Quantifying asymmetry: Ratios and alternatives

Traditionally, the study of metric skeletal asymmetry has relied largely on univariate analyses, utilizing ratio transformations when the goal is comparing asymmetries in skeletal elements or populations of dissimilar dimensions. Under this approach, raw asymmetries are divided by a size marker, such as a bilateral average, in an attempt to produce size‐free asymmetry indices. Henceforth, this will be referred to as “controlling for size” (see Smith: Curr Anthropol 46 (2005) 249‐273). Ratios obtained in this manner often require further transformations to interpret the meaning and sources of asymmetry. This model frequently ignores the fundamental assumption of ratios: the relationship between the variables entered in the ratio must be isometric. Violations of this assumption can obscure existing asymmetries and render spurious results. In this study, we examined the performance of the classic indices in detecting and portraying the asymmetry patterns in four human appendicular bones and explored potential methodological alternatives. Examination of the ratio model revealed that it does not fulfill its intended goals in the bones examined, as the numerator and denominator are independent in all cases. The ratios also introduced strong biases in the comparisons between different elements and variables, generating spurious asymmetry patterns. Multivariate analyses strongly suggest that any transformation to control for overall size or variable range must be conducted before, rather than after, calculating the asymmetries. A combination of exploratory multivariate techniques, such as Principal Components Analysis, and confirmatory linear methods, such as regression and analysis of covariance, appear as a promising and powerful alternative to the use of ratios. Am J Phys Anthropol 154:498–511, 2014. © 2014 Wiley Periodicals, Inc.     

蜘蛛抱蛋属植物的核型不对称性分析

报道了蜘蛛抱蛋属(Aspidistra)两种植物的染色体数目和核型,其中河口蜘蛛抱蛋(A.hekouensi)的染色体数目(2n=38)为首次报道,四川蜘蛛抱蛋(A.sichuanensis)染色体数目也为2n=38,但其核型与以往的报道有差别.使用染色体内不对称系数(A1)和染色体间不对称系数(A2)对该属34种植物核型的不对称性进行了分析,结果表明该属植物的核型似乎并没有向不对称性增强的方向演化.     

Left–right asymmetries and shape analysis on Ceroglossus chilensis (Coleoptera: Carabidae)

Bilateral symmetry is widespread in animal kingdom, however most animal can deviate from expected symmetry and manifest some kind of asymmetries. Fluctuating asymmetry is considered as a tool for valuating developmental instability, whereas directional asymmetry is inherited and could be used for evaluating evolutionary development. We use the method of geometric morphometrics to analyze left/right asymmetries in the whole body, in two sites and totally six populations of Ceroglossus chilensis with the aim to infer and explain morphological disparities between populations and sexes in this species. In all individuals analyzed we found both fluctuating asymmetry and directional asymmetry for size and shape variation components, and a high sexual dimorphism. Moreover a high morphological variability between the two sites emerged as well. Differences in diet could influence the expression of morphological variation and simultaneously affect body sides, and therefore contribute to the symmetric component of variation. Moreover differences emerged between two sites could be a consequence of isolation and fragmentation, rather than a response to local environmental differences between sampling sites.     

Morph‐dependent form of asymmetry in mandibles of the stag beetle Prosopocoilus inclinatus (Coleoptera: Lucanidae)

Abstract 1. The form of asymmetry in bilateral organs usually follows the same pattern within single populations. However, some exceptions may occur when a population consists of different phenotypes that are from different ontogenic backgrounds and under different selective pressures. We investigated the asymmetric patterns of mandibles of larvae, females, and males in the stag beetle Prosopocoilus inclinatus. 2. Larval mandibles exhibited directional asymmetry both in length and cross direction, whereas female mandibles showed directional asymmetry in cross direction. These asymmetric structures might be more effective in cutting wood fibres. 3. For the relation of male mandible length to body size, a model with a switch point showed a better fit to the data than a convex curve model. This shows that the males are dimorphic with two distinct morphs. 4. The form of asymmetry in male mandible length differed between the morphs. The smaller males exhibited left‐biased directional asymmetry in common with larvae, whereas the larger males exhibited fluctuating asymmetry. 5. This is a novel finding of a morph‐dependent asymmetry. The morph‐dependent asymmetry in males may be as a result of different selection on each morph or a developmental constraint from larval mandibles to adult ones.     

