A numerical analysis of the variation and correlation of crown elements in the upper cheek teeth of the european beaver, castor fiber (rodentia, castoridae), based on geometric morphometrics

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Variation and integration patterns of the complex anatomical structures, including their dynamics during the later stages of postnatal ontogenesis, became recently one of the focal points in the evolutionary morphology considered from an evo-devo perspective (Cheverud, 1996; Bolker, 2000; Callebaut, Rasskin-Gutman, 2005). However, specific studies of this type are still very scarce, such as those on the primate skull (Ackermann, 2002; Gkantidis, Halazonetis, 2011; Jung et al., 2021).

Mammalian dentition holds a great potential for its use in this regard (Ruf et al., 2020). Despite the centuries-long studies of its morphology, including age variation of dental crown elements, its detailed variation and integration (correlation) patterns in mammalian dentition still remain largely unknown, and this is true even for the most recent works (e. g., Laffont et al., 2009; Gόmez-Robles, Polly, 2012; Labonne et al., 2014; Wolsan et al., 2019; Boivin et al., 2022). The main reason is that in the previous studies of these patterns, the entire teeth were most usually considered the elementary units of the tooth row, so their deeper exploration, involving analysis of both variation of and correlations between particular crown elements, remained beyond their attention. However, the use of an “elementaristic” approach in such studies, which focused on the analysis of particular dental crown elements, has revealed a very interesting dental correlation patterns in two unrelated mammal species, a horse and a rodent (Pavlinov, Spasskaya, 2021; Pavlinov, 2022). With this, the just cited and other similar studies focused primarily on the dental crowns that were fully developed and minimally modified by wear, so any questions of possible age-related effects in the variation and especially integration patterns could not even been raised, and there seemed to be the only published attempt to reveal these effects (Scarano, Vera, 2017).

Since the 1950s, numerical studies of the variation and correlation of the anatomical structures became very popular. Those dealing with the individual variation used to employ standard coefficient of variation and some other dispersion-based estimates (Van Valen, 1965; Yablokov, 1974; Hayes, Jenkins, 1997), whereas the analyses of the age variation were based on some simple indices (Mina, Klevezal, 1976). In the studies of the morphological integration, the traditional correlation analysis became the most popular due to both its simple procedure and easily interpretable results (Olson, Miller, 1958; Terentiev, 1959; Gould, Garwood, 1969; Rostova, 2002; Pavlinov et al., 2008). In all these works, linear measurements were used to characterize particular anatomical structures. However, the recently developed methods of geometric morphometrics (GM) enable a direct comparison of these structures by their shapes and thus provide the new opportunities in the study of their morphological variation and integration (Zelditch et al., 2004; Vasil’ev et al., 2018; Machado et al., 2019). Of prime importance is that GM provides certain numerical estimates for the shape variation and covariation, with the reservation that many of them are approximate rather than precise because of certain specific calculation techniques (Rohlf, 1996). In the case of mammalian dentition, GM methods made it possible to analyze both the entire tooth crowns (Hallgrímsson et al., 2009; Klingenberg, 2009, 2014; Goswami, Polly, 2010; Lawing, Polly, 2010; Cardini, Loy, 2013; Klingenberg, Marugán-Lobón, 2013) and their particular elements (Pavlinov, Spasskaya, 2021; Pavlinov, 2022).

This article considers variation and correlation of the upper cheek teeth crown elements, described and evaluated by GM and some other numerical techniques, in the rodent species Castor fiber. The choice of this object is justified by that (a) the variation and correlation patterns of its dentition, which is classified as lophodont (Fig. 1), were not studied numerically “elementaristically” so far (unlike those of the cranium, see: Puzachenko, Korablev, 2016), (b) the basic crown elements are easily susceptible to an “elementaristic” analysis by means of GM, and (c) this rodent has a rather long lifespan (up to 20 years), with its dental crowns noticeably changing during postnatal ontogenesis.

Figure 1. Typical configurations of the upper cheek teeth crown surface in different age groups of Castor (schematically). Standard designations: juv, sad, ad – juveniles, subadults, and adults; dP4/P4 and M1–3 – teeth in the tooth row.

