Kinematics and Efficiency of Steady Swimming in Adult Axolotls (Ambystoma Mexicanum)

Swimming is a complex biological phenomenon comprising interactions between neural stimulation, muscle function, fluid dynamics and body kinematics (Carling et al. 1994). All these factors influence each other, making animal swimming a challenging topic for scientific inquiry [for reviews, see Lighthill (1975) on hydromechanics, Videler (1993), Wardle et al. (1995) and Van Leeuwen (1995) on kinematics and muscle function, and Carling et al. (1994) on neural stimulation].

Vertebrate swimming has been studied most extensively in fishes. Less is known about swimming in other vertebrate classes. In amphibians, the only primary swimmers besides the fishes, swimming remains largely unstudied.

For undulatory swimming fishes, a number of qualitatively distinct ‘swimming modes’ have been defined (Breder, 1926). This classification is based on the number of waves present on the body during steady swimming and ranges from anguilliform (more than half a wave) to ostraciiform (only the tail blade oscillates). Many studies have investigated the kinematics of steady swimming, and specific differences have been linked to body shape, muscle stimulation pattern and the animal’s ecological niche (Wardle and Videler, 1994).

In contrast, there is a lack of basic information regarding amphibian swimming, with the exception of anuran tadpoles (Wassersug and Hoff, 1985; Wassersug, 1989). Recent work suggests that the swimming mode of anuran tadpoles differs significantly from that of fish and that it appears to be tailored to their larval development (Liu et al. 1996). The few available studies on salamanders (Caudata) suggest that they show an undulatory swimming mechanism with kinematics resembling those of anguilliform fishes (Blight, 1976; Hoff et al. 1989; Frolich and Biewener, 1992).

The present study addresses steady swimming over a range of velocities in the adult axolotl Ambystoma mexicanum, an obligate aquatic, neotenic salamander. Its larval morphology differs in many aspects from that of typically anguilliform fishes, being more similar to that of tadpoles in possessing a distinct head region, a tapering tail and limbs. Moreover, external gills are present. We analysed the basic kinematics and hydromechanical efficiency of adult axolotls over as wide a swimming speed range as possible, and a functional comparison was made between the neotenic salamander’s swimming mechanism and that of both other amphibians and fishes.

Eight adult individuals of the neotenic Mexican axolotl Ambystoma mexicanum Shaw, 1789 (Amphibia: Caudata: Ambystomatidae) were used in experiments. Their total body length (L) and mass ranged from 0.135 to 0.238 m and from 22.2 to 92.1 g, respectively (Table 1).

During experiments, the animals were placed in an aquarium consisting of two open tanks (0.50 m×0.50 m×0.40 m) connected by a closed 1 m long glass tunnel (0.15 m wide×0.10 m high). A mirror was placed at 45 ° above the tunnel to permit filming of lateral and dorsal views simultaneously. The water temperature was 20±2 °C.

The animals were video-taped at 500 frames s⁻¹ using an NAC HSV-1000 high-speed video system, lit by three 650 W halogen spotlights (Trilite). They were stimulated to enter the tunnel section of the aquarium by gently touching the tail with a blunt stick. The animals then usually swam voluntarily through the tunnel to the opposite aquarium at the speed they preferred, with the limbs and gills fully adducted. The maximal burst speed might well be much higher than the speeds recorded here. For example, in Ambystoma californiense (total body length approximately 0.05 m), burst speeds of more than 15 L s⁻¹ have been measured (Shaffer et al. 1991). For detailed analysis, we selected 28 sequences (out of approximately 600 recorded) using the following criteria: (1) a constant swimming speed (i.e. a virtually rectilinear time–displacement plot), (2) a straight swimming direction (i.e. a virtually straight path of the least-oscillating body point), (3) positioning more than one body width away from the tunnel side walls and (4) showing at least three complete swimming cycles. The 28 sequences were also chosen to cover as wide a velocity range as possible. Our analyses were based on the dorsal views of the swimming sequences only. The lateral views were used to check the animal’s vertical position in the water during the swimming sequence but yielded no further information since the animals always swam along the bottom of the tunnel, with their ventral body surface in close proximity to the tunnel floor. The position of the dorsal midline was digitised every four frames (resulting in an effective sampling frequency of 125 frames s⁻¹) using an NAC-1000 XY coordinator connected to a computer. The dorsal midline was always clearly identifiable owing to the presence of a dorsal finfold over almost the entire body and tail region. In addition, preliminary studies in our laboratory showed that the kinematic variables did not differ significantly when either the directly digitised midline or a midline calculated from the animal’s outline was used.

