Geometry and evolutionary parallelism in the long bones of cavioid rodents and small artiodactyls O ROCHA-BARBOSA1 and A CASINOS2,* 1
Laboratório de Zoologia de Vertebrados (Tetrapoda) (LAZOVERTE), DZ, IBRAG, Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier, 524 – Maracanã –CEP: 20550-013 –Rio de Janeiro, RJ, Brazil 2 Departament de Biologia Animal (Vertebrats), Universitat de Barcelona, Diagonal, 645( 08028 Barcelona, Spain *Corresponding author (Email,
[email protected])
Morphological parallelism between South American cavioid rodents and small artiodactyls from the Old World has been postulated for a long time. Our study deals with this question from the point of view of biomechanical characteristics of the long bones. For this, cross-sectional area, second moment of the area, polar moment, athletic ability indicators and strength were calculated for the long bones (i.e. humerus, radius, femur and tibia) of five species of cavioids and two species of artiodactyls. Regressions of all these variables to body mass were established. Regarding the cross-sectional area, the confidence intervals show that the exponents calculated are not significantly different from the geometrical predicted value. The exponents obtained for the second moment of area and the polar moment are not significantly different from the geometrical prediction, except for the humerus. The two indicators of athletic ability scaled as expected, but the bending indicator of athletic ability of the femur was not correlated to body mass. The exponent calculated for femur strength is not different from zero, while the strength of the humerus decreases slightly with the body mass. Additional statistical tests (ANCOVAs) showed no difference between the values of these variables calculated for the samples studied of artiodactyls and rodents. The present results are consistent with the hypothesis that there is significant evolutionary parallelism between cavioid rodents and small artiodactyls. [Rocha-Barbosa O and Casinos A 2011 Geometry and evolutionary parallelism in the long bones of cavioid rodents and small artiodactyls. J. Biosci. 36 887–895] DOI 10.1007/s12038-011-9157-3
1.
Introduction
Species that are distantly related sometimes share similarities that do not reflect a common ancestry. These homoplastic characters are well documented and become a central concept in evolutionary biology when adaptation is studied (Gatesy et al. 2003; Wilcox et al. 2004; Harmon et al. 2005). Whether parallelism or convergence (see Wiley 1981 for the two possible kinds of homoplasy) is taken into consideration, it provides interesting insights in studies of ecological morphology (Savitsky 1983; Hibbitts and Fitzgerald 2005), constraints (Emerson and Koehl 1990; Herrel et al. 2004), palaeobiology (McGhee and McKinney 2000), adaptation (Larson and Losos 1996) and even evolutionary processes, such as adaptive radiation (Schluter 2000) and Keywords.
character displacement (Knouft 2003). Studying parallelism or convergence of shape for a particular function can improve our understanding of the causes and mechanisms that underlie morphological evolution. Parallelism of the traits of species occupying similar environments is generally considered to be evidence of adaptation (McLennan and Brooks 1993; Pagel 1994; Larson and Losos 1996; Schluter 1988, 2000). Most examples focus on adaptation of a limited set of traits to particular aspects of the environment, such as tooth morphometry (Ben-Moshe et al. 2001), head morphology (Hibbitts and Fitzgerald 2005) and limb length (McCracken et al. 1999). In general, parallelisms are recognized by striking visual resemblances (Begon et al. 1990). A conspicuous case of apparent parallelism is represented by two
Adaptation; artiodactyls; cavioids; long bones; mechanics; scaling; skeletal geometry
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J. Biosci. 36(5), December 2011, 887–895, * Indian Academy of Sciences
