Volume 11
Issue 3
Veterinary Medicine
JOURNAL OF
POLISH
AGRICULTURAL
UNIVERSITIES
Available Online: http://www.ejpau.media.pl/volume11/issue3/art02.html
ALLOMETRIC ANALYSIS OF CRANIAL PARAMETERS OF AMERICAN MINK, INCLUDING BONES OF MASTICATORY APPARATUS
Hubert Jakubowski^{1}, Marcin Komosa^{1}, Hieronim Frąckowiak^{2}
^{1} Department of Animals Anatomy,
University of Life Sciences in Poznań, Poland
^{2} Institute of Zoology, Department of Animal Anatomy, Poznań University of Life Sciences
The studies aimed at demonstration of uniqueness of American mink masticatory apparatus. The craniological relationships were defined in a sample of 25 skulls of adult minks (18 females, 7 males). The standard data, including 21 measurements, provided material for subsequent statistical analyses. The results demonstrated sexual dimorphism of some crania parameters. Most of characters of masticatory apparatus manifested high correlation with the total cranial length. In turn, equations of allometric analysis were constructed, in which the total cranial length was selected to represent the independent variable. Total lengths of dental rows, maxilla and mandible were markedly abbreviated, as compared to the total cranial length. In parallel, pronounced development was noted of the posterior part of mandible, which pointed to an extensive area for attachment of masticatory muscles. Length of hard palate exceeded markedly the length of dental rows. An isometry or proportional growth was noted of the total cranial length and the length of hard palate.
Key words: craniometry, skull, allometry, American mink.
INTRODUCTION
Both morphologically and functionally, the skull is one of the most complex structures in the body [15]. Total skull length was considered to represent an independent variable, reflecting overall size [16,17,20]. Allometric relationships can be useful for evaluating body size on the basis of individual measurements of body parts [18].
Determination of a relation between increase in one parameter as related to the other ones is known under term of allometric scaling. In morphological sciences the scaling permits to describe proportions of animal body. The term of allometry is derived from the Greek word of alloios, which means "distinct". Thus, allometry describes differences in relationships between studied parameters, including parts of animal body. The isometric growth, in which various body parts grow at the 1:1 ratio, or at the same rate, is relatively rare in living organisms.
Allometric analysis can estimate the covariation of characters [5] and provide a method to explicate the relationship between processes of growth and evolution [2]. Morphometric allometric relationships have been developed for bivariate allometric equations and for a multivariate generalization of the bivariate allometric equation. The formula of bivariate allometry [11] assumes a power function of the form y = ax^{b} where x and y are measurements and the constant b is often called the allometric coefficient. The special case when b = 1 is called isometry [19].
The studies aimed at presenting specific nature of masticatory apparatus structure in the American mink and of metric relationships between craniological parameters, using allometric scaling.
MATERIAL AND METHODS
The studies were performed on 25 bodies of American mink, including 18 females and 7 males, obtained from a large breeding farm. The animals manifested a variable age.
Heads were isolated and subjected to thermic processing. Cranial measurements were taken using the standard technique of von den Driesh [6]. The craniometry took advantage of slide caliper of accuracy up to 0.1 cm. The skulls were measured in two planes: the dorsal and the ventral one, the measurements were also conducted on bones of the mandible. The total of 21 measurements were taken, denoted by letter symbols (Fig. 1, Table 1). The numerical data were subsequently subjected to the following analyses: t test, correlation analysis and allometric regression (Fig. 2). The numerical material of cranial measurements was subjected to statistical appraisal using Statistica software, version 6.
