter the fitness of organisms through effects on components of fitness such as energy acquisition, metabolic cost, growth rate, survivorship, and reproductive output. Organisms, on the other hand, can alter aspects of their physiology and life histories through phenotypic plasticity as well as through genetic change in populations (selection). Researchers examining the effects of environmental variables frequently concentrate on individual components of fitness, although methods exist to combine these into a population level estimate of average fitness, as the per capita rate of population growth for a set of identical individuals with a particular set of traits. Recent advances in energetic modeling have provided excellent data on energy intake and costs leading to growth, reproduction, and other life‐history parameters; these in turn have consequences for survivorship at all life‐history stages, and thus for fitness. Components of fitness alone (performance measures) are useful in determining organism response to changing conditions, but are often not good predictors of fitness; they can differ in both form and magnitude, as demonstrated in our model. Here, we combine an energetics model for growth and allocation with a matrix model that calculates population growth rate for a group of individuals with a particular set of traits. We use intertidal mussels as an example, because data exist for some of the important energetic and life‐history parameters, and because there is a hypothesized energetic trade‐off between byssus production (affecting survivorship), and energy used for growth and reproduction. The model shows exactly how strong this trade‐off is in terms of overall fitness, and it illustrates conditions where fitness components are good predictors of actual fitness, and cases where they are not. In addition, the model is used to examine the effects of environmental change on this trade‐off and on both fitness and on individual fitness components.     

Facial fluctuating asymmetry is not associated with childhood ill-health in a large British cohort study

The idea that symmetry in facial traits is associated with attractiveness because it reliably indicates good physiological health, particularly to potential sexual partners, has generated an extensive literature on the evolution of human mate choice. However, large-scale tests of this hypothesis using direct or longitudinal assessments of physiological health are lacking. Here, we investigate relationships between facial fluctuating asymmetry (FA) and detailed individual health histories in a sample (n = 4732) derived from a large longitudinal study (Avon Longitudinal Study of Parents and Children) in South West England. Facial FA was assessed using geometric morphometric analysis of facial landmark configurations derived from three-dimensional facial scans taken at 15 years of age. Facial FA was not associated with longitudinal measures of childhood health. However, there was a very small negative association between facial FA and IQ that remained significant after correcting for a positive allometric relationship between FA and face size. Overall, this study does not support the idea that facial symmetry acts as a reliable cue to physiological health. Consequently, if preferences for facial symmetry do represent an evolved adaptation, then they probably function not to provide marginal fitness benefits by choosing between relatively healthy individuals on the basis of small differences in FA, but rather evolved to motivate avoidance of markers of substantial developmental disturbance and significant pathology.     

Fluctuating asymmetry of meristic traits: an isofemale line analysis in an invasive drosophilid, <Emphasis Type="Italic">Zaprionus indianus</Emphasis>

Metric (e.g., body size) and meristic (e.g., bristle number) traits are of general use in quantitative genetic studies, and the phenotypic variance is subdivided into a genetic and a non-genetic environmental component. The non-genetic variance may have two origins: a common garden effect between individuals and a developmental instability within the same individual. Developmental instability may be studied by considering the fluctuating asymmetry (FA) between the two sides of the body. The isofemale line technique is a convenient method for investigating the architecture of natural populations but has been rarely implemented for investigating FA. In this paper, we use this experimental design for analyzing four meristic traits in eight populations of the cosmopolitan Zaprionus indianus. A study of the correlation between left and right side of each line revealed that almost 90% of the variability was due to a developmental noise, while a much higher correlation among the means of the lines from the same population was observed. A slight trend toward a directional asymmetry was observed: more thoracic bristles on the left side. Four kinds of indices, scaled or non-scaled to the mean were used for comparing the different traits. Unscaled values (mean absolute values or standard deviation of each line) revealed a linear increase with the means. Interestingly the results of ovariole number were included in the same regression. With the scaled indices (mean absolute divided by each individual value or stadard deviation devided by the mean), the differences among traits were considerably decreased, but still remained significant. The mean FA of the various traits were not correlated, suggesting that each trait harbors its own developmental stability. The CVs of FA were high with a magnitude similar to those of the trait themselves, slightly less than 10%. Finally, even with the isofemale line design, which is a powerful means for unravelling slight genetic variations, we did not to find any clear indication of a genetic component of FA under the optimal environmental conditions used in this study.     