The basic issues addressed in this report were more methodological rather than proper biological. The author’s main task was to consider the principal possibilities of the approach, having been developed in his previous works (cited above), to study various aspects of variation and correlation of the dental crown elements in mammals. As far as the numerical analysis of shape variation of the latter, considered “elementaristically”, is in its infancy, only few and still rather simple specific hypotheses could be presently formulated about dentition in Castor fiber. Some of them concerned a possible dependence of the variation of dental crown elements on both their position in the tooth row and complexity. Others were about the general pattern of correlation between these elements: was it expressly hierarchical, which particular elements were most correlated, and which correlations were subject especially to certain age-related effects.

MATERIALS AND METHODS

The studied sample included 37 specimens of the European beaver (Castor fiber) collected in the 1970s and kept in the Research Zoological Museum at the Lomonosov Moscow State University. The sample was divided into several groups according to the age (Lavrov, 1953): (1) juveniles (n = 8) with milk dP4 and not fully erupted M3, (2) subadults (n =14) with completely developed permanent dentition and with minimally worn flexi on dental crowns, (3) adults (n = 15) with noticeably worn dental crowns, but with flexi on them not yet divided into isolated facets. Besides, subadults and adults were united in (4) a combined group; juveniles were not included in it because of their P4 and M3 not fully developed. Senile specimens were not studied, as they faced certain problems with the definite GM-description of their fragmented crown elements.

Our sample was strongly limited in its size by the availability of specimens, which were not so numerous in the collections as, say, the voles and mice most usually studied with regard to the dental variation and correlation. So one might reasonably suspect that such a scanty material made it hardly possible to apply standard statistical methods, based on the frequency distribution analyses. However, it is to be taken into account that GM methods do not presume such kind of analyses and normally consider the resultant numerical estimates without their traditional statistical evaluations (Rohlf, 1996). So, even with such limited data in hand, it was proved possible to attain certain interesting results (Scarano, Vera, 2017; Wolsan et al., 2019; Pavlinov, Spasskаya, 2021). With this, given the relatively small sample size used in this study, we opted for the more simple numerical methods to ensure their results more reliable and clearer for biological interpretations. Accordingly, the quantitative estimates were analyzed directly without considering their statistical significance; Shrader-Frechette (2008) and Wasserstein et al. (2019) have provided a general substantiation of the validity of such a “non-orthodoxal” approach.

The dental crown elements in Castor fiber were identified taking into consideration (a) the accuracy of both their standard individuation in the specimens of different ages and (b) certain requirements of GM methodology. The nomenclature of these elements was adopted after Korth (2002). The re-entrant flexi were treated as the elementary units to be compared (fig. 2), namely hypoflexus (Hyf), metaflexus (Mef), paraflexus (Paf), and posteroflexus (Pof). They were delimited at the tips of the salient angles (lophs) by either the latter’s maximal curvature or the points of enamel layer interruption on them.

Figure 2. Recognition and nomenclature of the upper dental crown elements in Castor. The analyzed crown elements (flexi) are marked with bold contour lines, with the gaps marking their boundaries. Element designations: Hyf – hypoflexus, Mef – metaflexus, Paf – paraflexus, Pof – posteroflexus. In each designation, the first part refers to a particular tooth (here M1), figure indicates the number of semilandmarks for respective contour lines.

The left-side upper cheek tooth row of each specimen was digitized by the camera Olympus SP-570 UZ, with tooth orientation being standardized with respect to a plane surface. For GM tools to be applied, the enamel layers of dental crowns were first manually outlined on their images in CorelDRAW program using its Shape tool, with the lines of minimum thickness being drawn along the midlines of the enamel layers. These vector contour lines were converted into high-resolution raster images to be processed by GM tools. Each crown element was initially described by an array of semilandmarks set automatically equidistantly along its contour line between two points fixed at its boundaries (Mitteroecker, Gunz, 2013), with semilandmark number, in our case, varying from 20 to 40 per a contour line depending on its length (see fig. 2). After that, some semilandmarks were appropriately “slided” by hand along the contour lines (in the sense of Bardua et al., 2019) to make them fitting more precisely to the shapes of respective flexi. The semilandmarks were set and their x, y coordinates were acquired with tpsDig2 program (Rohlf, 2017), and they were converted into the standard landmark data with tpsUtil program (Rohlf, 2019). Each crown element was run twice through tpsDig2, and its consensus configuration was calculated with tpsRelw program (Rohlf, 2019a) to become an actual studied shape. The initial x, y coordinates were transformed into Procrustes coordinates using generalized least-square Procrustes superimposition, and pairwise Procrustes distances were calculated between specimens in each group using PAST program (Hammer et al., 2001). In the subsequent specific analyses, either landmark x, y coordinates or pairwise Procrustes distances were used (see below for detail).