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mammalian ecological guilds, namely the South American cavioid rodents and the small Old World artiodactyls (Dubost 1968). Rodents and artiodactyls have a very old common ancestor around 88–110 Mya, prior to the K-T boundary, and constitute the clade Boreoeutheria, which is a sister group to the Xenarthra (Murphy et al. 2001; Eizirik et al. 2001; Archibald 2003). Molecular data for basal divergences within Boreoeutheria (79–88 Mya) suggest a gap during the Late Cretaceous, during which this clade dispersed and separated from the Laurasiatheria clade, which includes the Cetartiodactyla, and the Euarchontoglires clade, which includes the Rodentia (Murphy et al. 2001). Even though the evolutionary history of the cavioid rodents and Old World small artiodactyls followed different paths, Asiatic mouse-deer (Tragulidae) physically resemble other small forest-dwelling herbivorous mammals, such as the South American agouti (Dasyproctidae, Rodentia) and African duikers (Cephalophinae) in having forward-sloping shoulders and powerful hind quarters (Dubost 1968; Bourlière 1973; Nowak 1991; Rocha-Barbosa 1997). The cavioid rodents resemble the artiodactyls also in other characteristics (Gambaryan 1974; Casinos et al. 1996; Rocha-Barbosa 1997; Rocha-Barbosa et al. 2002, 2005, 2007; Weisbecker and Schmid 2006), such as the reduction of the clavicle (Rocha-Barbosa et al. 2002), and of the distal muscles of the fore and hind feet, the development of the autopodial skeleton and some locomotor characteristics (Rocha-Barbosa et al. 1996a, b). In addition, the cavioid rodents and small artiodactyls share similar environments in the rainforests of South America, Asia and Africa, respectively (Nowak 1991). As a consequence, we propose that similar selection pressure is working on the morphology, resulting in similar adaptations. The aim of this study was to analyse the morphological parallelisms at the fore and hind limbs of cavioid rodents and some small artiodactyls based on the biomechanical aspects of limb structures. Because of scaling issues due to varying sizes of the compared taxa, significant differences could exist between these two groups, despite their overall similarities. In general, the scaling of limbs in mammals fits the predictions of geometrical similarity (Alexander 1983), but ungulates are an exception to this rule. McMahon (1975) presented ungulates as an example of elastic similarity, i.e. as a case in which the diameter of a structure scales faster than predicted based on geometrical similarity, while the length scales more slowly than predicted. Economos (1983) suggested that the special case of ungulates was a matter of size, because mammals that are heavier than 20 kg would scale close to the predictions of elastic similarity, while mammals lighter than 20 kg would scale according to geometrical J. Biosci. 36(5), December 2011
predictions, irrespective of the taxonomic affiliation of the ungulates. At first view, there are no obvious reasons to think that the limbs of rodents would scale differently from the limbs of most mammals. However, considering the locomotor variability of rodents, it is difficult to calculate an allometric constant that is valid for the entire group. Different locomotor modes could have acted as selective pressures to generate particular proportions between the diameter and length of limb bones [see Bou et al. (1987) for a synthesis about long limb bone scaling in rodents]. The fact that the artiodactyls studied here are lighter than 20 kg and thus similar in size to the cavioid rodents, permits us to test the hypothesis of Economos (1983). If this hypothesis is correct, the different variables measured in this study on limb bones of cavioid rodents and small artiodactyls should scale similarly to body mass, according to the predictions of the geometric similarity. Two animals are geometrically similar if, when multiplying the linear dimensions of one animal by a constant factor, the linear dimensions of the other are obtained. Therefore, the cube of a linear dimension will be proportional to the volume, or to the body mass (Mb), for a constant density. Inversely, 1=3
l / Mb
ð1Þ
2 1=3 2=3 A / l2 / Mb / Mb
ð2Þ
where l is a linear dimension and A a surface area. According to the elastic similarity hypothesis (McMahon 1975), not all the linear dimensions scale to body mass in the same proportion. Lengths scale with body mass to 1/4 and diameters to body mass to 3/8 (McMahon 1975). Therefore,
2 3=8 A / d 2 / Mb / Mb0:75 2.
