The Denticle Multiverse: Morphological Diversity of Placoid Scales across Ontogeny in the Portuguese Dogfish, Centroscymnus coelolepis, and Its Systematic Implications

Abstract

Centroscymnus coelolepis is a deep-water sleeper shark and, like most sharks, it is covered in placoid scales, or dermal denticles. The morphological diversity of the dermal denticles in this species, however, has not been described in detail, and ontogenetic changes in denticle morphology are poorly understood in sharks. Combining scanning-electron microscopy and micro-CT imaging, we demonstrate the presence of eleven dermal-denticle morphotypes across the ontogeny and different regions of the body of Centroscymnus coelolepis. The snout, interspiracular, and trunk/tail regions have similar changes in denticle morphotype during development. For example, on the trunks and tails of juveniles (~350 mm TL), denticle crowns have two to three longitudinal ridges and three posterior cusps that are gradually replaced by ridgeless and cuspless crowns in adults (>800 mm TL). Sixteen measurements were obtained from the 3D models generated. A principal component analysis demonstrated that the eleven distinct dermal-denticle morphotypes observed were located in different regions of the morphospace. The denticle volume and surface area showed negative allometry with respect to body length throughout the ontogeny. The results reflect the considerable diversity within the denticle multiverse (ontogenetic and intraspecific variations), and much of this diversity remains to be explored to fully understand the role of dermal denticles in shark taxonomy, ecology, and biomechanics.

1. Introduction

Somniosidae, commonly known as sleeper sharks, are a small family of dogfish sharks from the order Squaliformes [1,2]. This family currently has six accepted genera and seventeen nominal species [3,4,5,6,7], although the status of some nominal species of Scymnodalatias and Somniosus are questionable [8]. These sharks live in deep water and are distributed worldwide [5,7,9,10]. Several aspects of the basic biology of these sharks are poorly understood, including their age at maturity, reproductive behavior, and dispersal and movement patterns [4,11]. We also know little about the intraspecific and ontogenetic variation of the dermal denticles covering the body surfaces of sleeper sharks, despite the importance of denticle shapes for identifying species and understanding their evolution and ecology.

Dermal denticles, or placoid scales, are present in the skin of most extant chondricthyans in various degrees, from entire-body coverage in mako sharks to very few denticles in specific organs of chimeras, or even the complete absence of scales in, for example, electric rays [4,12,13]. Dermal denticles are also present in the fossil record of stem-gnathostomes, such as “thelodonts” (e.g., Heterostraci, Anaspida), Galeaspida, Osteotraci, and “placoderms (e.g., Arthrodira), and crown-gnathostomes, such as “acanthodians” [14]. These tooth-like structures are made up of enameloid and dentine outer layers, with an inner pulp cavity [15]. These characteristics ensure that denticles persist throughout the fossil record [16]. Denticles also have a characteristic structure, with an outer crown that can vary in the presence of certain surface features (e.g., ridges, posterior cusps, or the lack thereof), a neck, and a basal root that is embedded in the dermis [7,17,18,19,20]. Dermal denticles most likely have multiple functions, such as altering the water flow on the body during swimming [21,22,23] and protection from predators [24,25]. Denticles are replaced throughout the life of an elasmobranch [26], with different species having distinct rates of replacement i.e., shedding [27]. Despite the numerous studies on variations in denticle morphology across shark species, only a small number document patterns of morphological variation on the body within a singular species e.g., [15,28]. Even fewer studies exist on the ontogenetic changes observed in the denticle morphology in any shark species e.g., [7,28,29,30,31,32,33,34,35].

The dermal-denticle variability in Somniosidae has been sparsely described in the literature, with results mainly focusing on the use of denticle morphology for taxonomic identification [9,10,18,29,32,36,37,38,39]. These studies usually analyzed a single sample, often from a single location. The most detailed accounts on the ontogenetic and topological variation of dermal denticles for species of Somniosidae are those by [7,30,31,40,41]. Garrick’s accounts, however, were limited by the low availability of materials and two-dimensional techniques. Vaz [7] was the first to provide a high-definition scanning-electron microscopy of the variation of dermal denticles across the ontogeny and topology of Scymnodon macracanthus.

Among the Somniosidae, Centroscymnus coelolepis [42] has one of the most striking patterns of ontogenetic variation in dermal-denticle morphology. The denticles of the juveniles of this species are so distinct from those in adults that Bigelow et al. [43] described juveniles of C. coelolepis as a new species, allocating it to a distinct genus (i.e., Scymnodon melas). A year later, Bigelow and Schroeder [29] had access to additional specimens and were able to recognize that the newly described species, Scymnodon melas, was a junior synonym of Centroscymnus coelolepis. Bigelow and Schroeder [29] also provided a brief description of the ontogenetic variation of the dermal denticles in C. coelolepis, but these accounts were limited by their small sample size and examination of single locations on the bodies of the specimens.

The overall goal of this study is to contribute new quantitative data on the ontogeny of shark denticles to better understand the extent of developmental variation in placoid scales. First, we describe in detail the ontogenetic variation in dermal denticles across the body of the sleeper shark, Centroscymnus coelolepis. We used both scanning-electron microscopic images and micro-CT scanning to allow the three-dimensional measurement of denticle shapes. Second, we analyze these data to document the diversity of denticle shapes in multivariate ontogenetic space and then assess the scaling relationships to document denticle parameters, such as surface and volume changes with body size. Third, we compare these data from Centroscymnus coelolepis to available data on other species of the Somniosidae family and consider the taxonomic implications of ontogenetic variation, building on the recent research by Vaz [7,8].

2. Materials and Methods

Terminology for dermal denticles follows Reif [17], Atkinson and Collin [44], Atkinson et al. [45], and Vaz [7]. Scanning-electron-microscopy images were obtained using the Zeiss DSM 940 available in the Instituto de Biociências, Universidade de São Paulo. Skin samples were scanned with a Bruker Skyscan 1173 (µCT-scan) with voxel resolution between 5.77 µm and 6.13 µm, voltage of 30 kV, current of 150 µA, rotation step between 0.35° and 0.4°, and frame average of 3.0 or 4.0. The raw images from the µCT were reconstructed using the software NRecon 2.0 (Bruker).

2.1. Examined Specimens and Skin Samples

A series of 178 specimens of Centroscymnus coelolepis and a total of 526 specimens of the family Somniosidae had their dermal denticles examined under a stereomicroscope. The complete list is attached in Appendix A. Institutional abbreviations follow Sabaj [46]. A subsample of specimens (

Table 1. Subsample of specimens examined with micro-computed tomography (µCT-scan) and scanning-electron microscopy (SEM).

Species and Catalog Number	Total Length (mm)	Method
Centroscymnus coelolepis
MCZ 132510	350	µCT
MCZ 38294	550	µCT
MCZ 38297	650	µCT
MCZ 57703	744	µCT
MCZ 39621	895	µCT
MZUSP 118097	328	SEM
MNHN 2001 3226	681	SEM
USNM 408586	837	SEM
NSMT-P 32586	949	SEM
Centroscymnus owstonii
MCZ 35038	280	SEM
MNHN 1989 0654	525	SEM
HUMZ 101723	627	SEM
TMFE 577	659	SEM
UERJ.AC 1460	950	SEM
BMNH 1973.7.9.9	1071	SEM
Centroselachus crepidater
AMNH 58099	283	SEM
MNHN 1998 1299A	768	SEM
USNM 408581	525	SEM
USNM 408582	426	SEM
Scymnodon macracanthus
MNHN 2008 1916	582	SEM
BMNH 1884.2.6.7 (holotype)	667	SEM
MNHN 2003 1708	691	SEM
NSMT-P 32079	1179	SEM
Scymnodon ichiharai
TMFE 1875	942	SEM
Scymnodon ringens
BMNH 1991.7.9.690	317	SEM
BMNH 1991.7.9.688	518	SEM
BMNH 1987.1.21.86	674	SEM
Scymnodalatias cf. garrick
ZMH 122774	417	Steromicroscope
Scymnodalatias albicauda
HUMZ 129360	170	SEM
Somniosus cf. microcephalus
UF 162500	1505	SEM
Somniosus cf. rostratus
MZUSP uncatalogued	1090	SEM
Zameus squamulosus
USNM 220496	341	SEM
USNM 220489	532	SEM

) had skin samples of 10 × 10 mm removed from five body locations (Figure 1): dorsal snout, the dorsal surface of the head between the nostril and the anterior edge of the eye; interspiracular region, skin surface between each spiracle; first gill region, surface of the skin dorsal to the first gill aperture; trunk, vertical middle of the trunk ventral to the first dorsal spine; and tail, vertical middle of the tail ventral to the second dorsal spine. The specimens of Centroscymnus coelolepis examined with µCT-scan had an additional sample extracted from the ventral snout, ventral surface of the head between the nostril and the mouth.

2.2. µCT Scanning Analysis and Dermal-Denticle Measurements

Materialize Mimics software (version 22.0) was used to segment individual denticles from each µCT scan. A total of 205 individual dermal denticles from across the six locations and five specimens of Centroscymnus coelolepis were segmented for imaging and measurements. Eleven measurements (Figure 2) were taken from each denticle using the “measurement tools” in Mimics: Crown length: largest distance from anterior margin to posterior margin of the crown. Crown width: largest distance between lateral margins of crown. Base width: direct distance between lateral edges of basal root. Base length: direct distance between anterior and posterior edges of basal root. Crown angle: the angle of the crown in relation to the basal root. Central cusp length: the height of the central cusp. Central cusp width: the distance between lateral edges at the base of the cusp. Lateral cusp length: the height of the lateral cusp. Lateral cusp width: the distance between the lateral edges at the base of the cusp (denticles without posterior cusps were scored as zero). Number of longitudinal ridges: the number of ridges arranged longitudinally in the dorsal surface of the crown, both extending partially or entirely across the crown. Surface area and volume of each denticle were calculated by exporting an STL file of a segmented denticle from Mimics and importing it in Materialize 3-Matic software (version 14.0). In the latter, the denticles had their pulp cavity and foramina closed, to make them watertight. The updated STL files were then exported to the MeshLab software (version 2022.02) for calculating surface area and volume. The raw data of individual denticles are provided on a table in Supplementary Materials S1.