To obtain the desired variables from the raw data files, the following procedures were used. (1) The animal was described in each frame by 20 segments of equal length (0.05 L), delimited by 21 equally spaced points numbered from head to tail and referred to below as ‘body points’. The slope at the tail tip was then calculated, i.e. the slope between the twentieth and twenty-first body point (Cheng and Blickhan, 1994). (2) The least-oscillating body point was then determined. The path of this body point, usually body point 5 (i.e. at 0.2 L), very closely approximated a straight line in all sequences analysed and defined the swimming direction (the x-axis, estimated using a linear regression through the path of the least-oscillating body point). (3) The positions of the body points in each frame were plotted with the x-axis vertical, i.e. with the animal swimming in the positive x-direction (upwards on the plots) and with each frame shifted a known distance to the right (Fig. 1). From these normalised plots, a number of measurements were taken to obtain the following kinematic variables (technique modified from Videler and Wardle, 1978; Fig. 1): swimming speed U (m s⁻¹), wave speed V (m s⁻¹), wave frequency f (Hz), wave amplitude A (m) and wavelength λ (m). U, V, A and λ were scaled to the total body length, yielding specific speed U_sp, specific wave speed V_sp, specific amplitude A_sp and specific wavelength λ_sp. The reciprocal of λ_sp gives the number of swimming waves present on the body at any instant during steady swimming. Although the use of the Reynolds number (Re) instead of body-length-specific values would allow direct comparison of kinematic variables under similar dynamic conditions (see Table 1), we chose instead to use the latter values. Since the swimming speed obtained at a given wave frequency is proportional to the body length (see Grillner and Kashin, 1976), dividing the swimming speed by the body length to give the specific swimming speed allows direct comparison of kinematic variables between differently sized individuals. We measured the wave amplitude A of every body point; the graph representing these amplitudes as a function of the position along the body is referred to below as the amplitude profile. A is defined as the maximal lateral deflection of a particular body point (or half the distance between the two extreme lateral positions of the body point). There was a large variation in A between the different sequences, but this could not be explained by individual variation (analysis of variance on body points 1, 6, 12 and 21, and on the intercept and slope of the line connecting body points 8 and 21, as an estimate of the ‘steepness’ of the increase in amplitude down the body).

In addition to a detailed kinematic analysis of 28 swimming sequences, we also measured the swimming speed in 150 other sequences (using simple distance/time measurements) to provide a larger data set for U and U_sp.

During steady swimming in Ambystoma mexicanum, waves of increasing amplitude travel down the body (see Fig. 2). At any instant, more than half a complete wave is visible on the body. According to Breder’s (1926) terminology, the axolotl’s swimming mechanism is thus of the anguilliform type.

In 150 swimming sequences, swimming speed (U) ranged from 0.106 to 0.610 m s⁻¹ and specific swimming speeds U_sp from 0.446 to 3.404 L s⁻¹ (Fig. 3). Almost the entire speed range was covered in the 28 sequences that were selected for detailed analysis (see Tables 1, 2). At lower speeds than those we observed, axolotls do not use an undulatory swimming mechanism but instead use their limbs to crawl along the bottom.

There is a strong bias towards slower swimming speeds (Fig. 3): more than half of the observations (82 out of 150) lie in the range 0.8–1.3 L s⁻¹. The mean relative swimming speeds, as well as the minimum relative speeds and maximum relative speeds, decrease as the body length increases: animals within the observed size range prefer to swim at equal absolute, rather than relative, swimming speeds (Fig. 4). This preferred swimming speed was also reflected in the 28 sequences that were selected for the detailed analysis (see Tables 1, 2; Figs 5–7).

