1. Ocypode ceratophthalma has a maximum speed of 2·1 m/sec when running on a measured track with a base of hard-packed sand. Speed increases linearly with the width of the carapace up to a certain size, beyond which larger crabs run slower than smaller ones.

  2. The crab does not run at these high speeds by making extremely rapid movements as these data seemed to require. The highest frequency of leg movements observed was 20 Hz.

  3. Electromyographs of muscles used in running, made from the freely running, intact crab, showed asymmetry in the motoneurone discharges. Extensors and flexors in the meropodites of legs on the leading side frequently showed only a maintained tonus and could not have contributed to the running movements. Those on the trailing side showed alternation synchronous with stepping.

  4. It is concluded that the crab mainly pushes itself along rather than using a push-pull combination.

  5. Three pairs of legs are commonly used in running. Legs 2 and 4 of one side move together with leg 3 of the opposite side and provide a tripod of support. At the highest speeds only legs 2 and 3 of one side are used to provide thrust alternately.

  6. The high speed is achieved by the crab leaping through the air as it steps, thereby increasing the effective length of the steps.

Of all crustaceans which move on land, crabs of the genus Ocypode living on tropical sandy beaches achieve the highest speeds. Their rapid, sideways running represents an escape response terminating in the surf or a burrow previously built at or above high-tide mark. When retreat into either of these safe havens is prevented the crab flees at great speed for a short distance but then either prostrates itself in any available depression on the beach or begins to dig itself a new burrow (Cott, 1929). It has been stated that they run sideways using three pairs of walking legs (Koepcke & Koepcke, 1953) or sometimes only two pairs (Gravier, 1922). The impression of high speed is enhanced by supreme agility; they can accelerate rapidly from a standing start, reverse direction abruptly without great loss of speed and rotate their body through 180° while continuing to run in the same direction (Koepcke & Koepcke, 1953).

Estimates of the speed of running have been made many times. Cott (1929) estimated that the O. ceratophthalma which he observed‘could hardly have been travelling at less than 10 m.p.h.’ (4·4 m/sec), while Koepcke & Koepcke (1953) estimated the O. gaudichaudii ran at 1·6 m/sec. Hafemann & Hubbard (1969) determined the speed of O. ceratophthalma over unspecified distances on sandy beaches and found an average speed of 1·8 m/sec. On the harder surface of a wooden ship’s deck the same authors found the average speed increased to 2·3 m/sec, with one individual recorded at 4 m/sec. They found that speed is correlated with body size, measured as width of the carapace, up to a particular size beyond which all the larger crabs ran at approximately the same speed.

Hafemann and Hubbard attempted to explain the high speed of running in terms of three specializations of the body. First, the length of the legs for a given body size is greater than for other species of crab from the same habitat; for example Sesarma (Cott, 1929) or Pachygrapsus (Hafemann & Hubbard, 1969). This would allow the length of a step and hence the‘gearing’ of the movement to be increased. Secondly, the extensor muscle in the meropodite is always larger than its antagonist, while the reverse is true in other crabs such as Pachygrapsus. This leads to the main power for running being developed about the mero-carpopodite joint in the form of a pushing thrust. Thirdly, since they found the muscles of the leg to have high tetanus fusion-frequencies, of the order of 90 Hz, this might allow the muscles to produce a high rate of cycling of leg movement. Hafemann & Hubbard (1969) calculated that stepping at 90–100 Hz would be necessary to explain the maximum speeds they observed.

We were attracted to the problem principally because we were searching for examples of experimentally analyzable central nervous motor programs. The high predicted stepping rates for Ocypode would require complete stepping cycles of only about 10 msec, leaving insufficient time for peripheral sensory feedback to adjust motor output. In addition, since the length changes are relatively large, whilst force requirements are high, specializations of the muscle fibres, a matter in which we are also interested, might have been expected to have occurred.

We first tested the ability of the muscles to produce unfused contractions of sufficient magnitude at the high rates required. Although the tetanus fusion-frequency is high, the muscles give very little tension variation at frequencies above 30 Hz, and we estimated that the maximum usable rate would be 25 Hz. This is well below the rate which Hafemann and Hubbard stated would be required and forced us to examine the various aspects of running. We also decided to study the actual rates of movement by electromyography from the running crab. Our findings were somewhat surprising, but they do allow us to offer an explanation of rapid running in terms of rates of stepping compatible with the contractile properties of the muscles. They also show a large disparity between the action of the legs on the leading side of the body compared with the trailing side. A difference, though much less than the differences we shall describe below, has recently been shown for Carcinus (Clarac & Coulmance, 1971).

Ocypode ceratophthalma were collected from beaches on the windward side of the island of Oahu, Hawaii. Crabs above 20 mm in carapace width were obtained in the late evening after sunset for they were not visible during the day. By contrast, smaller crabs were common during the daytime. They were kept in a tank with a sloping floor which allowed access to exposed sand or circulating sea water and thus simulated a sloping beach. Most runs were carried out with crabs which had been held captive for less than 24 h.

To examine the neuromuscular physiology of leg muscles a third leg was removed, and the muscles were exposed and bathed either in a Ringer’s solution containing, in mM/1: Na+, 466; K+, 8; Ca2+, 20; Mg24-, 2; Cl, 502; HCO2, 8; buffered to pH 7·0 or in filtered sea water, both at 24–26 °C.

Electrical responses of the muscle fibres were recorded with conventional intracellular electrodes, and the nerve fibres were stimulated with electrical shocks of variable duration and intensity through a pair of chlorided silver hook electrodes. Tension of the whole muscle was measured by grasping the muscle apodeme between forceps attached to a Grass FTO 3 mechano-electronic transducer.

The speed of running was measured using a race track 3 m long by 0·2 m wide having a base of moist, hard-packed sand 40 mm deep. The middle metre of the track was marked by photocells 10 mm wide on to which were focused beams of light. The resolution of the photocells was such that interception of the light beam by the individual legs of a crab as they passed could be detected.