2.3. Statistics

Denticles around the body and through ontogeny showed considerable variation, and for the purposes of describing this variation, we initially assigned denticles to general “morphotypes” that represent relatively distinct denticle shapes and sizes, based on their locations on the body and the measurements above. Morphotypes were defined by discrete and continuous characters, such as the number and the development of lateral ridges, presence or absence of posterior cusps in the crown, presence or absence of lateral depressions, central cusp aspect ratio, and the position of the anterolateral edge of the crown in relation to the lateral posterior cusp.

Table 2. Summary of the diagnostic characters for defining dermal denticle morphotypes in Centroscymnus coelolepis. The condition “reduced” in “Development of external lateral ridges” means the lateral ridge does not extend past the anterior region of the crown. The condition “complete” means the external lateral ridge reaches the posterior margin of the crown. Abbreviations: lpc, lateral posterior cusp; n/a, not applicable.

	Snout Morphotype			Spiracular Morphotype				Trunk Morphotype
Character	1	2	3	1	2	3	4	1	2	3	4
Number of longitudinal lateral ridges	2–4	4	6+	2	4	4	6	2	4	0	6+
Development of external lateral ridges	when present, reduced	complete	complete	absent	reduced	reduced or complete	complete	absent	reduced	absent	complete
Posterior cusps	absent	absent	absent	present	present	absent	absent	present	present	absent	absent
Central cusp aspect ratio	n/a	n/a	n/a	0.5–1.06	0.41–0.95	n/a	n/a	1.08–1.8	0.52–1.49	n/a	n/a
Lateral depressions	present	present	present	absent	present	present	present	absent	present	absent	present
Relative position of anterolateral edge of the crown	n/a	n/a	n/a	aligned with lpc	external to lpc	n/a	n/a	aligned with lpc	external to lpc	n/a	n/a

presents the summary of the diagnostic characters for each morphotype. Subsequent statistical classification using principal components analysis demonstrated the validity of these morphotype assignments.

To understand how body length affects size differences within the same morphotype, a simple linear regression was fitted using the base R stats package in R (version 4.2.2) to compare crown-length measurements across body length in each morphotype. Additionally, to determine whether denticles in the ventral snout and dorsal snout differed in size, a hypothesis test statistic (t-test) was used within each snout morphotype to determine whether the mean crown length differed significantly between dorsal and ventral denticles. Scaling relationships were analyzed for surface area, volume, crown length, crown width, basal root length, and basal root width versus body length using the slope of the linear regression line of the common logarithm of each measurement plotted against the common logarithm of body length.

A principal component analysis (PCA) was analyzed using the FactoMineR package (version 2.7) in R (version 4.2.2) to collapse the multidimensional measurement data into principal components to visualize denticle-shape transformation through ontogeny. Data were divided into snout denticles (dorsal and ventral snout), spiracle denticles (interspiracular region), and trunk denticles (first gill, trunk by first dorsal spine, and trunk by second dorsal spine). Each point on the PCA plots corresponds to a single denticle and overlaid on top of the PCA is a variable correlation plot and cos2 value, showing the direction and how much each individual measurement contributed to shape space. The R scripts of all statistics performed are available in Supplementary Materials S2. Note: this PCA function uses the mean for the group in cells with null values.

3. Results

3.1. Denticle Morphotypes

Dermal denticles cover most of the body, except for the mouth margins, the posterior margins of the fins, and the dorsal surfaces of the claspers. Our examination of the specimens of Centroscymnus coelolepis demonstrated three main regions where the denticles share similar changes across the ontogeny: the snout, spiracular, and trunk regions (which include the surface around the branchial apertures and caudal regions), similar to those described for C. owstonii [47]. Sexual dimorphism in the morphology of the dermal denticles was not observed. The summary used to distinguish the denticle morphotypes is presented in Table 2. The range of variation observed in each morphotype is presented in

Table 3. Range of variation within each variable from the dermal denticles of Centroscymnus coelolepis.

	Snout Morphotype			Spiracular Morphotype				Trunk Morphotype
	1	2	3	1	2	3	4	1	2	3	4
Character
Surface Area (mm2)	1.48–2.61	1.87–4.37	2.49–8.79	0.97–2.46	1.69–4.93	2.22–8.43	5.94–7.83	1.48–2.28	1.98–12.54	6.9–18.37	3.21–7.81
Volume (mm3)	0.03–0.1	0.07–0.21	0.12–0.60	0.02–0.11	0.06–0.26	0.08–0.63	0.39–0.55	0.04–0.09	0.08–1.03	0.43–1.98	0.13–0.47
Crown Length (mm)	0.49–0.9	0.75–1.32	0.7–1.62	0.53–0.93	0.7–1.35	0.84–1.94	1.5–1.72	0.71–1.0	0.91–2.43	1.88–2.89	1.29–1.78
Crown Width (mm)	0.58–0.90	0.8–1.27	1.13–2.11	0.47–0.63	0.64–1.22	0.9–1.77	1.65–1.93	0.49–0.71	0.62–2.23	1.61–2.94	1.09–1.96
Crown Aspect Ratio (Length/Width)	0.76–1.16	0.77–1.04	0.62–0.98	0.94–1.52	0.96–1.38	0.79–1.12	0.89–0.91	1.3–1.52	1.07–1.67	0.95–1.19	0.9–1.18
Central Cusp Length (mm)	-	-	-	0.11–0.4	0.18–0.44	-	-	0.29–0.43	0.27–0.53	-	-
Central Cusp Width (mm)	-	-	-	0.2–0.42	0.32–0.64	-	-	0.22–0.34	0.29–0.70	-	-
Central Cusp Aspect Ratio	-	-	-	0.5–1.06	0.41–0.95	-	-	1.08–1.8	0.52–1.49	-	-
Lateral Cusp Length (mm)	-	-	-	0.03–0.13	0.03–0.16	-	-	0.1–0.25	0.04–0.24	-	-
Lateral Cusp Width (mm)	-	-	-	0.07–0.18	0.09–0.24	-	-	0.11–0.23	0.08–0.29	-	-
Lateral Cusp Aspect Ratio	-	-	-	0.29–0.89	0.21–0.81	-	-	0.64–1.49	0.24–1.24	-	-
Central Cusp/Lateral Cusp Length	-	-	-	2.42–8.12	2.72–7.76	-	-	1.77–4.14	1.54–8.68	-	-
Central Cusp/Lateral cusp Width	-	-	-	1.89–5.6	1.79–5.56	-	-	1.26–2.5	1.37–5.94	-	-
Basal Root Length (mm)	0.64–1.08	0.49–1.01	0.53–1.01	0.4–1.06	0.63–1.14	0.66–1.28	0.87–1.02	0.68–0.89	0.59–1.28	0.88–1.28	0.52–0.81
Basal Root Width (mm)	0.77–1.12	0.81–1.42	1.13–1.8	0.68–1.21	0.84–1.38	0.90–1.75	1.33–1.52	0.85–1.06	0.79–1.91	1.06–2.36	1.01–1.76
Basal Root Aspect Ratio	0.69–0.98	0.55–0.92	0.46–0.63	0.59–1.03	0.67–1.0	0.63–0.88	0.65–067	0.68–0.94	0.57–1.6	0.51–1.06	0.4–0.61
Number Longitudinal Ridges	2–5	4–5	6–10	2–3	4–5	4–5	6	2–3	4–5	0	6–9
Crown Angle (degrees)	19.63–58.42	2.59–35.56	1.29–15.69	36.51–59.7	27.62–50.40	11.33–35.84	7.31–8.48	28.65–52.41	11.05–48.96	2.41–19.06	13.79–26.85

.

3.1.1. Snout

Morphotype snout one. The dermal denticles classified as morphotype snout one have surface areas ranging from 1.48 mm² to 2.6 mm² and volume areas from 0.03 to 0.09 mm³ (Figure 3). The crowns of morphotype snout one are rounded and drop-shaped, without any posterior cusps. The anterior margin is convex and has wide, rounded anterolateral edges. The lateral margins are convex, projecting posteriorly in the anterior region of the margin and posteromedially in the posterior portion. The crown has a wide, blunt, and angular posterior edge. The angle between the crown and the basal root is highly variable, ranging from 19.6 to 58.4 degrees. The dorsal surface of the crown is concave, with a rounded anteromedial central depression, anteriorly surrounded by the inner pair of longitudinal lateral margins. A pair of lateral depressions is also present, one on each side of the anterolateral regions of the crown. The number of longitudinal ridges in this morphotype varies from two to five. The innermost pair of longitudinal lateral ridges surround anteriorly the central depression and project posteriorly, reaching the posterior margin of the crown. The second (outer) pair of lateral ridges in this morphotype, when present, is small, restricted to the anterolateral edges of the crown. The outer pair of lateral ridges delineates the lateral depressions and extends posteriorly only to the anterior region of the lateral margins of the crown. The presence and extent of the central ridge is variable: in some denticles, the central ridge is short, restricted to the posterior edge of the crown (Figure 3A); in others, the central ridge extend from the posterior margin of the central depression to the posterior edge of the crown (Figure 3B); and in some denticles, the central ridge extends throughout the crown, from the anterior to the posterior margin (Figure 3C). The ventral surface is smooth and slightly concave.

The denticle peduncle, where the crown above the epidermis joins the basal root embedded within the epidermis and dermis, is narrow; its width is one-half the width of the basal root (Figure 3D,F,G). The basal root is diamond-shaped, with four angular edges (one anterior, one posterior, and two lateral; Figure 3E). The aspect ratio of the basal root varies from 0.7 to 1. The anterior and lateral edges have similar lengths, but the posterior edge is 1.5 times longer than the anterior edge. Both anterior and posterior margins of the basal root are concave. The dorsal surface of the basal root is concave and has four ridges, with each ridge extending from each basal-root edge to the ventral surface of the crown. A pair of foramina is present on the posterodorsal surface of the basal root, with each foramen positioned on opposite sides of the posterior ridge of the basal root. The ventral surface of the basal root is smooth and convex, and it delineates the ventral region of the pulp cavity. The pulp cavity is wide and trapezoid-shaped (Figure 3H,I).