The main characteristics of the propulsive wave are its wavelength λ, frequency f, speed V (where V=λf) and amplitude A.

The specific wavelength λ_sp did not correlate significantly with specific swimming speed U_sp and was 0.58±0.11 L (mean ± S.D., N=28) for all individuals and swimming speeds (Fig. 5).

Wave frequency f correlated linearly with U_sp: f=1.56U_sp+1.91 (r²=0.71, P<0.001; Fig. 6). Because λ_sp did not change with U_sp, a similar correlation was also found between the specific wave speed V and the wave frequency f (not shown).

The amplitude of the propulsive wave is commonly described by the amplitude at the tail tip (Fig. 7). While this is relevant for animals, such as most fish, whose amplitude profile remains constant, for Ambystoma mexicanum we found high variability in the amplitude profile during different swimming bouts, even at similar velocities (Fig. 8). Although the absolute amplitudes varied to a large extent (for example, tail-tip amplitude varied by more than twofold), some characteristics were similar in all amplitude profiles. First, the least-oscillating point was situated at 15±6 % L (mean ± S.D. N=28). Second, the amplitude increased from this point towards the snout as a passive result of movements in the trunk and tail region due to the immobility of the head–neck connection (Duellman and Trueb, 1986). Third, the amplitude increased greatly towards the tail tip (which has the greatest amplitude in all sequences at 0.097±0.022 L, mean ± S.D., N=28).

Several different variables can be used to estimate the mechanical efficiency of swimming animals. Simple estimates are the stride length (or distance travelled during one swimming cycle) and the propeller efficiency (also known as the slip factor), which is the ratio of the swimming speed to the propulsive wave speed, U/V (Webb, 1975). A longer stride length and a higher propeller efficiency are assumed to indicate a higher mechanical swimming efficiency. In Ambystoma mexicanum, the specific stride length is 0.35±0.08 (mean ± S.D., N=28) and the propeller efficiency is 0.60±0.09 (mean ± S.D., N=28; see Table 2; Fig. 9). These values are rather, but not extremely, low when compared with those of fishes (see Discussion).

While stride length and propeller efficiency can be used for comparative purposes, hydrodynamic theories allow the estimation of the hydrodynamic propulsive efficiency or the ratio of the power resulting in propulsion to the mechanical power delivered by the animal. In the present study, we calculated the hydrodynamic efficiency μ using both Lighthill’s (1960) classical elongated-body theory (μ_EBT) and Cheng and Blickhan’s (1994) expansion of this theory to include the slope at the tail tip (μ_AEBT, see Table 2; Fig. 10). Other theories (Lighthill, 1971; Yates, 1983; Cheng et al. 1991) are less suited to the analysis of anguilliform swimming with large wave amplitudes.

Mean μ_AEBT is 0.75±0.04 (mean ± S.D., N=28), which is 6 % lower than mean μ_EBT (0.80±0.05; mean ± S.D., N=28). The influence of the slope at the tail tip thus cannot be neglected in Ambystoma mexicanum, and we consider the adapted elongated-body theory to be the most appropriate for assessing the axolotl’s swimming efficiency (see Discussion for details). We found some variation in swimming efficiency between different swimming bouts (Table 2; Fig. 10), but this could not be explained by an individual effect (tested using ANOVA) and was not related to specific swimming velocity (see Fig. 10).

The present study has shown that the adult axolotl is an anguilliform swimmer, as defined for fish by Breder (1926) and characterised by the occurrence of more than half a wave on the body at any time during steady swimming. The adult axolotl differs in several morphological characteristics from anguilliform fish such as the eel (Grillner and Kashin, 1976) and the lamprey (Williams et al. 1989). The most striking differences are the presence of limbs, which are used for crawling at low speeds (<0.5 L s⁻¹), and the large feather-like external gills. The limbs and the gills are folded against the body during swimming, probably under active control (Hoff et al. 1989). The effect of adducted limbs on swimming kinematics and efficiency is likely to be small. Liu et al. (1996) have found that, in tadpoles before metamorphosis, the hindlimbs impose very little handicap on propulsion.