ð3Þ
Materials and methods
The long limb bones (i.e., humerus, radius, femur, and tibia) of five species of cavioid rodents [i.e. the domesticated Guinea Pig, Cavia porcellus (Linnaeus, 1758; Caviidae); the Lowland Paca, Cuniculus paca (Linnaeus, 1766; Cuniculidae); the Red Acouchi, Myoprocta acouchy (Erxleben, 1777; Dasyproctidae); the Red-rumped Agouti, Dasyprocta leporina (Linnaeus, 1758; Dasyproctidae); the Capybara, Hydrochoeris hydrochaeris (Linnaeus, 1766; Caviidae)] and two species of Artiodactyla [i.e. the Java Mouse-Deer, Tragulus javanicus (Osbeck, 1765; Tragulidae) and
Adaptation in cavioid rodents and small artiodactyls Maxwell’s Duiker, Philantomba maxwelli (C.H. Smith, 1827; Bovidae)] were measured [see Wilson and Reeder (2005) for taxonomy used, and table 1 for the number of specimens studied]. All specimens were from the vertebrate osteological collections of the Muséum National d’Histoire Naturelle of Paris (see table 1 for catalogue numbers). Moreover, some values referring to Hydrochoeris hydrochaeris were taken from Casinos et al. (1996). The only measurement taken directly on the actual bones was the total length (i.e. the length between the distal and proximal joint surfaces). The diameters of the limb bones were measured by sectioning the limb bones at midshaft. A Hitachi KP-C550 video camera, coupled to an optical stereomicroscope Olympus SZ-CTV, was used to record the cross-sectional images. Cross sections from larger animals were scanned on a Scanner EPSON GT-8000. The images were analysed by the IMAT software [‘Serveis Científico-Tècnics’, University of Barcelona; see Cubo and Casinos (1998) for details]. The following variables were measured from the images: (1) sagittal and transverse diameters; (2) cross-sectional area; (3) sagittal maximum second moment of area (i.e., second moment of inertia) and (4) polar moment of inertia to supplement the maximum and minimum second moment of the area (see below). The strength of a material (σ) is expressed by the following formula:
s¼
M y I
ð4Þ
where M is the bending moment at breaking, y the distance to the neutral axis, and I the second moment of
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area (Alexander 1983; Wainwright et al. 1976). For a constant σ
M/
I y
ð5Þ
The quotient I/y is known as the section modulus. Therefore, the strength of a bone equals the bending moment at breaking divided by the section modulus (Alexander 1983). On the other hand, the twisting strength (τ) is
t¼
M r J
ð6Þ
where M is the breaking moment, r is the radius of the section (calculated as quoted above) and J is the polar moment of inertia. The polar moment of inertia is defined as
J ¼ Ix þ Iy
ð7Þ
where Ix and Iy are the maximum and minimum second moment of area, respectively (Young 1989). Both were calculated on the cross-section area, as quoted above. The significance of the second moment of area and polar moment of inertia in a strength analysis is based on beam theory (Young 1989). The breaking moment (M) in bending was calculated for each bone using the allometric equations obtained by Bou et al. (1991) for a large sample of mammals (i.e. insectivores and rodents). The structural strengths (σ) of the humerus and the femur were calculated by substituting in equation (4) values from M (bending breaking moment), y (distance to the neutral axis) and I (second moment of
Table 1. Species, individuals, with catalog numbers, and number of long bones used Species Cavia porcellus Rodentia, Caviidae Myoprocta acouchy Rodentia, Dasyproctidae Cuniculus paca Rodentia, Cuniculidae Dasyprocta leporina Rodentia, Dasyproctidae Hydrochoeris hydrochaeris Rodentia, Caviidae Tragulus javanicus Artiodactyla, Tragulidae Philantomba maxwelli Artiodactyla, Bovidae
Collection number
Humerus
Radius
Femur
Tibia
1870-510; 1924–36; wi (female)
3
1
3
3
1924-357; 1890-44
1
2
1
1
1871-95; 1905–169; 1923-1024
3
2
3
3
1887-437; 1976–130; 1913-404
3
3
3
3
1929-492; wi (2 males)
3
2
3
2
A-3370; 1871–333; A-3383 GAC; wi
3
3
4
4
1930-266
1
1
1
1
wi = without identification. J. Biosci. 36(5), December 2011
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O Rocha-Barbosa and A Casinos area). Separate equations for the radius and tibia were not provided by Bou et al. (1991). The indicators of athletic ability were also calculated based on the following assumptions. Let us suppose an animal with a body mass of m and a bone whose cross-sectional area at midshaft is A. Therefore, its body weight would be mg, with g being the gravitational acceleration. Normally in a mammal, the body weight is not distributed uniformly on the fore and hind feet. For example, in most non-primates, 60% of the weight is supported by the forefeet and 40% by the hind feet (e.g. Jayes and Alexander 1978). We call a the fraction of the body weight that is supported by one foot (30% by one fore foot and 20% by one hind foot). Therefore, the axial force by surface area or axial loading (AL in figure 1), on the cross section of a long bone of a limb will be
ð8Þ
amg=A
Figure 1. Forces acting on a mammalian femur during locomotion and measurements taken on the bone. Abbreviations: AL, axial loading; BL, bending loading; l, total length of the femur; TL, twisting loading; x, distance between the point where the femur was sectioned to measure the cross-sectional area and the distal end.
