Two-module organization of the mandible in the yellow-necked mouse: a comparison between two different morphometric approaches

Authors

  • V. Jojić,

    Corresponding author
    • Department of Genetic Research, Institute for Biological Research “Siniša Stanković”, University of Belgrade, Belgrade, Serbia
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  • J. Blagojević,

    1. Department of Genetic Research, Institute for Biological Research “Siniša Stanković”, University of Belgrade, Belgrade, Serbia
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  • M. Vujošević

    1. Department of Genetic Research, Institute for Biological Research “Siniša Stanković”, University of Belgrade, Belgrade, Serbia
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Correspondence: Vida Jojić, Department of Genetic Research, Institute for Biological Research “Siniša Stanković”, University of Belgrade, Bulevar despota Stefana 142, 11060 Belgrade, Serbia.

Tel.: +381 11 2078330; fax: +381 11 2761433; e-mail: vjojic@ibiss.bg.ac.rs

Abstract

Mandibles of yellow-necked mouse (Apodemus flavicollis) were used to explore modularity. We tested a biological hypothesis that two separate modules (alveolar region and ascending ramus) can be recognized within the mandible. As a second research goal, we compared two different morphometric procedures under the assumption that methodological approaches that use either geometric or traditional morphometric techniques should give similar results. Besides confirmation of the predicted hypothesis of modularity, the application of both approaches revealed that: (i) modularity was somewhat more evident when it was analysed on the asymmetric (fluctuating asymmetry, FA) than on the symmetric (individual variation) component of variation; (ii) there is correspondence in the patterns of individual variation and FA, which indicates that integration of mandibular traits among individuals is primarily due to direct developmental interactions; and (iii) allometry does not obscure the hypothesized modularity for individual variation or for FA. In addition, traditional morphometric method allowed us to check whether allometry influenced each module to the same extent and to conclude that the ascending ramus is more heavily influenced by general size than the alveolar region. In studies of modularity, differences in methods can lead to discrepancies in the results, and therefore, some caution is required when comparing findings from different investigations. The substantial agreement between our results provides evidence that, when considering two-module organization of the mouse mandible, direct comparison among studies that use the methods applied herein is, in great part, reliable.

Introduction

Morphometrics could be defined as ‘the quantitative characterization, analysis, and comparison of biological form’ (Roth & Mercer, 2000). It has been demonstrated to be a valuable tool in numerous evolutionary studies for testing different hypotheses, examining various phenomena and establishing diverse concepts, such as morphological integration and modularity. Morphological integration refers to the relationships and connections among morphological traits within any complex morphological structure (Olson & Miller, 1958; Chernoff & Magwene, 1999; Marroig & Cheverud, 2001), whereas the concept of modularity assumes a general property of biological systems to be organized into modules whose parts are integrated internally by numerous or strong interactions but are relatively independent from other modules owing to few or weak interactions connecting different modules (Cheverud, 1996a; Wagner & Altenberg, 1996; Klingenberg, 2008, 2010). Morphological modularity occurs in developmental, genetic and functional contexts because morphological traits can be integrated through developmental, genetic and functional relationships. Additionally, evolutionary modularity is the result of correlated evolution in distinct sets of traits. Morphological integration could constrain the variability in individual traits. On the other hand, it could facilitate modifications of related traits (Wagner & Altenberg, 1996; Goswami, 2006). Thus, integration and modularity have important significance for morphological evolution.

Studies of morphological integration and modularity relied mostly on analyses of correlation/covariation among different traits starting from the defining quality of modules that correlations or covariances within one module are higher than between modules. In these studies, the symmetric component of variation, that is, patterns of covariation among individuals (individual variation, Ind), and the asymmetric component of variation, that is, patterns of covariation within individuals (fluctuating asymmetry, FA), were analysed. A phenotypic correlation/covariation structure could be considered as manifestation of multiple factors (developmental, genetic and environmental), as well as those related to allometry and functional integration. Moreover, some authors (Mitteroecker & Bookstein, 2007; Mitteroecker, 2009; Mitteroecker et al., 2012) emphasized the importance of other nonbiological sources of phenotypic covariances and correlations, such as geometric and spatial dependences among measurements. Thus, according to these authors, variational modularity does not necessarily reflect genetic or developmental modularity.

