Directional and fluctuating asymmetries in domestic pig skulls
P M Parés-Casanova (peremiquelp at prodan dot udl dot cat) #, C Esteve-Puig
Department of Animal Production, University of Lleida, Catalunya, Spain
# : corresponding author
Cite as
Research 2014;1:828

Morphological symmetry and asymmetry of skulls of domestic pig (n=29) were studied using geometric morphometric (GM) methods on the ventral aspect. Fluctuating asymmetry (FA) was used as an indicator of environmental stress, and directional asymmetry as a biomechanical constraint. The two-dimensional coordinates of 27 landmarks were digitized and analysed using GM. Multivariate analyses showed the presence of subtle but significant FA in the entire sample, and distinctive differences were detected between age groups. These results are indicative that environmental stress is present, but no symmetry alterations were noted. On the whole, morphometric studies should open up promising areas of research in this nearly unexplored field, to study environmental stress morphometrically in domestic ungulates.


Bilateral symmetry, a key feature of vertebrate body plans, is rarely perfect, and mild asymmetries can be found in normal growth and development as a typical adaptation of the organisms to their environments. Deviations from expected perfect symmetry can occur, and organisms can develop several kinds of asymmetries, including fluctuating asymmetry (FA) and directional asymmetry (DA). The former represents small random differences between corresponding parts on the left and right side of an individual, and because of its characteristics, it is usually considered to be a measure of developmental noise (Graham et al., 1993; Palmer 1994, 2004). DA occurs whenever one side on the plane of symmetry develops more than the other side, and has a proportion of genetic component (Van Valen, 1962; Palmer and Strobeck, 1986).

In the present study we analysed left-right ventral asymmetries in domestic pig skulls with geometric morphometric techniques, with the aim of quantifying asymmetries and to assess and describe differences based on age.

Materials and methods
Specimen collection

Twenty-nine skulls were obtained from a vulture feeding point located in Catalunya (NE Spain). The origin of these skulls represents dead farm animals of unknown sex, but different ages. Domestic pigs came from intensive local farms and were all raised for meat purposes. No inbreeding was supposed as animals were managed for productive purposes. Individuals corresponded to different age groups, according to molar teeth eruption: only M1 fully erupted (n=3), M2 fully erupted (n=10), and M3 fully erupted (complete molar series, n=16). Some cases of clear cheek tooth diseases (e.g. peg-shaped, dental agenesis, asymmetrical wear, chronic abscesses, etc.) were detected as well as osseous abnormalities (e.g. enthesopathies, osteomyielitis, periodontitis, etc.), which caused gross bony deformations intra vitam. These individuals were not excluded from the analyses.

Directional and fluctuating asymmetries in domestic pig skulls figure 1
Figure 1. Landmarks digitized on the surface of the skull.
Data collection and geometric morphometric analyses

Skulls were labelled and levelled dorsally on a horizontal plane, and then the ventral view was photographed. Image capture was performed with a Nikon® D70 digital camera (image resolution of 2,240 x 1,488 pixels) equipped with a Nikon AF Nikkor® 28–200 mm telephoto lens. The camera was placed on a tripod parallel to the ground plane so the focal axis of the camera was parallel to the horizontal plane of reference and centred on the ventral aspect of each skull. A scale was included in the images to standardize each specimen size (in mm). Skulls were digitized using tpsDig version 2.04 (Rohlf, 2006). In total, 27 two-dimensional (2D) landmarks (LMs, homologous anatomical points) were used on the ventral aspect of cranium (Figure 1). Twenty-three were bilateral, and four (1, 2, 3 and 27) were midline landmarks. All of these LMs are thought to encompass elements of the whole skull (both viscerocranium as esplachnocranium). As measurement error could be a confounding factor when assessing FA (Palmer and Strobeck, 1986), landmarks were digitized twice by the same person (CE) on two different days, in the same order. A NPMANOVA (Non Parametric Multivariate Analyses of Variance) with Bonferroni p-corrected values using Mahalanobis distances were used too to assess differences between replicas.

In order to compare Procrustes to tangent space distances between individuals, a Generalized Procrustes Analysis superimposition (equivalent to generalized least squares) procedure of Rohlf and Slice (1990) was performed on each data set using TPS-Small 1.20 (Rohlf, 2003). The approximation of shape space by tangent space presented a high correlation (1.000). This high degree of approximation of shapes in the sample (i.e. shape space) by the reference shape (i.e. tangent space) allowed accurate capture of the nature and extent of shape deformations in subsequent statistical analyses.