As mentioned above, A was calculated from the scanned images. We are now ready to consider the bending loading that acts at a right angle on a bone (BL in figure 1). This bending force originates from the fraction of the body weight acting on the bone. It can be significant because appendicular bones are relatively long and thin. The corresponding bending moment will be a×m×g×x, with x being the distance from the point, where the cross section is measured, to the joint. If Z is the section modulus, which is calculated from the cross section area [see equation (5)], the bending stress generated will be:
ð9Þ
amgx=Z
Table 2. Global allometric equations for the species of cavioid rodents and small artiodactyls studied for the cross-sectional area (A), polar moment of inertia (J), and maximum sagittal second moment of the area (Is) to body mass Bone Humerus
Radius
Femur
Tibia
A J Is A J Is A J Is A J Is
Equation
C.I. a 95%
Y=6.833×(X0.754) Y=19.519×(X1.558) Y=11.910×(X1.611) Y=4.145×(X0.732) Y=6.046×(X1.431) Y=4.333×(X1.387) Y=11.841×(X0.665) Y=70.980×(X1.298) Y=46.538×(X1.263) Y=10.186×(X0.670) Y=38.026×(X1.419) Y=23.828×(X1.432)
(5.561.) – (8.397) (13.590) – (28.033) (7.947) – (17.848) (3.489) – (4.925) (4.334) – (8.434) (3.200) – (5.867) (8.979) – (15.617) (43.812) – (114.995) (27.830) – (77.822) (7.383) – (14.054) (20.459) – (70.675) (11.665) – (48.676)
C.I. b 95%
R
N
– – – – – – – – – – – –
0.965 0.978 0.974 0.981 0.982 0.984 0.921 0.937 0.926 0.902 0.916 0.895
16 15 15 13 13 13 16 16 16 16 16 16
(0.636) (1.356) (1.386) (0.637) (1.249) (1.221) (0.497) (1.022) (0.969) (0.486) (1.065) (1.024)
(0.872) (1.759) (1.836) (0.826) (1.614) (1.553) (0.814) (1.574) (1.557) (0.854) (1.774) (1.841)
The equations correspond to the calculations carried out with all the values. 95% confidence intervals (C.I.) for the y-intercept (a) and the exponent (b) of the equations are given. Other abbreviations: N, sample size; R, correlation coefficient of the equations. J. Biosci. 36(5), December 2011
Adaptation in cavioid rodents and small artiodactyls
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Table 3. Global allometric equations for the species of cavioid rodents and small artiodactyls studied for the axial athletic ability indicator (A/amg) and bending athletic ability indicator (Z/amg) to body mass calculated for the humerus, femur and tibia Bone Humerus Femur Tibia
A/amg Z/amgx A/amg Z/amgx A/amg Z/amgx
Equation
C.I. a 95%
Y=3.528×(X–0.250) Y=116.079×(X–0.322) Y=4.049×(X–0.347) Y=229.141×(X–0.419) Y=3.468×(X–0.329) Y=83.367×(X–0.343)
(2.826) – (4.403) (86.906) – (155.043) (3.073) – (5.336) (136.379) – (384.997) (2.519) – (4.773) (48.737) – (142.601)
C.I. b 95%
R
N
– – – – – –
0.771 0.812 0.783 0.704 0.718 0.693
15 10 16 11 16 07
(−0.373) (−0.510) (−0.505) (−0.738) (−0.512) (−0.754)
(−0.126) (− 0.133) (−0.189) (−0.100) (−0.147) (−0.068)
As referred to in the text, values of the radius were not available. Abbreviations: C.I., 95% confidence intervals for the y-intercept (a) and the exponent of the equations (b); N, sample size; R, correlation coefficient of the equations.