The relationship between developmental instability of gudgeon Gobio gobio and abundance or morphology of its ectoparasite Paradiplozoon homoion (Monogenea)

Gudgeon Gobio gobio (Cyprinidae) were collected monthly from the Vlara Stream (Czech Republic) during 2004 and examined for the presence of the ectoparasite Paradiplozoon homoion (Diplozoidae; Monogenea). Over 26% of P. homoion showed abnormalities of the attachment sclerites, indicating either a stressful environment or that the quality of the fish host was suboptimal for parasite development. Here, the hypotheses that parasite abundance and the occurrence of morphological abnormalities are correlated with fluctuating asymmetry (FA, the random deviation from the perfect bilateral symmetry) in its fish host were tested. The FA and morphological abnormality are estimators of developmental instability. To estimate fish developmental instability nine meristic and two morphometric bilateral characters on the right and the left sides of the fish were measured. In general, there was no correlation between mean fish FA and parasite abundance or the proportion of parasites with abnormalities. There was, however, a significant relationship between the proportion of abnormal P. homoion and the number of asymmetric meristic traits per individual fish. This study thus indicates that developmental instability of P. homoion , measured as morphological abnormality of the attachment apparatus, is only weakly dependent on the fish quality as measured by FA.     

Does fluctuating asymmetry constitute a sensitive biomarker of nutritional stress in house sparrows (Passer domesticus)?

Small random deviations from left–right symmetry in bilateral traits, termed fluctuating asymmetry (FA), are theoretically predicted to increase with environmental stress and believed to constitute a potential biomarker in conservation. However, reported relationships between FA and stress are generally weak and variable among organisms, traits and stresses. Here we test if, and to what extent, FA increases with nutritional stress, estimated from independent feather growth measurements, in free-ranging house sparrows (Passer domesticus). Ptilochronological feather marks showed significant heterogeneity among study plots, indicating that house sparrow populations were exposed to variable levels of nutritional stress during development. However, individuals from more stressed populations did not show increased levels of fluctuating asymmetry in tarsus or rectrix length, nor was there evidence for significant between-trait concordance in FA at the individual or the population level. Lack of support for FA in tarsus and rectrix length as estimator of nutritional stress in house sparrows may indicate that developmental instability is insensitive to nutritional stress in this species, poorly reflected in patterns of fluctuating asymmetry due to ecological or statistical reasons, or highly context-specific. Such uncertainty continues to hamper the use of FA as a biomarker tool in conservation planning.     

Phenotypic variation and fluctuating asymmetry in sexually dimorphic feather ornaments in relation to sex and mating system

Secondary sexual characters have been hypothesized to demonstrate increased phenotypic variation between and within individuals as compared to ordinary morphological traits. We tested whether this was the case by studying phenotypic variation, expressed as the coefficient of variation (CV), and developmental instability, measured as fluctuating asymmetry (FA), in ornamental and non-ornamental traits of 70 bird species with feather ornamentation while controlling for similarity among species due to common descent. Secondary sexual characters differed from ordinary morphological traits by showing large phenotypic CV and FA. This difference can be explained by the different mode of selection operating on each kind of trait: a history of intense directional (ornaments) and stabilizing selection (non-ornaments). Phenotypic variation is reduced in the sex with more intense sexual selection (males), but does not differ among species with different mating systems. The strength of stabilizing selection arising from natural selection is associated with decreased CV (wing CV is smaller than tarsus or tail CVs). We found evidence of FA being reduced in ornamental feathers strongly affected by aerodynamics (tail feathers) compared to other ornaments, but only in females. In conclusion, CV and FA were not related, suggesting mat phenotypic plasticity and developmental instability are independent components of phenotypic variation.     

Beyond bilateral symmetry: geometric morphometric methods for any type of symmetry

Background

Studies of symmetric structures have made important contributions to evolutionary biology, for example, by using fluctuating asymmetry as a measure of developmental instability or for investigating the mechanisms of morphological integration. Most analyses of symmetry and asymmetry have focused on organisms or parts with bilateral symmetry. This is not the only type of symmetry in biological shapes, however, because a multitude of other types of symmetry exists in plants and animals. For instance, some organisms have two axes of reflection symmetry (biradial symmetry; e.g. many algae, corals and flowers) or rotational symmetry (e.g. sea urchins and many flowers). So far, there is no general method for the shape analysis of these types of symmetry.

Results

We generalize the morphometric methods currently used for the shape analysis of bilaterally symmetric objects so that they can be used for analyzing any type of symmetry. Our framework uses a mathematical definition of symmetry based on the theory of symmetry groups. This approach can be used to divide shape variation into a component of symmetric variation among individuals and one or more components of asymmetry. We illustrate this approach with data from a colonial coral that has ambiguous symmetry and thus can be analyzed in multiple ways. Our results demonstrate that asymmetric variation predominates in this dataset and that its amount depends on the type of symmetry considered in the analysis.

Conclusions

The framework for analyzing symmetry and asymmetry is suitable for studying structures with any type of symmetry in two or three dimensions. Studies of complex symmetries are promising for many contexts in evolutionary biology, such as fluctuating asymmetry, because these structures can potentially provide more information than structures with bilateral symmetry.