The output of the photocells was displayed on a pen recorder which allowed measurement of the time taken to cover 1 m to be made with an accuracy of ± 4 msec. Speed could thus be determined to within at least ± 0·5 % over a range 0·5–2·5 m/sec after a start (to permit acceleration) of at least 1 m. Crabs were induced to run in either direction along the track with either the left or right set of legs leading. Those with carapace widths below 12 mm were run on a second, smaller track 600 mm long and 10 mm wide but with the same base of hard-packed sand. The middle 200 mm of this track was monitored by photocells.

The gait of the crabs was investigated by first allowing them to run over smooth, moist but firm sand in which the tips of the dactyls left an impression. A clearer picture was obtained by dipping the tips of selected dactyls into acrylic paint of different colours and allowing the crab to run over white paper placed in the 3 m race track.

Electromyograms from freely moving crabs were made by inserting 50 μ m silver or copper wire insulated but for the tip into the appropriate muscle. The leads were sealed in place using Eastman 910 adhesive and wax of low melting point. The leads were taken to a central anchoring point on the carapace formed by a bracelet of 200 μ m copper wire which passed around the body and between the bases of the first and second pairs of legs. From this point the wires ran to a junction box 1 m above the track and then via shielded cables to a.c.-coupled pre-amplifiers with a band width of 80 Hz to 5 kHz. The output of these amplifiers was recorded on an Ampex d.c. tape-recorder for later display on a pen recorder or oscilloscope. The crabs were allowed to move freely across either a circular tank with a diameter of 1 m or along the 3 m track. All behavioural and electromyographic experiments were conducted at ambient air temperatures of 28–32 °C.

Neuromuscular physiology

We measured twitch time, tetanus fusion-frequency, time to peak tetanic contraction and the relaxation time from this for the opener and closer of the dactylopodite, the extensor and flexor of the carpopodite and the levator and depressor of the basipodite. Only the extensor and flexor of the carpopodite will be described in detail (summarized in Table 1) since the others were closely similar. We did not detect any properties which we consider would radically affect the speed of locomotion.

Of the two muscles in the meropodite the extensor is heavier by some 30% (Hafemann & Hubbard, 1969). Its fibres arise from a centrally placed apodeme and insert predominantly on the posterior wall of the meropodite, the majority being towards the proximal end of the segment. The colour of the fibres varies along the length of the muscle, there being a central portion of white, translucent fibres bounded proximally and dorsally by a small group of pinkish-brown fibres and distally by a larger group of pink fibres. Though the ultrastructure of this muscle has not been examined in detail it is known that the central white fibres have sarcomere lengths in the range of 2–4 μm. (Hoyle, 1966).

The tendon of the flexor muscle lies ventral to that of the extensor and fibres insert mainly on the anterior wall of the meropodite. They show a similar variation in colour with white fibres central, light pink fibres in a small distal group, and darker pink fibres in a larger proximal group.

The extensor muscle is innervated by two motor axons, fast and slow. The fast axon evoked a twitch contraction of the whole muscle lasting 70 msec, and individual twitches were still incompletely fused at 50 Hz, but the individual tension swings represented less than 20% of the fused tension. Complete fusion occurred at 100 Hz (Text-figs, 1, 4). Repetitive stimulation of the slow axon produced a slow, smoothly rising increase of tension in which individual contractions were not discernible (Text-fig. 1). At a stimulation rate of 100 Hz maximum tension was reached after 600 msec and relaxation was complete in 400 msec. By contrast, maximum tension was achieved after 100 msec and relaxation was complete in 150 msec when the fast axon was stimulated at the same frequency.

Text-fig. 1.

Neuromuscular transmission to the extensor carpopodite which receives two motor axons, (a) The fast axon was stimulated at 10, 15, 20, 25, 30, 40 and 50 Hz respectively. Upper traces, tension of the whole muscle; lower traces, stimulus marks. Each stimulus evokes a contraction increment which is still distinguishable at a stimulation frequency of 50 Hz. (b) the slow axon was stimulated at 20, 50 and too Hz. Upper traces, tension of the whole muscle; lower traces, intracellular activity of a single muscle fibre.

Text-fig. 1.

Neuromuscular transmission to the extensor carpopodite which receives two motor axons, (a) The fast axon was stimulated at 10, 15, 20, 25, 30, 40 and 50 Hz respectively. Upper traces, tension of the whole muscle; lower traces, stimulus marks. Each stimulus evokes a contraction increment which is still distinguishable at a stimulation frequency of 50 Hz. (b) the slow axon was stimulated at 20, 50 and too Hz. Upper traces, tension of the whole muscle; lower traces, intracellular activity of a single muscle fibre.

Comparable experiments were next carried out on the flexor muscle. This was found to have a much more complex innervation. There are four excitatory axons which evoked twitch durations of approximately 200, 120, 100 and 80 msec respectively. Fusion of the twitches produced by repetitive stimulation of the fastest axon was complete at 70 Hz, but at frequencies as low as 30 Hz the individual fluctuations in tension caused by each stimulus represented only 10% of the fused tension and at 50 Hz less than 5 % (Text-fig. 4). The twitch times for fast axon responses of the other leg muscles fell between those of the extensor and those of the flexor of the carpopodite.

In an attempt to simulate the optimal motor output which the muscle could receive during running, repetitive bursts of stimuli were applied to the fast axons (Text-figs. 2, 3). The following factors were varied over wide ranges : intervals between stimuli in the burst, burst duration and burst repetition rate. As far as possible these overlapped values that were used naturally, as determined by recording of electromyograms from the running crab (see below). Following a burst of three stimuli at 250 Hz the ensuing contraction and relaxation of the extensor was about 90% completed after 100 msec. When five stimuli at the same frequency were applied, 22% tension remained after 100 msec. These correspond to burst repetition rates of 10 Hz, and at this rate the muscle could be driven usefully with either 3 or 5 impulses per burst. This would not be the case at rates much higher than about twice the latter value, for as the burst repetition rate was increased above 10 Hz the relaxation became progressively less complete and individual contractions caused by the bursts of stimuli were a very small fraction of the fused tension. At a repetition rate of 15 Hz the contribution of the individual fluctuations in tension to the total tension of the muscle was 43 %, but at 20 Hz it had fallen to only 12% (Text-fig. 2b). At 25 Hz the swings comprised 5 % of the total and at 30 Hz a mere 1 %.

