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RELATIVE GROWTH OF THE SKULL OF THE COMMON MINKE WHALE
Balaenoptera acutorostrata USING A LASER SURFACE 3D SCANNER ... 2
Abstract ... 2
1. INTRODUCTION ... 3
1.1. From the archaeocetes to the modern whales ... 3
1.2. The minke whale and the other crown mysticetes (baleen whales) ... 6
1.3. The use of the 3D scanner and geometric morphometrics for morphological analyses of cetacean skeletons ... 13
2. MATERIALS AND METHODS ... 17
2.1. Images and mesasurements ... 17
2.2. Statistical analysis ... 22
2.3. Allometric growth ... 24
2.4. Surface areas ... 25
3. RESULTS ... 27
3.1. Correlations and linear regression analysis ... 27
3.1.1. Skull ... 28
3.1.2. Rostrum ... 30
3.1.3. Brain case ... 32
3.1.4. Nasal bones ... 35
3.1.5. Foramen magnum and condyles ... 36
3.1.6. Tympanic bullae ... 38
3.2. Results principal component analysis (PCA) ... 39
3.3. Allometry ... 40
3.4. Surfaces ... 43
3.4.1. Linear regression analysis of surface measurements ... 43
3.4.2. Principal Component Analysis (PCA) of surface measurements ... 45
3.4.3. Allometric analysis of surface measurements ... 46
4. DISCUSSION ... 47
5. CONCLUSIONS ... 49
LITERATURE CITED ... 51
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RELATIVE GROWTH OF THE SKULL OF THE COMMON MINKE WHALE
Balaenoptera acutorostrata USING A LASER SURFACE 3D SCANNER
Abstract
Growth-related morphological changes in the skulls of an ontogenetic series of 11 North Pacific common minke whales Balaenoptera acutorostrata were investigated using a laser surface 3D scanner. This is the first study to investigate developmental changes in skull morphology of baleen whales using a laser surface 3D scanner and based on the results obtained, this method will be very useful in future anatomical studies. Measurements were taken at 30 points on the skull to extract individual allometric equations relating the length and zygomatic width of the skull. Comparisons were made with estimates of the surface areas of various skull components. The results revealed that the anatomical portions involved in feeding, such as the rostrum, increased in size relative to the entire skull after birth. In contrast, the sensory organs and the anatomical regions involved in neurological function, such as the orbit, tympanic bullae, and foramen magnum, were fully developed at birth, and their relative size reduced over the course of development. The use of 3D has proved very useful for the study of surfaces, often missing in studies. Geometric morphometric studies could benefit from 3D images of specimens in museum collections and databases making the process of sample acquisition faster and less expensive.
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1. INTRODUCTION
1.1. From the archaeocetes to the modern whales
Cetaceans, whose name derives from the greek Ketos, meaning "sea monster", are an order of mammals whose origin dates back to the Eocene (56 Ma).
Figure 1. The changing cetacean body plan during the first ten million years of cetacean evolution. Five families of archaeocetes are shown, the oldest being the pakicetids, while the youngest are the basilosaurids (modified from Thewissen et al., 2009)
Although mesonychid condylarths, an extinct group of artiodactyls (even –toed ungulates) are traditionally recognized as closely related to cetaceans it is now generally accepted that raoellid artiodactyls are closer relatives (Thewissen et al., 2007). Most molecular data positions hippopotamid artiodactyls as their closest living relatives (e.g. Zhou et al., 2011).
Stem whales or archaeocetes have been found from early to middle Eocene (52–42 Ma) deposits in Africa and North America but are best known from Pakistan and India. Archaeocetes (Fig. 1) have been divided into five or six families, the
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Pakicetidae, Protocetidae, Ambulocetidae, Remingtonocetidae, and Basilosauridae (Dorudontinae is sometimes recognized as a separate family) (Thewissen et al., 1998; Thewissen et al., 2002; Uhen, 2004).
The constant search for food, led cetaceans from land to water and the evolution of a number of anatomical characters that can best support life in water. In the skull these modifications include movement of the external nares posteriorly but not yet positioned on the top of the skull, adaptations of the ear bones for hearing underwater. Among characters of the postcranial skeleton are reduction of the hind limbs, evolution of the tail and transformation of the spine to assist in swimming. The Pakicetidae are the oldest and most basal cetaceans (Thewissen et al., 1998). They possessed a very dense and inflated auditory bulla that is partially separated from the squamosal (cheek bone), a feature suggesting they were adapted for underwater hearing (Gingerich et al., 1990; Thewissen et al., 1993). However, pakicetids were predominantly land or freshwater animals and, except for features of the ear, had few adaptations consistent with aquatic life. Recent discoveries of pakicetid skeletons indicate that they had running adaptations as evidenced by their long, slender limbs (Thewissen et al., 2001). Ambulocetidae were a monophyletic group that possessed well-developed hind limbs and toes that ended as hooves of this so-called walking whale (Thewissen et al., 1994). Partial skeletons of
Protocetidae suggest that they swam using the robust tail as well as the fore limbs
and hind limbs (Gingerich et al., 2001). The Remingtonocetidae are characterized by long, narrow skulls and jaws and robust limbs. Morphology of the jaws of remingtonocetids suggests a diet of fast swimming aquatic prey (Thewissen, 1998). The paraphyletic Basilosauridae were late diverging archaeocetes that were gigantic, approaching 25 m in length, and they had very reduced hind limbs (Gingerich et al., 1990; Uhen, 2004).
According to the fossil record, crown (or modern) cetaceans diverged from a common archaeocete ancestor about 35 Ma (Fordyce, 1980; Barnes et al., 1985).
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Crown cetaceans differ from archaeocetes by possession of a number of derived characters not seen in archaeocetes. Arguably one of the most obvious features is the relationship of the bones in the skull to one another in response to the migration of the nasal openings (blowholes) to the top of the skull (Fig. 2) (Berta et al., 2006).
Figure 2. Telescoping of the skull in cetaceans. Note the posterior position of the nares and the different arrangement of the cranial bones in an archaic whale (archaeocete) (a), a modern odontocete (b), and mysticete (c). Cranial bones: premaxilla (stippled), frontal (f), maxilla (m), nasals (n), parietal (p), squamosal (sq), supraoccipital (s). (modified from Evans, 1987)
Changes in the conformation and arrangement of skull bones from ancestral archaeocetes to crown cetaceans is called telescoping. The telescoped skull, is a adapted for a fully aquatic life: the external nares (nostrils) have moved at the top of the skull to allow breathing without having to release the head from the water, the jaw bones are elongated, the premaxillae slide over the frontal bones and together with the maxillae they form a long rostrum. The occipital bone forms the back of the skull and the nasal, frontal, and parietal bones are sandwiched between the other bones.Other adaptations of the skull to a completely aquatic life can be found in the bones of hearing, particularly in the tympano-periotic complex. In terms of the postcranial skeleton, the laterally flattened paddle-like forelimbs are relatively short and rigid with an immobile elbow, rather than the flexible elbow joint, capable of rotation seen in archaeocetes (Berta et al., 2006).
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1.2. The minke whale and the other crown mysticetes (baleen whales)
Crown Cetacea are divided in two major groups, the Mysticeti (14 species), or baleen whales, and the Odontoceti (75 species ), or toothed whales (Committee on Taxonomy, 2014).