Morphotype snout two. The dermal denticles classified as morphotype snout two have surface areas ranging from 1.87 mm² to 4.37 mm² and volumes ranging from 0.07 to 0.21 mm³ (Figure 4). The crowns of morphotype snout two are drop-shaped and lack posterior cusps. The anterior margins are convex and continuous, with broad and rounded anterolateral edges. The lateral margins are convex and project posteromedially to form a broad, blunt posterior edge. The angle between the crown and the basal root varies greatly from 2.6 to 35.5 degrees. The dorsal surface of the crown is mostly concave, with an ample, rounded anteromedial central depression, anteriorly delimited by the inner pair of longitudinal ridges. A pair of additional lateral depressions is present in the anterolateral region of the crown, anteriorly surrounded by the origin of the outer pair of longitudinal ridges. Four to five longitudinal ridges are present on morphotype snout two. The inner pair of lateral longitudinal ridges surround anteriorly the central depression and project posteriorly, reaching the posterior edge of the crown. The outer pair of lateral longitudinal edges extends from the anterolateral region of the anterior margin and to the posterior region of the lateral margin of the crown (Figure 4A–F). The presence and extent of a central longitudinal ridge is variable. When present, this ridge can be restricted to the posterior region (Figure 4A), originating in the posterior region of the anterior central depression (Figure 4B), or it can cross the crown completely from the anterior to the posterior margin (Figure 4C). The ventral surface of the crown is smooth and concave.

The peduncle is broad. Its width is two-thirds the width of the basal root and wider than three-quarters of the crown’s width (Figure 4D,F,G). The basal root is diamond-shaped, with four angular edges, and its aspect ratio varies from 0.5 to 0.9 (Figure 4H). The lateral edges are angular, 1.5–2 times longer than their base width. The posterior edge is also angular, but broader, the width of its base similar to its length. The anterior edge is broad and short, and its length is half the length of its base width and twice as short as the length of the posterior edge. The antero-lateral margins of the basal root vary from straight to slightly concave, whereas the postero-lateral margins are deeply concave. The dorsal surface of the basal root is concave and has four ridges, each of which projects dorsally from the tip of each basal-root edge to the ventral margin of the crown. A pair of foramina is present on the posterodorsal surface of the basal root, with each foramen on opposing sides of the posterior ridge of the basal root. The ventral surface of the basal root is smooth and convex, delimiting the pulp cavity. The pulp cavity is wide and trapezoidal (Figure 4I).

Morphotype snout three. The dermal denticles defined as morphotype snout three have surface areas ranging from 2.49 mm² to 8.79 mm² and volumes from 0.11 to 0.59 mm³. The crowns of morphotype snout three are drop-shaped, without posterior cusps (Figure 5). The anterior margin is broad and convex, with broad and rounded anterolateral edges. The lateral margins are convex and project posteromedially to meet posteriorly, forming a blunt posterior edge. The crown angle in this morphotype varies from 1.3 to 15.7 degrees. The dorsal surface of the crown is mostly concave, with a large, rounded anteromedial central depression, which is anteriorly delimited by the inner pair of longitudinal ridges (Figure 5A–D). A pair of small lateral depressions is present on the anterolateral region of the crown, medially delimited by the inner pair of longitudinal ridges and laterally delineated by the first outer pair of longitudinal ridges. Six to ten ridges are present on the dorsal surface of the crown of morphotype snout three. The inner pair of longitudinal ridges extends from the anterior margin to the posterior edge of the crown. The first outer pair of longitudinal ridges is positioned on the lateral region of the crown, also originating on the anterior margin and projecting posteromedially to reach the posterior edge of the crown. The additional outer pairs of longitudinal ridges (e.g., the second and third) are relatively short and located adjacent to the lateral margin of the crown, projecting from the anterolateral region of the anterior margin and extending to the posterior region of the lateral margin of the crown. The presence of a central longitudinal ridge is variable, and it is absent in several denticles (present in Figure 5B; absent in Figure 5A,C). The extent of the central ridge, similar to that observed in other morphotypes, is also variable: it is restricted to the posterior edge of the crown, it extends from the central depression to the posterior edge, or it extends throughout the dorsal surface of the crown. The ventral surface of the crown is smooth and concave.

The denticle peduncle is broad, measuring more than three-quarters of both the basal root and the crown widths (Figure 5E). The basal root is rhomboid-shaped, with aspect ratio ranging from 0.6 to 0.9. The lateral edges are angular and long: the width of the edge-base is less than half of the length of the edge. The posterior edge is broad and blunt, and the base of the edge is wider than its length. The anterior edge is short, and its width two to three times the edge length. The shape of the margins of the anterior edge is highly variable. Some denticles have a basal cusp with a triangular anterior edge, whereas others have a rectangular anterior edge. In denticles with rectangular anterior edges, some denticles have straight and continuous edge margins, whereas others have indentations (Figure 5E,I). The dorsal surface of the basal root is concave and has four ridges, extending dorsally from the tip of each basal-root edge to the ventral surface of the crown. The basal roots of most morphotype-snout-three denticles have pairs of foramina on their posterodorsal surfaces, with one foramen adjacent to each side of the ridge extending from the posterior edge. In some denticles, an additional foramen is observable either on the left or the right side (Figure 5H). The ventral surface of the basal root is smooth and convex. The pulp cavity is ample and its shape varies from oval to elliptical, or triangular (Figure 5I,J).

3.1.2. Spiracular Region

Morphotype spiracular one. The dermal denticles defined as morphotype spiracular one have surface areas ranging from 0.96 mm² to 2.46 mm² and volumes from 0.02 to 0.10 mm³. The crowns of morphotype spiracular one have rounded anterior margins and posterior margins bearing one central and two lateral posterior cusps (Figure 6). The angle between the crown and the basal root varies from 36.5 to 59.7 degrees. The central cusp is 2.4–8.1 times longer and 1.9–5.6 times wider than the lateral cusps. The lateral margins of the lateral cusps are longitudinally aligned with the lateral edges of the anterior margin of the crown. The dorsal surface of the crown is concave, with a distinct central depression on its anterior region. Two lateral longitudinal ridges are present on the dorsal surface of the crown. The ridges surround the central depression anteriorly and project posteriorly adjacent to the lateral margins. The extent of the lateral longitudinal ridge is variable, reaching from the posterior half to the bases of the lateral cusps. The occurrence of a central ridge is variable; when present, the central ridge can be shallow and restricted to the longitudinal middle of the central cusp (Figure 6B), or it can extend through the entire dorsal midline of the crown (Figure 6C). The ventral surface of the cusp is smooth and convex.

The peduncle is narrow: its width is approximately half of the width of the basal root (Figure 6D). The basal root has four angular edges (tetracuspid; one anterior, one posterior, and two lateral edges; Figure 6F,H), and it is rhomboidal-shaped, with an aspect ratio varying from 0.6 to 1.0. The anterior and lateral edges are similar in length, but the posterior is less developed, at approximately a third of the anterior edge’s length. The dorsal surface of the basal root is concave, with four ridges extending dorsally from the edge of each basal root cusp to the ventral surface of the crown (Figure 6A–G). A pair of foramina is present in the posterodorsal surface of the basal root, with each foramen positioned on each side of the ridge on the posterior cusp of the basal root. The ventral surface of the basal root is slightly convex, delineating ample pulp cavity (Figure 6H,I).

Morphotype spiracular two. The dermal denticles classified as morphotype spiracular two have surface areas ranging from 1.69 mm² to 4.93 mm² and volumes of 0.05–0.25 mm³. The angle between the crown and the basal root varies from 27.6 to 50.4 degrees (Figure 7). The crown of this morphotype has a convex anterior margin, extending laterally to a rounded edge. The lateral margins of the crown extend posteromedially. Three triangular posterior cusps are present: one large central cusp and two small lateral cusps (Figure 7A–C). The central cusp is 2.7–7.7 times longer and 1.8–5.5 times wider than the lateral cusps. The lateral margins of the posterior lateral cusp are located medially in relation to the anterior edge of the crown. The dorsal surface of the crown is mostly convex, with a central depression in the anterior region of the crown. A pair of lateral depressions is present on the anterolateral edge of the crown, between the inner and outer lateral ridges (Figure 7A–D). Four to five longitudinal ridges are present on the dorsal surface of the crown of spiracular morphotype trunk two. The inner pair of longitudinal ridges surrounds anteriorly the central depression and projects posterolaterally to the bases of the posterior lateral cusps. The outer pair of lateral ridges are small, located on the lateral margin of the crown, extending only through to the anterior edge and delineating the lateral depression. The central ridge is present in all the crowns of morphotype spiracular two. The prominence of the central ridge, however, is variable, with some denticles’ central ridges restricted to the extent of the posterior central cusp, whereas others have a central longitudinal ridge extending from the anterior central depression to the edge of the posterior central cusp (Figure 7A–C). The ventral surface of the crown is smooth and slightly convex.

The peduncle of morphotype spiracular two is robust, measuring approximately three-quarters of the crown width and two-thirds of basal root width (Figure 7D,F). The basal root of morphotype spiracular two is trapezoidal and diamond-shaped, and it has four edges (tetracuspid; one anterior, one posterior, and two lateral edges). Both anterior and posterior edges of the basal root are broad, with the anterior cusp relatively small, measuring approximately half the length of the posterior edge (Figure 7H). The lateral edges are narrower and usually longer than the posterior, and they are angular in shape. The aspect ratio of the basal root is variable, ranging from 0.7 to 1. The dorsal surface of the basal root is concave and has four ridges extending dorsally from the edge of each cusp to the base of the crown. The posterodorsal surface of the basal root has a pair of foramina, each positioned on each side of the ridge projecting from the posterior cusp (Figure 7G). The ventral surface of the basal root is convex and forms an ample, spool-shaped pulp cavity (Figure 7H,I).