The inverse of equations (6) and (7), namely A/a×m×g and Z/a×m×g×x, are called the indicators of athletic ability (Alexander 1989) and are proportional to axial and bending stresses, respectively [see Casinos (1996) and Casinos et al. (1996) for two examples of the use of these indicators]. In this study, these indicators were only calculated for the humerus, femur and tibia, because measurements of the radius were not available. Global regressions against the body mass of the second moment of area, polar moment of inertia, strength, and the two athletic ability indicators were calculated for all the species studied by assuming the power expression (Huxley 1932):
y ¼ a xb
ð10Þ
where the body mass is always the independent variable (x). Since the body masses of the studied specimens were unknown (except for Cavia porcellus), we used the equation proposed by Alexander et al. (1979), which estimates the body mass (Mb) from the sagittal diameter of the femur:
Mb ¼ ðFemur sagittal diameter=5:2Þ1=0:36
Allometric equations were obtained by Model I (least squares method). According to Ricker (1973), this method is the most appropriate one when measurements of the dependent variable are not taken directly. Moreover, this is the model of regression used in previous studies of the same variables, and its use enabled us to make comparisons with the results obtained in those studies (see, for example, Cubo and Casinos 1998). The scaling equations were calculated first by considering all values separately and then also by using only the means of each variable for each species, since the sample sizes varied. No statistical difference was observed between the exponents calculated with either method. Therefore, the equations shown in the tables are those that correspond to the calculations with all the values. Finally, allometric equations regressing each variable to body mass in cavioid rodents and small artiodactyls were compared by ANCOVA. 3.
ð11Þ
The results obtained from equation (11) were checked against those in Silva and Downing (1995). For most of the species studied, the calculated values were within the range of body masses given in Silva and Downing (1995), except for D. leporina and M. acouchy. In these two species, we substituted the calculated values of body mass by the means of the ranges given by Silva and Downing (1995), namely 2.5 kg and 0.6 kg, respectively.
Results
Table 2 shows the scaling of the cross-sectional area, polar moment of inertia, and sagittal maximum second moment of area to the body mass. For the cross-sectional area, the confidence intervals of the exponents calculated always correspond to 0.66. Moreover, in the four bones studied, the confidence intervals also correspond to 0.75, which is to the elastic similarity prediction
Table 4. Global allometric equations for the species of cavioid rodents and small artiodactyls studied for the scaling of the strength (σ) to body mass for the humerus and femur Bone Humerus Femur
σ σ
Equation
C.I. a 95%
C.I. b 95%
Y=347.550×(X–0.224) Y=134.583×(X0.103)
(292.389) – (413.119) (101.393) – (178.637)
(−0.321) – (−0.128) (−0.059) – (0.264)
R
N
0.814 0.340
15 16
As quoted in the text, it was not possible to calculated strengths corresponding to radius and tibia. Abbreviations: C.I., 95 % confidence interval for the y-intercept (a) and the exponent (b) of the equations; N, sample size; R, correlation coefficient of the equations. J. Biosci. 36(5), December 2011
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O Rocha-Barbosa and A Casinos
This is the same to say that both the second moment of area and the polar moment of inertia must scale to body mass with an exponent of 1.33, if the cross-sectional area scales (according to equation (12)) with an exponent equal to 0.66 [see also Cubo and Casinos (1998)]. Exponents obtained for the radius, femur and tibia, irrespective of the second moment of area or the polar moment of inertia, are not significantly different from 1.33, whereas the confidence intervals for the humerus show that both moments scale faster than predicted. All the exponents are either not
significantly different from the value predicted for elastically similar animals (i.e. 1.50) (Cubo and Casinos 1998). Although predictions of elastic similarity are not statistically excluded, the important thing is that the high correlation coefficients obtained for the different equations show that both values from cavioid rodents and artiodactyls studied scale to body mass with a similar pattern. The use of ANCOVAs (see below) confirms this result. The regression equations to body mass calculated for the two indicators of athletic ability, A/amg and Z/amgx, are shown in table 3. The prediction for geometrically similar animals is an exponent not different from −0.33 (Alexander 1989). The bending indicator of athletic ability of the femur is not correlated with body mass. In all the other cases the confidence intervals show that all the exponents obtained fitted statistically the prediction. The expectation of the scaling of the structural strength (σ) to body mass, according to the results obtained by Biewener (1989), is a slope not different from 0. The confidence interval calculated for femur strength is not different from 0, while in the case of the humerus, the strength decreases slightly with body mass (table 4). Therefore, it seems that both for the cavioid rodents and artiodactyls studied, humerus strength is depending on body mass, while femur strength is not.