The Mysticeti, are also named “baleen whales” for their feeding apparatus: plates of baleen that hang from the roof of the mouth and are used to strain planktonic food items. Major evolutionary trends within the group include the loss of teeth, development of large body size and large heads, shortening of the intertemporal region, and shortening of the neck (Fordyce et al., 1994).
Two clades are typically recognized: Balaenopteroidea (includes two families Balaenopteridae and Eschrichtiidae) and Balaenoidea (includes two families Balaenidae and Neobalaenidae). While the Balaenoidea retain five digits (fingers) of ancestral mammals in the front flippers, the Balaenopteroidea have lost a digit, while the remaining four have very elongated so as to give the flippers a wing-like appearance (actually the term "Balaenoptera" is derived from the ancient Greek and means "whale with wings"). The skull of the two clades is fundamentally different. The rostrum of balaenoids (Fig. 3) is typically strongly arched, a characteristic that has earned them the English name of bowhead whales, that "whales from the bowed heads", while that of balaenopteroids (Fig. 4) is gently curved (Berta et al., 2006). In the mysticete form of telescoping, the emphasis is on the rostral bones that are positioned only as far posterior as the dorsal interorbital region, without any plate-like ascending supraorbital process on the maxilla; most mysticetes have a posteriorly produced infraorbital process of the maxilla. Further, in all but the most basal groups, the apex of the occipital shield is thrust anteriorly at least as far as the mid part of the temporal fossae. Crown mysticetes have rostral bones that are loosely sutured with the cranium, and this seems to be the case for most fossil mysticetes, but whether the pattern is diagnostic for Mysticeti is uncertain (Uhen et al., 2008a).
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Figure 3. Representative mysticete (Balaenoidea) cranial morphology. Skeleton of the bowhead whale (Balaena mysticetus). (Source: http://i13.photobucket.com/albums/a264/linky101/SIX.gif)
Figure 4. Representative mysticete (Balaenopteroidea) cranial morphology. A. Megaptera
novaeangliae skeleton, right lateral view, lacking forelimb ( after Van Beneden et al., 1880).
The Balaenopteridae, commonly called the rorquals, which include fin whale, minke, Sei, blue, and the humpback among others, and are the most abundant and diverse living baleen whales. They include eight species (Fig. 5) ranging from the small 9 m minke whale, Balaenoptera acutorostrata, to the giant blue whale, Balaenoptera musculus (Berta et al., 2006) which reaches a length of 30 meters and weight of 160 tons (earning the title of largest living animal). Balaenoptera omurai, was recently reported from Japan and distinguished from related species based on morphologic and molecular characters (Wada et al., 2003). Balaenopterids are characterized by the presence of a dorsal fin, unlike gray whales and balaenids, and by numerous throat grooves that extend past the throat region (Barnes et al., 1984).
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Figure 5. The rorqual family of whales. 8 to 100 ft; 2.5 to (Source: http://www.gmixdesigns.com/Marine_Mammals/Balaenopteridea_files/Balaenopteridae.05.png) The ability to dive longer and deeper is an essential component of foraging success and ecological function in a host of marine mammals and birds. In general, larger animals have greater diving capacity (Butler et al., 1982; Halsey et al., 2006) because body oxygen stores scale isometrically (Lasiewski et al., 1971; Hudson et al, 1986) and oxygen depletion rates scale negatively with body size (White et al., 2009); however, there is considerable variation around this trend because of differences in behavior, physiology and performance. For example, rorqual whales represent some of the largest divers of all time, but they exhibit relatively short dive durations because of the high energetic demands of their unique lunge-feeding strategy (Acevedo et al., 2002).
Feeding in balaenopterids is considered to be the „„largest bio-mechanical event that has ever existed on the earth‟‟ and it is referred to as engulfment feeding (Fig. 6). They swim rapidly at their prey (40–50 km/h), with an open mouth and lower jaw pulled wide open at a 90o angle. The mouth and ventral pouch engulf up to 60 m3 of water, then the mouth closes and food is swallowed after the expulsion of water through the baleen (Bouetel, 2005).
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Figure 6. Feeding stages of Balaenopteridae. A) Expansion of the ventral pouch. B) Forward movement of the tongue into the throat as the ventral pouch contracts, and water is expelled from the mouth (after Bouetel, 2005).
Feeding and locomotion are integrated in a dynamic process called lunge feeding. The great expansion of the ventral pouch wall presents a mechanical challenge for the physiological limits of skeletal muscle, yet its role is considered fundamental in controlling the flux of water into the mouth. From the study of Shadwick et al. 2013 it was shown that the ventral pouch muscle contraction modulates the rate of expansion and ultimate size of the ventral cavity, allowing it to adjust energy expenditure during engulfment.
This type of feeding is made possible by several major features of the skull and the lower jaw: a subrectilinear rostrum, short baleen, strong interdigitation of the rostrocranial bones, well developed coronoid process of the dentary, massive
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angular process of the dentary, frontomandibular stay apparatus, loose articulation of the dentary in the glenoid cavity of the squamosal, ligamentous symphysis of the lower jaw, ability of each dentary to rotate on its longitudinal axis, muscular and extensible ventral pouch, and movable tongue (Bouetel, 2005).
Figure 7. Balaenoptera acutorostrata
(Source: http://www.oceanwideimages.com/images/11314/large/minke-whale-50M1470-04.jpg) The subject of this study, the common minke whale Balaenoptera acuorostrata (Fig. 7), is the smallest of all mysticetes ranging in size from 2.5 to 9m. Much like the fin whale though more stocky; the snout is shorter and more pointed (hence the species name). The back is dark slate gray with lighter shades and features a conspicuous white stripe on the dorsal surface of the pectoral fins.
The common minke whale is a cosmopolitan species found in virtually all oceans (Fig. 8) and in virtually all latitudes, from 65°S to 80°N. It occurs in the North Atlantic, the North Pacific, and the Southern Hemisphere, but is not known from the northern Indian Ocean. In parts of its range it is very abundant, in other parts much less so. Its migration patterns are poorly known.
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Figure 8. Worldwide distribution of Balaenoptera acutorostrata. (Jefferson et al., 2011)
Until the 1990s, only one species of minke whale, Balaenoptera acutorostrata was recognized, the Antarctic minke whale B. bonaerensis was regarded as conspecific with B. acutorostrata. Most scientists prior to the late 1990s recognized B. acutorostrata for all minke whales including Antarctic minke whales. Since 2000, the International Whaling Commission (IWC) Scientific Committee has recognized Antarctic minke whales as the separate species B. bonaerensis, and provisionally assigned all northern hemisphere minke whales and all southern hemisphere "dwarf" minke whales to the single species B. acutorostrata (IWC 2001). This has been followed by management and treaty bodies, such as the Convention on International Trade in Endangered Species of Wild Fauna and Flora (CITES) and the Convention on Migratory Species (CMS). The dwarf minke whale is listed as an unnamed subspecies of B. acutorostrata in the southern hemisphere (Society of Marine Mammalogy Taxonomy Committee, 2014). It was originally described by Best (1985) and Arnold et al. (1987) and subsequently distinguished from the Antarctic minke whale on the basis of genetic data (Wada et al., 1991; Pastene et al., 1994). Two
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other subspecies of minke whale are recognized: B. a. actuorostrata, the North Atlantic minke whale and B. a. scammoni (Deméré, 1986), the North Pacific minke whale (Society of Marine Mammalogy Taxonomy Committee, 2014). However, given the limited sampling of dwarf minke whales to date, it may be premature to assume that southern hemisphere populations of B. acutorostrata are more closely related to each other than they are to either northern hemisphere population. For example, Pastene (2006) observed that dwarf minke whales from Brazil shared mitochondrial mtDNA haplotypes with individuals from both the North Atlantic and dwarf minke whales from the Antarctic. In addition, dwarf minke whales from Chile were closely related to animals from Brazil (Acevedo et al., 2006).