Fig. 1. Cranial measurements in American mink. For abbreviations see Table 1 
Table 1. Craniometric parameters in skulls of american mink 
Acronyms 
Explanation of acronyms 
AP 
(AkrokranionProsthion) – cranial length 
EctP 
(EctorbitaleProsthion) – facial length 
EctA 
(EctorbitaleAkrokranion) – length of cerebral cranium 
ZlP 
(ZygolacrimaleProsthion) – lateral length of visceral cranium 
ZyZy 
(ZygionZygion) – zygomatic width of cranium 
CbP 
(CondylobasalProsthion) – cranial length between posterior surface of occipital condyles and Prosthion (P) 
StP 
(StaphylionProsthion) – length of visceral cranium base (palatal length) 
GBP 
GBP – greatest breadth of the palatine 
BB 
(Bicanine breadth) – distance between canine sockets in maxilla 
LPTr 
(Alveolar length of Premolar Toothrow) 
LMTr 
(Alveolar length of Molar Toothrow) 
LTr 
(Alveolar length of Toothrow – canine not included) 
HP_{1}P_{2 } 
(Height of the mandible between P1 and P2) – the lowest height of mandible body between premolars 1 and 2 
IdGoc 
(InfradentaleGonion caudale) – the highest length of mandible 
HM1 
(Height of the mandible before M1) – maximum height of mandible body 
GovCr 
(Gonion ventraleCoronion) – height of mandibular ramus 
MolMol 
(MolareMolare) – the highest width of sockets for first molars 
BC 
(Bicanine Breadth) – distance between sockets for mandibular canines 
BMTr 
(Greatest breadth of the Molar Toothrow) – maximum width of molar socket 
BCP 
Greatest breadth of the Condyle Process 
GBR 
(Greatest breadth between vertical Ramus) – maximum width of mandible 
Fig. 2. Slope of regression line (in line with the logarythmic equation) 
Allometric regression was described by the following
equation: y = ax^{b}, equivalent to the logarythmic equation of
log y = log a + b log x
Where:
y – dependent variable
x – independent variable
a – constant (allometric coefficient)
b – allometric exponent (points to a relationship between x and y variables; represents
a slope of the straight line).
RESULTS
Evaluation of sexual dimorphism
Analysis using t test demonstrated sexual
dimorphism within 8 parameters, including cranial length (AP), length of
neurocranium (EctA), zygomatic width of cranium (ZyZy), the lowest height of
mandible body between premolars 1 and 2 (HP_{1}P_{2)}, the
highest length of mandible (IdGoc), height of mandibular ramus (GovCr), the
highest width of sockets for first molars (MolMol), the greatest breadth of
the condyle process (BCP).
Values of the parameters allowed to conclude that female skulls of American mink are smaller than skulls in males. The most pronounced sexual dimorphism occurred in the features such as cranial length (AP), length of neurocranium (EctA) and zygomatic width of cranium (ZyZy). These traits revealed maximum values higher by about 3 mm in males than females. The remaining features, as indicated by t test analysis, demonstrated insignificant differences between males and females.
Excluding the t test analysis, some of the cranial features could be concluded to demontrate values slightly higher in females than in males. These traits included length (StP), greatest breadth of the palatine (GBP), alveolar length of premolar tooth row (LPTr), alveolar length of molar tooth row (LMTr), distance between sockets for mandibular canines (BC) and the greatest breadth of molar tooth row (BMTr). The traits mentioned above involved a relationship between teeth and the palate.
In parallel, the analysis distinguished 12 traits which manifested no sexual dimorphism. This allowed to maintain significant size of the sample (Table 2). At subsequent stages of the studies the traits were used for the group of males and females forming a single set.
Table 2. Principal metric characteristic and t test (*p ≤ 0.05; **p ≤ 0.01; ***p ≤ 0.001), n – statistically insignificant) 
Measurement 
p 
Measure 
Males [mm] 
Females [mm] 
Males and females [mm] 
AP 
** 
min 
61.4 
58.4 
58.4 
max 
72.4 
71.0 
72.4 