Morphotype spiracular three. The dermal denticles classified as morphotype spiracular three have surface areas ranging from 2.21 mm² to 8.42 mm² and volumes of 0.07–0.63 mm³. The shape of the crown of this morphotype varies from oval to drop-shaped, without any posterior cusps (Figure 8). The anterior and lateral margins of the crown are rounded; the posterior margin varies from angular (Figure 8A,C) to rounded (Figure 8B). The angle between the crown and the basal root varies from 11.3 to 35.8 degrees. The dorsal surface of the crown is mostly concave, with a distinct central depression in its anterior region. Three to five longitudinal ridges are observed in the crowns of morphotype spiracular three: one central ridge and one to two pairs of longitudinal lateral ridges. The innermost pair of longitudinal lateral ridges surround the central depression anteriorly and extend posterolaterally (Figure 8A,C) or posteromedially (Figure 8B), reaching the posterior edge of the crown. The extent of the external pair of longitudinal ridges is highly variable, On MCZ 38297, the morphotype-spiracular-three denticles have an external pair of longitudinal ridges that is restricted on the anterolateral margin of the crown (Figure 8A). On MCZ 57703, the external pair of lateral ridges is also located on the margin of the crown, but these ridges extend posteriorly to the posterior half of the crown margin (Figure 8C). On adult MCZ 39621, the external pair of longitudinal ridges originates on the lateral portion of the anterior margin of the crown, projecting posteromedially over the lateral region of the crown (medial to the lateral margin), reaching the posterior margin of the crown (Figure 8B). The extent of the central longitudinal ridge is also variable: in some denticles, the central ridge is restricted to the posterior region of the crown (Figure 8A,B). In other denticles, the central ridge extends from the posterior edge to the anterior surface of the central depression of the crown (Figure 8C). The ventral surface of the crown is straight to slightly concave (Figure 8F,G,I).

The peduncle is relatively narrow, with a width approximately one-half of crown width (Figure 8D). The basal root is diamond-shaped, with an aspect ratio ranging from 0.6–0.9, and tetracuspid, with an anterior ridge, a posterior ridge, and two lateral edges (Figure 8H). All the edges are angular, with the lateral and anterior edges displaying similar dimensions. The posterior edge is slightly longer than and wider than the anterior. Both anterior and posterior margins of the basal root are slightly concave. The dorsal surface of the basal root is concave and has four ridges projecting dorsally from the edge of each cusp to the ventral surface of the crown (Figure 8A,C,D,F,G). On the posterodorsal surface of the basal root, a pair of foramina is present, with one on each side of the posterior ridge of the basal root. The ventral surface of the basal root is convex and forms an ample spool-shaped pulp cavity (Figure 8H,I).

Morphotype spiracular four. The dermal denticles classified as morphotype spiracular four have surface areas ranging from 5.91 mm² to 7.82 mm² and volumes of 0.39–0.55 mm³. The crown of morphotype spiracular four is round and pear-shaped, with a wider anterior region tapering posteriorly into a broad and convex posterior edge, without any posterior cusps (Figure 9). The anterior margin has a shallow indentation centrally. The anterolateral edges of the crown margin are broad and convex. The angle between the crown and the basal root varies from 7.3 to 8.5 degrees. The dorsal surface of the crown is slightly convex in its lateral portions, with a wide, deep central depression located anteromedially on the crown. The margins of the central depression are defined by the innermost pair of lateral ridges. Three pairs of longitudinal ridges are present on this morphotype. The innermost pair are anteriorly conjoined, delineating the anterior margin of the central depression. The anterolateral region of the innermost pair of longitudinal ridges projects posterolaterally, whereas the posterolateral portion of these ridges curves and projects posteromedially, reaching the margin of the posterior edge of the crown. Two additional pairs of lateral ridges are present, located on the lateral portion of the crown and extending from the anterior margin to the posterior region of the lateral margin of the crown. A short, central longitudinal ridge is present, restricted to the posterior edge of the crown. The ventral surface of the crown is smooth and mostly concave, except anteromedially, where the surface is convex (Figure 9F).

The width of the peduncle of morphotype spiracular four is half of the crown width and two-thirds of the width of the basal root (Figure 9B). The basal root is triangular, with a convex anterior margin and concave posterolateral margins (Figure 9D). The length of the basal root is approximately two-thirds of its largest width (with aspect ratios ranging from 0.65 to 0.67). The anterolateral edges of the basal root have acute edges. The posterior edge, conversely, is broad and rounded (Figure 9D). The dorsal surface of the basal root is slightly concave and has three ridges, each extending from each edge of the basal root to the base of the crown (Figure 9B,C,F). Two, three, or four foramina are present on the posterolateral surfaces of the basal root, adjacent to the posterior ridge (Figure 9E). The ventral surface of the basal root is smooth and convex, forming an ample trapezoidal pulp cavity (Figure 9F).

3.1.3. Branchial, Trunk, and Tail Regions

Morphotype trunk one. The denticles classified as morphotype trunk one have surface areas ranging from 1.49 mm² to 2.27 mm² and volumes of 0.03–0.08 mm³. The crown of this morphotype has a rounded anterior margin and its posterior margin bears a central cusp and two lateral cusps (Figure 10). The angle between the crown and the basal root (crown angle) varies from 28.6 to 52.4 degrees. The central cusp is 1.7–4.1 times longer and 1.2–2.5 times wider than the lateral cusps. The lateral margins of the posterior lateral cusps are longitudinally aligned with the lateral edge of the anterior margin of the crown. The dorsal surface of the crown is concave, with a distinct central depression on its anterior region. Two lateral longitudinal ridges are present on the dorsal surface of the crown of morphotype trunk one, surrounding the anterior depression and extending posteriorly adjacent to the lateral margins of the crown (Figure 10A–C). The lateral ridges project posteriorly to the distal tip of the lateral cusps (Figure 10C). The presence of a central ridge is variable; when present, the central ridge is shallow and restricted within the longitudinal middle of the posterior central cusp. The ventral surface of the crown is smooth and slightly convex (Figure 10D,E).

The peduncle is narrow: its width is approximately one-half of the width of the basal root (Figure 10B,D,E). The basal root is tetracuspid with an anterior cusp, a posterior cusp, and two lateral cusps. The basal root is rhomboid-shaped (Figure 10F), with an aspect ratio of 0.7–0.9. On morphotype trunk one, the posterior cusp is the longest, and the others have similar lengths. The anterior margins of the basal root are concave, whereas the posterior margins are straight. The dorsal surface of the basal root is concave and has four ridges, each of which extends from each tip of the basal root to the dorsal edge of the peduncle (Figure 10A–E). A pair of foramina is present in the posterodorsal surface of the basal root, with each foramen positioned on each side of the ridge on the posterior cusp of the basal root. The ventral surface of the basal root is slightly convex, and it forms an ample pulp cavity (Figure 10F). In the sagittal section, the outline of the pulp cavity is trapezoidal (Figure 10G).

Morphotype trunk two. The denticles classified as morphotype trunk two are characterized by surface areas ranging from 1.97 mm² to 12.53 mm², and volumes of 0.07–1.03 mm³. The angle between the crown and the basal root varies from 11.0 to 48.9 degrees. The crown of morphotype trunk two is rounded anteriorly, with its lateral margins projecting posteromedially, forming two anterolateral expansions. The posterior margin of the crown has one central and two lateral cusps (Figure 11 and Figure 12). The lengths of the cusps are highly variable, with the central cusp 1.5–8.6 times longer and 1.4–5.9 times wider than the lateral cusps (Figure 11). Centrally, the dorsal surface of the crown is concave, with a large central depression in the anterior region; the width of the central depression is more than half the width of the crown. The crowns of morphotype trunk two have four longitudinal lateral ridges. From the middle of the anterior region of the crown, the two inner lateral ridges surround the anterior depression and project posterolaterally, reaching either the base (Figure 11A–C,F) or the tip of the posterior lateral cusp (Figure 11D,E,G,H). The second pair of lateral longitudinal ridges are variable in length, extending from the anterolateral region of the anterior margin of the crown to either the anterior region (Figure 11A–D) or the middle of the lateral margin of the crown (Figure 11E–I). The lateral surface between the inner and outer lateral ridges forms the lateral depression on the anterolateral expansions. The length of the central ridge is variable, varying from restricted to the central posterior cusp (Figure 11C–E,G) to extending throughout the longitudinal middle of the crown (Figure 11H). The presence of the central ridge is also variable, and multiple crowns of morphotype trunk two might lack a central ridge entirely (Figure 11A,B,F,I). The ventral surface of the crown is smooth and slightly convex.

The peduncle is narrow. Its width is approximately one-half the width of basal root (Figure 12B,D,E). The basal root is rhomboidal, its aspect ratio varies from 0.6 to 1.6, and the lateral edges are longer and narrower than both anterior and posterior edges (Figure 12F). All the margins of the basal root are slightly concave. The dorsal surface of the basal root is smooth and slightly concave, with four ridges extending from each tip of the basal root to the dorsal edge of the peduncle. A pair of foramina is present on the posterodorsal surface of the basal root, with each foramen positioned on each side of the ridge on the posterior cusp of the basal root (Figure 12E). The ventral surface of the basal root is slightly convex. The pulp cavity is ample and it is trapezoid-shaped in the sagittal section (Figure 12F,G).

Morphotype trunk three. The denticles classified as morphotype trunk three have the largest absolute size observed in this series, with surface areas ranging from 6.89 mm² to 18.37 mm² and volumes from 0.42 mm³ to 1.98 mm³. The crown of morphotype trunk three is drop-shaped and lacks posterior cusps (Figure 13). In some denticles, the posterior margin of the crown may have a shallow indentation (Figure 13A,C), but cusps are absent. The angle between the crown and the basal root varies from 2.4 to 19 degrees. The dorsal surface of the crown is mostly smooth and slightly convex. The denticles have entirely smooth surfaces without ridges (Figure 13A–C,E). The anterior region of the dorsal surface of the crown has a shallow, circular depression. The ventral surface of the crown is smooth and slightly convex. In the smallest denticles of morphotype trunk three, the anterolateral wall of the central depression is sharper and vertically oriented (Figure 13C), but it is not surrounded by a lateral ridge (as observed in the other trunk denticles). In the smaller denticles of morphotype trunk three, some crowns might also have a shallow, sometimes inconspicuous, lateral depression.