Common minke whales have been observed to feed on a broad spectrum of prey and are more piscivorous than the other larger balaenopterids (e.g. Horwood, 1990; Haug et al., 1995). The common minke whale prefers to prey on small fish (Murase et al., 2007). The most important prey species include sand-eels (Ammodytes sp.), herring (Clupea haerengus), capelin (Mallotus villosus), euphausids and several species of larger bony fishes (Sigurjónsson et al., 1998; Víkingsson et al., 2010). Life-history data for minke whales in general indicates that calves are 2.5 – 2.8 m and 150 – 300 kg, at parturition, standard length at maturity of females and males are 7 – 7.5 and 6.5 – 7 m, respectively. Maximum standard length (meters) and mean-weight (tones) are 10.7 and 7 and 9.8 and 5.7, for females and males, respectively. Age at maturity is 5 – 7 years and 5 – 6 for females and males, respectively, and maximum longevity for both sexes about 50 years (Víkingsson et al., 2004).
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1.3. The use of the 3D scanner and geometric morphometrics for morphological analyses of cetacean skeletons
Next is a brief introduction to cetacean morphometric studies to date with an introduction to the 3D laser scanner that was used in this study.
Morphology is a key to understanding the diversity and evolutionary history of life, and the physical and biological interactions of species (Tsai et al., 2014). The origin and functional consequences of variation in the shape of biological organisms has intrigued biologists for centuries (Thompson, 1917). The description and analysis of shape differences was traditionally done by using multivariate techniques based on measured distances (Blackith et al., 1971). The development of geometric
morphometrics (GM) (Rohlf et al., 1993), based on the spatial relationships
between anatomical landmarks representing homologous biological structures, revolutionized the study of biological shape variation (Van der Niet et al., 2010). The main advantage of GM over traditional multivariate morphometrics is that, in addition to the shapes of structures, the geometric relationships among the structures are also quantified, allowing for powerful interpretation and visualization of the results, which was previously impossible (Rohlf et al., 1993; Adams et al., 2004). The number of studies applying this method has increased exponentially during the past few decades (Adams et al., 2004) and GM is now frequently applied to studies of ontogeny, evolutionary ecology, systematics and developmental genetics (Lawing et al., 2010). The application of GM has, however, been largely restricted to zoological and anthropological studies (Lawing et al., 2010; Slice, 2007).
Basic data for GM are usually recorded manually (using measuring tape) but in the last decade has been increasingly obtained from 2D and 3D images. At the present time it is relatively inexpensive and easy to obtain 3D digital models of specimens for morphometric analysis. They can be successfully obtained using CT scanners, or a surface scanner to capture a digital model of the external surface of a specimen, as was done in this research. It is also possible to obtain 3D models from 2D images but is very important that the digital camera have high resolution, accuracy, tonal range, color purity and take into account image noise, shadows and the reflective
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surfaces of the object (bone surfaces are often very reflective) which may impede visualization of important features like skull sutures and may distort portions of the skull.
With the availability of 3D estimation of surface measurement becomes a very simple practice, thanks to the existence of some software with which it is possible to select the area of interest in an image automatically to obtain the area calculation. This provides a tremendous advantage for 3D images of specimens to be studied as it is not possible to obtain accurate estimates of surface 2D images or manual measurement of specimens, as well as giving very precise measurements.
The method of GM data collection continues to advance rapidly. Today 3D scanners are increasingly common: laser scanners that image both surface and internal structures. In many ways, existing coordinate-based geometric morphometric methods are not easily extendable to 3D data, largely because of difficulties of mapping coordinates onto surfaces so that they are in at least geometrically, if not biologically, homologous positions (Lawing et al., 2010).
In this study, the new technology of 3D laser scanning was employed to examine the relationship between the area of the various components of the skull and the skull itself of a mysticete species (Balaenoptera acutorostrata) and then use this data to estimate specimen age and assess skull growth.
A 3D scanner is a device that analyzes a real-world object to collect data on its shape and possibly its appearance (e.g. color). The collected data can then be used to construct digital 3D models.
Many different technologies can be used to build these 3D-scanning devices; each technology comes with its own limitations, advantages and costs. Collected 3D data is useful for a wide variety of applications. These devices are used extensively by the entertainment industry in the production of movies and video games. Other common applications of this technology include industrial design, orthotics and prosthetics, reverse engineering and prototyping, quality control/inspection and documentation of cultural artifacts (Bernardini et al., 2002).
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3D scanners create a point cloud of geometric samples on the surface of the subject. These points can then be used to extrapolate the shape of the subject (a process called reconstruction). If color information is collected at each point, then the colors on the surface of the subject can also be determined.
3D scanners share several traits with cameras. Like cameras, they have a cone-like field of view, and like cameras, they can only collect information about surfaces that are not obscured. While a camera collects color information about surfaces within its field of view, a 3D scanner collects distance information about surfaces within its field of view. The "image" produced by a 3D scanner describes the distance to a surface at each point in the image. This allows the three dimensional position of each point in the image to be identified.
For most situations, a single scan will not produce a complete model of the subject. Multiple scans, even hundreds, from many different directions are usually required to obtain information about all sides of the subject. These scans have to be brought into a common reference system, a process that is usually called alignment or registration, and then merged to create a complete model. This entire process, going from the single range map to the whole model, is usually known as the 3D scanning pipeline (Bernardini et al., 2002).
The principal objective of this research is to examine an ontogenetic series of Balaenoptera acutorostrata using geometric morphometrics, and multivariate allometry of 3D images of skulls thereby increasing our understanding of skull growth in this species.
Not much is known about intraspecific variation especially allometric and sex related changes in the minke whale skull. Nakamura et al. (2014) reported no significant differences in skull morphology by sex except for width of occipital bone. The relative size of the various anatomical portions involved in feeding, such as the rostrum and mandible, increased in size after birth. In contrast, the sensory organs and the anatomical regions involved in neurological function, such as the orbit, tympanic bullae, and foramen magnum, were fully developed at birth, and their relative size
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decreased over the course of development. Nakamura et al. (2014) manually obtained skull measurements, using a 50-cm stainless steel caliper or a large 2-m caliper, when the distance between the two measurement points was less or more than 30 cm, respectively. Using landmark analysis of 2D images of the skull (dorsal surface only) Hampe et al. (2010) showed evolutionary changes in the shape of the skull from stem mysticetes (i.e. Aetiocetidae) to the living rorquals.
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2. MATERIALS AND METHODS
2.1. Images and mesasurements
All approaches to morphological study implemented until now, have been based on manually taken measurements of the various components of the skeleton and skull, or through the capture of 2D images. In this research, the skulls of Balaenoptera acutorostrata were collected using a laser surface 3D scanner, thus obtaining digital images of skulls in three dimensions. This approach to data collection has not been widely employed among cetaceans.