The kinematic variables determined here for swimming axolotls can be compared quantitatively with those of fishes measured in previous studies. Videler (1993) pooled kinematic data from a variety of fish species and found that, in general, U=0.71f (r²=0.93; N=45). In Ambystoma mexicanum, we found that U_sp≈0.64f−1.91, indicating that the axolotl needs a markedly higher tailbeat frequency than do fishes in order to attain a particular swimming speed. The mean specific tail-tip amplitude determined here for Ambystoma mexicanum (0.097±0.022 L) agrees very well with Videler’s (1993) general finding for fishes of 0.10L. However, axolotl and fish swimming kinematics differ in the distribution of the wave amplitude along the body.

While most kinematic parameters relate significantly to the specific swimming speed, the observed amplitudes clearly do not and, more puzzlingly, show a wide variability throughout the speed range investigated (Fig. 7). For example, we observed a more than twofold difference in tail-tip amplitude between two swimming bouts by the same animal at swimming speeds and frequencies that differed by only 0.7 % and 9.3 %, respectively. This unexpected and puzzling result can probably only be explained by the cumulative effects of several factors. First, small variations in swimming speed may have occurred, and these can have a marked effect on amplitude (Webb, 1975). Second, the noise in our amplitude data may account for some of the observed variability. Third, it is possible that increased drag due to subtle changes in gill or limb posture leads to an increased amplitude requirement in order to keep the swimming speed constant. However, we did not observe such changes during qualitative inspection of the high-speed video recordings.

We believe that the three explanations given above are likely to explain only part of the amplitude variability, and we therefore propose an alternative, additional hypothesis. In most studies, the amplitude profile along the body is considered to be constant, and therefore a description of the propulsive wave amplitude consists only of the amplitude at the tail tip. This is justifiable for most fish, in which the amplitude profile does not change drastically. However, it is clear from the present results that the axolotl has a highly variable amplitude profile and, therefore, that it is not sufficient to consider the tail-tip amplitude alone: one has to consider the entire amplitude profile. Indeed, for an anguilliform swimmer delivering thrust along almost the entire body length (Wardle and Videler, 1994; D’Août et al. 1996), this makes good sense. The same amount of propulsion, needed to counterbalance the drag (a prerequisite for steady swimming), can then be delivered in different ways, using different amplitude profiles with different tail-tip amplitudes.

It is unlikely that different amplitude profiles have equal efficiency, and one would expect evolution towards one optimal solution. So why has this not occurred in Ambystoma mexicanum? Ambystomatid salamanders live in the dense vegetation of shallow lakes (Smith and Smith, 1971; Scott, 1981). In such an environment, the ability to manoeuvre and to perform short strikes is important. These highly unsteady locomotor patterns impose totally different requirements on the locomotor system from those of steady swimming. It is likely then that adaptation towards an efficient steady swimming mechanism is not favoured in this environment.

This hypothesis is further supported by the relatively low hydromechanical efficiency of steady swimming in Ambystoma mexicanum. Great care must be taken when calculating values for efficiencies. The classical parameters, propeller efficiency (slip) and stride length, are easy to calculate but, as they do not yield the true efficiency, they can only be used to compare the swimming efficiency of animals using a similar swimming style. Their use is based on the assumption that the lower the slip and the higher the distance travelled per cycle, the higher the mechanical swimming efficiency will be. Hydrodynamic theories, in contrast, aim to provide values of the true hydrodynamic efficiency (the ratio of energy resulting in propulsion to mechanical energy delivered by the animal), but one must be aware that the available theories each have specific drawbacks. The widely used elongated-body theory (Lighthill, 1960) is the most appealing because of its simplicity, the efficiency μ_EBT being given by μ_EBT=(1+U/V)/2. However, its use is confined to small-amplitude motions, a point addressed by Lighthill’s (1971) large-amplitude elongated-body theory. While the latter theory has proved very useful for carangiform swimmers with a distinct trailing edge, for which the theory was developed, it is of questionable use for anguilliform swimmers with a tapering tail and has therefore not been used here. Both theories are based on a balance between (1) the moments imparted to the water by the animal and shed in the post trailing-edge wake and (2) the propulsion. Since anguilliform swimmers are thought to deliver propulsion along most of the body length (D’Août et al. 1996; Wardle and Videler, 1993; Wardle et al. 1995), the more recent three-dimensional waving plate theory (Cheng et al. 1991) seems more attractive for the study of anguilliforms because it is based on the vortex ring around the body (represented by a sequence of articulating plates of different heights). However, this theory requires more complex input from the experiments and is much more elaborate to calculate, which might be the reason why Lighthill’s (1960, 1971) theories remain standard in most studies. Moreover, a recent computational fluid-dynamic approach to tadpole swimming (Liu et al. 1996) yielded very similar efficiencies to Lighthill’s (1960) elongated body theory.