Fluctuating asymmetry, defined as minor, random differences between the two sides in bilaterally symmetric traits (Van Valen, 1962; Palmer & Strobeck, 1986, 2003), has been used as a useful tool for determination of the boundaries of developmental modules as well as for investigation of the developmental basis of morphological integration and modularity. These are important issues for understanding the evolution of morphological structures. Coordinated variation between morphological traits can originate from direct developmental interactions between the developmental pathways and from parallel variation in separate developmental pathways (Klingenberg & Zaklan, 2000; Klingenberg et al., 2001a; Klingenberg, 2002, 2003, 2004, 2005, 2008, 2010). Morphological integration by direct developmental interactions occurs when traits that originate from the same developmental precursor share variation accrued before or at the moment of partitioning of the precursor (Riska, 1986), or variation can be transmitted between different precursors by inductive signalling (Jacobson & Sater, 1988). Covariation of morphological traits derived from parallel variation in separate developmental pathways arises when some external factor (allelic or environmental variation) affects these pathways simultaneously. Covariation of morphological traits within a module is achieved primarily by direct developmental interactions, whereas morphological integration due to parallel variation does not reflect developmental modularity. Bilaterally symmetric traits develop under the same genetic and almost the same environmental conditions. Therefore, the study of fluctuating asymmetry provides almost complete control over external sources of variation that might produce parallel variation of separate pathways. Additionally, as FA originates from random perturbations that occur spontaneously within the developmental pathways themselves, it can only be transmitted among pathways by direct interaction. Thus, the patterns of covariation among traits for signed FA must result from direct interactions between developmental pathways and not from parallel variation of separate pathways, whereas the patterns of covariation among individuals can be of both developmental origins. By comparing patterns of covariation of FA with the patterns of covariation among individuals, it is possible to assess the relative importance of two mechanisms generating morphological integration.

Goswami & Polly (2010) summarized the majority of exploratory and confirmatory methods for studying morphological integration and modularity. By applying some of the methods, they tested three different models of cranial modularity in Japanese macaques to discuss similarities and differences in the results obtained and to illustrate strengths and weaknesses of the procedures used. Within the confirmatory methods, Goswami & Polly (2010) considered RV coefficient analysis introduced by Klingenberg (2009), as well as theoretical matrix correlation analysis developed by Cheverud (1995, 1996b). The first method relied on landmark-based geometric morphometrics, whereas the second is a traditional morphometric procedure based on linear distances. Goswami & Polly (2010) examined these methods and observed that all three models of cranial modularity were significant at the level of individual variation in the pooled adult sample for both analyses. For comparison between two different morphometric approaches, besides the main question (Whether the predicted hypothesis of modularity is confirmed?), several important issues remain to be addressed: (i) Do patterns of individual variation and FA reflect hypothesized modularity to the same extent? (ii) Is there correspondence or dissimilarity between the patterns of individual variation and FA? (iii) How does the effect of size on shape (allometry) influence modularity for individual variation and for FA?

The mouse mandible is a particularly suitable structure to address all of these questions, as it is composed of multiple parts, with different embryonic origins and timing of differentiation (Atchley, 1993), assembled into two main modules. The anterior module (alveolar region), which bears the teeth, includes the molar and incisor alveoli, whereas the posterior module (ascending ramus), which articulates with the rest of the skull and participates in the attachments of muscles, is composed of the central masseteric region as well as the coronoid, condylar and angular processes. Although some findings did not support the subdivision of the mandible into alveolar region and ascending ramus (Klingenberg & Leamy, 2001; Klingenberg et al., 2001b; Zelditch et al., 2008, 2009), a number of studies confirmed the hypothesis that two separate modules can be recognized within the mandible (Atchley et al., 1985; Cheverud et al., 1991, 1997; Leamy, 1993; Mezey et al., 2000; Klingenberg et al., 2003, 2004; Klingenberg, 2009). It is worth noting that other hypotheses propose more modules (Monteiro et al., 2005; Márquez, 2008; Zelditch et al., 2008, 2009; Fish et al., 2011), and some recent studies argue that the mandible is integrated but not modular (Zelditch et al., 2008, 2009; Roseman et al., 2009).

In this study, we used the mandibles of the yellow-necked mouse (Apodemus flavicollis) to explore modularity. We tested a biological hypothesis that two separate modules (alveolar region and ascending ramus) can be recognized within the mandible. As a second research goal, we compared two different morphometric procedures under the assumption that methodological approaches that use either geometric or traditional morphometric techniques should give similar results. Both modularity and methods for analysing it are of great general interest because modularity is now widely recognized as an important attribute of organisms, one that enables them to evolve, and methods for studying modularity are both debatable and clearly important.

Materials and methods

The analysed sample was composed of 226 individuals from four populations of yellow-necked mice (Apodemus flavicollis), trapped in Serbia (UTM coordinates are given in brackets): Ada (CQ82), 42 animals; Mt. Avala (DQ64), 86 animals; Mt. Cer (CQ84), 37 animals; and Mt. Jastrebac (EP30), 61 animals. Mandibles were cleaned by exposure to dermestid beetles. Only adult mandibles with complete eruption of the third molar were analysed. Images (2272 × 1520 pixels resolution) of the right and left hemimandibles in the labial view were obtained with a Nikon Coolpix4500 digital camera (Nikon Corporation, Tokyo, Japan). The images of left hemimandibles were reflected to their mirror images, and 14 two-dimensional landmarks around the outline of the mandible were recorded (Table 1; Fig. 1) using TpsDig software (Rohlf, 2008; SUNY, Stony Brook, NY, USA). Each image was digitized twice by the same observer in two separate sessions.

Figure 1.