3D images of the skulls of Balaenoptera acutorostrata were taken using a NextEngine Desktop 3D Scanner and measurements were taken using the software program of the instrument Scan Studio HD (Fig. 9).
Figure 9. Next Engine laser surface 3D scanner and the program Scan Studio HD. (Source: http://www.simit.it/grafica/scannerlaser/scanner_nextengine1.png; https://vcuarchaeology3d.files.wordpress.com/2012/11/editscreencap2.jpg)
The specimens examined in this study are housed in the following institutions: SDNHM, San Diego Natural History Museum, San Diego, CA, USA; LACM, Natural History Museum of Los Angeles County, Los Angeles, CA, USA; MVZ, Museum of Vertebrate Zoology, Berkeley, CA, USA; CAS, California Academy of Science, San
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Francisco, CA, USA; TMMC, The Marine Mammals Center, Sausalito, CA, USA; HSU, Humboldt State University, Arcata, CA, USA.
Table 1. Study specimens of minke whales (Balaenoptera acutorostrata) (4 male, 5 female and 2 unknown sex) in collections in the museums listed above.
SEX: F, female; M, MaleAGE: C, calf; J, juvenile; M, mature, U=unknown
SPECIMEN TAXON SEX AGE
CAS 23867 Balaenoptera acutorostrata F M
HSU 2670 Balaenoptera acutorostrata M C
HSU 7503 Balaenoptera acutorostrata F M
HSU 7504 Balaenoptera acutorostrata F M
LACM 54573 Balaenoptera acutorostrata U M
LACM 54808 Balaenoptera acutorostrata F M
LACM 72507 Balaenoptera acutorostrata M C
LACM 95388 Balaenoptera acutorostrata M J
MVZ 126873 Balaenoptera acutorostrata M J
TMMC Balaenoptera acutorostrata F J
SDNHM 23642 Balaenoptera acutorostrata U M
The skulls were positioned on a slightly raised horizontal plane, so as to make the mobility around the specimen easier. The scanner was positioned at an optimal distance from the skull, perpendicular to the horizontal plane of it. Gradually moving the scanner along the same plane, 3D images of the dorsal portion skull were taken covering the entire 360 degrees. The ventral portion of the skull was next scanned.
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The images were aligned using the software Scan Studio HD. The scanning and alignment process is shown in figure 10.
Figure 10. Photos of Balaenoptera acutorostrata specimens to illustrate use of the 3D laser scanner.
I followed the measurements taken by Nakamura at al. (2014). A total of 30 measurements (Fig. 11) were taken to encompass all components of the skull bones in length, width and height.
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Anatomical abbreviations are as follows: CBL, Condylobasal length; MaL, Maxilla
length; PmL, Premaxilla length; RL, Rostrum length; RW ½, Rostrum width at the middle; RW, Rostrum width at the antorbital notch; SWPMa, Skull width at the outer edge of posterior edge of maxilla; SWPPF, Skull width at postorbital process of the frontal bone; ZW, Zygomatic width of the skull; GWOB, Greatest width of the occipital bone; UFM-SPOB, Length from the upper ridge of foramen magnum to superior part of the occipital bone; NL, Nasal length; NWA, Nasal width at the anterior edge of the process; NW ½, Nasal width at the middle; MWP, Minimum width of the parietal bone; FMW, Foramen magnum width; FMH, Foramen magnum height; OCsW, Width of occipital condyles; OCH, Occipital condyles height; OCW, Occipital condyles width; TPm-PS, Tip of premaxilla to the posterior edge of the squamosal; TPm-POB, Tip of premaxilla to the posterior edge of the occipital bone; PaL, Palatine length; PaWP, Palatine width at posterior end; TBL, Tympanic bulla length; GWTB, Greatest width of tympanic bulla; MWTB, Minimum width of tympanic bulla; SH, Skull height; OH, Orbit height; OW, Orbit width.
The growth of the skull of Balaenoptera acutorostrata was assessed by examining ontogenetic variation among skulls with a range of ages between calf, juvenile, and mature (adult).
Figure 11. Measurements on a skull of Balaenoptera
acutorostrata. (Modified from Nakamura et al., 2014) A, dorsal view; B, nasal bones; C, ventral view; D, tympanic bulla; E, lateral view; F, posterior view.
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The approximate age of the skulls was established, with reference to total body length when known, using the data obtained by Walsh (2006). When the age of the skulls could not be determined from body length, I determined age based on various skull proportions of the specimens examined. The age established was in agreement with the age listed in the records of the various museum collections housing the examined specimens.
With the availability of males and females, but not with similar size specimens of the opposite sex, it was not possible to evaluate dimorphism among them but, assuming that "No significant differences in skeletal morphology were observed between the sexes except for in the width of the occipital bone in the present study "(Nakamura et al. 2014, page 1120), a fairly homogeneous sample of skulls was obtained that were treated without regard to sex.
The statistical analysis was conducted using the principal component analysis (PCA) to extract the correlation matrix, used to correlate the size of the components of the skull and to obtain the value of the eigenvectors, in the allometric study. Linear regression analysis was also performed to assess the mode of skull growth and that of its components and to extract the allometric equation.
Having available 3D image I also took measurements of the surface of various parts of the skulls, with the purpose to understand if and which of these parts has an increase of the surface during development. As already mentioned, using specific software selection and the calculation of surfaces of 3D images has become a very simple procedure. The surfaces obtained were then analyzed by linear regression and allometric analysis.
22 2.2. Statistical analysis
The relative growth of the skulls of minke whales was assessed by multivariate analysis of allometry conducted using Principal Components Analysis, thus using the table of correlations of every single measurement. This method served to assess the relative growth of each individual component of the skull as well as the length and width of the different components.
Principal components analysis was used to obtain a series of data considering the
specimens as the table of correlations, the eigenvectors. Principal component analysis (PCA) (Pearson, 1901; Hotelling, 1933) is a statistical methodology for reducing size as a factor. PCA is particularly useful when a certain aspect is not directly quantifiable, but you have multiple indicators of the same dimension.
Correlation was examined to determine whether there is a certain degree of
correlation in the growth of the various components of the bony skull. In statistics correlation is a relationship between two statistical variables such that each value of the first variable corresponds "fairly regularly" with a value of the second. This is not necessarily a cause-and-effect, but simply the tendency of one variable to change as a function of another. Sometimes the changes in a variable is dependent on the variation of the other, and other times they are mutually dependent.
The degree of correlation between two variables is expressed by the so-called correlation indices. These indices assume values between - 1 (when the considered variables are inversely related) and + 1 (when there is no absolute correlation that is, when the variation of a variable corresponds to a variation rigidly dependent on the other), obviously a correlation index equal to zero indicates an absence of correlation. Two independent variables have a correlation index equal to 0, but on the contrary, a value of 0 does not necessarily imply that the two variables are independent.
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Linear regression was used to assess the growth of various component bone of the
skull compared to a fixed value as the CBL or GWD and to extrapolate the equation and the allometric coefficient.
Linear regression analysis was performed to obtain the growth lines of the various components, comparing them with the length and width of the skulls.
Regression is defined as dependence of a variable (dependent) from another variable (independent).