Effect of the 1990 die-off in the northern Italian seas on the developmental stability of the striped dolphin Stenella coeruleoalba (Meyen, 1833)

Developmental stability of the community of striped dolphins, Stenella coeruleoalba (Meyen, 1833), that died during the Mediterranean epizootic of 1990 was compared with that of the population prior to and after the epizootic, to assess whether animals that died were the developmentally less stable individuals in the population. Significantly higher levels of fluctuating asymmetry (FA) were found in those individuals that died. Tissue levels of organochlorine pesticide residues and PCBs were determined and the correlation between contaminant concentration and FA was tested. No correlations were found between the contaminant level and FA.     

Mandible asymmetry and genetic diversity in island populations of the common shrew, Sorex araneus

Mandibles from 13 island and six mainland populations of common shrews from the west coast of Scotland were subjected to geometric morphometric analysis in order to investigate the relationship between genetic diversity and fluctuating asymmetry. Although population mean shape fluctuating asymmetry (FA) and size FA were significantly inversely correlated with population genetic diversity this result was substantially due to one island. Sanda, the smallest island with by far the lowest genetic diversity, also had the highest FA. When Sanda was removed from the analysis, the relationship was not significant. There was no relationship between genetic diversity and FA at the individual level, whether measured as mean locus heterozygosity or d(2). In general, if genetic variation affects FA at all, the effect is weak and may only be of biological interest in very small populations.     

An asymmetric parental investment conflict with continuous strategy sets

In the parental investment conflict each of the sexes decides how much to invest in its brood, where its decision influences both sexes' fitness. In nature, each species is usually characterized by a common parental care pattern, male-only care, female-only care or biparental care. A possible way for understanding the factors that have led each species to adopt its unique parental care pattern is to analyse a male's and a female's decision process using a game-theoretical model. This paper suggests a two-stage game-theoretical model with two types of players, male and female. During the game each parent makes three decisions. The interval between the beginning of the game, i.e. after mating and having offspring, and the moment a parent starts to care for them is a random variable. Thus, in the first stage a parent chooses the cumulative probability distribution of this interval, and its amount of parental care. In the second stage the other parent chooses its probability for cooperation. It is assumed that as long as parental care is not provided the offspring are at risk, and that parental caring accrues a different cost for each sex. We compute the Evolutionary Stable Strategies (ESS) under payoff-relevant asymmetry, and show that uniparental and biparental care are possible ESS. We also characterize cases where the sex having the lower cost "forces" the sex having the higher cost to care and vice versa.     

Abnormal erythrocyte membrane phospholipid organisation in chronic myeloid leukaemia

The membrane phospholipid organisation in the red cells of humans suffering from chronic myeloid leukaemia has been analysed using the amino-group labelling reagent trinitrobenzenesulphonic acid and the fluid-sensing fluorophore, Merocyanine 540. Unlike the normal human erythrocytes, trinitrobenzenesulphonic acid in intact chronic myeloid leukaemia erythrocytes modified about 30% phosphatidylserine, under controlled conditions. Also, the chronic myeloid laukaemia red cells, but not the normal cells, were found to bind the fluorescent dye Merocyanine 540. These results demonstrate that loss of the transmembrane phospholipid asymmetry in chronic myeloid leukaemia erythrocytes is accompanied by an enhancement in the outer surface fluidity and, therefore, suggest that the red cells membrane phase-state asymmetry originates probably from the asymmetric arrangements of phospholipids across the membrane bilayer.     

Directional and anteroposterior asymmetry of common white markings in the legs of the Arabian horse: response to selection

Arabian bay horses manifest, on the average, more common white markings in their hind legs than their forelegs (anteroposterior asymmetry) and more common white markings in their left legs than their right legs (directional asymmetry). To determine if genetic variation exists for these types of asymmetry, the phenotypic response was studied in bay foals when their dams and sires were selected for the directions of fore-hind and left-right differences. In the fore-hind studies, the quantitative shifts in the bay foals were in the direction specified by the selection scheme and the observed deviations were all statistically significant. The shifts were also consistently in the direction favored by selection in the left-right studies, but only two of six observed deviations were statistically significant using a one-tailed test of significance. Thus, only marginal statistical evidence is available to support the observed consistent responses to selection in the left-right studies. These differential responses are reflected in the magnitudes of the heritability estimates. Based on the overall results, it is concluded that both types of asymmetry have a genetic basis in the Arabian horse, but much more genetic variation is present for anteroposterior asymmetry than for directional asymmetry. This revised version was published online in July 2006 with corrections to the Cover Date.     