Two kinds of comparisons of crown elements were undertaken, either within or between teeth, with variation and correlation of these elements being considered in two following combinations. In within-teeth comparisons, each tooth was taken for a basic unit of comparison, so all of its crown elements were mutually compared. In between-teeth comparisons, each crown element was taken for such a unit, so all elements were mutually compared across all teeth in the tooth row.

Individual variation of the shapes of crown elements was estimated by the averaged Procrustes distances calculated as an arithmetic mean for each element in each age group (Pavlinov, 2011). These distances were then averaged for within- and between-teeth comparisons to estimate general levels of individual variation of the shapes of dental crown elements.

To characterize the age differences in the shapes of these elements, principal component analyses of the latter’s x, y coordinates were run for the pairwise combinations of age groups using the above-mentioned tpsRelw program. The PC (relative warp) scores thus obtained were analyzed by ANOVA using STATISTICA program (StatSoft, 2012). The magnitude of age difference between groups was estimated (Pavlinov, 2011) as a ratio of the sum of squares of the explained variance (EV) to the total variance of the first ten PCs that explain cumulatively (in our case) about 95–99 percent of the total variance. This measure seemed to be similar methodologically to the index CR defined as a ratio of between- to within-covariances (Adams, 2015). For the final comparisons, the average EV estimates were calculated, as in the case of means of Procrustes distances, for both within- and between-teeth comparisons.

To reveal correlation patterns in each of the age groups, the Procrustes distance matrices were vectorized, and the pairwise Pearson correlations and Euclidean distances were calculated between these vectors for all crown elements using STATISTICA program. The average correlation values were next calculated, based on the pairwise ones, for within- and between-teeth comparisons. Following N. Rostova (2002), these average correlations were treated as a measure of the overall integration of respective anatomical units, either teeth or crown elements in our case. Being rather simple in its calculation and straight forward in its interpretation, this integral estimate was shown to be fully comparable with a more sophisticated index based on the covariance matrices analysis (Pavlicev et al. 2009; Machado et al., 2019). The age differences between groups in these correlations, both for withtin- and between-teeth comparisons, were numerically estimated by pairwise rank (Spearman) correlation R_M of correlation matrices for particular crown elements. The index AD = (1 – R_M) was actually used for illustrating just the differences instead of similarities.

The hierarchical cluster analysis of the Euclidean distance matrices was applied to reveal the overall correlation patterns of dental crown elements in each of the age groups. The phenograms illustrating these patterns were produced by the Ward algorithm with bootstrap estimations of cluster support (1000 replicates). This support was considered a rough quantitative estimate of the “constancy” of association of respective elements. An average bootstrap support of the cluster hierarchy was calculated for each of the phenograms as a measure of the structuredness of the overall correlation pattern in respective age group. Such measure seemed to be more appropriate for our purposes as compared to the analysis of cluster structure borrowed from standard phenetic techniques (e. g., Young, 2008).

RESULTS

Individual variation of the shapes of dental crown elements was shown to be somewhat higher on average in the adults (Table 1). Among particular teeth, M1 appeared the least and M3 the most variable in general (0.14 and 0.21, respectively), and among the elements, Paf appeared the least and Hyf the most variable (0.14 and 0.20, respectively). The age differences may be assessed in general as average to rather high, with the ratio of EV varying from 0.16 to 0.52 (the same Table). The differences between subadults and adults appeared the least and those between juveniles and two other groups the most expressed (0.18 and 0.35–0.38, respectively). In average, M3 and P4 were the most stable and M2 was the most variable with age (0.20–0.25 and 0.40, respectively). Of particular crown elements, Hyf appeared the least variable in average as compared to others (0.19 and 0.36–0.38, respectively).

Table 1. Individual variation and age differences of the upper cheek teeth crown elements in Castor fiber

Notes. See fig. 2 for the designations of crown elements; see text for the explanation of indices.

Correlations between crown elements, both for within- and between-teeth comparisons, were not especially high on average, with their most frequent values being located between 0.15–0.35, and their upper limits rarely reaching 0.85. Three principal kinds of frequency distributions of correlations were revealed in different pairwise comparisons, namely symmetrical unimodal, asymmetrical unimodal, and slightly bimodal (fig. 3), of which the former appeared the most common.

Figure 3. Three principal kinds of frequency distributions of the correlations between dental crown elements in the combined age group: a – symmetrical unimodal (M3-Pof), b – asymmetrical unimodal (M2-Paf), c – bimodal (M3-Hyf).