Text-fig. 2.

Modulation of tension development by the extensor carpopodite produced by repetitive bursts of stimulation applied to the fast axon, (a) Each burst contained 3 pulses at a frequency of 250 Hz. Repetition rates were to, 15, 20, 25 and 30 Hz respectively. Fusion was almost complete at 30 Hz. (b) Each burst contained 5 pulses at 250 Hz. Burst rates were 10, 15, 20 or 25 Hz. Fusion was almost complete at 25 Hz. Upper traces, tension of the whole muscle ; lower traces, stimulus marks.

Text-fig. 2.

Modulation of tension development by the extensor carpopodite produced by repetitive bursts of stimulation applied to the fast axon, (a) Each burst contained 3 pulses at a frequency of 250 Hz. Repetition rates were to, 15, 20, 25 and 30 Hz respectively. Fusion was almost complete at 30 Hz. (b) Each burst contained 5 pulses at 250 Hz. Burst rates were 10, 15, 20 or 25 Hz. Fusion was almost complete at 25 Hz. Upper traces, tension of the whole muscle ; lower traces, stimulus marks.

Text-fig. 3.

Modulation of tension of the flexor carpopodite produced by patterned stimulation, (a, b) Separate stimulation of two of the four motor axons to this muscle with bursts containing 5 stimuli each at a frequency of 250 Hz repeated at 10, 15, 20 and 25 Hz respectively. The tension fuses at repetition rates of 20 Hz. Upper traces, tension of the whole muscle; lower traces, stimulus marks.

Text-fig. 3.

Modulation of tension of the flexor carpopodite produced by patterned stimulation, (a, b) Separate stimulation of two of the four motor axons to this muscle with bursts containing 5 stimuli each at a frequency of 250 Hz repeated at 10, 15, 20 and 25 Hz respectively. The tension fuses at repetition rates of 20 Hz. Upper traces, tension of the whole muscle; lower traces, stimulus marks.

Text-fig. 4.

The relationship between frequency of unpattemed stimuli and fluctuation of tension produced by each stimulus expressed as a percentage of the total tension. At 50 Hz only the extensor carpopodite shows significant individual fluctuations which are 20 % of the total tension. Tetanic fusion of all the muscles except the extensor carpopodite occurs below 70 Hz.

Text-fig. 4.

The relationship between frequency of unpattemed stimuli and fluctuation of tension produced by each stimulus expressed as a percentage of the total tension. At 50 Hz only the extensor carpopodite shows significant individual fluctuations which are 20 % of the total tension. Tetanic fusion of all the muscles except the extensor carpopodite occurs below 70 Hz.

Comparable experiments on the flexor of the carpopodite (Text-fig. 3) showed that for the antagonist the useful range of repetition rates of bursts is somewhat less than it is for the extensor. Similar experiments were also carried out, with similar results, on the opener and the closer muscles of the dactylopodite and the levator and depressor of the basipodite. The results are summarized graphically in Text-fig. 5. Stimuli were delivered in bursts containing five impulses each at a frequency of 250 Hz, corresponding to the naturally occurring stimuli, at burst repetition rates of 10, 15, 20, 25 and 30 Hz. At rates above 20 Hz the swings in tension were below usable amplitude for all the muscles except the extensor carpopodite.

Text-fig. 5.

The relationship between stimuli patterned in bursts and fluctuation in tension produced by each burst expressed as a percentage of the total tension. The stimuli (at a frequency of 250 Hz), were delivered in groups of 5 and repeated at 10–30 Hz. Only the extensor carpopodite shows significant modulation of the total tension above repetition rates of 20 Hz. Tetanic fusion of all the muscles occurred at repetition rates below 30 Hz.

Text-fig. 5.

The relationship between stimuli patterned in bursts and fluctuation in tension produced by each burst expressed as a percentage of the total tension. The stimuli (at a frequency of 250 Hz), were delivered in groups of 5 and repeated at 10–30 Hz. Only the extensor carpopodite shows significant modulation of the total tension above repetition rates of 20 Hz. Tetanic fusion of all the muscles occurred at repetition rates below 30 Hz.

Although our electromyograms showed that bursts of impulses, not single impulses, are used during running, the single impulse is of course the theoretical minimum for muscle activation, so simple trains also needed to be tested. Accordingly, we present in Text-fig. 4 graphs of the tension fluctuations for the four muscles studied as a function of frequency of single stimuli applied. These results show that only the extensor carpopodite could, even in principle, be used at frequencies as high as 80 Hz. Smooth tetanus fusion of all the muscles except the extensor occurs below 70 Hz, and at this frequency the peak-to-peak tension swings of the extensor are a mere 4% of the total tension. For other leg-joint muscles the fluctuations are reduced to this level at less than 50 Hz.

Speeds of running crabs

The speeds of 62 crabs with all limbs intact were measured, and the fastest of six to ten runs by each crab were selected. We were interested in the fastest sprint performance of each crab, not its average speed.

It was found that the speed of running increases as a function of the carapace width up to 20 mm (Text-fig. 6). Thereafter the speed decreases with increasing carapace width. The maximum speeds were in the range of 1·8–2·0 m/sec with only one crab exceeding 2·0 m/sec.

Text-fig. 6.

The speed of running of Ocypode ceratophthalma as a function of the width of the carapace. The points represent the maximum speed achieved in 6–10 trials by sixty-two different crabs given a flying start over a measured track. The base of the track was of hard-packed, moist sand. Speed increases with size up to a carapace width of 20 mm but then decreases with increasing size.

Text-fig. 6.

The speed of running of Ocypode ceratophthalma as a function of the width of the carapace. The points represent the maximum speed achieved in 6–10 trials by sixty-two different crabs given a flying start over a measured track. The base of the track was of hard-packed, moist sand. Speed increases with size up to a carapace width of 20 mm but then decreases with increasing size.

