ABSTRACT
The locomotion of free, intact cockroaches, Periplaneta americana, was studied with the aid of high speed motion pictures.
The insects used a single gait, alternating triangle, at all speeds of locomotion (5–80 cm/s) except the very lowest ones (below 5 cm/s).
Both forward (protraction) and rearward (retraction) movements of the legs relative to the body decreased in duration as the insect’s rate of forward progression increased, but at different rates. In addition, protraction was usually shorter for the two middle legs than for the remaining four.
The ratio of protraction to retraction increased as the locomotor rate increased. The rate of change of this ratio was the same for each of the legs.
Phase relationships between adjacent ipsilateral legs were constant at about 0·5 at all walking speeds above about 5 cm/s. Phase between legs in a single segment (i.e. contralateral pairs) was constant at about 0·5 at all speeds.
The locomotion of Periplaneta was compared to that of other insects. Despite the differences, a single mechanism could account for walking in each.
INTRODUCTION
Much attention is currently being directed toward the problem of control and co-ordination of leg movements during locomotion in insects (Wilson, 1965, 1966; Runion & Usherwood, 1966, 1968; Pearson & Iles, 1970). Yet, a detailed, quantitative description of the leg movements of insects during walking does not exist for the most common experimental animals. Wendler (1964) supplied such a description for leg movements in the stick insect, but this insect is little used in physiological studies of locomotion. A description of locomotion in cockroaches was given by Hughes (1952), but it is in general a qualitative one, and no longer provides the depth of detail required by the physiologist.
The present work was undertaken to provide a firm foundation of behavioural data on which to base hypotheses concerning the mechanisms of control and co-ordination of leg movements (Delcomyn, 1971). The main finding has been that the gait used by the cockroach, Periplaneta americana, the alternating tripod or alternating triangle gait, is essentially the same over nearly the entire range of observed speeds of locomotion. Only at very low speeds is there any significant deviation.
MATERIAL AND METHODS
All animals used in this study were intact adult American cockroaches, P. americana L. Each subject was placed in an oblong Perspex box for observation. The bottom of the box was lined with graph paper to give a reference grid for movements, and its walls were coated with petroleum jelly to prevent the animal from escaping. The cockroaches were photographed with a Hycam rotating-prism, high-speed motion picture camera (Red Lake Labs, Santa Clara, California) at 200 or 500 frames per second as they moved freely along the length of the box. The camera was arranged so that four to seven full steps of each leg could be captured on the film. Lighting was provided by two Photoflood lights, one above each end of the box. These lights were turned off periodically for brief periods during the photographic sessions to prevent overheating of the animal.
The films were examined with the aid of an analytical motion picture projector (L-W Photo, Inc., Van Nuys, California). Analysis consisted of counting the number of frames occupied by protraction and retraction (definitions below) during each cycle of movement, for each leg. The parameters of interest, protraction, retraction, cycle duration, protraction/retraction ratios, and relative phase positions were calculated from the frame data with the aid of a digital computer. Graphs of the pattern of leg movements (e.g. Fig. 2) were drawn for each walking sequence and used as the basis for editing the computer output. Steps during which the animal abruptly changed speed or direction were excluded, since the parameters under these conditions often bore different relationships to frequency of leg movement than they did during steady locomotion.
The terms used in describing the results are similar to those already established in the literature (Hughes, 1952; Wilson, 1966), and are as follows:
Protraction: the forward movement of a leg relative to the body and the ground.
Retraction: the backward movement of a leg relative to the body. No movement relative to the ground.
Lag: the time from the beginning of protraction of one leg to the beginning of protraction of another.
Phase: the lag between two legs divided by the cycle duration of the leg which moved first, i.e. the time relation between the movements of two legs.
RESULTS
Cockroaches do not generally run straight for long distances. However, the long narrow structure of the running box and the petroleum jelly on the walls combined to produce a large number of relatively straight runs through the field visible to the camera. In addition, the lighting was arranged so that the ends of the box were not as well lit as the centre, which tended to increase the probability that the negatively phototactic cockroach would continue through the well-lit centre rather than stop in mid-run.
The cockroaches did not appear to be excessively disturbed by the lights, for after 10–15 min in the box some moved about quite slowly. In addition, they tended to carry their bodies well off the floor of the box. Dragging the body is a mode of behaviour characteristic of cockroaches in poor condition. The range of speeds observed was about 2·80 cm/s (at a maximum temperature of 29° C). The maximum speed observed here is similar to that reported by others (Hughes, 1965).