Landmarks recorded on the labial view of the mandible of the yellow-necked field mouse (Apodemus flavicollis). See Table 1 for landmark definitions and their membership in two modules.

Table 1. Definitions of landmarks digitized on the labial view of the mandible of the yellow-necked field mouse (Apodemus flavicollis). Landmarks membership in the alveolar region (alv) and the ascending ramus (asc) is given in brackets
1Posterior tip of the condyle (asc)
2Anterior tip of the condyle (asc)
3Maximum of curvature between coronoid and condylar processes (asc)
4Tip of the coronoid process (asc)
5Posterior intersection of the molar tooth row with the coronoid surface (alv)
6Anterior edge of the molar tooth row (alv)
7Extreme of the diastema invagination (alv)
8Antero-dorsal border of the incisive alveolus (alv)
9Antero-ventral border of the incisive alveolus (alv)
10Anterior-most point on the baseline perpendicular to the landmark 6 (alv)
11Dorsal-most point on the ventral border of the mandible (alv)
12Ventral-most point on the ventral border of angular process (asc)
13Tip of the angular process (asc)
14Maximum of curvature on the curve between the condylar and angular processes (asc)

Landmark-based geometric morphometric approach

The landmark coordinates of right and left mandibles of both replicates were superimposed using a generalized Procrustes analysis (GPA) to obtain centroid size (CS) and Procrustes coordinates (Rohlf & Slice, 1990). Centroid size is a geometric measure of size, whereas Procrustes coordinates contain complete shape information after removing variation due to scaling, position and orientation. Centroid size and Procrustes coordinates were subjected to conventional two-factor anova (Palmer & Strobeck, 1986, 2003) and Procrustes anova of shape (Klingenberg & McIntyre, 1998; Klingenberg et al., 2002), respectively. In the conventional two-factor and Procrustes anovas, individuals and sides were the main effects, where the former accounted for individual variation and the latter for the directional asymmetry (DA). The individuals x sides interaction estimated the measure of fluctuating asymmetry (FA), whereas residual variance component between replicates quantified measurement error. In the analyses of the shapes of morphological structures with matching symmetry, such as mandibles, the variation among individuals in the averages of the right and left configurations constitutes the symmetric component of shape variation, and the variation within individuals in the signed differences between configurations from the right and left sides constitutes the asymmetric component of shape variation or FA (Klingenberg et al., 2002). When analysing FA, it is important to distinguish FA from DA and antisymmetry. Parametric F-tests in the conventional two-factor and Procrustes anovas were used to determine whether variation among individuals, FA and DA were significant. To check for potential antisymmetry, log CS asymmetry and asymmetric components of shape variation were inspected for signs of bimodality using the Kolmogorov–Smirnov test of normality. A preliminary two-way multivariate analysis of variance (manova) was carried out to test for significant differences in asymmetric component of shape variation among populations and between sexes. No significant differences were detected, either for main factors or interaction term (population: F72,583.6 = 1.18, P = 0.1549; sex: F24,195.0 = 0.91, P = 0.5888; interaction: F72,583.6 = 0.86, P = 0.7859), and therefore, populations and sexes were pooled throughout all subsequent analyses.

The covariance matrices of symmetric and asymmetric components of shape variation were used to test the modularity of the mandible following the procedures described by Klingenberg (2009). As a measure of the strength of the association between hypothesized modules (alveolar region and ascending ramus), the RV coefficient of Escoufier (1973) was calculated and compared with RV coefficients obtained for alternative partitions of the configuration into subsets of landmarks. These subsets contained the same number of landmarks as the hypothesized modules, and alternative partitions were spatially contiguous. Spatial contiguity was defined using an adjacency graph. The values of RV coefficient could be from zero to one. Lower values of RV coefficient reflect weaker correlation between two subsets of landmarks. If the calculated value of RV coefficient between hypothesized modules is the lowest value or it falls in the lower tail of distribution of RVs observed for alternative partitions, the predicted hypothesis of modularity is confirmed.

However, by affecting all traits of the entire morphological structure jointly, the effect of size on shape (allometry) can lead to overall integration throughout the whole morphological structure, counteracting modularity (Klingenberg, 2009). To test for allometry, we used multivariate regressions of Procrustes coordinates on log CS. The symmetric component of shape variation was regressed onto symmetric log CS, and the asymmetric component of shape variation was regressed onto log CS asymmetry. Allometry tests were based on regression by a permutation test with 10 000 iterations under the null hypothesis of independence between size and shape, by randomly exchanging the value for log CS among individuals (Good, 1994). The covariance matrices of residuals from these multivariate regressions were used to test the modularity of the mandible, after removing the influence of allometry, following the same procedures (Klingenberg, 2009) described previously.

Patterns of variation among individuals (symmetric) and FA (asymmetric) components of shape variation were compared by computing matrix correlations (R) between the respective covariance matrices. Additionally, after the correction for allometric effects, the covariance matrices of residuals were also compared by computing matrix correlation. The significance of these correlations was obtained using the matrix permutation test with 10 000 iterations against the null hypothesis of complete dissimilarity between the respective covariance matrices (Cheverud et al., 1989), by permuting landmarks. The matrix permutation test excluded the diagonal entries of the matrices.