Figure 2. Plot of the axial athletic ability indicator (A/amg) to body mass for the humerus of the cavioid and small artiodactyl species studied. The plot shows a similar distribution of values for both groups. Abbreviations: A, Agouti paca; C, Cavia porcellus; D, Dasyprocta leporina ; H, Hydrochoeris hydrochaeris; M, Myoprocta acouchy; T,Tragulus javanicus; P, Philantomba maxwelli; Mb, body mass.
Figure 3. Plot of the bending athletic ability indicator (Z/amg) to body mass (Mb) for the femur of the cavioid and small artiodactyl species studied. The plot shows a similar distribution of values for both groups. Abbreviations: A, Agouti paca; C, Cavia porcellus; D, Dasyprocta leporina; H, Hydrochoeris hydrochaeris; M, Myoprocta acouchy; T, Tragulus javanicus; P, Philantomba maxwelli; Mb, body mass.
According to the equations (4) and (5), and assuming that for a given material σ and τ can be considered as constants,
I /M y
ð12Þ
J /M r
ð13Þ
and
Since y and r are linear dimensions proportional to Mb1/3 and since any breaking moment (M) must be proportional to l3 or Mb (Bou et al. 1991), from equations (12) and (13), we have 1=3
I; J / Mb Mb
4=3
/ Mb
J. Biosci. 36(5), December 2011
ð14Þ
Adaptation in cavioid rodents and small artiodactyls The distribution of the values of the axial strength indicator of the artiodactyls Tragulus javanicus (T) and Philantomba maxwelli (P) (figure 2) is similar to that of the cavioid rodents of similar body size. The distribution of the values of the femur bending strength indicator of the artiodactyls Tragulus javanicus (T) and Philantomba maxwelli (P) is slightly below the regression line (figure 3), but it does not seem very different from that of the cavioid rodents of similar body size. The points corresponding to the humerus strength indicator of the artiodactyls Tragulus javanicus (T) and Philantomba maxwelli (P) are distributed on both sides of the regression line (figure 4), even though most points are above the line. Overall, the scatter plots of figures 2, 3 and 4 show a similar distribution for both values of cavioid rodents and artiodactyls. Considering the results obtained with ANCOVAs to compare the cavioid rodents and the studied artiodactyls, there is no evidence against the null hypothesis that the slopes corresponding to the rodents and artiodactys are not different, since for all variables P>0.05 (table 5). Hence, ANCOVA results confirm the results obtained with the
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allometric equations for a uniform scaling pattern of the cavioid rodents and artiodactyls studied, irrespective of which parameter is considered 4.
Discussion
The ecological parallelism between forest-dwelling large cavioid rodents and small artiodactyls is mentioned by several authors (Bourlière 1973; Dubost 1968; RochaBarbosa 1997). The question is, at which point the corresponding selective pressures can overcome the constraints that are imposed by the morphotype of the group. For the same body size, the morphotype of rodents is very different from that of ungulates, such as antelopes (Casinos et al. 1996). Regarding the strength indicators, the largest extant rodent, the Capybara, is not very athletic for its size (Casinos et al. 1996) in comparison to three other species of mammals (e.g. buffalo, elephant and rhinoceros), according to the results of Alexander et al. (1979) and Alexander and Pond (1992). The corresponding correlation coefficients of the different regressions referring to second moments of area and Table 5. Results of the ANCOVAs comparing separate regressions of each variable to body mass for the caviod rodents and small artiodactyls studied
Figure 4. Plot of the strength (σ) of the humerus to body mass of the cavioid and small artiodactyl species studied. For the humerus, the strength is correlated to body mass. The regression line shows that the strength slightly decreases with the body mass as indicated by the exponent of the corresponding equation (see table 4). The values appear similar for the cavioid rodents and small artiodactyls studied. Abbreviations: A, Agouti paca; C, Cavia porcellus; D, Dasyprocta leporina; H, Hydrochoeris hydrochaeris; M, Myoprocta acouchy; T, Tragulus javanicus; P, Philantomba maxwelli; Mb, body mass.
