Sexual dimorphism in the walrus mandible: comparative description and geometric morphometrics

Biological sample

The dataset includes two Odobenus rosmarus mandibles from the Institut Royal des Sciences Naturelles de Belgique (IRSNB) and 38 mandibles from the United States National Museum of Natural History (USNM). The sample comprises specimens from various geographical regions, from off Russia to Greenland, through the Bering Strait and Alaska, representing the two currently recognized subspecies (Odobenus rosmarus divergens and O. r. rosmarus) (Table S1). Therefore, potential differences between subspecies have not been further investigated in this work. IRSNB 1150B and IRSNB 1150D are adult female and male, respectively. Of the 38 USNM specimens, 10 have been identified as males, six as females, and sex was not recorded at collection time for 22 specimens. With the exception of specimens USNM 220151 and USNM 267962, the mandibular symphysis is fused in all specimens. The two specimens from the IRSNB form the basis for the comparative description, with pictures from the USNM specimens used to validate whether or not the morphological differences observed between IRSNB 1150B and IRSNB 1150D are recovered in other males and females of the studied sample.

The ontogenetic stage (adults, subadults, juveniles) has been recorded for each specimen. The proxies used to determine the ontogenetic stage are: the relative size of specimens, tooth wear (especially for canines), the increase in roughness with age of the mandibular condyle, and the reduction of the porosity of the mandibular bone (Fay, 1982; Storå, 2000; Reitz & Wing, 2008). The sample includes 23 adults (including at least ten males and one female), nine subadults (including at least one male and four females) and eight juveniles (including at least two females). Due to the small morphological and size difference between the subadult and adult stages for sexed individuals, subadult individuals were grouped within the adult stage. The complete assignment of each specimen is provided in Table S1.

Anatomical description

The anatomical terminology used in the present study follows Deméré (1994a); Deméré (1994b) and Kryukova (2012) for the walrus and Evans & deLahunta (2013) for the domestic dog, as a representative for (caniform) Carnivora. Names of mandibular teeth have been abbreviated (incisors = i, canine = c, premolars = p, second premolar = p2, third premolar = p3, fourth premolar = p4, molars = m). TMJ = temporomandibular joint.

Geometric morphometrics

To quantify the shape variation in the mandibles of our sample we used two-dimensional geometric morphometrics, which is the statistical study of morphological variations (shape and size components) through the use of landmark coordinates (Bookstein, 1991; Mitteroecker & Gunz, 2009). We carried on the landmark placement on photographs of the selected specimens in lateral view. Photographs were taken with a Nikon D5300 camera and with a Nikon AF-S DX 18–140 mm f/3.5−5.6G ED VR lens. The camera was located at 50 cm from the specimens, which were positioned with sand and modelling putty to fix them. Eight fixed landmarks were selected and adjoined by 75 semi-landmarks to better capture the mandibular shape (Gunz & Mitteroecker, 2013). Eight curves were placed between the eight fixed landmarks, along which the sliding semi-landmarks were positioned. The number of semi-landmarks per curve was chosen according to the shape and length of the surface to adequately capture the curve shape (Viscosi & Cardini, 2011). The morphological characteristics, represented by the fixed landmarks, are visualized in Fig. 1 and numbered in Table 1.

The landmark coordinates were collected with the tpsDig software (Rohlf, 2006), utility operations were performed using tpsUtil32 (Rohlf, 2018). Landmarks and semi-landmarks raw coordinates are provided in .tps file (Supplemental Dataset S1). Analyses were carried out using the Geomorph and Morpho packages in the R Studio v4.1.0 environment (R Development Core Team, 2008). First, landmark coordinates were imported using the readland.tps function (Rohlf, 2010), then we performed the Generalized Procrust Analysis (GPA) with the gpagen function using bending energy for sliding (Schlager, 2017; Adams, Collyer & Kaliontzopoulou, 2020). To visually assess the morphological differences between males and females we performed a principal component analysis (PCA) using the gm.prcomp function (Baken et al., 2021). After this first visualization two Procrustes ANOVA were carried out on the landmark coordinates with 1,000 permutations using the procD.1m function (Sherratt, 2016). The first one on the sexed specimens only, to determine if sex truly has a significant influence on mandibular shape without considering the age, and then a second on the whole dataset, to test for the influence of the ontogenetic stage (juvenile vs. non-juvenile), not considering the sex. Then, to test for the allometric influence in our dataset we also performed a Procrustes ANOVA to test for the influence of the log centroid size on the shape. Finally, to make sure that sex is actually a good predictor of mandibular shape, we performed a linear discriminant analysis (LDA) using the lda function on the landmark coordinates with a Box’s M-test (Box, 1949) as a prerequisite (Supplemental Dataset S2) on the sexed specimens only. Because of the small size of our dataset we cross validated our LDA results using the ‘CV’ argument of the lda function.