With linear regression the dependence of a variable (dependent, y) to another (independent, x) is analyzed. One begins from the premise that a change of x will lead directly to a change in y. However, in general, we are not allowed to conclude that x caused y rather we are able to predict the value of y for a given value of x. The relationship between x and y is summarized by the equation of a straight line (regression line):
Y= α + βx
α intercepts: is the value of the equation when x = 0
β regression coefficient or slope of the line when x increases by one unit, the average value of y changes of β units.
The regression of the population is a model: the parameters α and β are estimated (a and b) using a random sample of observations (xi, yi).
When β=1 x and y increase in the same way, if β 1 x increase faster than y and when β 1 x increase slower than y.
24 2.3. Allometric growth
In this study, I used two methods for analyzing allometric growth. The first method obtains the allometric equation from the regression line, from which was extrapolated from the allometric coefficient for each measurement and compared between them. The second method was that of eigenvectors obtained from the PCA. Allometry is important in biology to describe mathematically a relative growth of non-proportional body structures. For example, relative growth of the head and the rest of the body in animals: the head of a newborn, in many species, is greater respect to the body than in the adult.
Allometric analysis can estimate the covariation of characters (Cock A.G., 1966) and provide a method to explicate the relationship between processes of growth and evolution (Blackstone N.W., 1987). Morphometric allometric relationships have been developed for bivariate allometric equations and for a multivariate generalization of the bivariate allometric equation.
Fig 12. Different types of allometry. α is the allometric coefficient.
The following allometric equation was used to extract growth patterns at each point: Y = β x Xα
equivalent to the logarithmic equation of: log Y = log β + α log X
25
where X defines the straight distance between the anterior end of the premaxilla and the posterior end of the occipital condyles, that is, the condylobasal length (CBL); Y, the length (cm) of the target anatomy; α, the allometric coefficient; and β as a constant.
If α is negative, Y characteristic decreases with increasing X. If α is positive, but <1, Y increases as X, but not very fast. If α is> 1, it has a rapid growth and not proportional of Y to the increase of X (Fig. 12).
The data were grouped into three different growth patterns: hyperallometry (positive allometry) when the allometric coefficient was significantly greater than 1, isometry (isometric allometry) and hypoallometry (negative allometry) when the allometric coefficient was less than 1.
I obtained the eigenvectors by PCA. The eigenvectors were used to evaluate the type of allometric growth. I estimated the isometric vector (1/p)1/2, where p is a number of traits (p=30). Values above this value were found to have positive allometry, values the same were identified as isometric allometry and lower values indicate negative allometry.
2.4. Surface areas
In this study estimates of the surface areas of various parts of the skull were also made (Fig. 13) including the rostrum, brain case, maxilla, occipital bone, frontal bone, parietal, palatine, condyles and the complex of zygomatic process – squamosal - postglenoid process of squamosal (ZSP).
The surfaces were estimated using the software Geomagic Verify Viewer, by selecting the areas of interest (by following the margins that surround the bones comprising the skull), and then the software calculates the surface. Requirements for a good selection are distinctions between the margins and the sutures of the bones, as well as a good quality of scanned images of specimens.
Once the surface estimates were obtained allometric and linear regression analysis were conducted to assess the rate and pattern of growth.
26
27
3. RESULTS
3.1. Correlations and linear regression analysis
To better understand the data obtained from correlation, linear regression and allometric growth of the various components of the skull, the 30 measurements employed were grouped into the following subdivisions: skull, rostrum, braincase, nasal bones, foramen magnum & condyles and tympanic bullae. For abbreviations see Materials and Methods.
SKULL: CBL, TPm-PS, TPm-POB, SH, ZW. ROSTRUM: MaL, PmL, RL, RW1/2, RW.
BRAIN CASE: MWP, SWPMa, UFM-SPOB, SWPPF, GWOB, OH, OW, PaL, PaWP. NASAL BONES: NL, NWA, NW1/2.
FORAMEN MAGNUM & OCCIPITAL CONDYLES: FMW, FMH, OCsW, OCH,
OCW.
TYMPANIC BULLAE: TBL, MWTB, GWTB.
In the graphs of the correlations, the Y axis is the value of the correlation coefficient; the X axis is the measurements arranged as described in the Materials and Methods (Fig. 14).
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3.1.1. Skull
Measurements of skull height (SH), condylobasal length (CBL), zygomatic width (ZW), tip of the premaxilla to the posterior edge of the squamosal (TPM-PS) and tip of the premaxilla to the posterior edge of the occipital bone (TPM-PS), appear to be highly correlated with values greater than 0.9 for most elements of the rostrum and the skull (Fig. 15). Previous measures mentioned are less well correlated with the palatine bones (PaL and PAWP) values between 0.6 - 0.8 with no correlation (values close to 0) for the size of the tympanic bullae (TBL, GWTB, MWTB) and the foramen magnum (FMW, FMH).
Fig. 15. Correlation of skull height (SH), condylobasal length (CBL), zygomatic width of the skull (ZW), tip of premaxilla to the posterior edge of the squamosal (TPm-PS) and tip of premaxilla to the posterior edge of the occipital bone (TPm-POB).
Linear regression of the data showed a trend of linear growth of SH, ZW, TPM-PS, TPM-POB based on the condylobasal length (CBL) and CBL relative to zygomatic width (ZW).The data show that after an irregularity in the size and initial growth in calves during later development, the growth trend becomes uniform along the regression line (Fig. 16).
29
Fig. 16. Linear regression of skull height (SH), condylobasal length (CBL), zygomatic width of the skull (ZW), tip of premaxilla to the posterior edge of the squamosal (TPm-PS) and tip of premaxilla to the posterior edge of the occipital bone (TPm-PS).
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3.1.2. Rostrum
The correlation of the main components of the rostrum with maxilla length (MaL), premaxilla length (PML) rostrum length (RL), rostrum width at the middle (RW1 / 2), rostrum width (RW), appear to have a high degree of correlation, with values close to 1 with the components of the rostrum and the skull, except for the palatine bones that have a correlation of 0.4 with PaL and 0.3 with PAWP (Fig. 17). Negative values were found in the correlation of the foramen magnum and the tympanic bullae with values of 0.3 with TBL, GWTB, MWTB and foramen magnum height (FMH) and values of 0.4 with foramen magnum width (FMW). Near-zero values, were found for OH, while values greater than 0.9 were obtained with orbit width (OW).
Fig. 17. Correlation of maxilla length (MaL), premaxilla length (PmL), rostrum length (RL), rostrum width at the middle (RW1/2) and Rostrum width at the antorbital notch (RW).
The rostrum exhibits a pattern of linear growth and also in this case, the data show that after an irregularity in the size and initial growth in the calf stage during later development, the growth trend becomes uniform along the regression line (Fig. 18).
31
Fig. 18. Linear regression of maxilla length (MaL), premaxilla length (PmL), rostrum length (RL), rostrum width at the middle (RW1/2) and Rostrum width at the antorbital notch (RW).
32
3.1.3. Brain case
As seen in the previous correlations SWPMa, SWPPF, GWOB, FOM-Spob and OW also have a high degree of correlation with most of the elements of the rostrum and of the skull with values greater than 0.9. Braincase measures were found to be less correlated with the palatine bones (PaL and PAWP), with values between 0.6 - 0.8 and have no relationship to the tympanic bullae (TBL, GWTB, MWTB) and foramen magnum (FMW, FMH) having a degree of correlation close to 0 (Fig. 19). Minimum width of the parietal bone (MWP) has the same degree of correlation of the measures described above but with a greater degree of variability between individuals, while orbit height (OH) is found not to show any correlation.