The average correlation between crown elements within particular teeth was equal to 0.08–0.38 (table 2). The most integrated were P4 and M2 (0.26–0.28 on average) and the least so M1 and M3 (0.16–0.17 on average). Regarding particular homologous elements on different teeth, the lowest estimates were obtained for Paf and the highest for the rest (0.13 and 0.19–0.22 on average, respectively). On average, within-teeth correlations were slightly higher than between-teeth ones (0.16–0.28 and 0.13–0.22, respectively), and both particular teeth and homologues were the most integrated in the adults as compared to the juveniles and subadults (0.28 and 0.20 against 0.16–0.17 and 0.12–0.16, respectively). It is to be noted that the combined age group (subadults + adults) demonstrated the highest or nearly so level of dental integration (0.26) in both within- and between-teeth comparisons.

The AD values indicating the age differences in dental correlations (table 2) varied from 0.01 to 0.95 for particular pairwise comparison: the former meant no difference and the latter corresponded to no similarity between age groups. For within-teeth comparisons, the least different with age were the correlations between crown elements of M2 and the most different were those of dP4/P4 and M1 (0.38 and 0.89–0.90, respectively). For between-teeth comparisons, the least different with age were the mutual correlations of Mef and the most different were those for Hyf and Paf (0.22 and 0.59–0.62, respectively). Regarding particular age groups, within-teeth correlations appeared the most different between juveniles and subadults (0.82) and the least different between subadults and adults (0.56); between-teeth correlations revealed an opposite relation, with the former pair being the least and that latter pair the most different (0.29 and 0.69, respectively).

The averaged bootstrap supports of the overall correlation patterns of dental crown elements vary from 37–42 percent in adults and juveniles to 70 percent in subadults and in the combined group. A visual analysis of the structure of phenograms illustrating between-elements correlations in particular age groups (fig. 4) indicated the following. In the juveniles, the most stable were associations between Mef and Hyf in dP4 and less so between Pof in dP4 and Paf in M1 (bootstrap support is 90 and 78 percent respectively), whereas all other associations were much weaker. In subadults, most of the branching points had rather strong bootstrap supports exceeding 50 percent. Most strongly supported (90 and higher percent) were the associations between some homologues in different teeth (Hif in P4 and M3, Paf in M1 and M3) and also strongly to moderately supported (about 70–80 percent or higher) between some elements in the same teeth (Hyf and Pof in M3, Mef and Pof in each of P4 and M2). In the adults, there were several noteworthy rather strongly supported associations of homologues in different teeth (Hif in P4 and M3, Paf in M2 and M3). Regarding the combined group, all branching points had strong bootstrap supports exceeding 50 percent. Among quite strongly supported associations, of interest were those of the elements in the same teeth (Hyf and Pof in M1, Mef and Pof in M2), though one seemingly “odd” association (Paf in M3 with Mef in M1) was also highly supported.

DISCUSSION

To begin with, it is to be noted once more that the numerical analysis of the shape variation in mammal dentition, considered “elementaristically”, is in its earliest infancy. So any findings in this new field of odontology may bear new light on the general trends of dental variation and correlation patterns. In particular, it seems very important to have numerical estimates of these patterns, which make them commensurable in some respects. Thus, the following principal results of our study of the European beaver (Castor fiber) deserve a closer consideration.

First, it is to be pointed out that a certain correspondence seems to exist between individual variation of particular teeth and their position in the tooth row. The least individual variability is characteristic of M1 and M2 taking middle position in the row (0.14–0.16), as compared to anterior P4 and especially posterior M3 (0.18–0.21). This result largely agrees with the previous observations: the teeth in the middle position of the tooth row were usually reported to be the least variable individually in various mammals (e. g., Gingerich, 1974; Gingerich, Schoeninger, 1979; Polly, 1998; Pavlinov, 2022). Regarding particular crown elements, the interior most simple Hyf is the most variable, the anterior moderately complex Paf is the least variable, whereas the most complexly shaped Mef and Pof do not tend to be more variable, as one might expect. Thus, no clear-cut relation of individual variation of crown elements is revealed with respect to either their position in the tooth crown or their complexity.