x 
67.0 
62.9 
64.1 

s.d. 
4.7 
3.3 
4.1 

EctP 
n 
min 
20.3 
17.6 
17.6 
max 
25.8 
24.2 
25.8 

x 
22.7 
21.0 
21.5 

s.d. 
2.0 
1.5 
1.8 

EctA 
* 
min 
41.7 
38.7 
38.7 
max 
49.4 
48.6 
49.4 

x 
44.7 
42.5 
43.1 

s.d. 
3.4 
2.7 
3.0 

ZlP 
n 
min 
13.7 
11.3 
11.3 
max 
15.7 
15.2 
15.7 

x 
14.6 
13.1 
13.5 

s.d. 
0.8 
1.0 
1.2 

ZyZy 
* 
min 
34.6 
32.2 
32.2 
max 
44.9 
41.8 
44.9 

x 
38.8 
36.3 
37.0 

s.d. 
3.7 
2.6 
3.1 

CbP 
n 
min 
62.7 
60.6 
60.6 
max 
74.8 
72.8 
74.8 

x 
68.6 
64.8 
65.8 

s.d. 
4.9 
3.7 
4.3 

StP 
n 
min 
28.1 
26.7 
26.7 
max 
34.7 
35.0 
35.0 

x 
31.4 
29.8 
30.3 

s.d. 
2.6 
2.2 
2.4 

GBP 
n 
min 
19.0 
20.0 
19.0 
max 
24.6 
23.7 
24.6 

x 
22.0 
21.6 
21.7 

s.d. 
2.0 
1.1 
1.4 

BB 
n 
min 
12.4 
12.0 
12.0 
max 
16.4 
15.8 
16.4 

x 
14.5 
13.8 
14.0 

s.d. 
1.6 
1.0 
1.2 

LPTr 
n 
min 
14.1 
13.7 
13.7 
max 
15.9 
16.1 
16.1 

x 
14.9 
14.6 
14.7 

s.d. 
0.6 
0.6 
0.6 

LMTr 
n 
min 
2.5 
2.5 
2.5 
max 
3.9 
4.0 
4.0 

x 
3.2 
3.3 
3.3 

s.d. 
0.6 
0.4 
0.4 

LTr 
n 
min 
14.6 
14.6 
14.6 
max 
18.5 
18.5 
18.5 

x 
17.3 
16.8 
17.0 

s.d. 
1.5 
0.8 
1.0 

HP1P2 
*** 
min 
5.2 
5.0 
5.0 
max 
8.2 
8.2 
8.2 

x 
7.0 
6.2 
6.5 

s.d. 
0.9 
0.8 
0.9 

IdGoc 
** 
min 
37.4 
35.1 
35.1 
max 
45.4 
44.0 
45.4 

x 
41.2 
38.3 
39.1 

s.d. 
3.4 
2.4 
2.9 

HM1 
n 
min 
6.9 
6.3 
6.3 
max 
8.9 
8.6 
8.9 

x 
8.0 
7.3 
7.5 

s.d. 
0.8 
0.7 
0.8 

GovCr 
*** 
min 
16.3 
16.2 
16.2 
max 
21.2 
21.0 
21.2 

x 
19.3 
17.6 
18.1 

s.d. 
2.0 
1.4 
1.7 

MolMol 
** 
min 
14.7 
14.2 
14.2 
max 
18.9 
18.4 
18.9 

x 
16.8 
15.9 
16.2 

s.d. 
1.6 
1.1 
1.3 

BC 
n 
min 
7.0 
7.3 
7.0 
max 
9.7 
9.0 
9.7 

x 
7.7 
7.9 
7.8 

s.d. 
0.9 
0.5 
0.6 

BMTr 
n 
min 
3.0 
2.5 
2.5 
max 
3.8 
3.9 
3.9 

x 
3.4 
3.2 
3.3 

s.d. 
0.2 
0.3 
0.3 

BCP 
** 
min 
9.2 
8.4 
8.4 
max 
11.8 
11.7 
11.8 

x 
10.5 
9.8 
10.0 

s.d. 
1.0 
0.9 
0.9 

GBR 
n 
min 
22.5 
15.9 
15.9 
max 
28.4 
27.2 
28.4 

x 
24.9 
23.7 
24.1 

s.d. 
2.2 
2.3 
2.3 
Traits which demonstrated no significant intergender differences were subjected to analysis of linear correlation according to Pearson, in relation to the highest cranial length (CbP). The analysis distinguished 9 variables which manifested high correlation with the CbP variable (Table 3).
Variables which manifested low extent of correlation (< 0.40) were excluded from subsequent analyses. These traits involved lateral length of visceral cranium (ZlP), alveolar length of molar tooth row (LMTr) and mandibular bicanine breadth (BC).
Table 3. Analysis of linear correlation according to Pearson between metric traits of the skull 

CbP 
EctP 
0.71 
ZlP 
0.21 
StP 
0.84 
GBP 
0.79 
BB 
0.91 
LPTr 
0.79 
LMTr 
0.34 
LTr 
0.74 
HM1 
0.74 
BC 
0.37 
BMTr 
0.51 
GBR 
0.40 
Correlation coefficients at the significance level of p≤0.05 N=25 