Directional and fluctuating asymmetries in domestic pig skulls figure 2
Figure 2. Scatter plot of CVA showing differences between age groups, for symmetric component of variation.
Size study and shape asymmetry

Cartesian x-y coordinates were then extracted with a full Procrustes fit (Rohlf and Slice, 1990; Dryden and Mardia, 1998), a procedure that removes information about position, orientation and rotation and standardizes each specimen to unit centroid size (CS), which is a measure computed as the square root of the summed squared Euclidean distances from each landmark to the specimen centroid, and provides an estimation of the size of the structure. Differences in CS were analysed with the Kruskal-Wallis test. Due to the symmetry of the structure, reflection was removed, including the original and the mirror images of all configurations in the analysis, and they were superimposed simultaneously (Klingenberg et al., 2002), and all information on the asymmetry of the studied structure was used to observe the eventual phenomena of FA and DA. Within a symmetrical structure, DA happens whenever one character developed more on one side of the plane or planes of symmetry than on the other, while FA is defined as the non-directional deviation from bilateral symmetry (right-left differences, r-l). We used Procrustes ANOVA, as it has been used in studies on symmetry (Klingenberg and McIntyre, 1998; Klingenberg et al., 2002; Klingenberg and Monteiro, 2005), to quantify the amount of symmetric variation and asymmetry; results are reported as the sums of squares (SS) and mean squares (MS), which are dimensionless. Additionally, to avoid the assumption of having isotropic (equal and independent) variation on all LMs, we performed a MANOVA test for both symmetric and asymmetric components (Klingenberg et al., 2002). Differences in shape were analysed with NPMANOVA using Euclidean distances and p-Bonferroni corrected values.

Directional and fluctuating asymmetries in domestic pig skulls figure 3
Figure 3. Scatter plot of CVA showing differences between age groups, for asymmetric component of variation.

Shape asymmetry can be viewed as the distance of the actual shape from its closest symmetrical variant. FA and DA as assessed using landmark-based methodology are different from traditional methods of asymmetry analysis (Palmer and Strobeck, 1986) but measure the same biological phenomena as in traditional morphometrics (Palmer and Strobeck, 2003). However, we cannot expect absolute numbers with respect to particular landmarks, as asymmetry is a measure of distance between complete landmark configurations (Procrustes distance).

We then assessed shape variation in the whole dataset by performing a principal component analysis (PCA), taking into account both symmetric and asymmetric components of variation; the symmetric component is the average of the left and right sides and represents the shape variation component, whereas the asymmetry component represents the individual left-right differences. Differences between the three sampled populations were assessed with a canonical variate analysis (CVA), a multivariate statistical test that allows finding shape characteristics that best distinguish among several groups of individuals. Results are reported as the Mahalanobis distance, a multivariate measure of distance relative to the within sample variation. All analyses were computed with 10,000 permutation runs.

Size asymmetry

Additionally, centroid size (Bookstein, 1991) was used as a basic characteristic describing size differences between age groups. Centroid size is a unit-less measure and can only be used for comparison of samples described by the same set of landmarks.

All analyses were performed using MorphoJ v. 1.05 by Klingenberg (2011), which can handle data by using full multivariate analysis (MANOVA), and PAST- “Paleontological Statistics Software Package for Education and Data Analysis” (Hammer et al., 2001).


The results of the measurement error assessment are presented in Table 1 and show that the variance as a result of repeated measurement was significantly smaller in comparison with the FA variance. The NPANOVA also showed no difference in Procrustes values between the two digitizing trials (p=0.298), thus indicating that precision is unlikely to constrain the results of subsequent statistical analyses in the present study.

SS MS Df F P (param.)
Shape Individuala 0.06193162 0.0000884737 700 9.06 <0.0001
Sideb 0.00036047 0.0000144189 25 1.48 0.0633
Ind x Sidec 0.00683303 0.0000097615 700 24.60 <0.0001
Error 0.00057541 0.0000003968 1450
Size Individual 4534094.723380 161931.954406 28 20623.20 <0.001
Error 227.706036 7.851932 29
Table 1. ANOVA for skull size and shape for Sus domestica (n=29), on the basis of the position of all 27 landmarks. .a Individual effect represents the variation between individuals in the symmetric component of shape. .b Side, systematic difference between the original and mirrored copy of each individual, directional asymmetry. .c Ind x Side quantifies FA, effects of Side and Ind x Side represent asymmetric component of the shape. Error, the residual variation due to measurement error, includes both symmetric and asymmetric components.

For the three age groups considered, the samples differed significantly from each other in size (p<0.05), which were progressively larger with increasing age. They also presented differences in shape (p<0.05).

Procrustes ANOVA indicated that variation between individuals was significant based on size (Table 1) as well as shape. Additionally, both DA and FA emerged as highly significant.

We then used PCA to assess and describe this pattern of individual variation and asymmetry. PCA for the symmetric component of variation showed that the first three PCs explained 65.8% of the total shape variation, with all of the other PC, which account for no more than 8% of variation (see Table 2 for details); all LMs contributed quite equally to the whole shape variation. The reverse PCA for the asymmetric component of shape variation (FA) showed that the first three PCs contributed 71.7% to the total variation (refer to Table 2 for details). Age groups appeared differentiated for both symmetric and asymmetric components (Figures 2 and 3).