An explanation of the lower speed of large-sized crabs may lie in the relationship between width of the carapace (or length of the legs) and total weight of the body. The length of the legs as measured from the base of the basipodite to the tip of the dactylopodite increases linearly with increasing carapace width (Text-fig. 7 a). However, body weight increases approximately exponentially with both increasing carapace width (Text-fig. 7 b) and leg length (Text-fig. 7c). Thus if a crab with a carapace width of 30 mm is compared with one of 20 mm the leg length is 60 % larger but body weight is 400% greater. The increased weight which must be carried could significantly reduce the speed of running. Another behavioural factor is that the very large crabs are always males, which are more inclined to stand and fight than to run. Even when running, the relatively larger claws of large crabs were held in what we assumed to be an aggressive posture and often the crab would stop and rear up defensively. Thus it may be that rapid running, which is an escape response elicited by any startle stimulus, is replaced in older males by aggressive behaviour.

Text-fig. 7.

The relationships between carapace width, length of the third (longest) leg and total body weight, (a) Length of the third leg increases linearly with carapace width. (b) Body weight increases approximately exponentially with carapace width and with increasing leg length (c).

Text-fig. 7.

The relationships between carapace width, length of the third (longest) leg and total body weight, (a) Length of the third leg increases linearly with carapace width. (b) Body weight increases approximately exponentially with carapace width and with increasing leg length (c).

The speed at a given cycling rate will depend upon the length of a step. This is defined as the distance the animal is propelled during a single stepping cycle. It can be measured as the distance between an initial contact point with the ground of a leg tip, and the next contact point of the same tip. It is desirable to be able to judge the maximum step-length capability, assuming the traditional concept of the mechanism of locomotion by crabs, from some simple measurement of the whole crab. Clearly leg length is the most important parameter. Carapace size must also be considered, because at rest the body is held close to the ground, so that the meropodite— carpopodite (M–C) joint is higher than the dorsal surface of the carapace (Hafemann & Hubbard, 1969). When the crab starts to run the body is raised from the ground so that the M–C articulation is level with the dorsal surface of the carapace (Stebbing, 1893; Hafemann & Hubbard, 1969). This means that the leg can now be put down at some point in its cycle of movement immediately beneath the body with a consequent increase in step length.

The step length is a function of the effective extended leg length and the angle through which the leg swings. If this is 6o° the step length is twice the extended leg length; for more obtuse angles it is greater and for more acute angles it is less. The maximum possible step length, assuming the traditional view of crab locomotion (Bethe, 1897 a, b) is equal to twice the extended leg length, if the leg is in fact fully extended. Hafemann and Hubbard, for reasons which they did not explain and which we are at a loss to understand, give a value equal to the extended length of the longest (i.e. third) leg as the maximum step length. The step length determines the theoretical stepping rate in relation to running speed. During our investigation we soon came to consider their values to be gross underestimates.

Gait

In order to estimate stepping rates it is also necessary to know the type of gait being used. A large number of stepping gaits is possible, in principle, for an effectively eight-legged animal which need not be using all legs at the same time. Considering only the legs on one side, they could be used in the following ways: all four in sequence with several sequences possible; three legs in sequence, two legs or two pairs of legs alternately; one pair alternately and one pair synchronously; and so on. In order to determine the actual gaits utilized by the crab we first dipped the dactyls into differently coloured paints and then let the crabs run on white paper. The gaits were determined by studying the points of contact of the tips with the ground in successive steps. Fortunately only a small number of patterns, representing the simplest possible gaits, were found.

The commonest gait at moderate speeds is two pairs alternating. Legs 2 and 4 of one side are placed down together and alternate with legs 3 and 5 of the same side (Text-fig. 8 a). At moderate speeds of running leg 5 of each side is raised from the ground (Text-fig. 8b), so that when two legs of one side are in contact with the ground only one leg of the opposite side touches down at the same time. If legs of both sides are actively and equally contributing to the movement, by combined pulling and pushing, then alternate strides will be of the same length. But if either pulling or pushing predominates then at alternate steps first one leg (leg 3), then two legs (legs 2 and 4), will contact the ground. Two legs might be expected to produce more thrust or pull than one leg, leading to long steps alternating with shorter ones. What we found is that succeeding steps are of approximately equal length (Text-fig. 8). This could be due to the compensatory effect of leg 3 being considerably larger and therefore having stronger muscles than either of legs 2 and 4. The pairs of legs on opposite sides were about 1800 out of phase with their counterparts, but tended to become unrelated and to give strange patterns at high speeds. This matter will be dealt with below.

Text-fig. 8.

Stepping patterns during rapid running. The tips of the dactylopodites of the right legs were dipped in paints of different colours and the crab was allowed to run to its left across sheets of paper. The actual records are shown and circled in (b). (a) Sequence in which right-side leg 2 (R2) and right-side leg 4 (R4) move together and alternate with R3. The crab was a female with a carapace width of 27 mm. (b) Stepping sequence from a male crab of 25 mm carapace width in which legs R3, R4 and R5 are recorded. R3 and R5 move together and alternate with R4. As the crab’s speed increases R5 is lifted clear of the ground (arrows).

Text-fig. 8.

Stepping patterns during rapid running. The tips of the dactylopodites of the right legs were dipped in paints of different colours and the crab was allowed to run to its left across sheets of paper. The actual records are shown and circled in (b). (a) Sequence in which right-side leg 2 (R2) and right-side leg 4 (R4) move together and alternate with R3. The crab was a female with a carapace width of 27 mm. (b) Stepping sequence from a male crab of 25 mm carapace width in which legs R3, R4 and R5 are recorded. R3 and R5 move together and alternate with R4. As the crab’s speed increases R5 is lifted clear of the ground (arrows).

At the highest running speeds leg 4 in addition to leg 5 of the trailing side was found to be commonly held raised up. Then only two legs, 2 and 3, are contributing thrust to the movement and these legs are alternating.