The peduncle of morphotype trunk three is wide, approximately two thirds of the width of the basal root (Figure 13D,F,G). The basal root of morphotype trunk three is triangular, without an anterior edge as observed in the roots of the other trunk morphotypes (Figure 13H). The anterior margin of the base is convex, laterally extending into two sharp lateral edges. The posterior margins of the basal root are slightly concave, forming a broad posterior cusp with a rounded posterior edge. The dorsal surface of the basal root is smooth and slightly concave. In contrast to the base observed in other morphotypes, the dorsal surface of the basal root lacks ridges on both anterior and posterior regions (Figure 13D,G). The lateral edges have ridges projecting medially, extending dorsally to the middle of the peduncle (Figure 13F). The posterior surface of the basal root has at least one pair of foramina positioned centrally. Additional foramina (single or a pair) are observed in multiple denticles of morphotype trunk three (Figure 13G). The ventral surface of the basal root is convex and the pulp cavity is relatively smaller, flattened antero-posteriorly. In the sagittal section, the pulp cavity is spool-shaped (Figure 13H,I).

Morphotype trunk (branchial) four. This morphotype has a very narrow distribution, and it is observed only in the area dorsal to the gill openings in the smallest adult specimens of Centroscymnus coelolepis. The denticles of morphotype trunk (branchial) four have surface areas ranging from 3.20 mm² to 7.80 mm² and volumes of 0.12–0.47 mm³. The angle between the crown and the basal root varies from 13.8 to 26.8 degrees. Similar to morphotype trunk three, the crown of morphotype trunk four is drop-shaped, with straight posterior margins, without cusps. In contrast to morphotype trunk three, however, the crowns of morphotype trunk four have six to nine shallow longitudinal ridges in all their denticles (Figure 14). The inner pair of longitudinal ridges surrounds the anterior central cavity and extends posteriorly to the posterior region of the crown. The other lateral pairs of ridges extend from the anterior region to the middle of the lateral margin of the crown. The dorsal surface of the crown is mostly convex, except anteromedially, where the anterior depression of the crown with a concave surface is located. The ventral surface of the crown is mostly straight to slightly concave.

The peduncles of morphotype trunk four are wide, measuring approximately three-quarters of the crown width (Figure 14D,G). The basal root of this morphotype is trapezoidal, with a reduced anterior cusp, and a wide and rounded posterior cusp (Figure 14H). The lateral cusps of the basal root are large and angular. The dorsal surface of the basal root of morphotype trunk four is concave, with three ridges projecting dorsally from the tip of the posterior and lateral edges of the basal root and extending to the ventral surface of the crown (Figure 14D,F,G). On the posterior surface of the basal root, at the boundary with the peduncle, a pair of foramina are present, one on each side of the ridge projecting from the posterior cusp. The ventral surface of the basal root is convex, forming a semi-cylindrical and ample pulp cavity (Figure 14H,I).

3.2. Denticle Replacement

The replacement of denticles through the ontogeny among the different morphotypes in Centroscymnus coelolepis is not simultaneous, but gradual. The proportions of each denticle morphotype vary topologically and ontogenetically. Sexual dimorphism in the replacement was not observed in any of the regions.

3.2.1. Denticle Replacement in the Snout

In neonates, both the dorsal and the ventral anterior regions of the head, from the tip of the snout to the anterior edge of the eye aperture, are completely covered by morphotype snout one denticles (MCZ 38452, 269 mm TL). Across the snout, the replacement of different morphotypes consistently occurs earlier across ontogeny in the ventral region (Figure 15). In specimen MCZ132510 (350 mm TL), 97% of the denticles on the dorsal surface of the snout are from morphotype one, with only 3% being from morphotype snout two (Figure 15A); ventrally, 12% of the denticles are already morphotype snout two, with the remaining 88% from morphotype snout one (Figure 15F). In MCZ 38294 (550 mm TL), 71% of the denticles on the dorsal surface of the snout are from morphotype snout one and 29% are from morphotype snout two. No denticles from morphotype three are present (Figure 15B). On the ventral surface, however, morphotype snout three are already present and correspond to 19% of all denticles. Additionally, denticles from morphotype snout one are not the predominant morphotype ventrally as in the dorsal region; only 21% of denticles correspond to morphotype snout one. The predominant morphotype is snout two, with 62% of the denticles (Figure 15G). Similar proportions are observable in MCZ 38297 (650 mm TL; dorsal: SN1: 83%, SN2: 17%; ventral: SN1: 20%, SN2: 59%, SN3: 20%). The MCZ 57703 (744 mm TL) was the first specimen in which the dorsal surface of the snout was predominantly covered by morphotype snout two denticles (63%), whereas the remaining 37% were still from morphotype snout one (Figure 15C). The ventral surface of the snout is still predominantly covered by morphotype snout two (64%), with morphotype snout one representing only 10% of the denticles. Morphotype snout three accounts for 26% of denticles on the ventral surface of the snout (Figure 15H). The USNM 408586 (837 mm TL) was the first specimen observed in this series in which the dorsal surface of the snout was covered predominantly by morphotype snout three (59%), and it lacked morphotype snout one; the remaining denticles are all morphotype snout two (41%) (Figure 15D). No data are available for the ventral region of USNM 408586. In adults (e.g., MCZ 39621), both the dorsal and the ventral surface of the snout are completely covered by morphotype snout three (Figure 15E,I).

We also observed that that the crown lengths of dorsal-snout morphotypes seemed larger than those of the same morphotypes in the ventral region. However, the results of the t-test comparing the crown lengths reported no significant differences in mean crown length between the dorsal and ventral snout denticles for morphotype snout one (t-value = 0.3, p-value = 0.7). In the morphotype snout two denticles, the mean crown length of dorsal denticles is significantly larger than those of the ventral denticles, with a t-value of 2.9 and a p-value of 0.02. The morphotype three denticles showed the strongest difference in mean-crown-length measurements between the dorsal and ventral denticles, with the dorsal denticles displaying significantly longer crowns (t-value = 5.9, p < 0.001).

3.2.2. Denticle Replacement in the Spiracular Region

From neonates to individuals measuring 396 mm TL (MNRJ 30244), the spiracular region is entirely covered by denticles of morphotype spiracular one (Figure 16A). The first occurrence of morphotype spiracular two was found in a specimen measuring 421 mm TL (MNRJ 30249). In specimen MCZ 38294 (550 mm TL; Figure 16B), the spiracular region is mostly covered by denticles from morphotype spiracular two (64%). The remaining denticles are morphotype spiracular one (36%). In MCZ 38297 (650 mm TL), most of the denticles covering the spiracular region are still of morphotype spiracular two (53%). In this specimen, the denticles of morphotype spiracular three are present and represent 36% of the denticles in this region. The remaining denticles (13%) are morphotype spiracular one. Specimen MCZ 57703 (744 mm TL; Figure 16D) has a similar morphotype distribution (SP1: 14%; SP2: 51%; SP3: 35%). Although it was slightly smaller (725 mm TL; Figure 16C), USNM 206061 was the first specimen to have a single denticle from morphotype spiracular four (2%). In this specimen, morphotype spiracular one was not present. However, in USNM 206061 (725 mm TL), morphotype spiracular two comprises only 18% of denticles in the spiracular region; the remaining denticles (80%) are morphotype spiracular three. In adults, denticles of morphotype spiracular two are not present. In USNM 408586 (837 mm TL; Figure 16E), 46% of the denticles covering the spiracular region are morphotype spiracular three, whereas 54% are morphotype spiracular four. In MCZ 39621 (895 mm TL; Figure 16F), morphotype spiracular three comprises only 36% of the denticles in this region. The remaining 66% is composed of morphotype spiracular four.

3.2.3. Denticle-Replacement Patterns in the Branchial, Abdominal, and Caudal Regions

From neonates to individuals measuring 350 mm TL (MCZ 132510; Figure 17A,G,M), the branchial, abdominal, and caudal regions are covered by denticles from morphotype trunk one. The first appearance of morphotype trunk two occurs in the caudal region of MCZ 132510, as a single denticle. Replacement across different morphotypes in this region occurs in the tail first and progresses to the branchial region through ontogeny. In the branchial region of specimen MCZ 38294 (550 mm TL; Figure 17B), 47% of the denticles are from morphotype trunk one, whereas 54% of the denticles are from morphotype trunk two. In the abdominal region of MCZ 38294 (Figure 17H), morphotype trunk one comprises 17% of the denticles, with the remaining 83% composed by morphotype trunk two. In the caudal region of MCZ 38294 (550 mm TL; Figure 17N), fewer than one percent of the denticles are morphotype trunk one and 79% of the denticles covering this region are from morphotype trunk two. The remaining 21% of the denticles are composed of morphotype trunk three. In specimens MCZ 38297 (650 mm TL) and MCZ 57703 (744 mm TL), both the abdominal and the caudal region lack morphotype trunk one denticles. In the abdominal region of MCZ 38297 (650 mm TL), 55% of the denticles are of morphotype trunk two and 45% are of morphotype trunk three; in the caudal region, morphotype trunk two comprises 40% and, morphotype trunk three, 60%. The branchial region of MCZ 38297 is covered by morphotype trunk one (29%) and trunk two (71%) only. In the abdominal region of MCZ 57703 (744 mm TL; Figure 17I), 88% of the denticles are of morphotype trunk two and 13% are of morphotype trunk three; in the caudal region, morphotype trunk two comprises 41% and, in trunk three, 59% (Figure 17O). The branchial region of MCZ 57703 (Figure 17C) is covered by morphotype trunk one (11%) and trunk two (89%) at this size. In sub-adults and adults (>830 mm TL), both the abdominal and the caudal region are entirely covered by denticles of morphotype trunk three (Figure 17J–L,P,R). Variation occurs only in the branchial region. From 800 mm TL to 900 mm TL, the branchial region is mostly covered by morphotype trunk (branchial) four. In MCZ 39621 (895 mm TL; Figure 17E), all the denticles examined are from morphotype trunk (branchial) four. In USNM 408586 (837 mm TL; Figure 17D), however, 92% of the denticles are from morphotype trunk (branchial) four, and the remaining 8% are from morphotype trunk three. In specimens larger than 950 mm TL, the denticles covering the branchial region were entirely replaced by morphotype trunk three, similar to the abdominal and caudal regions (NSMT-P 32586, 949 mm TL; Figure 17F).