The age differences in the shape of dental crown elements may occasionally be very significant by reaching up to half of the total variance. For both within- and between-teeth comparisons, the juveniles appear the most specific in this respect, and the least differences occur between the subadults and adults, thus indicating that the tooth crowns remain nearly unchanged in them. An overall trend of relations between the levels of individual and age variation seems to be the same for both within- and between-teeth comparisons: the least individually variable dental units (either total teeth or particular elements) appear in general the most variable with age. However, one cannot exclude a possibility that this result, though looking interesting from a biological perspective, may be of a pure “statistical” nature: it is normal for the ANOVA that the higher is the within-group (individual) dispersion, the lower, other things being equal, is the between-group (age) dispersion.

The general level of correlations between dental crown elements is not very high, with within-teeth correlations (0.16–0.28) being slightly stronger than between-teeth ones (0.12–0.26). This ratio between within- and between-teeth correlations differs from those obtained earlier for Equus and Ondatra (Pavlinov, Spasskaya, 2021; Pavlinov, 2022), which indicate that the crown integration patterns may differ among different types of mammalian dentition. The correlations are somewhat stronger in the adults in both within- and between-teeth comparisons, so one may speculate that a slight wear of the dental crown surface entails a certain strengthening of its “elementary” integration, probably by an elimination (wiping away) of some “random” variations in the elements. It is to be noted also that the correlations in question are the highest or nearly so in the combined group, which indicates that a mixture of subadults and adults better reveals correlation patterns in the lophodont dentition.

The correlations between crown elements vary with age, though at a different magnitude for different dental units. It is of interest that the trends of the differences between age groups appear opposite for within- and between-teeth comparisons. Indeed, juveniles and subadults are the most different with regard to within-teeth correlations and the least different with regard to between-teeth ones. The most intriguing moment in this difference is that the elementary units of comparisons are the same in both cases, which are particular crown elements, so it remains unclear what might be a cause of such an “opposite” effect.

With regard to within-teeth correlations, the most stable with age are those within M2 and the least stable are those within dP4/P4 and M1, whereas of particular crown elements, the most stable is Mef and the least so are Hyf and Paf. With regard to the relation between general levels of correlations and the magnitudes of their age differences, it is nearly absent for within-teeth comparisons and is evidently negative for between-teeth comparisons; the latter means that the less intercorrelated crown homologues generally are, the less stable their intercorrelations tend to be with age.

Our analyses of relations between different aspects of variation and correlation of dental crown elements in Castor fiber do not reveal any clear-cut trends in them deserving a more detailed consideration. With this, however, certain findings are to be highlighted that may indicate some possible biologically interesting trends worthy of further exploration. For instance, for both within- and between-teeth comparisons, the least individually variable dental unit (M1 and Paf, respectively) appears also the least correlated with others, although other units display no relation of such kind. In this regard, an absence of a clear relation between the magnitudes of age differences in crown elements proper and their correlations may deserve a more close attention, as it concerns an important issue of the ontogenetic regulation of dental crown pattern in general.

The frequency distributions of correlations seems to be quite indicative for a preliminary consideration of the basic properties of the general correlation pattern of cheek teeth (see fig. 4). The nearly symmetrical unimodal distribution indicates an absence of any clear-cut hierarchy in it, and this was the most common correlation pattern in the studied sample. The asymmetrical strongly left-skewed distribution indicates certain elements of the hierarchy in the correlation pattern, though without a clear-cut discreteness. The bimodal distribution clearly indicates the occurrence of two-level basic nearly discrete levels in the pattern in question, with the major peak of the distribution corresponding to the prevailing lower-level correlations and its minor peak corresponding to the higher-level one. Such discrete correlation pattern was revealed in the studied dentition for but a few pairwise comparisons.

Table 2. Correlations between upper cheek teeth crown elements and their age differences in Castor fiber

Notes. Designations of crown elements are the same as in Table 1; see text for the explanation of indices.

Both overall correlation patterns and their age-related differences are clearly illustrated by the distributions of particular dental crown elements over cluster phenograms (see fig. 4). In general, judging by their bootstrap supports, the overall patterns in both the juveniles and adults are evidently more “loose” as compared to the subadults; or in other terms, the hierarchical arrangement of these patterns in the two former is expressed much weaker than in the latter. With interpreting the most supported groupings of crown elements as the so-called “correlation pleiades” (in the sense of Rostova, 2002), it becomes evident that the overall “pleiade” structure of cheek teeth dentition in Castor fiber is not well-defined in general and fairly unstable with age in particular. Indeed, (a) not many crown elements are assembled in such “pleiades”, and (c) there are but two “pleiades” that coincide in subadults and adults. Only few of these “pleiades” seem to be biologically sound, some uniting within-teeth correlations (those of dP4/P4 in the juveniles and subadults, of M2 in the subadults), while others corresponding to the correlations between homologous elements in different teeth (Paf of M1 and M3, Mef in M1 and M2 in subadults, Hif of P4 and M3 in subadults and adults).