The Kolmogorov–Smirnov test of normality and manova were performed using Statistica (StatSoft Inc, 1997). All other analyses were conducted using MorphoJ software (Klingenberg, 2011).

Linear distance–based traditional morphometric approach

A set of 35 linear measurements (interlandmark distances) was calculated from the landmark coordinate data of right and left mandibles of both replicates (Fig. 2) using the TMorphGen6 program (Sheets, 2000; SUNY, Buffalo, NY, USA). The geometric mean (GM) of all variables was used as overall size (Mosimann, 1970). Size adjustment was obtained by dividing each variable by the geometric mean of all variables (Darroch & Mosimann, 1985). ‘Size extracted by Mosimann's ratio method can be called “isometric size” (Oxnard, 1978)’; (Jungers et al., 1995), and in all further analyses, size-adjusted variables were used. Geometric mean and each of 35 variables were subjected to a conventional two-factor anova (Palmer & Strobeck, 1986, 2003) to obtain the significance of individual variation, DA and FA. Following analogy of the geometric morphometric studies of shape with bilateral symmetry where the total shape variation is partitioned into symmetric and asymmetric components, we also obtained the variation among individuals for the averages of the right and left linear distances (symmetry of linear distances) and the variation within individuals in the signed differences between linear distances from the right and left sides (asymmetry of linear distances or FA). The presence of antisymmetry was tested on GM asymmetry and signed differences (right minus left differences) using the Kolmogorov–Smirnov test of normality (Palmer & Strobeck, 1986, 2003). Additionally, asymmetry of linear distances was subjected to two-way multivariate analysis of variance (manova) to test for significant differences among populations and between sexes. No significant differences were detected, either for the main factors or interaction term (population: F105,551.9 = 1.11, P = 0.2234; sex: F35,184.0 = 0.79, P = 0.7969; interaction: F105, 551.9 = 0.79, P = 0.9267), and therefore, populations and sexes were pooled throughout all subsequent analyses.

Figure 2.

Linear measurements (interlandmark distances) recorded from the labial view of the mandible of the yellow-necked field mouse (Apodemus flavicollis). Fifteen of them were assigned to the alveolar region (black lines) and 20 to the ascending ramus (grey lines).

The correlation matrices of symmetry (individual variation) and asymmetry (FA) of linear distances were used to test the modularity of the mandible according to the procedures introduced by Cheverud (1995, 1996b). Fifteen and 20 of these linear distances were assigned to the alveolar region and the ascending ramus, respectively (Fig. 2). Selected linear measurements exactly corresponded to the edges of the adjacency graph, which was used for definition of spatial contiguity of modules. The assignment of linear measurements to the hypothesized modules was used to construct two 35 × 35 theoretical matrices. If two traits belonged to the specified mandibular module, a value of one was entered, otherwise, a value of zero was entered. By combining these two matrices, that is, by summing them, a single theoretical connectivity matrix was obtained, where the value of one was entered if two traits shared the same functional and developmental module, and otherwise, the value of zero was entered. These three theoretically derived matrices were compared with the observed correlation matrices, and matrix correlation (R) was obtained as a measure of the structural similarity between pairwise matrix correlations. The statistical significance of the observed matrix correlation for all comparisons was assessed by the quadratic assignment procedure (Mantel's test), under the null hypothesis of no correlation between compared matrices (Mantel, 1967). This procedure includes 999 random permutations of one matrix followed by correlation of each randomized matrix with the reference matrix to generate a distribution of matrix correlations (Cheverud et al., 1989). If the observed matrix correlation exceeds 95% of the random correlations, the similarity between two matrices is considered to be higher than what one would expect due to chance (Marroig & Cheverud, 2001). We also calculated the overall mean of the observed Pearson's correlation coefficients for functionally and developmentally related and unrelated traits in each of the empirically derived matrices (Marroig et al., 2004). It is worth noting that the use of Mantel's test for testing the matrix correlation has been criticized by Mitteroecker & Bookstein (2007), who have argued that Mantel's test is not a valid significance test, but is a measure of the average difference between within-module and between-module correlations. However, in accordance with our second research goal (a comparison between two different morphometric approaches), we followed the original procedures given by Cheverud (1995, 1996b).

To eliminate the influence of allometry, the symmetry and asymmetry of linear distances were regressed onto symmetric GM and GM asymmetry, respectively. The correlation matrices of residuals from these regressions were used to test the modularity of the mandible free of the effects of size according to the same procedures (Cheverud, 1995, 1996b; Marroig et al., 2004) described previously.

The matrix correlation pattern between individual variation (symmetry of linear distances) and FA (asymmetry of linear distances) was compared by calculating matrix correlation (R) between the respective correlation matrices. Additionally, after the correction for allometry was made, the correlation matrices of residuals for individual variation and FA were also compared by computing matrix correlation. The significance of these correlations was obtained by Mantel's test with 999 iterations against the null hypothesis of complete dissimilarity between the respective correlation matrices (Mantel, 1967).