Fig. 19. Correlation of minimum width of the parietal bone (MWP), skull width at the outer edge of posterior edge of maxilla (SWPMa), skull width at postorbital process of the frontal bone (SWPPF), greatest width of the occipital bone (GWOB), Length from the upper ridge of foramen magnum to superior part of the occipital bone (UFM-SPOB), orbit height (OH), orbit width (OW), palatine length (PaL) and palatine width at posterior end (PaWP).
33
While minimum width of the parietal bone (MWP) shows dispersion of points along the regression line but still shows growth. Skull width at the outer edge of posterior edge of maxilla (SWPMa), skull width at postorbital process of the frontal bone (SWPPF), greatest width of the occipital bone (GWOB) and length from the upper ridge of foramen magnum to superior part of the occipital bone (FOM-Spob) show linearity of growth, having points arranged along the regression line, but like the other measurements, there are irregularities in the size and initial growth of individual calves (Fig. 20). Orbit height (OH) shows no signs of growth, but rather seems to be the same size in the three individuals where it was possible to measure it. The palatine bones (PaL, PAWP) show only a slight increase in both length and width.
34
Fig. 20. Linear regression of minimum width of the parietal bone (MWP), skull width at the outer edge of posterior edge of maxilla (SWPMa), skull width at postorbital process of the frontal bone (SWPPF), greatest width of the occipital bone (GWOB), Length from the upper ridge of foramen magnum to superior part of the occipital bone (UFM-SPOB), orbit height (OH), orbit width (OW), palatine length (PaL) and palatine width at posterior end (PaWP).
35
3.1.4. Nasal bones
The nasal bones are more strongly correlated in width than in length with the other parts of the skull, having values between 0.8 and 0.9 for the nasal width at the anterior edge of the process (NWA) and nasal width at the middle (NW1/2), and values of 0.5 to nasal length (NL) (Fig. 21). Like the other components their growth trajectories differ from the palatine bones, the tympanic bullae and the foramen magnum.
Fig. 21. Correlation of nasal length (NL), nasal width at the anterior edge of the process (NWA) and nasal width at the middle (NW1/2).
From the results obtained the nasal bones are uneven both in size and growth. From the plotted data one can see the variability in the distribution of points along the regression line. The bones, with a low rate of growth, seem to grow more in width than in length (Fig. 22).
Fig 22. Linear regression of nasal length (NL), nasal width at the anterior edge of the process (NWA) and nasal width at the middle (NW1/2).
36
3.1.5. Foramen magnum and condyles
The foramen magnum height (FMH) is found not to have any correlation with the other components of the skull, as well as width (FMW), to the exclusion of the latter with the nasal bones and the palatine bones, with which respectively, share a degree of correlation of 0.6 and 0.7. The size of the condyles are, instead, correlated with the size of the other components of the skull with values greater than 0.9 for the measures of width and 0.8 values for the measures of length, while they are not related to the size of the foramen magnum, palatine bones and tympanic bullae with values between 0.3 and -0.3 (Fig. 23).
Fig. 23. Correlation of foramen magnum width (FMW), foramen magnum height (FMH), width of occipital condyles (OCsW), occipital condyle height (OCH) and occipital condyle width (OCW).
By linear regression the foramen magnum shows a small increase in width from calves to adult, while remaining more or less unchanged in height if not showing decrease in proportion with the condylobasal length (CBL). The condyles show growth both in height and in width. From the graphs it can be seen that the condyles Increase more in width than length (Fig. 24).
37
Fig. 24. Linear regression of foramen magnum width (FMW), foramen magnum height (FMH), width of occipital condyles (OCsW), occipital condyle height (OCH) and occipital condyle width (OCW).
38
3.1.6. Tympanic bullae
The tympanic bullae, as already noted in all previous correlations, are not correlated with the other components of the skull (Fig. 25).
Fig. 25. Correlation of tympanic bulla length (TBL), greatest width of tympanic bulla (GWTB) and minimum width of tympanic bulla (MWTB).
By linear regression the tympanic bullae do not increase in size from juvenile stage to adult, indeed it seems that the growth rate relative to condylobasal length (CBL) decreases (Fig. 26).
Fig. 26. Linear regression of tympanic bulla length (TBL), greatest width of tympanic bulla (GWTB) and minimum width of tympanic bulla (MWTB).
39 3.2. Results principal component analysis (PCA)
Fig. 27. Principal component analysis of 30 measurements made on the skulls of Balaenoptera
acutorostrata.
As shown in the figure 27, PCA shows that the increase in size of the tympanic bullae (TBL, GWTB, MWTB), foramen magnum (FMW, FMH), palatine bones (PaL,PaWP) and nasal bones (NL, NW1/2), differs in growth from the other components of the skulls analyzed. The graph shows that the increase in width of the foramen magnum (FMW) differs from the its increase in height (FMH). The differences in the growth of these components was confirmed by the analysis of correlation and linear regression.
CBL MaL PmL RL RW1/2 RW SWPMa SWPPF GWOB ZW UFM-SPOB NL NWA NW1/2 MWP FMW FMH OCsW OCH OCW TPm-PS TPm-POB PaL PaWP TBL GWTB MWTB SH OH OW -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 F2 (12,28 %) F1 (71,40 %) Variables (axes F1 e F2: 83,68 %)
40 3.3. Allometry
The allometric relationships of various components of the minke whale skull.
Table 2.Relative growth coefficients and relative growth patterns of each part of the skull of minke whales. α indicates relative
growth coefficient, lnβ indicates growth constant, R2
indicates the coefficient of determination: values close to 1 means that the values obtained predict well the value of the dependent variable in the sample, and if it is equal to 0 means that they do not. The relative growth pattern was classified as “Positive” when the relative growth coefficient was significantly larger than 1, “Negative” when the coefficient was significantly smaller than 1, and “Isometric” when the coefficient did not differ significantly from 1.