Fluctuating asymmetry in bank vole populations (Rodentia, Arvicolinae) reflects stress caused by landscape fragmentation in the Mont-Saint-Michel Bay

In intensively farmed, reclaimed areas (polders) of Mont-St-Michel Bay, France, bank voles ( Clethrionomys glareolus ) live in fragmented hedgerows, where populations are small and dispersal rates and genetic diversity are low. These small populations are likely to have been exposed to potential environmental and/or genetic stress. The sensitivity of development to stress can be measured by fluctuating asymmetry (FA). FA was calculated for three samples from a disturbed area and one sample from an adjacent, more connected and undisturbed landscape. Size FA was estimated from 16 measurements of the skull and teeth whilst shape asymmetry was estimated from the skull alone. Bank voles in fragmented hedgerows of the disturbed area had a higher degree of FA than bank voles from the more extensive and more connected hedges of the undisturbed area. These results were confirmed by the study of shape asymmetry, body mass and centroid size of the skull. There were no differences in FA between the three disturbed area samples. We conclude that FA does not reveal differences in the development of bank voles living in isolation under different local conditions in the various parts of the disturbed area. However, FA may allow differentiation between populations from greatly contrasting landscapes.  © 2003 The Linnean Society of London, Biological Journal of the Linnean Society , 2003, 80, 37–44.     

Directional asymmetry in the forelimb of Macaca mulatta

Asymmetry was investigated in the forelimbs of 150 rhesus monkey (Macaca mulatta) skeletons using measurements of right and left humerii, radii, ulnae, second metacarpals, and femora. Seven of the ten forelimb dimensions were larger on the right than on the left side. Paired t-tests revealed that the mean of the right side was significantly larger than that for the left for two measurements of the ulna and two of the humerus. No measurement was significantly larger on the left than on the right side. These results indicate a small but significant asymmetry in the forelimb bones of rhesus monkeys and, as is the case for humans, the direction of asymmetry favors the right side. Our findings are consistent with an interpretation of hypertrophy of certain muscles and opens the question of whether rhesus monkeys preferentially use their right forelimbs for manipulative tasks that require manual dexterity, as is the case for humans. These forelimb skeletal asymmetries are discussed in light of the recent literature on cortical asymmetry and handedness in nonhuman primates.     

Tolerance assessment of Cistus ladanifer to serpentine soils by developmental stability analysis

Developmental instability is the result of random environmental perturbations during development. Its absence (developmental stability) depends on an organism's ability to buffer environmental disturbances. Both genotype and environment influence the phenotypic expression of developmental instability and it is susceptible to selection pressure. We studied developmental instability (as indicated by increased within-individual asymmetry of repeated traits) in vegetative and reproductive structures of three populations of Cistus ladanifer L. living in different soil substrates (serpentine, siliceous and contact zone) to detect tolerance to serpentine soils. Serpentine soils, characterized by high concentrations of heavy metals (Ni, Cr, and Co), low levels of Ca/Mg ratio and high water deficit, can adversely affect plant performance. In this study we demonstrated that asymmetry and within-plant variance were higher in the contact zone population than either the silica or serpentine populations, proving the adaptation of C. ladanifer to serpentine soils. Within-population estimates of developmental instability were concordant for both vegetative and reproductive traits. There was little or no within-individual correlation among estimates of developmental instability based on different structures, i.e., plants that had highly asymmetric leaves always had high developmental instability in translational symmetry. Radial asymmetry of petals was negatively correlated with petal size, especially in silica soil plants, providing evidence of selection for symmetric and large petals. While leaf size was positively correlated with absolute fluctuating asymmetry, suggesting selection for small or intermediate size leaves. Serpentine soils presented the largest foliar and floral traits, as well as shoot elongation, while silica soil plants had the smallest scores. On the contrary, aboveground plant biomass was larger in silica soil plants, while the contact zone plants had the lowest biomass.     

