Biology_of_Turtles

suggesting that they do not always maintain stable equilibrium (Jayes & Alexander, 1980; Zug, 1971). The lateral sequence of limbs in this case is dominant.

The most likely reason for the existence of slow locomotor speeds in tortoises is that their muscles are remarkably slow. Slow muscles are not able to produce abruptly changing forces. In mammals, the maximum possible isometric stress of leg muscles is about 0.3 MPa, although these high values are apparently required only in very strenuous activities. During walking, tortoise leg muscles exert maximum stresses between 0.1 MPa and 0.2 MPa (Van Leeuwen & Jayes, 1981). These maximum values of turtle legs are still lower than the lowest values recorded in mammals. For tortoises, one possible advantage of having these particular muscles is the ability to maintain tension at low metabolic costs, which in turn facilitates higher energy efficiency (Alexander, 1982).

There are two parameters that illustrate the extent to which walking in tortoises is different from other tetrapods. The first is duty factor, which is the percentage of the stride duration for which the corresponding foot is on the ground. Tortoises walk with duty factor values of 0.75 or more, which are unusually high relative to duty factor values observed in mammals (Jayes & Alexander, 1980; Hildebrand, 1976). Consequently, the forces that tortoises exert while walking are not much higher than those exerted while standing. For mammals to exhibit similarly high duty factor values, they would have to maintain three feet on the ground at all times to maintain adequate equilibrium. In contrast, tortoises often walk with as many as two feet off the ground. Experiments with force platforms have shown that the gait used by tortoises is close to optimal for such slow muscles.

The second parameter is the equilibrium number, equal to

where g is the gravitational acceleration, f is the stride frequency, and h is the length of the leg (Alexander, 1993). This dimensionless parameter can be used as an index of the animal’s necessity to preserve equilibrium when walking. Assuming that 1 f is the duration of a stride, an animal

submitted to gravitational acceleration g will fall a distance g 2 f 2 . Remember that frequency is the inverse of time, and the general expression for distance as function of time (t) and any acceleration

(a) is 12 at2 . The distance that it will fall without hitting the ground will be a little less than h, the length of the leg. In mammals, the highest value of the equilibrium number observed is about 5, corresponding to a dog that is slowly walking. In tortoises, much higher values have been recorded, up to 200 for Geoemyda (Alexander, 2003).

According to Romer (1968), the peculiarities of the chelonian limb structure appear to be more related to the presence of the shell rather than to the nature of the habitat frequented by a particular turtle species. This is exceptional relative to other tetrapods (e.g., rodents), where habitat and the corresponding locomotion required in that habitat exert an important selective pressure on limb structure, either for the bones or muscles (Bou et al., 1987, 1990; Casinos, 1994; Castiella & Casinos, 1990). Moreover, Romer (1968) reported that in amphibious reptiles limb length is positively related to the active role that the limbs play as propulsive organs: smaller limbs tend to be associated with a tail that is the primary propulsive element in swimming. Again, this appears to be exceptional among tetrapods, where limb scaling is probably in accordance with geometrical similarity criteria (Alexander, 1985), except in the case of adaptive variations (Casinos et al., 1993).

In this chapter, we compare bone diameters and lengths across various families of turtles to test whether limb scaling in chelonians follows the patterns described previously for other tetrapods and whether there are differences in limb scaling between aquatic and terrestrial species—which may be related to locomotor adaptations, as previously reported in mammals.

88 Biology of Turtles

Table 4.1

List of Species and Samples Used in This Study

Table 4.1

List of Species and Samples Used in This Study (continued)

Table 4.2

Regressions of Length to Diameter for the Different Bones Studied; Confidence Interval (CI) for a and b Parameters of the Regression Line Are Given

4.4Discussion

With the exception of metapodial bones, all the regressions produced exponents significantly less than 1 (the predicted outcome of the geometrical similarity hypothesis) but not as low as 2/3 (the predicted outcome of the elastic similarity hypothesis). On the basis of these results, it appears that turtle bones have more in common with the shape of avian hind limb bones (Olmos et al., 1996) than with the long bones of normal quadrupedal mammals (Alexander et al., 1979). The relationship between chelonian locomotion and limb bone length/diameter proportions deserves attention in future research.