3.3. Size Variation within Each Dermal-Denticle Morphotype

The results from the linear regressions of the denticle-crown length versus the body length within each morphotype demonstrate that in the snout, both morphotype snout one and morphotype snout two have a significant positive correlation between crown length and body length, with p-values of 0.003 and 0.008, respectively, and R-correlation values of 0.58 and 0.63, respectively. Morphotype snout three does not have a significant correlation, displaying a p-value of 0.80 and an R-correlation value of 0.08. Morphotypes spiracular one, two, and three did not show significant correlations between their crown lengths and body lengths, with respective p-values of 0.2, 0.9, and 0.5, and R-correlation values of 0.30, 0.03, and 0.21. Denticles of morphotype spiracle four did not have sufficient data to fit a regression as they were only observed in one individual (895 mm TL). Morphotypes trunk one and three also did not show a correlation between crown length and body length, with p-values of 0.3 and 0.2, respectively; the R-correlation values for both morphotypes were 0.30. However, morphotype trunk two denticles showed a significant positive correlation between crown length and body length, with a p-value of <0.001 and an R-correlation value of 0.47. Since morphotype trunk four (branchial) denticles were only seen in one body length (895 mm TL), there were not sufficient data to run a regression.

3.4. Principal Component Analysis of Dermal-Denticle Morphotypes

Principal component analyses (PCA) facilitate comparisons of denticle-size and shape change across body location and ontogeny by collapsing the eleven denticle measurements (Figure 2) into a lower-dimension multivariate space. The PCA analysis also analytically reinforces the morphotype groupings described in Section 3.1. The first and second principal components captured the two axes with the highest percentage of variation. Therefore, they are presented in Figure 18, Figure 19 and Figure 20 (PCA plots for denticles on the snout, spiracle, and trunk regions, respectively).

For the snout denticles (Figure 18), the first principal component accounts for 69.7% of the denticle-shape variation, while the second principal component accounts for 19.3% of the variation. Together, both axes account for 89% of the total shape variation. Lower PC1 values correspond to smaller denticles, and movement along PC1 reflects an increase in denticle size and crown growth. Along PC2, lower values represent rounder denticles with a lower crown angle, while denticles with higher PC2 values have larger crown angles and fewer longitudinal ridges. Variables including surface area, volume, and crown width, with crown length and base width, drive the change along PC1. Crown angle, base length, and the number of longitudinal ridges are variables that, while displaying low cos2 values, contribute to PC2. Morphotype snout one denticles have predominantly low PC2 values and zero-to-high PC1 values, which correspond to smaller denticles with high crown angles. Morphotype snout two denticles had higher PC1 values and a wide spread of values along PC2, ranging from smaller denticles with larger crown angles to medium- and larger-sized denticles with more longitudinal ridges. Morphotype snout three denticles showed a high PC1 value, mostly negative PC2 values, and a larger, rounder denticle shape with low crown-angle values and an increase in longitudinal ridges. The distribution of the points in the PCA shows substantial separation in morphospace among each of the three snout morphotypes (SN1, SN2, and SN3). Although there is some overlap, different morphotypes cluster separately in the snout-denticle morphospace, as shown by the 95% confidence ellipses, which occupy distinct locations in the multivariate space (Figure 18).

The PC1 of the denticles from the spiracular region (Figure 19) accounts for 56.5% of the measurement variation, while PC2 accounts for 18.3%. Together, the two axes explain 74.8% of total spiracular denticle variation. The shape change along PC1 is size-dependent, with smaller denticles having lower PC1 values and larger denticles displaying higher PC1 values. The crown length, crown width, volume, surface area, base width, and number of longitudinal ridges are positive on PC1, and in the negative PC2 quadrant. Crown angle is negative in PC1 and loads positively on PC2. The lateral cusp length, lateral cusp width, central cusp length, central cusp width, and basal-root length all load positively on PC1 and PC2 in the morphospace. Morphotypes spiracular one and two have low PC1 values and a wide spread of values along PC2, corresponding to smaller denticles with high crown angles and lateral and central cusps. Morphotypes spiracular three and four have high PC1 and a low PC2 values, reflecting a shape change in the crown, base, and overall growth, an increase in the longitudinal ridges, and the eventual loss of posterior cusps. Despite some overlap between individual denticles, different morphotypes cluster at different locations in the morphospace, as indicated by the 95% confidence ellipses (Figure 19).

The denticles from the branchial, trunk, and tail regions show size variation along PC1 similar to both the snout and spiracle regions, with smaller denticles positioned in the left quadrants of the morphospace and larger denticles in the right quadrants of the PC1 axis (Figure 20). The PC1 explains 52.5% of the total measurement variation, and PC2 explains 15.4%; combined, they explain 67.9% of the trunk-denticle-shape variation. The variables that contribute to the shape change along PC1 are the crown angle, central cusp width, base length and width, crown measurements, surface area, and volume. Along PC2, lateral and central cusp measurements drive the differences in shape, along with the number of longitudinal ridges. Small, tricusped denticles with large crown angles (morphotype trunk one) are positioned in the left (negative) quadrants of PC1. Morphotype trunk two denticles are spread around all quadrants of both PC1 and PC2, reflecting the wide range of crown shapes observed in this morphotype (Figure 11). The largest, oval-shaped, non-cusped denticles with small crown angles (morphotype trunk three) are found in the positive quadrants of PC1. Morphotype trunk four (branchial) denticles are clustered with low PC1 and low PC2 values. There is a high level of clustering in the morphospace of morphotypes trunk one, three, and four (branchial). Morphotype trunk two, however, is widespread throughout the morphospace.

3.5. Denticle Scaling

The results of the scaling regressions are presented in

Table 4. Scaling results from the linear regression of the common logarithm of the measurement against the common logarithm of total length.

Denticle Variable	Expected Isometric Slope	Slope	Standard Error of Slope	Adjusted R2	Regression p-Value
Surface Area	2	1.38	0.11	0.42	<0.001
Volume	3	2.23	0.17	0.47	<0.001
Crown Length	1	0.81	0.08	0.33	<0.001
Crown Width	1	1.05	0.07	0.51	<0.001
Basal Root Length	1	0.12	0.05	0.03	0.01
Basal Root Width	1	0.47	0.05	0.32	<0.001

. The denticle surface area, volume, crown length, basal root length, and basal-root width all show negative allometry. The crown width, conversely, shows slight (although not statistically significant) positive allometry. The scaling plots for these measurements can be found in Figure 21. The regression fits for the log of the surface area and the log of the volume against the log of the body length show slopes of 1.38 and 2.23, respectively. The observed slopes are both less steep than is expected for isometric growth (Table 2: a slope of two for surface area, and a slope of three for volume); they therefore show strong negative allometry. The dermal denticle surface area and volume in the samples measured thus increase less than expected from the isometric growth over the ontogeny. If the denticles were to grow isometrically, variables like crown and base length and width would be expected to have a slope of 1.0 when plotted against the body length. The crown length is also negatively allometric, with a slope of 0.81. The denticle base length and width both show strong negative allometry, with slopes of 0.12 and 0.47, respectively (Table 4). The near-zero slope for the basal-root length shows that this denticle measurement is nearly constant as Centroscymnus coelolepis increases in total body length.

4. Discussion

Research on elasmobranch placoid scales or dermal denticles has grown considerably in recent years, following the pioneering studies by Reif [17,25,48], who first explored in depth the diversity of shark denticles. Since then, researchers have continued to document denticle diversity, emphasizing differences in morphology around the body [15,20,49,50,51,52], using differences between dermal denticles to make inferences in terms of taxonomy and systematics [7,28,53], constructing biomimetic models of denticles [54,55], and testing shark-skin-like surfaces for their propulsive and hydrodynamic functions [22,23,56,57]. In addition, shark denticles have served as a means of understanding shark-community structures [58,59]. Sibert and Rubin [16] used dermal denticles as vehicles for studying changing abundances of sharks through geological time. The use of solitary denticles, however, incurs the risk of overestimating the extent of interspecific variation due to the diversity of denticle morphotypes, which vary considerably during ontogeny and around the body, as suggested by other authors [60,61], as well in our study. Denticles can be present around the eye [62] and inside the mouth [20,63], and the homology of denticle and tooth developmental patterning is a recent focus of analyses of gene-expression patterns [64,65].

As research continues, the extent of known denticle diversity expands, and what we term the “denticle multiverse” grows as new axes of structural and functional variation are uncovered. However, one area that has not been actively studied is ontogenetic change in denticle morphology and patterning. How do skin denticles around the shark body change during growth? We know that denticles are shed and replaced in adult sharks [27,51], but few authors have considered that variation during ontogeny could be more extensive than interspecific variation, and that changes in denticle shape and size around the bodies of adult sharks could themselves be highly ontogenetically variable.

The overall goal of this paper is to document the dramatic ontogenetic changes we observed during growth in the somniosid Portuguese Dogfish shark (Centroscymnus coelolepis). Ontogenetic changes in denticle morphology at different locations around the body are so extensive in this species that they necessitated the development of nomenclature (morphotypes) and the use of statistical approaches, such as principal components analysis, to describe this variation. Furthermore this extensive ontogenetic denticle variation has considerable implications for taxonomy when considered within the context of other species within the family Somniosidae.