It is to be noted also that the overall correlation pattern of dental crown elements is generally more evident in the combined (subadults + adults) age group. This finding seems to be of a certain relevance to the methodology of the analyses of dental correlations in mammals. It indicates that the correlation patterns in question could be uncovered more definitely and profoundly if the dentitions at several wear stages are jointly studied in this respect – of course, as long as the particular crown elements remain clearly identifiable.

Figure 4. Phenograms illustrating correlation patterns of dental crown elements in different age groups. Designations of the crown elements as in fig. 2.

It would be more than premature to consider here in detail any possible causes, either biological or “statistical”, of variation and correlation patterns of the “elementaristically” interpreted dental crowns in Castor fiber. However, our findings presented in this article, together with the earlier ones (referred to above), allow us to conclude positively that such an “elementaristic” approach provides apparently a more thorough and informative picture of these patterns. Therefore, I would suggest that the further explorations of both the variation and integration patterns of mammalian dentition, including age-related effects in them, should adopt this approach applied to different dental crown types (bunodont, solenodont, lophodont, prismatic, etc.). This would provide a more comprehensive knowledge of both specific and common features in the regularities of the variation and correlation patterns in dentition in various groups of mammals.

CONCLUSIONS

The principal results of this study can be summarized as follows.

1. The least individual variability is characteristic of the teeth taking middle position in the cheek tooth row. No clear-cut relation of the levels of individual variation of crown elements is revealed with respect to either their position in the tooth crown or their complexity.
2. The age differences in the shape of crown elements may occasionally be very significant, with the juveniles being the most specific in this respect. The least individually variable dental units (either total teeth or particular elements) appear in general the most variable with age, though this result may be of a pure “statistical” nature.
3. The correlation between dental crown elements is generally not very high, with within-teeth correlations being slightly stronger than between-teeth ones. The correlations are generally stronger in the adults than in other age groups.
4. The dental correlations vary with age, with crown elements differing significantly in this regard. The general trends of age differences in correlations are shown to be opposite for within- and between-teeth comparisons. The general levels of correlations and the magnitudes of their age differences are inversely related in the case of between-teeth comparisons.
5. The overall correlation pattern of dental crown elements is more evident in the combined (subadults + adults) age group.
6. The further explorations of both the variation and integration patterns of mammalian dentition should be based on an “elementaristic” description of dental crown.

ACKNOWLEDGEMENTS

The author is grateful to Dr. Andrey Puzachenko (Institute of Geography, Russian Academy of Sciences) for his valuable comments on some numerical methods applied in this study.

FUNDING

This work was supported by ongoing institutional funding (The Governmental Theme no. 121032300105–0). No additional grants to carry out or direct this particular research were obtained.

ETHICS APPROVAL AND CONSENT TO PARTICIPATE

This work does not contain any studies involving human and animal subjects.

CONFLICT OF INTEREST

The author of this work declares that he has no conflicts of interest.

About the authors

Igor Ya. Pavlinov

Author for correspondence.
Email: igor_pavlinov@zmmu.msu.ru
Russian Federation, ul. Bolshaya Nikitskaya 2, Moscow, 125009

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2. Figure 1. Typical configurations of the upper cheek teeth crown surface in different age groups of Castor (schematically). Standard designations: juv, sad, ad – juveniles, subadults, and adults; dP4/P4 and M1–3 – teeth in the tooth row.

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3. Figure 2. Recognition and nomenclature of the upper dental crown elements in Castor. The analyzed crown elements (flexi) are marked with bold contour lines, with the gaps marking their boundaries. Element designations: Hyf – hypoflexus, Mef – metaflexus, Paf – paraflexus, Pof – posteroflexus. In each designation, the first part refers to a particular tooth (here M1), figure indicates the number of semilandmarks for respective contour lines.

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4. Figure 3. Three principal kinds of frequency distributions of the correlations between dental crown elements in the combined age group: a – symmetrical unimodal (M3-Pof), b – asymmetrical unimodal (M2-Paf), c – bimodal (M3-Hyf).

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5. Figure 4. Phenograms illustrating correlation patterns of dental crown elements in different age groups. Designations of the crown elements as in fig. 2.

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