When the lengths of steps were measured directly after fast runs they were often found to be consistently greater than the value we considered to be the theoretical maximum possible value for the crab being tested (Text-fig. 9b). Of 49 crabs tested only six had step lengths below the theoretical maximum value and these were the same crabs which in separate tests had shown speeds of running below average for their-size. All crabs with a carapace width below 25 mm produced step lengths significantly greater than the theoretical maximum, whereas crabs above 25 mm made steps which were equal to or below it. Again this will be a contributory factor to the reduction in speed with increasing size. If the measured step length exceeds the theoretical maximum without help from other legs then neither member of the pair of legs can have constant contact with the ground and the crab must be leaping. Once we realized this we took test photographs of the crab during rapid running. The crab was induced to run on a wooden table-top past the camera and its motion was‘stopped’ by an electronic flash of 0·5 msec duration. The resulting photographs (Plate 1) unequivocally show that there are times during a run when the legs are clear of the ground. The crab is thus achieving a high speed of running by leaping from the dactyl of leg 3, alternating with leg 2, or alternating with legs 2 and 4 acting together.

Text-fig. 9.

The relationship between carapace width and (a) theoretical maximum step length assuming traditional explanation of crab locomotion with legs in contact with the ground; (b) experimentally determined step length. The line on graph (b) is the line of best fit for theoretical step length from graph (a). Theoretical maximum possible step length is defined as twice the leg length.

Text-fig. 9.

The relationship between carapace width and (a) theoretical maximum step length assuming traditional explanation of crab locomotion with legs in contact with the ground; (b) experimentally determined step length. The line on graph (b) is the line of best fit for theoretical step length from graph (a). Theoretical maximum possible step length is defined as twice the leg length.

Plate.1

M. BURROWS AND G. HOYLE

Plate.1

M. BURROWS AND G. HOYLE

The increase in length achieved by leaping through the air is 40–60%. Hence the frequency at which the leg movements must be repeated to cover a given distance in a given time can be reduced (Text-fig. 10). Actual stepping rates were calculated from the measured maximum speed of the crab and its measured step length. The stepping rate that a crab would need to achieve the same speed if it were to use its theoretical maximum step length was then calculated. Crabs with carapace widths below 25 mm were found to have stepping rates of about one-half those needed to achieve the same speed without leaping. For larger crabs where the actual step length approximates to the maximum calculated value there is no saving. The highest stepping rate found was 20 Hz, in a tiny crab with a carapace width of 7 mm travelling at 1·0 m/sec. Our fastest crab, which travelled at 2·1 m/sec, needed to cycle its legs at only 18 Hz because of its particularly strong leap.

Text-fig. 10.

Improvement over theoretically required cycling rate as a function of carapace width. The open circles show the measured cycling rate which would be necessary to produce the same maximum speed if the theoretical maximum stride length were being used. For the smaller, lighter crabs there is a considerable reduction (i.e. relative increase in speed). The effect is small for large crabs.

Text-fig. 10.

Improvement over theoretically required cycling rate as a function of carapace width. The open circles show the measured cycling rate which would be necessary to produce the same maximum speed if the theoretical maximum stride length were being used. For the smaller, lighter crabs there is a considerable reduction (i.e. relative increase in speed). The effect is small for large crabs.

Electromyography

Muscle activity was recorded with implanted leads in freely moving animals. The small number of axons which innervate the muscles means that in fortunate electrode placements single-unit discharges can be identified. The recording leads apparently did not greatly impede the movements of the legs though they restricted the distance over which the crab could run. The maximum running speed obtained under such conditions was 1·8 m/sec. In the circular tank 5–10 steps at maximum speed could be recorded, compared with 10–30 on the 3 m track. The studies were made on the crabs which were fastest in test runs and all had widths in the 20–32 mm range (Text-fig. 6).

When the crab moved away from a stationary position, electrical activity always occurred first in the muscles of the trailing legs (Text-fig. 11a). Therefore, even at the start of a run the crab is thrust into motion rather than pulled. Activity always occurred first in muscles of the meropodite : a low-frequency discharge in the flexor, followed by the‘opener’ of the dactylopodite and the levator of the fused basi-ischiopodite, which extend the leg. On the return part of the cycle the carpopodite is first flexed about the meropodite, then the basi-ischiopodite is depressed and finally the dactylopodite is‘closed’. Twenty-five to thirty milliseconds elapse before activity occurs in the contralateral flexor, and about 10 msec more elapse before the contralateral extensor fires.

Text-fig. 11.

Electromyograms of the opener of the dactylopodite (top traces), extensor carpopodite (beam 2) and depressor basipodite (beam 3) of leg L3. The extensor carpopodite of right-side leg 3 (R3) of shown on beam 4. (a, b) Continuous sequence of a run to the crab’s left from a stationary start, (c, d) Continuous sequence from the middle of a run to the crab’s right. Male with carapace width of 25 mm. Note that there is almost no activity except weak constant background in the muscles of the left legs when they are leading. By contrast, rhythmic bursts of large spikes occur in the muscles of the right leg. When the direction of the run is reversed there are no spikes in the carpopodite but strong rhythms in the three muscles of the left legs.

Text-fig. 11.

Electromyograms of the opener of the dactylopodite (top traces), extensor carpopodite (beam 2) and depressor basipodite (beam 3) of leg L3. The extensor carpopodite of right-side leg 3 (R3) of shown on beam 4. (a, b) Continuous sequence of a run to the crab’s left from a stationary start, (c, d) Continuous sequence from the middle of a run to the crab’s right. Male with carapace width of 25 mm. Note that there is almost no activity except weak constant background in the muscles of the left legs when they are leading. By contrast, rhythmic bursts of large spikes occur in the muscles of the right leg. When the direction of the run is reversed there are no spikes in the carpopodite but strong rhythms in the three muscles of the left legs.

While the trailing leg is extending or flexing, its contralateral homologue goes through the opposite phase of the cycle. Its sequence of contractions is similar during flexion but the relative phasing of closing of the dactylopodite and depression of the basipodite may be changed so that closing may precede depression. During extension, levation of the basipodite may precede depression followed by extension of the carpopodite and finally opening of the dactylopodite. The sequence is similar to that of Carcinus legs when stepping at 1–2 Hz (Clarac & Coulmance, 1971).

Recordings from the basipodite depressor muscles of the legs of one side showed that activity in leg 2 is in phase with that in leg 4 but in anti-phase with that in legs 3 and 5. When legs on opposite sides are considered, leg 3 on one side is in phase with legs 2 and 4 of the opposite side but in anti-phase with its opposite partner (Text-fig. 12). Depressor and levator activity in one joint alternate, but in a trailing leg levation follows depression with a phase relationship which is always less than 0·5 (Text-fig. 12 c). The complexity of the discharge, due to the firing of several motoneurones to each muscle, has precluded any inferences about the pattern of individual motoneurone activity during running.