This study includes morphological measurements. These include the measurement of the minimum mandible thickness (MT), following Wiig et al. (2007). The MT is the minimum transverse thickness of the mandible posterior to the last postcanine. The MT has been measured using a digital caliper with an accuracy of ±0.01 mm. Five angular measurements have also been taken, following Mohr (1942) and Deméré (1994a): angle between (a) the anterior and dorsal margin; (b) the anterior and ventral margins; (c) the ventral and dorsal margins; (d) the horizontal and vertical rami; and e) the coronoid process and the mandibular condyle. All measurements are provided as supplemental information (Fig. S1).

Comparative description of sexual dimorphism in mandibles of Odobenus rosmarus

O. rosmarus has a highly pachyostosic mandible with mandibular dental formula i0c1p3m0. In the absence of lower incisors, the mandibular terminus of O. rosmarus is pinched transversely and displays a sagittal symphyseal furrow. The mandibular symphysis is sexually dimorphic: it is transversely thinner in females (Fig. 2). In female walruses, the anterior margin of the mandible is generally straight in lateral view. Towards the mandibular terminus, anterodorsally, this margin becomes abruptly convex (Fig. 3). Adult males differ from females in having a clearly marked convexity of the anterior margin of the mandible in lateral view. Towards the mandibular terminus, this margin is narrowly concave before transitioning to convex in its lower part (Fig. 3). In males, a variable convexity is observed between individuals, with certain—presumably old—adult specimens having a conspicuous rounded anterior margin largely exceeding the anterior tip of the mandibular terminus, as observed by Mohr (1942). The posteroventral margin of the mandibular symphysis corresponds to the genial tuberosity, which is usually the lowest part of the mandible. This tuberosity is better defined in females due to the absence of a swelling for the anterior margin of the mandible (Fig. 3). As a consequence of the important development of the anterior part of the mandible in male walruses, their genial tuberosity expands anterior to the canine and the mandibular terminus. This condition differs from females, in which the genial tuberosity extends anterior to the level of p2. Posterior to the genial tuberosity, the ventral margin of the mandible starts at different levels in males and females: at p2 in males and at p3 in females. Due to the swelling of the anterior margin, males possess a more obtuse angle between the anterior and ventral margins, compared to females. The ventral margin of the mandible is more rectilinear in males (Fig. 3), whereas it is slightly concave in females.

The digastric prominence is located at the posterior end of the ventral margin and serves as the insertion area for the digastric muscle. This prominence is more rugose and robust in males. Due to the strong development and convexity of the anterior part of the mandible in males, the dorsal margin of the horizontal ramus of their mandible is oriented more posterodorsally compared to females. The MT is higher in males compared to females, corroborating previous studies (Wiig et al., 2007; Taylor et al., 2020). The pre-angular space separates the ventral margin anteriorly from the angular process posteriorly. The pre-angular space is located posteriorly to the genial tuberosity and ends at the articular part of the angular process; it is usually ventrally concave. This space is proportionally shorter and more curved posterodorsally, hook-like, in females.