Regressions were made in Statistica (StatSoft Inc, 1997), whereas Mantel's tests were performed using PopTools (Hood, 2010).

Results

Geometric morphometrics

The two-factor anova for centroid size (CS), as well as Procrustes anova of shape (Table 2), showed highly significant (P < 0.0001) differences among individuals, between sides and fluctuating asymmetry (FA). Variation among individuals contributed the most to the total variation. The mean squares for individual variation and FA exceeded measurement error by more than 3498- and 26-fold (for CS) and 99- and 11-fold (for shape), and therefore, all the subsequent analyses of individual variation and FA are warranted. Directional asymmetry (DA), although statistically significant, accounted for a fairly small percentage of the total variation for both size (0.11%) and shape (1.46%). Kolmogorov–Smirnov tests disclosed that log CS asymmetry was normally distributed and that only one of the 28 signed asymmetry distributions showed significant departure from normality. Thus, these asymmetries could be assigned to fluctuating asymmetries.

Table 2. Two-factor anova of centroid size (CS) and Procrustes anova of shape. Significance levels are from parametric F-tests. % Total indicates the relative amount of the total variation
 Effect MS d.f. F P % Total
CSIndividual43714.673750225134.14< .000199.09
Side11165.057422134.26< .00010.11
Individual × side325.89314822526.08< .00010.74
Measurement error12.496772452  0.06
ShapeIndividual0.000238027654008.62< .000186.72
Side0.00090341512432.72< .00011.46
Individual × side0.0000276085540011.49< .000110.06
Measurement error0.000002402010848  1.76

The a priori hypothesis of a two-module (alveolar region–ascending ramus) organization of the mandible was confirmed for both individual variation (symmetric component of shape variation) and FA (asymmetric component of shape variation) (Fig. 3). None (for variation among individuals) and only one (for FA) of the 322 alternative spatially contiguous partitions produced a lower RV coefficient than that observed for the partition into hypothesized modules. The value of the RV coefficient between the alveolar region and ascending ramus was lower for FA (RV = 0.194) than for individual variation (RV = 0.249). Additionally, we obtained similar RVs for all alternative partitions of the mandible for individual variation (about 0.2–0.4) and for FA (about 0.2–0.3).

Figure 3.

Evaluation of an a priori hypothesis of a two-module (alveolar region – filled circles and ascending ramus – open circles) organization of the mandible of the yellow-necked field mouse (Apodemus flavicollis) for individual variation (Ind) and fluctuating asymmetry (FA). Histograms of the RV coefficients for those partitions for which the subsets of landmarks are spatially contiguous. The values of RV coefficients (Escoufier, 1973) observed for the partition into alveolar region and ascending ramus and proportions (P) of partitions with RV lower than that observed for the subdivision into alveolar region and ascending ramus are indicated by arrows.

For both symmetric and asymmetric components of shape variation, a statistically significant (P < 0.0001) effect of size on shape was observed. Allometry accounted for 7.9% of individual variation and 3.2% of FA. After the correction for allometry was made, the RV coefficient between alveolar region and ascending ramus had the lowest value compared with the RV coefficients for the alternative partitions, supporting partition of the mandible into hypothesized modules for both individual variation and FA (Fig. 4). Moreover, allometry correction reduced the RV coefficient between alveolar region and ascending ramus from 0.249 to 0.208 for individual variation and from 0.194 to 0.190 for FA. After the effect of size was removed, the ranges of RVs for all alternative partitions remained almost the same (about 0.2–0.4 for individual variation and about 0.2–0.3 for FA).

Figure 4.

Evaluation of an a priori hypothesis of a two-module (alveolar region – filled circles and ascending ramus – open circles) organization of the mandible of the yellow-necked field mouse (Apodemus flavicollis) for individual variation (Ind) and fluctuating asymmetry (FA) after correction for allometry. Histograms of the RV coefficients for those partitions for which the subsets of landmarks are spatially contiguous. The values of RV coefficients (Escoufier, 1973) observed for the partition into alveolar region and ascending ramus and proportions (P) of partitions with RV lower than that observed for the subdivision into alveolar region and ascending ramus are indicated by arrows.

The matrix correlations between the symmetric (variation among individuals) and the asymmetric (FA) components of shape variation were significantly (P < 0.0001) similar before (R = 0.667) as well as after removing the influence of allometry (R = 0.704).

Traditional morphometrics

As revealed by two-factor anovas, the main effects of individuals (variation among individuals) and the individuals x sides interaction (FA) were all highly significant at P < 0.0001 for geometric mean (GM) and for each character tested. Variation among individuals contributed the most to the total variation. The mean squares (MS) for individual variation and FA were from 31.3- to 4129.6-fold and from 4.7- to 95.6-fold higher than the MS for measurement error, respectively. Directional asymmetry (DA), although statistically significant (P < 0.05) for all except two characters (after a sequential Bonferroni adjustment), accounted for smaller percentages (0.02–6.21%) of the total variation than FA (0.79–19.24%). Besides normal distribution of GM asymmetry, Kolmogorov–Smirnov tests showed that one of 35 signed differences was not normally distributed. However, its kurtosis was positive, suggesting the absence of platykurtotic distribution and antisymmetry (Palmer & Strobeck, 1986, 2003).