The statistical analysis of fluctuating asymmetry: REML estimation of a mixed regression model

The unbiased estimation of fluctuating asymmetry (FA) requires independent repeated measurements on both sides. The statistical analysis of such data is currently performed by a two-way mixed ANOVA analysis. Although this approach produces unbiased estimates of FA, many studies do not utilize this method. This may be attributed in part to the fact that the complete analysis of FA is very cumbersome and cannot be performed automatically with standard statistical software. Therefore, further elaboration of the statistical tools to analyse FA should focus on the usefulness of the method, in order for the correct statistical approaches to be applied more regularly. In this paper we propose a mixed regression model with restricted maximum likelihood (REML) parameter estimation to model FA. This routine yields exactly the same estimates of FA as the two-way mixed ANOVA . Yet the advantages of this approach are that it allows (a) testing the statistical significance of FA, (b) modelling and testing heterogeneity in both FA and measurement error (ME) among samples, (c) testing for nonzero directional asymmetry and (d) obtaining unbiased estimates of individual FA levels. The switch from a mixed two-way ANOVA to a mixed regression model was made to avoid overparametrization. Two simulation studies are presented. The first shows that a previously proposed method to test the significance of FA is incorrect, contrary to our mixed regression approach. In the second simulation study we show that a traditionally applied measure of individual FA [abs(left – right)] is biased by ME. The proposed mixed regression method, however, produces unbiased estimates of individual FA after modelling heterogeneity in ME. The applicability of this method is illustrated with two analyses.     

Dental arch asymmetry in an isolated Adriatic community

Developmental stability reflects the ability of a genotype to develop in the same way under varying environmental conditions. Deviations from developmental stability, arising from disruptive effects of environmental and genetic stresses, can be measured in terms of fluctuating asymmetry, a particularly sensitive indicator of the ability to cope with these stresses during ontogeny. In an inbred Adriatic island population, we expected dental arch fluctuating asymmetry 1) to be higher than in an outbred sample from the same island, and 2) within this population, to increase with the level of inbreeding. Due to environmental stress, we also expected to find higher fluctuating asymmetry in the outbred island population than in an urban reference group from the same country. The material consisted of 506 dental casts of 253 children from 1) the island of Hvar, and 2) Zagreb, Croatia. Three-dimensional coordinates of 26 landmarks spanning the arches were digitized. The analysis partitioned the asymmetry of arch forms into components for directional and fluctuating bilateral asymmetry, using the appropriate Procrustes method (geometric morphometrics). The results corroborated the hypotheses. Fluctuating asymmetry was found to be higher on the island than in Zagreb in all groups and in both jaws, and increased significantly with endogamy level in the lower jaw. There was no significant directional asymmetry in the Zagreb sample and likewise none in the upper jaws of the outbred island group, but significant directional asymmetry in both jaws of the inbred population and also in the lower jaws of the outbred island group. These results suggest an environmental as well as a genetic influence on dental arch asymmetry. Although the lower jaws expressed these two stresses almost additively, the upper jaws appeared to be better buffered. The role of directional asymmetry as a potential indicator of craniofacial developmental instability clearly merits further attention.     

Occurrence of four‐spined Gasterosteus aculeatus in an isolated Croatian river population

An isolated population of the three‐spined stickleback Gasterosteus aculeatus in Croatia was found to have a high incidence of specimens either having a fourth dorsal spine or showing remnants of a fourth spine. Juvenile individuals showed a 9·4% incidence of a fourth spine. The population was examined for asymmetry of the skeletal defensive complex in order to determine whether the additional spine could be the result of developmental instability, a response to predation or environmental conditions.     

Acid stress increases pelvic spine asymmetry in juvenile three-spined sticklebacks

In the evaluation of the effect of acidic water on the symmetrical development of the pelvic spines in juvenile three-spined sticklebacks Gasterosteus aculeatus , directional rather than fluctuating asymmetry was found, with left spines being, on average, longer than the right. Fish that were exposed for a period of c. 2 months to acidic pH levels grew significantly more asymmetrical pelvic spines than their control full-siblings held in unmanipulated water. Average spine size was not affected by the experimental treatment.     

Correspondence between enamel hypoplasia and odontometric bilateral asymmetry in Australian twins

Four aspects of enamel hypoplasia of the maxillary central incisor and mandibular canine (hypoplasia presence, width, cumulative width, and crown position) were correlated with directional and fluctuating measures of bilateral odontometric asymmetry in a large panel (n = 950) of South Australian twins. Hypoplasia and asymmetry are thought to reflect general developmental disruption, but they show few correlations beyond the expected statistical type I error. This may relate to differences in their specific etiology, the composite nature of overall crown dimensions, a general lack of stress, and the extended period of formation of dental crowns. In contrast, asymmetry is marginally more detectable in a subsample separated according to hypoplastic teeth, suggesting that correspondence may be clearer in comparisons at the population rather than individual level. The most notable difference is the greater variability of asymmetry measures in hypoplastic individuals.