4.1. Denticle Morphology in Centroscymnus coelolepis

The variability of the dermal denticles of Centroscymnus coelolepis has intrigued ichthyologists through history. Bigelow et al. [43] examined three juvenile specimens of Centroscymnus coelolepis (MCZ 37420, MCZ 37424, MCZ 37452) and observed the presence of dermal denticles bearing crowns with three posterior cusps. At the time of Bigelow et al.’s study, dermal denticles with tricuspidated crowns were thought to be present exclusively in the genus Scymnodon [36,37], leading these authors to not only describe these individuals as a new species (i.e., Scymnodon melas), but also to allocate this putative new taxon to the genus Scymnodon. A year later, however, Bigelow and Schroeder [29] had access to a gravid female of Centroscymnus coelolepis with late embryos, and they were able to compare late embryos of this species with an adult specimen. Bigelow and Schroeder [29] were not only able to observe the occurrence of distinct dermal denticles among embryos, juveniles, and adults (confirming a brief observation made by Tortonese, [66]), but they were also able to determine that their recently described new species, Scymnodon melas, was actually a junior synonym of Centroscymnus coelolepis. Bigelow and Schroeder [29] also provided a brief description and illustration of the ontogenetic variation of dermal denticles on the trunk of C. coelolepis. These accounts, however, were limited because of the low size range of their sample, which was focused on a single topological location (the vertical middle of the trunk, aligned with the first dorsal fin). A complete description of the ontogenetic variation in the dermal denticles of Centroscymnus coelolepis eluded researchers for years, given the difficulty in obtaining a complete ontogenetic series. C. coelolepis is a deep-water species, and it is not commonly caught in either commercial or research fleets. Therefore, the scarcity of specimens in museums (in comparison to coastal species) led previous studies to focus mostly on the dermal denticles of adults e.g., [9,67]. Now, after a decade-long endeavor that included visits to multiple museums around the globe, in conjunction with the incorporation of CT-scanning and SEM techniques, we can now describe the considerable extent of the ontogenetic morphological variation in dermal denticles in C. coelolepis. This new dataset not only reveals morphological variability, but also allows new taxonomic and systematic inferences similar to those as described by White et al. [33,34,35].

4.2. Denticles and the Taxonomy of Centroscymnus coelolepis and C. owstonii

The close phylogenetic relationship between Centroscymnus coelolepis and C. owstonii and the recognition of these taxa as two distinct species is widely accepted in the literature [4,5,6,9,11,32,36,37,38,67,68,69,70,71,72]. One of the previous characteristics based on dermal denticle morphology used to distinguish these two species was relative size, since the placoid scales of Centroscymnus coelolepis are larger than those from C. owstonii [6,38,67,68]. The present study, continuing from the studies from Vaz [8] and Weigmann et al. [6], confirmed that not only adults, but also juveniles of Centroscymnus coelolepis larger than 550 mm TL have denticles on the trunk and tail that are 1.5–2.0 times larger than those from C. owstonii (Figure 22).

Cadenat and Blache [32], Yano and Tanaka [9], Last and Stevens [71], and Weigmann et al. [6] proposed that denticles dorsal to the gill-arch apertures and in the trunks of C. coelolepis lack posterior cusps in the posterior edge of the crown, whereas C. owstonii has cuspidated denticles in this region (Figure 22). Our series of examined materials also revealed this feature to be distinctive between these species. Cadenat and Blache [32], Compagno [70], and Last and Stevens [71], however, considered that all denticles of adults of C. coelolepis are smooth, without ridges. We, conversely, demonstrated that, not only in adults, but throughout growth, most of the head of C. coelolepis is covered by denticles, with three or more (up to nine) ridges in their crowns (Figure 3, Figure 4, Figure 5, Figure 6, Figure 7, Figure 8, Figure 9, Figure 15 and Figure 16).

Yano and Tanaka [9] proposed that adults of Centroscymnus coelolepis have dermal denticles with rounded crowns on the head, similar to those on the trunk, whereas the head of C. owstonii supports denticles with tridentate margins and three to five longitudinal ridges. Yano and Tanaka [9], however, generalized their observations from the region dorsal to the first branchial aperture to the entire head ([9], Figure 6). We demonstrate here that adults from both species of Centroscymnus have rounded crowns bearing three to nine longitudinal ridges around the snout, mouth, and spiracular region (Figure 2, Figure 3, Figure 4, Figure 5, Figure 8, Figure 9, Figure 15, Figure 16 and Figure 22), similar to those described for Centroscymnus owstonii by Rincon et al. ([47], Figure 7A,B). The variation between C. coelolepis and C. owstonii occurs only in the region dorsal to the branchial apertures. Indeed, adults of Centroscymnus owstonii have denticles bearing crowns with three posterior cusps in the region dorsal to the branchial apertures, with three to five longitudinal ridges (Figure 22K), whereas adults of Centroscymnus coelolepis have the region dorsal to the branchial apertures supporting denticles with rounded crowns, similar to described by Yano and Tanaka [9] (Figure 17D–F). The surfaces of the crowns of the denticles in the region dorsal to the branchial apertures, however, is variable in adults of C. coelolepis. In smaller adults (up to 950 mm TL), crowns of denticles might have six to nine longitudinal ridges, which are distinct from the trunk and tail denticles, which have smooth surfaces. Denticles with triangular crowns and smooth surfaces in the region dorsal to the branchial apertures, similar to those on the trunk, are present only in larger adults of C. coelolepis (larger than 950 mm TL; Figure 17D–F).

Weigmann et al. [6] described denticles dorsal to the branchial region of C. coelolepis with one pair of lateral ridges. This statement, however, was based on the use of scanning-electron microscopy, which often does not allow the visualization of parts of denticles that overlap with adjacent denticles. The use of computed tomography scanning allowed the examination of individual denticles of C. coelolepis, including the regions that overlap with nearby denticles. This technique demonstrated that the branchial denticles of adult Centroscymnus coelopis can have up to four pairs of longitudinal ridges, rather than only one pair, as suggested by Weigmann et al. [6]. We also demonstrated that the crowns of denticles with longitudinal ridges dorsal to the branchial region are present only in the smallest adults. Specimens larger than 950 mm TL have branchial denticles with smooth crowns, similar to those observed in the trunk and tail (NSMT-P 32586; Figure 17F). Rincon et al. [47] describe the trunk of adults of C. owstonii, at the level of the first dorsal fin, with denticle crowns bearing up to 12 posterior cusps. This feature was not observed in any of our samples (which included UERJ 1634). Such high number of cusplets seems to be an anomaly. Similar to C. coelolepis, C. owstonii oval trunk denticles with three to five posterior cusps (morphotype trunk two; Figure 22F,I) are replaced by denticles without cusps, with their posterior margins, when present, bearing only small indentations (Figure 22L; similar to the description, by Rincon et al. [47], of denticles on the lateral line).

A potential new characteristic that allows the distinction between juveniles up to 525 mm TL of Centroscymnus coelolepis and C. owstonii is the crown ratio of the denticles in the dorsal region of the snout. In most examined denticles from C. coelolepis, the crown ratio ranges from 0.8 to 1.0, with a single denticle displaying a ratio of 1.1. Most of the examined denticles from the dorsal region of the snout in C. owstonii have a ratio higher than one, varying from 1.0–1.2 (Figure 22A,D). The effectiveness of this characteristic, however, needs to be assessed with three-dimensional data, as the crown-ratio measurements of the C. owstonii were taken from two dimensional images.

4.3. Monophyly of Centroscymnus: Additional Support from Dermal Denticles

The composition of the genus Centroscymnus has varied through time [18,31,36,38] and, currently, only two species are included in this genus: Centroscymnus coelolepis and C. owstonii [4,7,8,11,72,73]. One of the features previously used to support the argument for the close relationship among these two species was the morphology of the dermal denticles from the trunk and tail of adults, which have large oval crowns with smooth dorsal surfaces, and an anterior circular cavity and lacking longitudinal ridges [5,7,38,47]. The phylogenetic hypotheses of Naylor et al. [1], Straube et al. [2], and Silva and Vaz [74], however, consistently recover the genus Centroscymnus as a polyphyletic assemblage.

The data presented here, conversely, present additional morphological features shared by Centroscymnus coelolepis and C. owstonii that further suggest their monophyly. At 550 mm TL, the tail of Centroscymnus coelolepis presents denticles with large, oval crowns, classified here as morphotype trunk three (Figure 17). In specimens of Centroscymnus owstonii of a similar size (MNHN 1989 0654, 525 mm TL; Figure 22F), a large denticle, with wide, rounded crowns, lacking longitudinal ridges and bearing an anterior, circular cavity is present in similar proportions to morphotype trunk three in C. coelolepis. The change in replacement observed in larger specimens is also similar across these two species. On specimens of C. owstonii HUMZ 101723 (627 mm TL) and TMFE 577 (659 mm TL; Figure 22I), the proportions of denticles similar to those from morphotype trunk three are close to those observed in MCZ 38297 (650 mm TL). Therefore, both species not only share this morphologically unique dermal denticle (morphotype trunk three) on the trunks and tails of adults, but they also share similar rates of denticle replacement across ontogeny.

4.4. Ontogenetic Variation and Phylogenetic Inference within the Family Somniosidae

The family Somniosidae currently comprises six genera: Somniosus, Centroscymnus, Scymnodon, Centroselachus, Scymnodalatias, and Zameus [4,5]. Their interrelationships are not entirely clear, and the monophyly of this family was previously questioned [1,2,74]. Dermal-denticle morphology was used in the past for inferring phylogenetic relationships between sleeper sharks [18,31]. As previously mentioned by Bigelow and Schroeder [29], a large series of specimens is needed to properly assess the phylogenetic signal, not only for dermal-denticle morphology, but for any character in general [75]. The examination of complete ontogenetic series allows the recognition of new morphological characters that are potentially phylogenetically informative.

Somniosus is unique among genera of Somniosidae in having conical denticle crowns, without a pair of lateral posterior cusps, and for having a broad crown peduncle, continuous with the tip of the crown. In Centroscymnus, Scymnodon, Centroselachus, Scymnodalatias, and Zameus, denticles have peduncles that are narrower than the crown width throughout the ontogeny (Figure 23). The determination of the apomorphic state, however, is highly dependent on the phylogeny, as similar variations occur intragenerically across the diversity of Squaliformes. The phylogenetic hypothesis by Silva and Vaz [74] recovered a polyphyletic Somniosidae, with species of Somniosus established as the sister group of a clade formed by species of Squaliolus and Euprotomicrus. The remaining species of Somniosidae and Oxynotus form a monophyletic group, which is a sister of the clade comprising species of Etmopteridae. Assuming the hypothesis proposed by Silva and Vaz [74], the conical crowns shared by species of Somniosus could be a putative synapomorphy supporting the monophyly of this genus. Euprotomicrus and Squaliolus have rectangular crowns (with independent occurrences in other Dalatiinae and some species of Etmopteridae [32,76]). Denticles with crown widths 1.5–2.0× wider than the width of the peduncle are shared by Centroscymnus, Scymnodon, Centroselachus, Zameus, and Scymnodolatias, and this feature could be a putative synapomorphy, suggesting the close relationship among genera, with a reversion in Oxynotus. Although a combined analysis is needed to properly assess the optimization of these characters, denticle morphology shows potential for supporting the non-monophyly of Somniosidae, as suggested by Naylor et al. [1], Straube et al. [2], and Silva and Vaz [74].