Observed correlation patterns for individual variation (symmetry of linear distances) and FA (asymmetry of linear distances) were compared with correlation patterns theoretically derived under the hypothesis that two separate modules (alveolar region and ascending ramus) can be recognized within the mandible. Comparisons of empirically and theoretically derived correlation matrices, together with the average correlations among functionally and developmentally related and unrelated traits, are presented for individual variation and FA in Table 3. Similarities of the matrix correlation patterns between observed and theoretical matrices were all highly statistically significant. Within the overall mandible, as well as within each module, the average correlations of functionally and developmentally related traits exceeded the average correlations among unrelated traits. Thus, individual variation and FA are both structured by predicted functional and developmental influences underlying disunion of the mandible into two distinct modules. However, the average correlations between functionally and developmentally related traits for FA were somewhat higher than the average correlations among functionally and developmentally related traits for individual variation. Additionally, the observed Pearson's correlation coefficients for functionally and developmentally related traits within the alveolar region were more than four times higher than those within the ascending ramus for both individual variation and FA.

Table 3. Evaluation of an a priori hypothesis of a two-module (alveolar region and ascending ramus) organization of the mandible of the yellow-necked field mouse (Apodemus flavicollis). Average correlations of functionally and developmentally related (r(+)) and unrelated (r(−)) traits and matrix correlations (R) between observed and theoretically derived matrices for individual variation (Ind) and fluctuating asymmetry (FA). Probability (P) indicates the statistical significance of similarity between compared matrices
 r (+)r (−) R P
Ind
Alveolar region0.111−0.0460.219< 0.001
Ascending ramus0.025−0.0390.1090.001
Overall mandible0.056−0.0910.269< 0.001
FA
Alveolar region0.120−0.0460.241< 0.001
Ascending ramus0.027−0.0380.115< 0.001
Overall mandible0.060−0.0930.291< 0.001

The hypothesized modularity of the mandible was also confirmed for individual variation and FA after elimination of the influence of size (allometry) (Table 4). The empirically derived correlation matrices of residuals were highly significantly (P = 0.001 and P < 0.001) correlated with theoretically derived matrices for both individual variation and FA. The exception was individual variation of ascending ramus traits for which the statistical significance of similarity between compared matrices was considerably lower (P = 0.037). Within each module and within the mandible as a whole, the average correlations among functionally and developmentally related traits were higher than the average correlations among unrelated traits. The average correlations among functionally and developmentally related traits for FA were higher than the average correlations among functionally and developmentally related traits for individual variation, and this difference became more pronounced after removal of allometric size from the data. In addition, the observed Pearson's correlation coefficients for functionally and developmentally related traits within the alveolar region were higher than those within the ascending ramus (almost four times for FA and more than 13 times for individual variation).

Table 4. Evaluation of an a priori hypothesis of a two-module (alveolar region and ascending ramus) organization of the mandible of the yellow-necked field mouse (Apodemus flavicollis) after correction for allometry. Average correlations of functionally and developmentally related (r(+)) and unrelated (r(−)) traits and matrix correlations (R) between observed and theoretically derived matrices for individual variation (Ind) and fluctuating asymmetry (FA). Probability (P) indicates the statistical significance of similarity between compared matrices
 r (+)r (−) R P
Ind
Alveolar region0.079−0.0380.172< 0.001
Ascending ramus0.006−0.0280.0620.037
Overall mandible0.032−0.0660.1890.001
FA
Alveolar region0.100−0.0440.208< 0.001
Ascending ramus0.026−0.0390.115< 0.001
Overall mandible0.053−0.0880.266< 0.001

The correlation patterns of individual variation (symmetry of linear distances) and FA (asymmetry of linear distances) were significantly (P < 0.001) similar to one another before (R = 0.794) and after removing the influence of allometry (R = 0.813).

Discussion

This study explored the pattern of coordinated variation of mandibular traits among individuals (individual variation, Ind) and fluctuating asymmetry (FA) in the yellow-necked mouse (A. flavicollis). We applied two different methodologies, one based on geometric and the other on traditional morphometrics, to test whether the alveolar region and the ascending ramus are distinct modules within the mouse mandible. Either way, the predicted hypothesis of modularity was confirmed; so two general conclusions can be drawn. The first, biological in nature, is that the alveolar region and the ascending ramus are two modular units within the mandible. The second, a methodological inference, is that the application of geometric morphometric and traditional methods to studies of modularity produces very similar results.