Variables
P
σ-F σ-H A/amg - H A/amg - F A/amg - T Z/amgx -H Z/amgx -F Z/amgx -T A-H A-R A-F A-T J-H J-R J-F J-T I-H I-R I-F I-T
0.007 0.24 0.92 0.39 0.98 0.92 0.12 0.17 0.62 0.93 0.23 0.37 0.47 0.71 0.21 0.29 0.45 0.72 0.18 0.24
Abbreviations and terms: A, cross-sectional area; A/amg, axial strength indicator; F, femur; H, humerus; I, maximum saggital second moment of area; J, polar moment of inertia; P, probability; R, radius; T, tibia; Z/amgx , bending strength indicator; σ, strength. J. Biosci. 36(5), December 2011
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O Rocha-Barbosa and A Casinos
polar moments are very high. This is not surprising since the corresponding ANCOVAs show no difference between the two samples of cavioid rodents and artiodactyls. Therefore, we can infer that the variability of the variables studied, even considering the rodents and artiodactyls together, is very restricted. The correlation coefficients corresponding to the indicators of athletic ability are lower, but they are within the range of those obtained by Fariña et al. (1997) when analysing the bending indicator of athletic ability in a sample of fossil and extant land tetrapods. Again, the results obtained with the ANCOVAs are more conclusive. They show no difference between the allometric coefficients of the cavioid rodents and the ungulates studied. Concerning the agreement of the predictions of the geometrical and elastic similarities, the results are not very clear because in several cases, the confidence intervals of the exponents included values from both predictions, but that was also the case in a more uniform sample of extant birds (Cubo and Casinos 1998). In fact, the aim of this study was not to ascertain whether animals are geometrically or elastically similar. Instead, our results show that the scaling particularities of artiodactyls, as considered by McMahon (1975), do not in fact exist. Small artiodactyls do not scale differently from rodents of similar body size. The idea of Economos (1983) is probably correct in that both predictions can be right, with small mammals fitting the geometrical prediction and large mammals fitting the elastic prediction. Since volume increases at a higher rate than the surface, loads on bone cross sections of larger animals would be proportionally higher than in small animals. Given that bone structural strength tends to be constant, as it has been shown, the only solution for avoiding greater risks of bone fracture in large animals is to scale the diameters of their long bones at higher rates than in small animals to stabilize bone stress irrespective of the body size (Alexander 1985). The statistical results obtained in this study support the hypothesis of a parallelism between cavioid rodents and small artiodactyls, at least at the level of appendicular bones. The studied geometrical or mechanical variables scale in both subsamples in a similar manner as shown both by the allometric equations and the ANCOVAs. The mechanical constraints linked to body size are strong, and at least in the case of long bones, the constraints due to morphotype do not seem to be relevant, even though the morphotype of cavioid rodents and small artiodactyls is very different Acknowledgements Prociência/UERJ Fellowship Program, Capes Process number 4123-07-7 (Pós-Doc) provided financial support CRBIO 02085. The ‘Serveis Científico-Tècnics’ (Universitat de Barcelona) made the software according to the specifications of the authors. Jorge Cubo (Paris 6 University), José J. Biosci. 36(5), December 2011
Domingo Rodríguez-Teijeiro (University of Barcelona), Eloy Gálvez López (University of Barcelona), and Mariana Fiuza de Castro Loguercio (Rio de Janeiro State UniversityUERJ) helped with technical questions and suggestions. The contribution of AC is part of the research programmes CGL2005-04402/BOS and CGL2008-00832/BOS.
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MS received 18 December 2009; accepted 29 August 2011 ePublication: 3 November 2011 Corresponding editor: DOMINIQUE G HOMBERGER
J. Biosci. 36(5), December 2011