Text-fig. 12.

Electromyograms from the basipodite during rapid running, (a, c) Run to the crab’s right, (b) Run to the crab’s left. Traces are (a, b) beam 1, L3 depressor basipodite; beam 2, R3 depressor basipodite; beam 3, R4 depressor basipodite; beam 4, L3 extensor carpopodite; (c) beam 1, L3 depressor basipodite; beam 2, R3 depressor basipodite; beam 3, R3 levator basipodite; beam 4, L3 extensor carpopodite. Note the increased activity in the legs that are on the trailing side. Male with carapace width 32 mm.

Text-fig. 12.

Electromyograms from the basipodite during rapid running, (a, c) Run to the crab’s right, (b) Run to the crab’s left. Traces are (a, b) beam 1, L3 depressor basipodite; beam 2, R3 depressor basipodite; beam 3, R4 depressor basipodite; beam 4, L3 extensor carpopodite; (c) beam 1, L3 depressor basipodite; beam 2, R3 depressor basipodite; beam 3, R3 levator basipodite; beam 4, L3 extensor carpopodite. Note the increased activity in the legs that are on the trailing side. Male with carapace width 32 mm.

Activity in the closer muscles of legs 2 and 4 of one side alternates with that in legs 3 and 5 of the same side but is in phase with activity in legs 3 and 5 of the opposite side. The relative time is nevertheless labile and in a few sequential steps may change from the left side leading (phase +0·3) through synchrony (phase 1·0) to right side leading (phase –0·7) (Text-fig. 13 a). Phasing between muscles of adjacent legs on the same side may also vary (Text-fig. 13, b). The peak amplitude, which reflects the amount of facilitation, is markedly different, depending on whether the leg is leading or trailing when recorded with the same electrode placements from the same crab in two successive runs in opposite directions (Text-fig. 13). Both the number and frequency of impulses carried by a single motoneurone are increased to the muscle of a trailing leg.

Text-fig. 13.

Extracellular myograms from the closer muscles of the dactylopodite during rapid running. Beam 1, L3 closer; beam 2, R3 closer; beam 3, R4 closer; beam 4, L3 extensor carpopodite. (a) Run to the crab’s right. The left leg is active first. (b) Run to the crab’s left. The right leg is active first. Note the increased activity of closer muscles of the trailing legs. Again the extensor carpopodite is most active when the leg is on the trailing side. Male with carapace width 32 mm.

Text-fig. 13.

Extracellular myograms from the closer muscles of the dactylopodite during rapid running. Beam 1, L3 closer; beam 2, R3 closer; beam 3, R4 closer; beam 4, L3 extensor carpopodite. (a) Run to the crab’s right. The left leg is active first. (b) Run to the crab’s left. The right leg is active first. Note the increased activity of closer muscles of the trailing legs. Again the extensor carpopodite is most active when the leg is on the trailing side. Male with carapace width 32 mm.

We have analysed recordings made from the muscles of the meropodite, in particular the extensor, but even the most favourable electrode placements always recorded the activity of both flexor and extensor together. The extensor activity could be identified by its relative simplicity, there being only two motoneurones compared with four to the flexor. It was found necessary to make an exact identification by correlation of the activity with the resultant movements (Text-fig. 14). This was done using a moving-wand transducer (Sandeman, 1968) which monitored the change in angle of the carpopodite about the meropodite. Two receiving antennae of 50 μ m silver wire were attached to the posterior face of the meropodite and a third similar wire, the signal wire, was run along the opposite wall of the meropodite but attached to the posterior face of the carpopodite (Text-fig. 14). Movement of the carpopodite moved the signal wire in an arc between the two antennae which by connexion to suitable electronic circuitry converted the movement to a d.c. signal. Apparently movement of the limb was not impeded.

Text-fig. 14.

Identification of activity in flexor and extensor carpopodite muscles in extracellular recordings from the meropodite. Despite cross-talk between the two pairs of electrodes, flexor (larger amplitude burst on the middle trace) and extensor activity (lower trace) are distinguishable by reference to the movement monitor (upper trace where down represents an extension movement). Further details of the movement detector are given in the text.

Text-fig. 14.

Identification of activity in flexor and extensor carpopodite muscles in extracellular recordings from the meropodite. Despite cross-talk between the two pairs of electrodes, flexor (larger amplitude burst on the middle trace) and extensor activity (lower trace) are distinguishable by reference to the movement monitor (upper trace where down represents an extension movement). Further details of the movement detector are given in the text.

The number of impulses carried by the single fast axon to the extensor muscle was found to decrease with increasing frequency of stepping (Text-fig. 15). At low stepping rates of 2–4 Hz, 30–40 impulses were recorded but during rapid running at a stepping rate of 16–18 Hz, only 5–8 impulses occurred for each step. The initial high frequency of 300–350 Hz at the start of the burst remained the dominant one over the whole range of stepping speeds examined. At higher stepping rates a frequency of 500 Hz was reached. The duration of the bursts was approximately linearly related to the frequency of stepping, implying that the longer bursts must contain relatively more long intervals than the shorter ones.

Text-fig. 15.

Structure of single fast motoneurone discharges to the extensor of the carpopodite at different rates of stepping. The data was obtained from extracellular myograms from several crabs and is presented as instantaneous frequency plots; the reciprocal of the interval between successive pulses is plotted against the instant in time midway between those two pulses. ○, One burst; •, a second. The rates of stepping were: (a) 2–3; (b) 4–5; (c) 6–7; (d) 8; (e) 12; (f) 16Hz.

Text-fig. 15.

Structure of single fast motoneurone discharges to the extensor of the carpopodite at different rates of stepping. The data was obtained from extracellular myograms from several crabs and is presented as instantaneous frequency plots; the reciprocal of the interval between successive pulses is plotted against the instant in time midway between those two pulses. ○, One burst; •, a second. The rates of stepping were: (a) 2–3; (b) 4–5; (c) 6–7; (d) 8; (e) 12; (f) 16Hz.