Cheng and Blickhan (1994) adapted Lighthill’s (1960) elongated-body theory to remove the assumption of zero slope at the tail tip. Indeed, in the axolotl (and also in most fish), the tail tip does not move parallel to the sagittal plane during most of the swimming cycle, but has a certain slope (see Fig. 2). This slope will result in a decreased efficiency relative to that calculated according to the elongated-body theory.

Cheng and Blickhan’s (1994) results demonstrate that the adapted elongated-body theory approaches the results from the three-dimensional waving plate theory and remains simple to apply. We consider this theory the most appropriate for estimating the axolotl’s hydromechanic swimming efficiency. Only Cheng and Blickhan (1994) have used the adapted elongated-body theory to date, and the axolotl’s efficiency can therefore best be compared with that of other swimmers using published values for propeller efficiency and stride length and using elongated-body theory.

Hoff et al. (1989), using small Ambystoma larvae, reported much higher relative swimming speeds than those in the present study, which agrees with our observation in adult axolotls that the smaller the individual, the higher the specific swimming speed. The larvae swam with a propeller efficiency of 0.65 at swimming speeds greater than 6 L s⁻¹. At lower velocities, the propeller efficiency was slightly lower, making our results (mean propeller efficiency 0.60) consistent with their findings. Anuran tadpoles (of Bufo, Rana and Xenopus) perform markedly better, with propeller efficiencies of 0.68–0.72 (Wassersug and Hoff, 1985; Hoff and Wassersug, 1986). Much better propeller efficiencies are achieved by several fishes, e.g. 0.8 for Salmo (Webb, 1975). A similar pattern emerges for the stride length data. Larval Ambystoma have a stride length of 0.5 L (Hoff et al. 1989), Bufo and Rana tadpoles 0.6 L (Wassersug and Hoff, 1985; Hoff and Wassersug, 1986) and subcarangiform fishes 0.7 L (Bainbridge, 1958). Our result for Ambystoma mexicanum, 0.35 L, is markedly lower. The knifefish, Notopterus notopterus, has an even shorter stride length of 0.3 L (Blake, 1983).

Wassersug and Hoff (1985) calculated the swimming efficiency of anuran tadpoles to be 0.83, slightly higher than that found here for Ambystoma mexicanum (0.80). They also found that efficiency tended to be lower at lower swimming speeds. Liu et al. (1996) calculated the hydrodynamic efficiency of anuran tadpoles using a computational fluid-dynamic (CFD) approach and found an efficiency of 0.82, in very close agreement with the elongated-body theory values for these tadpoles (0.83). Fishes and some mammals swim much more efficiently and elongated-body theory efficiencies greater than 0.9 are not uncommon.

The kinematics and the estimates of mechanical swimming efficiency reported in the present study show that Ambystoma mexicanum uses an anguilliform swimming mechanism with a highly variable wave amplitude profile and with a low efficiency. This is consistent with their ecological niche and the likely constraints imposed by this environment.

We thank Dr Frits De Vree for his expertise and support during the research in his laboratory, and Dr R. Van Damme and two anonymous reviewers for their input and constructive comments on an earlier version of the manuscript. This research was supported by grant 943012 from the Flemish Institute for the Encouragement of Scientific Research in Science and Technology (I.W.T.) to K.D. P.A. is a research associate from the Fund for Scientific Research – Flanders (F.W.O.).