In the present study the animals’ rates of forward progression were measured directly from the films in cm/s, and also estimated by measuring the frequency of leg movement in Hertz (Hz). The latter measure has the dual advantage of allowing cycle-by-cycle plotting of parameters, and of freeing the experimenter from the necessity of measuring directly the animal’s rate of progression, a measurement which is not possible under some experimental conditions. For these reasons, frequency of leg movement was substituted for rate of forward progression as the independent parameter in this study. The nearly linear relationship between average frequency of leg movement and rate of forward progression (Fig. 1), shows that the substitution is a straightforward one.
The movement of an animal’s legs during locomotion can be visualised with the aid of diagrams of stepping patterns, such as those shown in Figs. 2 and 3. These diagrams illustrate typical sequences of leg movements at stepping frequencies from 1·5 to 23 Hz, and show qualitatively the behaviour of both the individual step parameters, protraction and retraction, and the inter-leg timing parameter, phase. The behaviour of each of these parameters as a function of the frequency of leg movements is described in detail in the following sections.
Individual leg movements
The durations of both protraction and retraction decrease as the cockroach moves at progressively higher speeds, but they do so at different rates. This may be seen in the diagrams of stepping patterns (Figs. 2 and 3), and in Fig. 4. Retraction is nearly three times longer than protraction at the lowest frequency of leg movement, but it falls more rapidly than protraction as frequency of leg movement increases, until at the highest observed stepping frequencies it is often shorter than the latter.
This differential rate of decrease is also reflected in the protraction/retraction (p/r) ratio (Fig. 5), which increases linearly with increases in frequency of leg movement. The relationship between p/r and frequency is nearly the same for each of the legs. The parameters of the regression lines and other statistics for the data for each leg are shown in Table 1. There is no significant difference between the slopes of any of the distributions, i.e. the rate at which p/r increases as stepping frequency increases is essentially the same for each of the legs.
However, the mean p/r ratios of each of the legs do not show such uniformity, those of the middle legs (R2 and L2) being lower than those of the remaining four legs (Table 1). This difference between the mean p/r of R2 and L2 and each of the remaining legs is significant statistically to at least the 97·5% level of confidence in each case. There is no significant difference between the mean ratios of legs R2 and L2, nor between those of any of the remaining four legs. Graphically, therefore, the regression lines for R2 and L2 are depressed vertically compared to those from the remaining legs (Fig. 5). Since all the slopes are the same, the p/r ratio at any given frequency of leg movement is lower for legs L2 and R2 than for legs R1, L1, R3 or L3. This means that the middle legs are off the ground for shorter periods at any given speed of locomotion than are any of the four other legs. Although there is, in fact, a great deal of variation in the p/r ratio at any speed, thus necessitating the statistical treatment, this phenomenon may be seen quite clearly in the R2 steps in Figs. 2B and 3 A.
Timing of leg movements
Except at the very lowest speeds of locomotion (stepping frequencies less than about 3 Hz), Periplaneta always uses the alternating tripod gait. This may be seen qualitatively in the stepping patterns shown in Figs. 2 and 3. Clearly, the leg movements are rarely synchronous; that is, the three legs comprising one tripod do not usually begin protraction at exactly the same instant. Nevertheless, the overall consistency of the stepping pattern is also clear.
This consistency is reflected in the distributions of phase values. Except at the extreme low end of the range of walking speeds, there is no significant change in phase as a function of the frequency of leg movement (Fig. 6). Statistical tests support this statement (Table 2), since in no case is there a significant correlation between phase and frequency of leg movement when phase values corresponding to frequencies less than 5 Hz are omitted. This is not surprising, of course, since phase is simply a measure of the timing relationships between the legs, which in turn determine the gait employed during walking. The fact that the average phase of L1 on L3 and of R1 on R3 is 0·954 indicates that each of the front legs generally begins protraction slightly earlier than the corresponding rear legs, rather than at exactly the same time, as would be demanded for a rigid alternating triangle gait. At very low walking speeds, t stepping frequencies of about 3–4 Hz, the protraction of each front and middle leg egins earlier than usual relative to the ipsilateral rear legs, as shown in Fig. 3 B, so the corresponding phase values are reduced (Fig. 6A). This change in phase at low walking speeds occurs only in ipsilateral legs. The phases of contralateral leg pairs, that is, legs in a single body segment, do not show any reduction at low walking speeds.
This finding suggests the possibility that the mechanism(s) responsible for the phasing of leg movements may be different for contralateral leg pairs than for ipsilateral legs.
Description of the behaviour of another parameter of the timing of leg movements, lag, is implicit in the description of phase given above. Phase is simply lag divided by cycle duration. Since phase is constant over nearly the entire range of locomotor speeds, lag must bear a constant relationship to cycle duration, which is simply a reciprocal function of frequency of leg movement.