The rodent mandible has long been examined as a model for morphological integration and modularity in complex morphological structures (Atchley et al., 1985, 1992; Atchley & Hall, 1991; Atchley, 1993; Cheverud et al., 1991, 1997; Leamy, 1993; Mezey et al., 2000; Ehrich et al., 2003; Klingenberg & Leamy, 2001; Klingenberg et al., 2001b, 2003, 2004; Monteiro et al., 2005; Márquez, 2008; Zelditch et al., 2008, 2009; Klingenberg, 2009). A number of studies have employed different morphometric approaches to examine whether the alveolar region and the ascending ramus could be recognized as two separate mandibular modules. Although the majority of them supported this hypothesis (Atchley et al., 1985; Cheverud et al., 1991, 1997; Leamy, 1993; Mezey et al., 2000; Klingenberg et al., 2003, 2004; Klingenberg, 2009), there were some cases where the two-module hypothesis was not confirmed (Klingenberg & Leamy, 2001; Klingenberg et al., 2001b; Zelditch et al., 2008, 2009. Goswami & Polly (2010) tested three different models of cranial modularity in Japanese macaques by applying some exploratory and confirmatory methods and found that the exploratory approaches (cluster analyses of various sorts) were less consistent with one another than were the results of model testing or comparative approaches. Thus, it is possible that support for the two-module organization of the mouse mandible in some cases but not in others could depend upon the methodology. Differences in methods can lead to discrepancies in the results, and therefore, findings from different studies can be difficult to compare.

Using the geometric morphometric approach (Klingenberg, 2009), we confirmed the hypothesis of the two-module organization of the mandible. Covariation between the alveolar region and ascending ramus was the lowest (for individual variation) and almost the lowest (for FA) after comparison with the strength of covariation between alternative partitions of the mandibular configuration into two subsets of landmarks. Analysing potential modularity of pleiotropic quantitative trait loci (QTL) effects on the morphology of the mouse mandible, Klingenberg et al. (2004) compared the covariation between the alveolar region and ascending ramus with other possible partitions of the mandible into two sets of landmarks, as well as with those partitions that divided the mandible into two subsets of landmarks that were spatially contiguous along the outline of the mandible. They confirmed the two-module organization of the mandible by finding that the division corresponding to the hypothesized boundary between modules yielded lower squared trace correlations between the two modules than the correlations between arbitrary subsets of landmarks. The lowest trace correlations of landmark positions between the alveolar region and ascending ramus were also obtained by Klingenberg et al. (2003) for both individual variation and FA. The RV coefficient is similar to the trace correlation and is a replacement for it in more recent publications. Furthermore, our study revealed that the RV coefficients for alternative partitions varied within limited ranges (about 0.2–0.4 for individual variation and about 0.2–0.3 for FA), agreeing with the earlier findings for mouse mandible (Klingenberg et al., 2003, 2004; Klingenberg, 2009) and underscoring that the alveolar region and the ascending ramus are not totally independent of each other. Once again, it is shown that mandibular modularity in mice is a matter of degree rather than a black-or-white phenomenon, which has also been reported for other morphological structures of various organisms (Klingenberg, 2010). In addition, we found that the RV coefficient between the hypothesized modules was lower for FA than for individual variation. This result is consistent with those reported previously for mouse mandible (Klingenberg, 2009), vole dental row (Laffont et al., 2009) and dog, wolf and Carnivora skull (Drake & Klingenberg, 2010), and may indicate that modularity is somewhat more apparent for the asymmetric component of shape variation. Moreover, as suggested by Laffont et al. (2009), higher values for the RV coefficient between modules observed for individual variation may be due to the presence of an additional part of shape covariation acting between modules at the level of individual variation; namely trait covariation within individuals is solely due to direct interactions between developmental pathways, whereas trait covariation among individuals can arise both from direct interactions and from parallel variation of developmental pathways caused by additional factors, such as genetic or environmental effects.

Following the traditional morphometric approach (Cheverud, 1995, 1996b; Marroig et al., 2004), we compared the predicted pattern of correlation among mandibular traits to the observed one for individual variation and fluctuating asymmetry (FA). The observed pattern among mandibular characters corresponded to the pattern of developmental and functional interrelationship among the traits for both, individual variation and FA. This agreement was largely due to high correlations among characters within each of the modules in comparison with those among characters in different modules. Analysing morphological integration of fluctuating asymmetry in the mouse mandible, Leamy (1993) also found that asymmetries of linear measurements were more strongly correlated within hypothesized modules (incisor and muscle) than between them. Our results showed that the average correlations among characters within each of the modules were higher (for the alveolar region double) than those among characters in different modules. Similarly, Leamy (1993) found the highest level of integration of FAs within the two character (incisor and muscle) groupings, especially within the incisor character group. Furthermore, it should be noted that although two mandibular modules were identified for individual variation (symmetry of linear distances), as well as for FA (asymmetry of linear distances), the average correlations among functionally and developmentally related traits for FA were higher than those for individual variation, especially when the influence of size was eliminated. Therefore, it seems that modules appear more clearly in the asymmetric component of variation. Likewise, in their study of craniofacial variability and modularity in macaques and two strains of mice, Hallgrímsson et al. (2004) tested three hypotheses of modularity by comparing phenotypic (among individuals), signed asymmetry (FA) and genetic correlation matrices to hypothetical matrices of developmental and functional integration and found that in both strains of mice only the signed asymmetry matrices showed the pattern of modularity.