Measurement site Abbreviation α lnβ Relative growth pattern R2 α lnβ Relative growth pattern R2 Condylobasal length CBL 0.91 1.2 negative 0.966 Maxilla length MaL 1.12 0.84 positive 0.985 1.04 1.03 positive 0.984 Premaxilla length PmL 1.12 0.85 positive 0.988 1.03 1.04 isometric 0.978 Rostrum length RL 1.19 0.77 positive 0.993 1.1 0.96 positive 0.977 Rostrum width at the
middle RW1/2 1.53 0.46 positive 0.953 1.44 0.6 positive 0.982 Rostrum width at the
antorbital
notch RW 1.15 0.69 positive 0.962 1.08 0.84 positive 0.992 Skull width at the outer
edge of posterior edge of
maxilla SWPMa 1.1 0.79 positive 0.969 1.04 0.95 positive 0.994 Skull width at postorbital
process of the frontal bone SWPPF 1.1 0.8 positive 0.966 1.03 0.97 isometric 0.991 Zygomatic width of the skull ZW 1.06 0.84 positive 0.966
Greatest width of the occipital
bone GWOB 1.11 0.76 positive 0.961 1.04 0.92 positive 0.99 Length from the upper ridge
of foramen magnum to superior part of the occipital
bone UFM-SPOB 1.09 0.63 positive 0.944 1.03 0.81 isometric 0.983 Nasal length NL 1.52 0.33 positive 0.542 1.37 0.44 positive 0.515 Nasal width at the anterior
edge of the process NWA 1.83 0.23 positive 0.81 1.77 0.3 positive 0.884 Nasal width at the middle NW1/2 2.75 0.09 positive 0.743 2.65 0.14 positive 0.817 Minimum width of the
parietal
bone MWP 1.5 0.4 positive 0.811 1.4 0.52 positive 0.825 Foramen magnum width FMW 0.13 0.82 negative 0.155 0.13 0.83 negative 0.17 Foramen magnum height FMH -0.62 0.99 negative 0.112 -0.54 0.88 negative 0.095 Width of occipital condyles OCsW 0.69 0.73 negative 0.88 0.66 0.81 negative 0.927 Occipital condyle height OCH 0.7 0.59 negative 0.633 0.71 0.64 negative 0.749 Occipital condyle width OCW 1.81 0.21 positive 0.868 1.7 0.29 positive 0.896 Tip of premaxilla to the
posterior edge of the
squamosal TPm-PS 0.93 1.06 negative 0.989 0.87 1.25 negative 0.99 Tip of premaxilla to the
posterior edge of the occipital
bone TPm-POB 0.92 1.07 negative 0.984 0.86 1.26 negative 0.99 Palatine length PaL 1.96 0.31 positive 0.174 1.8 0.45 positive 0.175 Palatine width at posterior
end PaWP 1.47 0.41 positive 0.108 1.98 0.53 positive 0.111 Tympanic bulla length TBL -4.97 12.02 negative 0.141 -3.81 3.41 negative 0.093 Greatest width of tympanic
bulla GWTB -4.76 8.82 negative 0.13 -3.65 2.61 negative 0.085 Minimum width of tympanic
bulla MWTB -4.98 8.76 negative 0.141 -3.76 2.4 negative 0.09 Skull height SH 1.13 0.69 positive 0.967 1.05 0.84 positive 0.972 Orbit height OH -0.6 0.45 negative 0.001 1.38 0.13 positive 0.004 Orbit width OW 1.23 0.47 positive 0.989 1.11 0.6 positive 0.94
41
Condylobasal length (CBL) of the skull of Balaenoptera acutorostrata exhibits negative allometry. This is in contrast to growth observed in the length of the rostrum (RL) and the occipital plate (FOM-Spob) which instead shows positive allometry. Even the height of the skull is found to have positive allometry seen in the allometric coefficient both in relation to the condylobasal length, and the zygomatic width (ZW) (Table 2). The allometry of the width of the skull of Balaenoptera acutorostrata is positive for all measurements made (i.e. RW, RW1 / 2, MWP, SWMPa, SWPPF and ZW; the width of the occipital plate (GWOB)). Maxilla length (MaL), premaxilla length (PML) and rostrum length (RL) were found to have among the highest allometric coefficients observed, demonstrating positive allometric growth of the rostrum. Allometric coefficients of very high value were found in the measurements of the nasal bones (NL, NWA, NW1 / 2) and palatine bones (PaL, PAWP), but the low value of R2 obtained leads me to question the result, when compared with the result obtained with the eigenvectors, they are always positive, excluding nasal length (NL) which is instead found to be negative, but with more reliable coefficients (Table 3). Negative allometry was found for length measurements of the ventral part of the skull, tip of premaxilla to the posterior edge of the squamosal (TPm-PS) and tip of premaxilla to the posterior edge of the occipital bone (TPm-POB), while positive allometry was found by the method of the eigenvectors. Negative allometry was found for the foramen magnum measurements. The condyles, however, were found to have positive allometry in width of the single condyle (OCW) and negative in height (OCH) and in the overall width of the two (OCsW) (Table 2); a different result was found with the method of the eigenvectors showing isometric height and positive allometry (Table 3) for the two measures in width. Positive allometry was also found for orbit width (OW) and negative orbit height (OH).
42
Table 3. Relative growth patterns of each part of the skull of minke whales based on eigenvectors, where p is the number of measurements. The difference is the allometric coefficient: if greater than 0 indicates positive allometry, if the value is 0 isometric and if less than 0 indicates negative allometry.
Measurement site Abbreviation Eigenvectors (1/p)^1/2 Difference Relative growth pattern
Condylobasal length CBL 0.213 0.183 0.03 positive
Maxilla length MaL 0.214 0.183 0.031 positive
Premaxilla length PmL 0.215 0.183 0.032 positive
Rostrum length RL 0.214 0.183 0.031 positive
Rostrum width at the
middle RW1/2 0.214 0.183 0.031 positive
Rostrum width at the antorbital
notch RW 0.214 0.183 0.031 positive
Skull width at the outer edge of posterior edge of
maxilla SWPMa 0.215 0.183 0.032 positive
Skull width at postorbital
process of the frontal bone SWPPF 0.212 0.183 0.029 positive
Zygomatic width of the skull ZW 0.215 0.183 0.032 positive
Greatest width of the occipital
bone GWOB 0.215 0.183 0.032 positive
Length from the upper ridge of foramen magnum to superior part of the occipital
bone UFM-SPOB 0.213 0.183 0.03 positive
Nasal length NL 0.166 0.183 -0.017 negative
Nasal width at the anterior
edge of the process NWA 0.197 0.183 0.014 positive
Nasal width at the middle NW1/2 0.193 0.183 0.01 positive
Minimum width of the parietal
bone MWP 0.198 0.183 0.015 positive
Foramen magnum width FMW 0.099 0.183 -0.084 negative
Foramen magnum height FMH -0.071 0.183 -0.254 negative
Width of occipital condyles OCsW 0.210 0.183 0.027 positive
Occipital condyle height OCH 0.188 0.183 0.005 isometric
Occipital condyle width OCW 0.206 0.183 0.023 positive
Tip of premaxilla to the posterior
edge of the
squamosal TPm-PS 0.215 0.183 0.032 positive
Tip of premaxilla to the posterior
edge of the occipital
bone TPm-POB 0.215 0.183 0.032 positive
Palatine length PaL 0.100 0.183 -0.083 negative
Palatine width at posterior
end PaWP 0.082 0.183 -0.101 negative
Tympanic bulla length TBL -0.078 0.183 -0.261 negative
Greatest width of tympanic
bulla GWTB -0.075 0.183 -0.258 negative
Minimum width of tympanic
bulla MWTB -0.077 0.183 -0.26 negative
Skull height SH 0.214 0.183 0.031 positive
Orbit height OH 0.006 0.183 -0.177 negative
43 3.4. Surfaces
3.4.1. Linear regression analysis of surface measurements
In the linear regression the data show a trend of linear growth in the maxilla, occipital bone, palatine, frontal, condyle, parietal, the complex of zygomatic process-squamosal-postglenoid process of squamosal (ZSP), the rostrum and brain case surfaces based on the total surface area of the skulls. From the results obtained it appears that the condyles do not undergo an increase in surface area during development. The other estimates, however, were found to have a surface area growth more or less uniform, except for the ZSP complex which is less uniform than other measures. Of the components of the cranium analyzed, the frontal bones are the component with the highest rate of growth of surface. The surface of the maxilla and especially the total area of the rostrum, appears to be that the part of the skull with the largest surface area (Fig. 28).