DISCUSSION
While early work on insect locomotion had been concerned primarily with the correct description of leg movement (e.g. Carlet, 1879; Morgan, 1886; Demoor, 1890), current attention has turned to investigations of mechanisms by which patterns of leg movements might be generated (e.g. Hughes, 1957; Wilson, 1965, 1966; Pearson & Iles, 1970; Delcomyn, 1971). The present work is especially relevant to some of these. Pearson & Iles (1970) have shown that alternating bursts of flexor and extensor motoneurone activity can be obtained in partially de-afferented preparations of Periplaneta, suggesting that the production of these bursts may be under the control of a central programme generator. Their results show an increase in both extensor and flexor burst durations as the burst period increases (i.e. as the frequency at which the bursts occur decreases), although the latter relationship is a weak one. Their findings fit reasonably well with the behavioural observation that as leg-cycle time increases, the duration of both protraction and retraction increase. (In the leg they examined, R3, flexion causes protraction, extension retraction.) The weak relationship between flexor burst duration and burst period would be accounted for if few or none of the flexor muscles were active during the entire period of protraction (cf. the lobster swimmeret system, Davis, 1968), so that the duration of a burst of activity in any one flexor muscle would not accurately reflect the duration of protraction. In this case, the relationship between flexor activity and burst period would not necessarily be similar to that between protraction and leg-cycle time, and their results would be fully compatible with the behavioural data.
The data reported above are also relevant to Wilson’s (1966) model of insect Wilson pointed out that with three conditions fulfilled, an insect’s gait would be a direct function of its speed of locomotion, over the whole range of speeds. These conditions were that as speed of walking increased: (1) protraction remained constant, (2) lag between ipsilateral legs remained constant, resulting in increasing phase between them, and (3) phase between contralateral leg pairs in each body segment remained constant at 0·5. Conditions 1 and 2 clearly do not hold for Periplaneta, so that the gait of this insect does not change over most walking speeds. Wilson has suggested (personal communication) that Periplaneta might be considered a ‘fast walker’, that is, an insect in which gait is affected by speed of walking only at very low speeds, and stays constant at higher speeds. While the data are not complete for low-speed walking, they do suggest a change of gait as the animal slows down, and thus support this notion.
Wilson based his model primarily on the work of Wendler (1964, 1966) on the stick insect, Carausius morosus, and Hughes (1952, 1957) on the cockroach, Blatta orientalis. The locomotion of Carausius differs from that of Periplaneta in several respects. As in Periplaneta the p/r ratio increases and retraction decreases with increasing speed of walking, but protraction is constant. The phase of leg pairs within a single body segment (e.g. L2 and R2) is independent of speed, as in the cockroach, but phases of ipsilateral leg pairs drift, increasing as speed of walking increases. Thus, in this insect gait is a function of the speed of locomotion, over the whole range of walking speeds.
The results of Hughes (1952) on Blatta have been interpreted similarly (Wilson, 1966; Wendler, 1966). However, examination of his results suggests that Blatta walks more like Periplaneta than Carausius. Hughes states: ‘Cockroaches use very nearly the same rhythm (R1, L2, R3, etc.) at all speeds from 1 to 15 cm/s [about 1–8 Hz]… ‘(p. 279), and:’ The same basic rhythm of leg movements is found at all speeds of cockroach movement, although at the very slowest ones different rhythms may be observed. But these grade insensibly into the normal rhythm with an increase in speed… ‘(p. 280). The basic rhythm is the alternating triangle gait (cf. Fig. 3 A above), as shown in some of the graphs of leg movements appearing in his papers (Hughes, 1952, 1957). None of the phase values which can be calculated from his data are substantially different from those for Periplaneta shown in Figs. 4 and 5 above. Thus, in Blatta, gait is independent of the speed of walking at medium and fast speeds, and is a continuous function of speed during very slow locomotion.
Mechanisms of locomotion in stick insects and cockroaches need not be as different as the above descriptions of their patterns of locomotion might suggest. In Periplaneta the data suggest that at stepping frequencies below 3–4 Hz, gait is a direct function of velocity. The data of Hughes (1952, 1957) suggest that non-alternating tripod gaits in Blatta also appear only below this stepping frequency (equivalent to about 5–7 cm/s, see Fig. 1). Carausius is a much more slowly moving animal, and while the alternating triangle gait is used only at the highest walking speeds, the speed at which it appears is only about 7 cm/s (Wendler, 1964, 1966), approximately the same as the critical speed for the two cockroaches. (Calculations from Wendler’s data suggest this is equivalent to a stepping frequency of about 2 Hz.) Thus, a mechanism of locomotion which would be adequate to generate the stepping patterns in the cockroaches could possibly generate those of the stick insect as well with little modification.
ACKNOWLEDGMENTS
This work was supported by a U.S. Public Health Service Physiology Training Grant to the University of Oregon and by N.S.F. grant GB-7413 to Dr G. Hoyle. I wish to thank Drs Hoyle, P. N. R. Usherwood and C. Walther for helpful criticisms of this paper.