Within Somniosidae, denticle ontogeny along distinct denticle developmental trajectories (morphotypes) is a feature shared by species of Centroscymnus, Scymnodon, and Centroselachus. In addition to Centroscymnus coelolepis, the first denticle morphotype to appear on the trunk of small juveniles (usually smaller than 400 mm TL) of Centroscymnus owstonii, Scymnodon macracanthus, Scymnodon ringens, Scymnodon ichiharai (see [10]), and Centroselachus crepidater is morphologically similar to the morphotype trunk one described here for Centroscymnus coelolepis (Figure 10 and Figure 17A,G,M). The crowns of the denticles in these juveniles have three elongated posterior cusps (Figure 24), with the central cusp extending anteriorly to approximately half or more of the crown length (in C. coelolepis, 0.4–0.5 of the crown length; two-thirds in S. ringens; Figure 10 and Figure 17A,G,M). The crowns of the denticles of the adults in the Scymnodon species are leaf-shaped (Figure 23 and Figure 24; see also [7,10]); in Centroscymnus, crowns are oval-shaped without longitudinal ridges (Figure 13, Figure 17 and Figure 22); and in Centroselachus, the crown is also oval, but bears five longitudinal ridges (Figure 24G). In Zameus, Scymnodalatias, and Somniosus, the crowns of the denticles are morphologically similar throughout the ontogeny (Figure 25; see also Taniuchi and Garrick [18]) and have short central cusps (Zameus: 0.22 times the crown length; Scymnodalatias: 0.34 times the crown length; Somniosus lacks posterior cusps).

The available accounts of dermal-denticle morphology in other Squaliformes species suggest that most of the genera from this order present little ontogenetic variation in denticle morphology [32,37,38,43]. The main exception is the genus Centrophorus. In this genus, juveniles of Centrophorus longipinnis and C. leslei have dermal denticles with distinct peduncles and elongated, elliptically shaped crowns, whereas the denticles of adults have short peduncles and broad, tear-drop-shaped crowns [32,34]. In Centrophorus uyato, juveniles have pyramidal crowns, with short and broad peduncles, which are gradually replaced by denticles with wider and flatter crowns, resulting in a tear-drop shape [35]. The dermal denticles of adults of Centrophorus granulosus are similar to those from the other species of Centrophorus, but the juvenile denticles have distinct, broad pedicels and tricuspidate crowns, similar to morphotype trunk one, described herein, in Centroscymnus coelolepis [33]. Assuming the phylogenetic hypothesis presented by Silva and Vaz [74], juveniles bearing dermal denticles with tricuspidate crowns (i.e., morphotype trunk one) that are replaced with distinct denticles in the later stages of ontogeny could be considered a putative synapomorphy for the clade, including Centroselachus, Zameus, Centroscymnus spp., Scymnodon spp., and Oxynotus, with reversions in Zameus, Oxynotus, and an independent occurrence in Centrophorus granulosus. A similar optimization was recovered when mapping this character in the phylogenetic hypothesis by Naylor et al. [1].

Additionally, Zameus and Scymnodalatias both present microreliefs (i.e., transverse ridges) among the longitudinal ridges of their crowns (Figure 25; see also [18]). No other species of Somniosidae and none of the other squaliform sharks examined have microreliefs among the longitudinal ridges of the crowns of the dermal denticles that can be interpreted as a potential synapomorphy, suggesting the monophyly of Zameus and Scymnodalatias, as previously proposed by Taniuchi and Garrick [18].

4.5. Denticle Replacement and Function

Shark-skin denticles are extremely diverse in size and shape, and our results on denticle ontogeny in Centroscymnus coelolepis expand the boundaries of the denticle multiverse by showing that considerable changes in spacing, size, crown-ridge number and morphology, and base shape can all occur within a single individual during growth. These changes most likely occur through denticle replacement and the eruption of new denticles in the gaps between existing denticles as sharks grow through ontogeny. Dillon et al. [27,59] have shown that shark denticles are shed through time and can be collected from both sediments on the ocean floor and the bottoms of laboratory tanks holding captive sharks. Sibert and Rubin [16] recovered shark denticles from deep-sea sediment cores, used them to reconstruct shark abundances through time, and identified a Miocene shark-extinction event. Thus, denticles must be shed from the skin, and Popp et al. [51] were able to observe the process of denticle replacement in skin samples from adult thresher sharks. Replacement denticles can be seen emerging from below the epidermis into the gap formed by a shed denticle, and examination of the skin surface reveals numerous gaps between denticles that have been previously shed [51].

What are the functions of this diversity of shark-skin denticles in general and of the different denticle morphotypes identified here specifically? Most researchers have suggested that shark-skin denticles function by reducing drag forces and, hence, they reduce the effort of swimming through the water [77,78,79,80]. Furthermore, experimental evidence strongly suggests that longitudinally arranged denticle ridges can function in a similar manner to engineered riblets, which are known to reduce drag [81,82,83]. In addition, the close packing of denticles in many adult pelagic sharks (e.g., [49]) may create a smooth hydrodynamic surface with exposed riblets, which can further reduce drag. One additional aspect of denticle function has been demonstrated by testing shark-skin surfaces and biomimetic models in a robotic propulsive device [22,54,55,56,57]: shark denticles can act not only to reduce drag, but also to increase thrust and, thus, enhance propulsion by altering the attachment of leading-edge vortices on the posterior body and tail.

While these hypothesized functions of shark denticles could be reasonable for the adult denticles observed here in Centroscymnus coelolepis, where the skin surface is covered with closely-spaced denticles with few gaps (e.g., Figure 15E,I; Figure 16E,F; Figure 17K,L,Q,R), hydrodynamic explanations would seem unlikely for skin denticle patterns early in ontogeny. At that time, denticles are spaced more widely, there are noticeable gaps in the denticle field (e.g., Figure 17E,G), and denticle crown angles are large relative to adults and the posterior cusp points project away from the skin surface and into the water flowing over the body. Such denticle configurations would be better suited to another function such as deterring predation by cephalopods by limiting attachment of arm suckers. Smaller and slower moving C. coelolepis may be more vulnerable to attack by predators that attempt to attach to or grab the body, and denticles with sharply pointed cusps and projecting crowns may limit the extent to which individual suckers can attach.

One noteworthy result of our analysis of denticle ontogeny is the negative scaling that we observed between surface area, volume, and linear measurements with the sole exception of denticle crown width which scales nearly isometrically. At present, no other studies of denticle scaling are available for comparison to these data, but previous studies of shark body scaling reveal that many aspects of shark body shape scale isometrically, with negative allometry observed only for some aspects of tail shape [84]. Irschick et al. [85] concluded that for eight shark species, large sharks are in general geometrically similar to smaller individuals based on 12 linear measurements that captured overall body and tail shape characteristics.

Gayford et al. [86] studied body scaling in the brown smoothhound shark Mustelus henlei and observed a mixture of positive and negatively allometric linear variables, with five linear body measurements scaling isometrically, and tail measurements displaying negative allometry. Regions showing positive allometry include body width (span) at the pectoral fin location, and the circumference of the caudal peduncle.

The scaling relationships of denticles observed here may reflect the necessity of packing denticles onto the skin surface as sharks grow and the relative increase in crown surface area which results in a nearly complete covering of the skin by denticle crowns in large individuals. Denticle bases may be constrained in how much they can grow given the relative expansion of crown surfaces in adults which overlap with adjacent denticles. Denticle bases remain separate from nearby denticle bases despite the overlap of the crowns of these same denticles.

5. Conclusions

We discovered considerable variation in denticle shape through ontogeny in the squaliform shark Centroscymnus coelolepis, which has eleven distinct morphotypes that are expressed during development and in different regions on the body. The extent of this variation is larger than most of the currently described interspecific differences in denticle shape and size. Three distinct regions of the body of C. coelolepis have denticle replacement in a distinct series of morphotypes across ontogeny: the snout, spiracular, and trunk regions (the latter ranging from the gill openings to the tail). Within the trunk region, replacement to the end point of larger denticles of the same morphotype or to distinct morphotypes occurs in a tail-to-head direction, with juvenile specimens possessing larger denticles and with morphotypes trunk two and three being the most common in the tail, whereas the branchial region of the same specimen presents large percentages of morphotype trunk one.

Smaller adults (830–950 mm TL) of Centroscymnus coelolepis have a transitory denticle morphotype on the surface dorsal to the branchial apertures (morphotype trunk four). In adults larger than 950 mm TL, the branchial region is replaced by denticles from morphotype trunk three, which is similar to the remaining regions of the trunk and tail. The growth in the dermal denticles of Centroscymnus coelolepis is negatively allometric with the denticle-surface area, volume, crown length, basal-root length, and basal-root width, with lower-than-isometric scaling exponents. The scaling equation for the basal-root length shows that the basal-root length is nearly constant as the body length increases. The crown width, conversely, shows slight positive allometry.

Centroscymnus coelolepis shares with Centroscymnus owstonii the presence of denticles from morphotype three in the trunk and tail regions. These species also share similar rates of denticle replacement across morphotypes through ontogeny. Centroscymnus coelolepis shares with Centroscymnus owstonii, Centroselachus crepidater, Scymnodon ringens, Scymnodon macracanthus, and Scymnodon ichiharai the presence of denticle morphotype trunk one in the branchial, trunk, and tail regions of its juveniles.

While the functional significance of the dramatic changes in denticle size and shape during ontogeny in C. coelolepis is unknown, we hypothesize that the denticles of smaller individuals have a primarily anti-predator function, while adult denticles may function to reduce drag and the cost of swimming. Future analyses are needed to demonstrate the extent to which this high level of ontogenetic variation among denticles is common among Squaliformes and other shark orders.