44
45
3.4.2. Principal Component Analysis (PCA) of surface measurements
Fig. 29. Principal component analysis of the surfaces measurements made on the skulls of
Balaenoptera acutorostrata.
PCA shows that increase in the area of the condyles and the ZSP complex proceed in different ways from the other components of the skulls analyzed. As shown in Figure 29, the line of the condyles (condyles) and complex process of zygomatic-squamosal-postglenoid process of squamosal (ZSP) differ from those of the other measures and differently between the two of them, as seen in the results of the linear regression. Maxilla top Maxilla ven Maxilla tot Occipital Palatine Frontal Condyl Parietal ZSP Rostrum Brain case Tot Surface -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 F2 (12,41 %) F1 (84,40 %) Variables (axes F1 e F2: 96,81 %)
46
3.4.3. Allometric analysis of surface measurements
Table 4. Relative growth patterns of each part of the skull of minke whales based on eigenvectors, where p is the number of measurements. The difference is the allometric coefficient: if greater than 0 indicates positive allometry, if the value is 0 isometric and if less than 0 indicates negative allometry. From the allometric analysis of the surfaces, the rostrum has the highest allometric coefficient, as well as the surface of the maxillary bone that covers most of the surface of it. Despite the brain case being allometrically negative, many of its components were found to show positive allometry such as the occipital bone, the palatine bones, the parietal and frontal bones. The frontal bones were found to have a higher allometric coefficient between the components of the brain case. The condyles were found to have a negative allometric coefficient, showing that growth of this surface area is insignificant. Also, the ZSP complex was found to have a negative allometric coefficient. However, overall allometric growth of the skull of Balaenoptera acutorostrata is still positive.
Measurement site Eigenvectors (1/p)^1/2 Difference Relative growth pattern
Maxilla top 0.309 0.289 0.02 positive
Maxilla ven 0.314 0.289 0.025 positive
Maxilla tot 0.313 0.289 0.024 positive
Occipital 0.302 0.289 0.013 positive Palatine 0.304 0.289 0.015 positive Frontal 0.308 0.289 0.019 positive Condyl 0.124 0.289 -0.165 negative Parietal 0.301 0.289 0.012 positive ZSP 0.219 0.289 -0.07 negative Rostrum 0.314 0.289 0.025 positive
Brain case 0.279 0.289 -0.01 negative
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4. DISCUSSION
Many of the components of the skull of Balaenoptera acutorostrata that exhibit growth in size, appear to have a high degree of correlation, except for the palatine bones, nasal bones, condyles, the foramen magnum and tympanic bullae, which follow a different growth pattern.
This study confirms the results obtained by Nakamura et al. (2014) in which those skull regions that grew proportionally larger during development are the rostrum, frontal and squamosal bones, the width and length of the occipital bone. The orbit, tympanic bullae, foramen magnum, occipital condyles, the sensory organs such as vision and hearing, and other regions involved in neural functions, instead, grew proportionally smaller during development. The negative allometric coefficients and regression line obtained in the present study indicates that the growth of the tympanic bullae was near completion at birth. Some of the data obtained in this study, however, differ from those obtained by Nakamura et al. (2014). For example, GWOB which was found to be isometric by Nakamura et al. was found to have positive allometry in this study. This study also found differences in the analysis of the allometry of the nasal bones (NL, NW, NW1 / 2), the palatine bones (PaL, PaWP) and occipital condyle width (OCW). These differences could be attributed to various factors such as the differences in specimen availability, or materials and methods used since this study employed 3D , instead of manual measurements or 2D images as is more commonly done. Comparison of different materials and methods (e.g. 2D vs 3D) in a single study may be useful for evaluating the effectiveness of both.
A major advantage of using 3D images instead of manually measured specimens or 2D images, is the ease in calculating the surface areas of the specimens. Geometric morphometric analysis of shape based only on linear measurements, often, does not represent the real growth of the specimen. This study of the surface areas of the skull, in addition to confirming the increased growth rate of the rostrum compared to the brain case, showed that the squamosal, the zygomatic and postglenoid process show negative allometry, despite measurements in width (ZW, SWPMa, SWPPF)
48
which displayed positive allometry. This may be due to the fact that this area, restricts movement of the coronoid process of the mandible, and is subject to considerable stress during engulfment feeding.
The irregularity of growth and size of some components of the skull of Balaenoptera acutorostrata found in the distribution of the points along the regression line, can be explained as different growth patterns of the minke during development from juvenile to mature adult. This has been described by Walsh (2006) who noted that the cranial growth rates of B. acutorostrata are not uniform across ontogenetic stages. The braincase dimensions of the calves grow at the same growth rate relative to the body length. However, this changes in juveniles and adults. Overall, the rates of growth for the skull dimensions in the juvenile stage are slower than the postcranial rate of growth, while they are greater than the postcranial rate of growth in adults. This indicates that growth in B. acutorostrata is focused on growth of the entire body as a calf, with special emphasis on the feeding apparatus. During the juvenile stage growth of the postcranial skeleton is emphasized. Finally, as a mature adult growth is focused on the cranial region (Walsh 2006).
All balaenopterids feed through engulfment, a process that is very expensive in terms of energy. The size of the skull and jaws play a fundamental role in this process, resulting in Balaenoptera species having a proportionally increased head size compared to body size, compared with other mammals. The common minke whale prefers to prey on small fish, which may explain why the condylobasal length shows negative allometry, despite the positive allometry exhibited by length of the rostrum and the occipital plate. The dimensions of the body in the minke whale are smaller than other Balaenoptera species and the relatively small head of B. acutorostrata might help to reduce drag and enhance locomotor performance when feeding, providing the capacity to feed on agile prey.
49
5. CONCLUSIONS
The growth of the skull of Balaenoptera acutorostrata appears to have different regions of growth during development from calves to juveniles to mature adults. Skull growth is proportional to its component portions with the exception of the foramen magnum, tympanic bullae, palatine bones that appear to be almost fully developed at birth.
The largest growth of the rostrum than the braincase was also confirmed by the study on areas, frontal bones turn out to be the bones with the most development in the surface of the brain case and the complex process of zygomatic-squamosal-postglenoid process of squamosal (ZSP). It is already highly developed at birth. The study of the surface areas of the skull is a very useful method for the study of geometric morphometrics and 3D images makes the procedure for estimation of surface areas very fast.
The use of the laser scanner 3D surface was found to be very time consuming both the processes of acquiring images as well as the reconstruction of the 3D model. This method, however, is still useful given the results and the quality of the images obtained because the margins and the suture of bones are clearly visible. It takes much less time to scan skulls smaller than a balaenopterid, such as a dolphin. The existence of a support structure onto which to place the skull, or a small object, so that the scanner works directly without interrupting the process to reorient the specimen, makes the process much quicker. The sampling and processing of data from 3D images provides many possibilities in the type of data obtainable from these images. Until now it was only possible to obtain linear measurements of the samples, with the 3D images and the use of special software you can also easily obtain surface and volumetric measurements, which could expand the field of geometric morphometrics. This is a valid reason for use of a 3D surface scanner despite the challenges of scanning large objects like the skull of a large whale.
In the future more consideration should be given to the collection of digital images from specimens in museum collections. Museum collections play a fundamental role