At the fastest speeds the successive bursts to the extensor varied both in the number and frequency of impulses within a burst (Text-fig. 16), but the first intervals were the shortest and subsequent ones were progressively larger.

Text-fig. 16.

Instantaneous frequency plots of the fast motoneurone discharge to the extensor carpopodite during seven successive steps at a frequency of 15 Hz. From five to ten impulses occur per burst, at variable frequency. The interburst interval is also variable.

Text-fig. 16.

Instantaneous frequency plots of the fast motoneurone discharge to the extensor carpopodite during seven successive steps at a frequency of 15 Hz. From five to ten impulses occur per burst, at variable frequency. The interburst interval is also variable.

Extensor muscle activity of leg 2 is in phase with that of leg 4 of the same side and so is that of legs 3 and 5, whilst these two sets are in antiphase to each other, as are the dactylopodite closer and basipodite depressor muscles (Text-fig. 17). There is no apparent difference in the structure of the bursts in legs 2 and 4 compared with leg 3 which could account for the equality of the stride lengths when first legs 2 and 4 and then leg 3 are used. Often at high frequencies of stepping cyclical activity in the extensor muscle of leg 4 ceases (Text-fig. 17b), becoming continuous and therefore tonic. At this time the leg is lifted clear of the ground and contributes no force; the crab is now running with only two pairs of legs participating in the movements.

Text-fig. 17.

Extracellular myograms from the extensor and flexor carpopodite of leg R2 (upper traces), R3 (middle traces) and R4 (lower traces) of a freely moving crab, (a) Run to the crab’s left in which all three legs participate; R2 and R4 move together and alternate with R3 but their phase relationships are not constant. (b) Run to the crab’s left in which R4 is not used. Male, with carapace width 30 mm.

Text-fig. 17.

Extracellular myograms from the extensor and flexor carpopodite of leg R2 (upper traces), R3 (middle traces) and R4 (lower traces) of a freely moving crab, (a) Run to the crab’s left in which all three legs participate; R2 and R4 move together and alternate with R3 but their phase relationships are not constant. (b) Run to the crab’s left in which R4 is not used. Male, with carapace width 30 mm.

The most striking feature of extensor muscle activity is the complete asymmetry of discharge to muscles of a pair of legs, one of which is leading and the other trailing (Text-fig. 18). Extensor muscles of leading legs show little or no cyclical activity but merely a maintained tonus. Cyclical modulation of this tonus can sometimes be observed but often is completely absent after the first few cycles of movement (Text-fig. 18 a, b). Discharges to the flexor muscles show a similar asymmetry, with continuous tonic activity in the leading legs and cyclical activity in the trailing legs (Text-fig. 18 c, d).

Text-fig. 18.

Extracellular myograms from the carpopodite of leg L3 (upper traces) and R3 (lower traces) during very fast running, (a) Continuous sequence in which the crab runs first to its left, then to its right and finally to its left again. (b) Different crab which runs first to its right, then left, then right again, (c, d) Faster records of a single right run (c) and a single left run (d). Only the muscles on the trailing side were activated cyclically. The carapace sizes of the crabs were: (a) 25 mm (male); (b) 27 mm (male); (c, d) 30 mm (female). In these examples both the extensor (larger spike bursts) and the flexor activity were recorded by the electrodes. Scale : (a, b) 1 sec ; (c, d) 200 msec.

Text-fig. 18.

Extracellular myograms from the carpopodite of leg L3 (upper traces) and R3 (lower traces) during very fast running, (a) Continuous sequence in which the crab runs first to its left, then to its right and finally to its left again. (b) Different crab which runs first to its right, then left, then right again, (c, d) Faster records of a single right run (c) and a single left run (d). Only the muscles on the trailing side were activated cyclically. The carapace sizes of the crabs were: (a) 25 mm (male); (b) 27 mm (male); (c, d) 30 mm (female). In these examples both the extensor (larger spike bursts) and the flexor activity were recorded by the electrodes. Scale : (a, b) 1 sec ; (c, d) 200 msec.

These observations imply that there is no significant pulling force in the running movement. The tonus developed by meropodite muscles is just sufficient to hold the leg raised. The propulsive force must therefore be developed by the pushing muscles in the trailing legs. Graphic illustration of this finding was obtained from marks made on paper placed in the runway after dactylopodites of the right and left third legs had been coated with wet paint (Text-fig. 19). The dactylopodite of a leg on the trailing side left a precise round spot when the animal was moving at high speed, such as could only have been caused by the tip of the dactylopodite being placed firmly on the ground. By contrast, dactylopodites of the leading legs left either no mark at all or a long, imprecise smear. This means that during a very fast run the leading legs are only partly extended, with the dactyl tucked under the body to serve as a skid.

Text-fig. 19.

Movements made by legs L3 and R3 during very fast running. The tips of the dactylopodites of both legs were dipped in paints of different colours and the crab was allowed to run to its right across a sheet of paper. The tip of the dactylopodite of trailing leg 3 was put down precisely at each step leaving neat spot impressions (circled). Leading leg 3 leaves a long smear impression, indicating that it is used as a skid for balance without contributing sideways force to the movement.

Text-fig. 19.

Movements made by legs L3 and R3 during very fast running. The tips of the dactylopodites of both legs were dipped in paints of different colours and the crab was allowed to run to its right across a sheet of paper. The tip of the dactylopodite of trailing leg 3 was put down precisely at each step leaving neat spot impressions (circled). Leading leg 3 leaves a long smear impression, indicating that it is used as a skid for balance without contributing sideways force to the movement.

We have sought to explain physiologically the remarkably fast running by ghost crabs. Hafemann & Hubbard (1969) had suggested that the crab would have to use stepping cycles up to 90 Hz to achieve the highest speeds. They proposed that this was possible because the fusion frequency of some of the leg muscles was higher than the required stepping rate. However, in moving a limb it is necessary for the muscle to show considerable length changes in the absence of any amplifying mechanism at the joint articulation. None exists in the joints of Ocypode. The amplitudes of the individual peak-to-peak fluctuations of tension at 50 Hz are barely 20% of the total muscle tension, and much less at higher frequencies. For other leg muscles the amplitudes are even less. The problem is further increased when it is borne in mind that the animal does not use single impulses to excite the muscles but brief bursts. Under burst stimulation we found that the leg muscles reached fusion when the bursts, of which each represents behaviourally a single step, were repeated at the low rate of 25 Hz.