Symmetric Asymmetric
PC Eigenvalues % variance Cumulative % Eigenvalues % variance Cumulative %
1 0.0003811 34.462 34.462 0.0000465 38.105 38.105
2 0.0002358 21.325 55.787 0.0000288 23.567 61.672
3 0.0001113 10.063 65.850 0.0000122 10.022 71.695
4 0.0000850 7.688 73.538 0.0000071 5.812 77.506
5 0.0000614 5.552 79.090 0.0000058 4.743 82.249
6 0.0000517 4.677 83.767 0.0000044 3.562 85.812
7 0.0000446 4.037 87.804 0.0000040 3.312 89.124
8 0.0000339 3.069 90.872 0.0000027 2.168 91.292
9 0.0000204 1.843 92.715 0.0000020 1.625 92.917
10 0.0000159 1.441 94.156 0.0000018 1.502 94.419
11 0.0000151 1.363 95.519 0.0000016 1.301 95.721
12 0.0000128 1.160 96.679 0.0000013 1.076 96.797
Table 2.Principal component analysis (PCA) of shape variation, for both symmetric and asymmetry components. Values reported are the eigenvalues and percentages for which each principal component accounts.

Morphological variability between age groups was assessed and displayed with CVA, which showed highly significant differences (in each case, p<0.01) between the three age groups analysed in both the symmetric component (Mahalanobis distances: 1M vs. 2M=82.619; 1M vs. 3M=49.299; 2M vs. 3M=37.837) and the asymmetry component (Mahalanobis distances: 1M vs. 2M=15.564; 1M vs. 3M=11.621; 2M vs. 3M=11.232) of variation.


Since a large proportion of individuals in a population will have asymmetries close to zero for any given trait due to chance alone, it may be necessary to study deviations from symmetry in multiple traits to obtain reliable measures of developmental competence for individuals. The use of FA and DA is not prevented for comparison, because shape variability relative to proportions of asymmetry is preserved. The effect of different sizes does not play as important a role as in traditional morphometry, because asymmetry is considered to be a property of normalized objects with respect to a sample. The method used allowed the decomposition of the total shape variation into components of symmetric variation (i.e. differences among individuals) from components of asymmetry (multiple components might occur according to the symmetry of the object). Using this approach, purely symmetric variation spanned only about 65.8% of the total variation, which is similar to the variation described by individual patterns of asymmetry, which did account for 71.7% of the total morphological variation in all three age groups for the first three PCs. But the differences expressing the deviation from symmetry obviously will depend on the selection of a landmark set, because Procrustes analysis distributes the error equally among the landmarks.

Some authors (Herring and Teng, 2000; Rafferty et al., 2000; Herring et al., 2002) have reported that muscle contraction in juvenile pigs increases strain in the braincase. If muscle action had an effect on symmetry, symmetry differences would appear both in splachnocranium (where the muscles dilatator naris apicalis, depressor labii superioris and buccinator pars buccalis are inserted, for example) as in the neurocranium (insertion of orbicularis oculi and malaris, for example). An increased strain can be supposed to be localized to specific portions of the skull that correspond directly to masticatory action. Fibres that attach to different surfaces of an aponeurosis must have different orientations, raising the possibility that the differential contraction of fibres could change the direction of muscle pulls, a possibility that has been confirmed in a variety of masticatory muscles (Herring et al., 1979; Turkawski et al., 1998). Shape variation is explained by general conformation, not by specific points. Moreover, individuals with asymmetrical muscular development as a result of either chewing side preference or simply a product of pathologies are expected to have increased levels of DA, but this is not the case; moreover, some individuals which presented clearly ad visu asymmetrical oclussal wearings did not appear separated. Thus, although the action line could vary dynamically throughout a masticatory cycle, its action must be globally constant in domestic pig. Pathological skulls did not appear separated.

Since both sides of any bilateral trait are produced by the same genome, the degree of symmetry reveals the individual’s ability to canalize development in the face of stress. While individual random asymmetry often is proximately caused by environmental stress, the ability to execute developmental programs correctly and uniformly in the face of such stress has a genetic basis. We believe that, in our samples, ventral pig craniofacial FA could just reflect responses to stress factors, which are different for each of the considered age groups. On the whole DA displayed no clear shape variation patterns.

To conclude, from our study emerged the presence of FA but not DA in domestic pig skull, but its value, although statistically significant, appeared as subtle. These results on the whole indicate the presence of some asymmetries in the structure, which are apparently insufficient to infer developmental stability; instead, they appear to act to counteract stressors and maximize fitness.

These morphometric studies should open up promising areas of research in this nearly unexplored field of morphometry and stress in domestic ungulates.


We wish to thank Marta Caballero who kindly allowed access to the feeding vulture point. Irina Kucherova helped us to collect samples.

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