Sex-related differences are also noted in the shape of the mandibular condyle. The latter is more elongated posteriorly and more rectangular in posterior view in males; in females, it is more globular and oval. The articular surface of the condyle, connecting the latter with the squamosal, forms a depression where the temporomandibular joint (TMJ) is located (Winer et al., 2016). In males, this depression is located dorsally on the condyle, whereas it is located rather dorsoposteriorly in females (Figs. 3 and 4). Wear of the TMJ is significantly more prevalent in males (Winer et al., 2016). The shape of the mandibular notch, between the mandibular condyle and the coronoid process, varies also between male and female walruses. In males, this notch forms a right or slightly acute angle and the posterior margin of the coronoid process either is vertically straight or slightly overhangs the mandibular notch. In females, the mandibular notch is open, forming an obtuse angle between the mandibular condyle and the coronoid process (Fig. 3), and the posterior margin of the coronoid process is slightly slanted anterodorsally. In females, the coronoid process reaches dorsally a higher level than the mandibular terminus and the anterior part of mandible. On the contrary, due to the important development of the anterior part of the mandible, the coronoid process of males does not reach dorsal to the level of the mandibular terminus, giving a more concave angle between the dorsal margin and the coronoid process (Fig. 3, Table S2). The distance between the last tooth (p4) and the anterior limit of the coronoid process is proportionally greater in females (Fig. 3), where this distance is approximately twice the mesiodistal length of p4, whereas it is closer to the length of p4 in males. On the lateral surface of the coronoid process, the masseteric fossa is deeper in males. A large, oval mental foramen opens antero-laterally on the lateral margin of the horizontal ramus of the mandible of O. rosmarus, (Figs. 3 and 5). This foramen is located at the level of c in males and at the level of the diastema between c and p2 in females. Other, smaller mental foramina are present, but their number and position on the mandible varies widely between the specimens of the studied sample, seemingly not following any sexual pattern.

Morphologically, juvenile mandibles from our sample (including 2 females and 6 individuals with no sex identification) have a more sinuous ventral margin and an anterior margin that is not swollen, generally straight in lateral view (one exception is USNM 16445, which displays a slightly concave anterior margin). The genial tuberosity is relatively pronounced, the pre-angular space presents a hook-like form, and the mandibular notch is open, forming an obtuse angle between the mandibular condyle and the coronoid process, with a mandibular condyle being more rounded and the dorsal margin of the horizontal ramus being oriented more anterodorsally (Fig. 6). These characteristics are also found in adult females.

Geometric morphometrics

First, to visualize the effect of sex on mandibular shape we performed a principal component analysis (PCA) that retrieved 39 components (Fig. S2), the first three axes explaining a total of 64,19% of the morphological variation (32.26%, 19.20%, and 12.73%, respectively).

Males and females are well differentiated on those first two PCs with almost all females showing positive values along both axes (the only exception is USNM 267965 (21), showing negative PC1values and positive PC2 values), resulting in two distinct areas of morphospace occupation for males and females (Fig. 7). Except for USNM 22014 (16), males show negative for either PC1 or PC2, or both. PC1 encompasses the development of the anterior margin, or chin, of the mandible. Higher, positive values of PC1 represent a slightly convex or flat anterior margin of the mandible, and lower, negative, values represent a strongly convex, i.e., bulging, anterior margin. In addition, higher values for PC1 correspond to a more pronounced genial tuberosity, a rather concave pre-angular space, and a rather rounded coronoid process in lateral view, contrasting with a less conspicuous genial tuberosity, a less concave pre-angular space, and slightly more angular coronoid process in lateral view for lower values for PC1. PC2 captures the relative dorsal expansion of the anterior portion of the mandible, with lower values representing proportionally higher anterior portions of the mandible, dorsally exceeding the level of the coronoid process, and higher values representing lower anterior portions of the mandible. In addition, PC2 captures the proportion in size between the horizontal and vertical ramus, with lower values for PC2 corresponding to a shortening of the horizontal ramus and higher values representing an elongation of this part compared to the vertical one.

For the ontogenetic aspect, four juvenile specimens of unknown sex (5, 9, 35, and 39, representing USNM 121177, 16445, 550413, and 7156, respectively) occupy the female area. Two others (32 and 33, representing USNM 550408 and 550409, respectively) are nearby. One juvenile female specimen (24, representing USNM 276625) defines one of the boundaries of the female convex hull, with the highest PC1 value, and the other (20, representing USNM 267963) falls within this hull. No juvenile specimens fall within or close to the convex hull of males.