Objections may be raised to our experiments on the basis that the conditions were abnormal, perhaps permitting anoxia. But no differences were seen in muscles tested with the leg still attached to the body and with the circulatory system intact and those of isolated preparations. Also, our experiments were performed at constant temperature (24–26 °C) and so did not allow for a possible improvement in performance at higher muscle temperatures after a‘warm-up’ period. In an escape run there would be no time to permit an increase in body temperature, and the increase in running speed at a later stage in the run is small. We found no increase in the stepping rate during a run.

From all of this we reach the conclusion that there is a physiological upper limit for stepping which lies between 20 and 25 Hz. A possible way in which the upper limit might be extended slightly is for there to be a close coupling between firing of the peripheral excitor and inhibitor neurones to a muscle. Perfect timing of the latter, late in each excitatory burst, would accelerate each relaxation. Close coupling with the correct timing is known to occur during passive resistance reflexes of another crab (Bush, 1962), but has not yet been found to occur during centrally driven behaviour (Evoy, Barnes & Spirito, 1970).

The actual maximum stepping rate observed during our experiments was 20 Hz, well within the limits required by burst excitation even without suitably timed peripheral inhibition. We would have been obliged then, to seek an explanation in an unexpected form of gait and a very long step. The realization that the crab can leap resolved the problem.

The maximum possible step length for one cycle, in which the legs stay on the ground, is equal to twice the effective leg length, for a swing angle of 6o°. If the angle through which the legs swing can be made more than 6o°, which is unlikely, it will be a little more. Hafemann & Hubbard (1969), for reasons which they do not give and which we consider must be erroneous, gave a value equal to the extended length of the longest (third) leg as the step length. Acceptance of a step length equal to twice this value would of course lead to a halving of their theoretical maximum stepping rates. But since these are four times the maximum physiologically permissible rates there is still a discrepancy of the order of a factor of 2.

We found that the actual step lengths made by fast-running crabs were about 50% greater than the maximum possible step length assuming contact with the ground, or about four times the extended length of the middle leg. A small-sized, vigorous crab with a 15 mm carapace width and a third leg length of 3 cm should have a maximum possible theoretical step length – without leaping – of 6 cm. We have registered steps for such crabs in excess of 12 cm. Our interpretation, that the legs must have lost contact with the ground, i.e. that the crab leaps from one position to the next, is the only possible one. By thereby increasing the effective length of the stride the crab can reduce the number of times each leg must go through a cycle of movement in order to produce a given speed. It is remarkable that, since the leading legs are lifted up and trailing legs 4 and 5 likewise do not touch the ground, the fastrunning Ocypode is acting like a two-legged runner.

The simple expedient of leaping through the air, of running instead of walking, means that our fastest crab, a male with a carapace width of 22 mm which ran at 2· 1 m/sec, needed to cycle its legs at only 18 Hz, well within the capabilities of all the leg muscles. Thus a high speed has been achieved without any need for specialization of the muscles.

It is of interest to know whether there is any limit of this jumping mode in fast locomotion in other crabs which might serve as the evolutionary starting-point, as it were, for leaping. Fortunately, an analysis has recently been made of locomotion by the less spectacular, but fairly fast crab Carcinus maenas (Clarac & Coulmance, 1971). The electromyographs from running Ocypode showed that there is an extreme disparity between the action of the leg muscles, the flexor and extensor of the carpopodite in particular, on the leading and trailing sides. During rapid running these muscles in a leading leg may show no cyclic activity at all but merely a maintained tonus. Those on the trailing side meanwhile show vigorous cyclical activity. A similar, though less pronounced disparity occurs between the action of muscles of the meropodite of leading and trailing legs during the walking of Carcinus in which the legs are moved at only 2–3 Hz (Clarac & Coulmance, 1971). Also, in Carcinus the joints of legs on the trailing side, in particular leg 3, show greater angular excursions than do the same joints of legs on the leading side. These differences are to be expected from the disparity of motor discharge to the legs of the two sides but are complicated by passive movements due to the crab’s speed and weight. However, Clarac and Coulmance considered that pulling by the leading legs as well as pushing by the trailing legs contributed to the movement, though often the pushing by the trailing legs would dominate. In Carcinus the leading legs are lifted up as if seeking points of contact with the ground. Thus in these aspects of locomotion of an ordinary shore crab we can see the basis for evolution towards superfast leaping and bipedal running.

Finally, and to return to the initial focus of our research, although we have shown that Ocypode steps at rates which give sensory-feed back time to control the steps, the extreme differences in behaviour of legs on the two sides shows that there is an overriding central motor program. This program must directly drive the extensors on the trailing side and inhibit them on the leading side. An evolutionary precedent for this may be found in a general mechanism, since it also happens in movements of the flagella of the maxillipeds of several species of crab (Burrows & Willows, 1969). In tackling some of the detailed questions of neural control mechanisms, we would like to commend Ocypode for wider attention. It is a hardy crab which lives equally well on land and/or in water, and is a very promising experimental animal.

We would like to thank the Director and staff of the Hawaiian Institute of Marine Biology for their hospitality during the Summer of 1970 when the experimental work was carried out and Mr L. H. Vernon for technical assistance. This work was supported by Research Grant GB 16962 from the National Science Foundation.

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Pictures taken with electronic flash showing Ocypode during rapid running. The crab is moving from right to left across the picture. The crab shown in frontal view (a) was a male with a carapace width of 32 mm and the crab shown back view, (b) was a male with a carapace width of 29 mm. The upper crab had just thrust with trailing legs 2 and 4. Leg 3 is about to come down and under the body for the next thrust. Leading legs are all lifted up except 3, which is in the skid position. The lower crab is at a stage just slightly more advanced and is in the air after the thrust. Trailing leg 3 is about to be placed on the ground, whilst leading leg 3 is also in the skid position.