Based on research of limb proportions in terrestrial mammals, Raich and Casinos (1991) reported that most of the locomotor specialization took place in the autopod (metacarpals and metatarsals) rather than in the long bones. Our present results suggest a similar situation in turtles. The scaling of length to diameter of the longest metacarpal and metatarsal bones revealed a greater dispersion of values than that observed when other appendicular bones were studied, or even when both long bones of a limb together were considered. In general, it appears that chelonian families that are highly adapted to an aquatic environment have metacarpals and metatarsals that are relatively long and narrow—for example, the Trionychidae and Dermochelyidae, or only long and thin metacarpals, like the Cheloniidae. Note that these three turtle families have flippers. However, families with metacarpals and metatarsals that tend to be short or wide are more difficult to characterize. None of them have flippers, and among these families the most remarkable shape is present in the Testudinidae, the family that includes the most terrestrial turtle forms, with both extremely short metacarpals and metatarsals. When the scaling of total lengths of the forelimb to hind limb was analyzed, the pattern was very different; although the dispersion of the cluster was not great, the Testudinidae, together with two marine families (the Cheloniidae and Dermochelyidae) display rather longer fore limbs.

There remain basic questions about bone size as related to mechanical behavior. For instance, is parameter (1) an adequate index of the speed exhibited by a turtle, i.e., the lower the value, the faster the animal? Renous (1995) showed that aquatic turtle forms are able to attain moderate running speeds. Combined with low values of parameter (1), this information predicts that aquatic animals should have longer limb bones than terrestrial species. However, the data presented above reveal that limb length is mainly a function of the length of the metacarpal or metatarsal. It has been observed that aquatic turtle families have the longest autopodial bones, in accordance with the previous observation by Guibé (1970). Moreover, the Testudinidae—which are the most terrestrial chelonians— have the shortest bone lengths. Interestingly, within the Emydidae terrestrial species tended to have shorter bones whereas aquatic species tended to have longer bones, concordant with the predicted adaptation to aquatic or terrestrial environments exhibited by different species in this family. In general, we conclude that locomotor adaptation is an important factor acting on appendicular bone shape as has been observed in mammals, although the typology does not appear to be the same. Casinos (1994) showed that long bones in aquatic rodents tended to be relatively slender. This could be true for metapods also, based on the results described previously concerning the Dermochelyidae. However, this has not been observed in the ulna and tibia bones as they tend to be rather robust. One possible explanation for this difference is that while swimming, rodents propel themselves with their body and marine turtles produce thrust by beating their flippers (Alexander, 2003).

The results reported in this chapter represent a first pass on the subject. More work is needed to fully understand the role of locomotor adaptation on appendicular shape in turtles, particularly within families that include both terrestrial and aquatic forms, such as the Emydidae. The influence of other factors also deserves attention—for example, geographic variations or sexual dimorphism, whose importance has been highlighted in other types of anatomical studies (Fairbairn, 1997; Kamezaki & Matsui, 1995; Wyneken et al., 1999). Also, methods used to study other species such as birds can inform this type of research. For instance, in turtles it would be useful to study cross-sectional parameters with mechanical significance, such as the area of the cross sections,

the second moment, and the polar moment (Cubo & Casinos, 1998). Similarly, more work on bone curvature is needed, given its importance in terrestrial turtles. Although the mechanical meaning of bone curvature is currently under discussion, there is an indication that the sagittal long bone curvature in birds increases very quickly with body mass (Cubo et al., 1999). From this, it can be predicted that curvature must also increase in a similar manner with any other size parameter, such as the total length of the animal.

Acknowledgments

Funds from program BOS2000-0997 (Ministerio de Educación y Ciencia of Spain) awarded to A. Casinos made this research possible.

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