Ten adult specimens of unknown sex (1, 6, 8, 10, 12, 15, 18, 34, 38 and 40, representing USNM 108344, 14397, 16437, 16446, 16756, 21331, 22200, 550410,7139 and 9475, respectively) fall within the convex hull of males; an eleventh adult specimen, USNM 6780 (37), falls in the area occupied by females.

When plotting PC1 against PC3, the reduction to 44.99% in the percentage of morphological variation explained, due to PC3 explaining only 12.73% of variance, resulted in an overlapping of the areas occupied by males and females (Fig. 8). Females show negative PC3 values except for USNM 267962 (19) and USNM 276030 (22). Males generally occupy lower PC1 values and higher PC3 values than females. The convex hulls of males and females show only little overlap, with IRSNB 1150B (2) being the only female falling within the observed range for males, and USNM 287993 (26) being the only male falling within the range for females. PC3 captures the development and the elongation of the coronoid process posteriorly and the concavity of the angle between the dorsal margin of the mandible and the coronoid process. Lower values for PC3 represent a proportionally less elongated and less posteriorly developed coronoid process. The opposite is true for higher values for PC3. In addition, lower values for PC3 correspond to a more pronounced concavity between the dorsal margin and the coronoid process.

Two juvenile specimens of unknown sex (35 and 39, representing USNM 550413 and 7156, respectively) occupy the female area, and two others (5 and 32, representing USNM 121177 and 550408, respectively) fall just outside the known range of female morphology. Seven adult specimens of unknown sex (6, 10, 12, 28, 34, 38, and 40, representing USNM 14397, 16446, 16756, 35683, 550410, 7139, and 9475 respectively) fall within the male area, and three others (1, 7 and 15, representing USNM 108344, 144995 and 21331, respectively) fall within the female convex hull. One adult specimen, USNM 6780 (37), falls in the area corresponding to the two overlapping hulls. The two juvenile female specimens (20, 24, representing USNM 267963 and USNM 276625, respectively) make two corners of the female field. No juvenile specimens fall within or close to the convex hull of males.

As for the plot showing PC2 against PC3 (36.93% of variation explained, Fig. S2), males and females show more overlap than in the two previous plots, showing thus that males and females are mainly distinguished by PC1.

Following those first graphical results, we performed a Procrustes ANOVA with 1,000 permutations on the sexed specimens to assess if the sex truly has a significant influence on landmark coordinates. We isolated the identified males and females in the dataset to perform this analysis and the p-value obtained was far below the significance level (0.001), indicating significant differences between males in females in terms of mandibular shape (Table S3). Then we performed a second Procrustes ANOVA with 1000 permutations to test for statistical differences between adults and juveniles on the whole dataset (males, females and unidentified) and also obtained a significant p-value of 0.001, implying an influence of the ontogenetic stage on the mandibular shape. A last Procrustes ANOVA was performed to test for the influence of size (Log centroid size) on the shape and again the p-value obtained was significant: 0.001. We performed a principal component analysis (PCA) to obtain graphical representation of this last Procrustes ANOVA with Log centroid size. We observed the same results and arrangements as in our first ANOVA (Fig. S2). As for the influence of allometry in our dataset, our regression between the log centroid size and the first four PCs show different allometric patterns in males and females on PC1 (Fig. S2). Finally, we performed a linear discriminant analysis to test if sex is truly a good predictor of mandibular shape. To do so we randomly split the identified males and females (18 individuals) into a training (80%, 15 individuals) and a test set (20%, three individuals), created a model with the training set and tried to assess the sex of the test set based on this model. The prediction of our model was 100% accurate, our three test specimens were always assigned to the correct sex by our model meaning that sex is an extremely good predictor of mandibular shape. To make sure this was not simply due to the low number of individuals in the test set, we performed other LDAs with increasing ratio of training/test: 70/30 (five test individuals), 60/40 (six test individuals), 50/50 (nine test individuals), and 40/60 (10 test individuals). Our prediction accuracy remained at a 100% until the 50/50 training/test ratio, where it dropped to 87.5%. However, the cross validated error rate was 44%, meaning that these results must be treated carefully. We then computed another linear discriminant analysis without the juvenile specimens and our accuracy remained at 100% until the 30/70 training/test ratio, where it dropped to 90%. Again, the cross validated error rate was high (52%), so those results must be treated carefully.