Allometry
The model of Huxley [11] is the one of the most useful
methods to study the allometry phenomenon. The subsequent stage involved
analysis of allometric regression. For the analysis, the variables highly
correlated with the maximum cranial length (CbP) variable were used. In the
studies the maximum cranial length of CbP was used as the independent
variable.
Coefficient b value of 1 points to isometric growth of analysed parameters, value of b higher than 1 points to positive allometry while the values below 1 are typical for negative allometry. Individual values for the consecutive traits are listed in Table 4.
Most of the features directly related to the visceral cranium demonstrated the negative allometry. These features involved the maximum width of mandible (GBR), the maximum width of molar socket (BMTr), facial length (EctP), alveolar length of tooth row (LTr), alveolar length of premolar tooth row (LPTr) and the greatest breadth of the palatine (GBP).
Table 4. Values of growth coefficient b and the resulting types of allometry demonstrated for selected craniometric traits (dependent variables) in relation to maximum cranial length CbP (the independent variable) 
Dependent variable 
Value of coefficient a 
Value of coefficient b 
Type of allometry 
GBR 
2.72 
0.52 
negative 
BMTr 
0.14 
0.76 
negative 
EctP 
0.42 
0.94 
negative 
LTr 
0.94 
0.70 
negative 
LPTr 
1.69 
0.52 
negative 
GBP 
0.87 
0.77 
negative 
StP 
0.41 
1.02 
isometry 
HM1 
0.05 
1.21 
positive 
BB 
0.08 
1.22 
positive 
Positive allometry was found in two features, including the maximum height of mandible body (HM1) and distance between canine sockets in maxilla (BB). Isometric growth occurred only in the length of visceral cranium base (StP). Simultaneously, the neurocranium underwent intense extension.
DISCUSSION
The studies revealed that most of cranial parameters demonstrate larger values in males than females. The male skull of Mustela lutreola is characterised by a relatively high neurocranium, widely arranged zygomatic arches, a wide rostrum, and by wider auditory bullae and higher mandibles [1].
Masticatory muscles in carnivores manifest extremely vast development. In such animals the mandibulotemporal joint moves mainly upward and downward, acting like scissors [7]. Radinsky [16,17] suggested that Mustelidae may manifest the strongest occlusion among all carnivores as they manifest relatively vast temporal muscles, strong maxilla and mandible.
Studies of Radinsky [16,17] and Greaves [8,9] revealed a general model for carnivorous mammals, which possess carnassial teeth. One of the arguments involved the fact, that the most pronounced shearing force developes at the carnassial tooth level, when the muscular resultant force acts onethird of the way along the mandible and the carnassial teeth are situated halfway along the jaw.
The animals prey on small mammals (muskrats, hares, shrews) as well as on frogs, invertebrates and, equally frequently, on fishes and aquatic birds. Minks consume also eggs of birds [3,4].
This has been confirmed in present studies since maximum height of mandibular body demonstrated positive allometry in relation to the total cranial length. Undoubtedly, the traits make Americal mink a deft hunter.
The trait related to the length of visceral cranium base (StP) revealed isometric growth in relation to maximum cranial length (CbP). In African wild dogs, similarly to domestic dogs, the length of mandible demonstrates an isometric growth in relation to cranial length [13].
Most of analysed traits manifested a negative allometry, which might be linked to abrupt growth of the total cranial length and of cerebral cranium in particular. This might reflect the fact that in prenatal and early postnatal periods nervous system and its surrounding structures grow much more rapidly than facial skeleton does [14].
Our studies revealed that some of the
features related to teeth and the palate show larger metric values in females
than males. Similar observations were made by Kieser and Groeneveld [13] who
studied mandibulodental allometry in the African wild dog. However, their studies
cannot fully explain this phenomenon, because this relationship has not occurred
to a comparable extent in domestic dogs. One factor which might be of relevance
is the increased dietary demand of pregnancy. It has been suggested that
relatively larger teeth in females is an evolutionary consequence of the
elevated masticatory demands placed upon them during pregnancy and lactation [10,12,21].
CONCLUSIONS
Positive allometry of the height of mandible body was
decisively linked to growing surface area of attachment for the muscles of
masticatory apparatus. Most of craniometric traits subjected to analysis of
allometric regression demonstrated a negative allometric growth. The allometric
growth was expressed in marked elongation of the entire skull, in particular in
elongation of temporal fossae, providing vast areas for attachment of temporal
muscles. The phenomenon of isometry was observed in the case of the total
length of osseous palate (StP), which was also typical of other carnivores.
The characteristic traits included also the fact that length of dental rows
manifested a negative allometry versus the CbP parameter. Moreover, dental
rows in adcaudal parts of maxilla did not reach the level of choanae (posterior
nares). In females certain traits linked to teeth and palate manifested values
slightly higher than those in males.
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Accepted for print: 25.06.2008
Hubert Jakubowski
Department of Animals Anatomy,
University of Life Sciences in Poznań, Poland
Wojska Polskiego 71C, 60625 Poznań
Marcin Komosa
Department of Animals Anatomy,
University of Life Sciences in Poznań, Poland
Wojska Polskiego 71C, 60625 Poznań, Poland
Hieronim Frąckowiak
Institute of Zoology, Department of Animal Anatomy, Poznań University of Life Sciences
ul. Wojska Polskiego 71 C
60625, Poznań
email: hierofro@up.poznan.pl
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