The developmental origin of morphological integration and modularity is one of the central issues in evolutionary developmental biology. Similarity between the patterns of FA and individual variation indicates that direct interactions between developmental pathways is the primary mechanism that produces trait covariation among individuals, whereas discrepancy of these patterns means that trait covariation among individuals arises primarily by parallel variation of separate pathways (Klingenberg & Zaklan, 2000; Klingenberg et al., 2001a; Klingenberg, 2002, 2003, 2004, 2005, 2008, 2010). Both geometric and traditional morphometric analyses in the mandibles of A. flavicollis revealed correspondence in the patterns of FA and individual variation, indicating that integration of mandibular traits among individuals is primarily due to direct developmental interactions. These results are in agreement with an earlier traditional morphometric study of mouse mandibles (Leamy, 1993). However, a geometric morphometric study of 90 mouse mandibles revealed that the patterns of FA and individual variation were only partly consistent, indicating that different developmental processes are involved in generating the variation observed at the two levels (Klingenberg et al., 2003). The developmental origin of morphological integration has important effects on the potential for evolutionary change, as the pattern of covariance generated by direct interactions between developmental pathways is more robust evolutionarily than integration due to parallel variation of separate pathways (Klingenberg, 2004, 2005).

Size is a potentially important factor contributing to the pattern and level of correlation among traits (Zelditch, 1988). The effect of size on shape (allometry) can produce global integration throughout the whole morphological structure, counteracting modularity (Klingenberg, 2009). By comparing the values of RV coefficients before and after correction for allometry, we detected slightly weaker integration between the hypothesized mandibular modules for individual variation, as well as for FA after the effect of allometry had been removed. Moreover, after the effect of size was removed, the ranges of RVs for all alternative partitions remained almost the same for both individual variation (about 0.2–0.4) and FA (about 0.2–0.3). Thus, it seems that allometry does not obscure the hypothesized mandibular modularity. Additionally, size could be a confounding factor when testing morphological integration hypotheses given that some traits or even regions can be more strongly associated with overall size than others (Marroig et al., 2004). Theoretical matrix correlation analysis (Cheverud, 1995, 1996b) allowed us the possibility to check whether allometry influenced each module to the same extent. In contrast, RV coefficient analysis (Klingenberg, 2009) provides evaluation of allometric effects only on the mandible as an overall structure and is not suitable for determination of whether or not individual regions are more strongly associated with allometry than others. Generally, we observed higher correlations among characters within the alveolar region relative to those within the ascending ramus. For individual variation, traits within the alveolar region were about four times more strongly associated than traits within the ascending ramus. After the correction for size-related shape variation was made, the alveolar region traits were more than 13 times more closely correlated than the ascending ramus traits. Thus, it seems that allometry contributed more to the integration of characters within the ascending ramus, namely the posterior part of the mandible, which is tightly related to the insertion of the masticatory muscles, is more heavily influenced by general size than the anterior region associated with the molar and incisor alveolar area. Likewise, studying morphological diversity of mandibles of Old World rats and mice in relation to phylogeny and adaptation, Michaux et al. (2007) observed allometric shape changes that were associated with the massive posterior part of the mandible and provided a larger surface for insertion of the masticatory muscles.

In conclusion, our study disclosed that two different morphometric methods for evaluation of an a priori hypothesis of the two-module (alveolar region–ascending ramus) organization of the mandible produce very similar results when applied to the patterns of covariation/correlation in morphological data for individual variation and FA of the yellow-necked field mouse (A. flavicollis). Besides confirmation of the predicted hypothesis of modularity, the application of both approaches revealed that: (i) modularity was somewhat more evident when it was analysed on the asymmetric (FA) than on the symmetric (individual variation) component of variation; (ii) there is correspondence in the patterns of individual variation and FA, which indicates that integration of mandibular traits among individuals is primarily due to direct developmental interactions; and (iii) allometry does not obscure the hypothesized modularity for individual variation or for FA. In addition, traditional morphometric method allowed us to check whether allometry influenced each module to the same extent and to conclude that the ascending ramus is more heavily influenced by general size than the alveolar region. As already mentioned, in studies of modularity, differences in methods can lead to discrepancies in the results, and hence, some caution is required when comparing findings from different investigations. However, the substantial similarity between the results obtained provides evidence that direct comparison among studies using the methods applied herein is, in great part, reliable when considering two-module organization of the mouse mandible.

Acknowledgments

This work was supported by the Ministry of Education, Science and Technological Development of Serbia, Grant No. 173003. The authors are grateful to Dr. Philipp Mitteroecker and an anonymous reviewer for their helpful comments on the earlier version of this manuscript.

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