Stepping Movements Made by Jumping Spiders During Turns Mediated by the Lateral Eyes

Jumping spiders use their four lateral eyes when making turns towards moving objects. Once a stimulus has been detected by the retina of one of these eyes, the spider turns accurately through the appropriate angle, whether or not it receives the visual feed-back it would expect from its movements (Land, 1971). Since this is an ‘open-loop’ system, each region of the retinae is capable of specifying in advance the size of the turn to be made. This leads to the interesting question of how these ‘commands’ from the eyes (turn 65° left, 140° right, etc.) are executed by the part of the nervous system that controls the legs. Turning is a complex manoeuvre involving all eight legs, and may in a large turn require several steps of each leg for its completion. The question of how accuracy of turning is achieved can thus be put : ‘what aspect or aspects of this pattern of leg movements (e.g. timing, final leg position, number of steps) is actually under the control of the instruction from the eyes?’

This paper examines three aspects of the stepping pattern during turning. First, the patterns of leg movements made during both walking and turning are described and compared; it is found that walking follows the loosely coupled alternating tetrapod pattern that Wilson (1967) found in tarantulas, and that turning is very similar to walking, except that legs on opposite sides walk in opposite directions, spinning the animal about a vertical axis. Secondly, the nature of the ‘oscillators’ responsible for stepping are considered, and on the basis of a variety of observations it is concluded that proprioceptive afference from the legs is essential both for the maintenance of the stepping rhythm and for attaining constancy of step amplitude under a wide range of external conditions; a model of the possible control system of each leg is presented to account for these findings.

Finally, the question of how accuracy of turning is achieved is discussed. Four classes of possible explanation are eliminated, leaving one which is compatible with the results described. This supposes that the eye specifies the number of steps that have to be taken, and turns stop when the appropriate number of steps have been made and counted.

Metaphidippus harfordi were collected locally from California redwoods (Sequoia sempervirens) and were kept in Petri dishes containing moist cotton-wool until required. They were fed on houseflies at about one per week.

To examine walking and turning behaviour the spiders were restrained by waxing a piece of stiff card to the back of the prosoma, while the animals were briefly narcotized with CO₂ from which they recovered in 2–5 min. By means of this ‘handle’ the spiders were clamped to a support and given a 1·3 cm diameter card ring of about their own weight (15 mg) to hold between their feet. In some experiments (see RESULTS) larger rings were used.

To elicit turns, the spiders were placed in the apparatus described by Land (1971), which consists of a white drum on which a small (5°) black spot could be moved around the animal in short (5°) steps in the horizontal plane (Fig. 1). The velocity of the spot during these steps was 25°/sec, which had been found to be optimal for eliciting turns. The response to movement of the spot may be either a complete turn (in which the spider turns the ring through an angle equal to that between the target and the animal’s longitudinal axis), apartial turn of 10–20° whose size is independent of target position, or no response at all. Under these conditions the spider receives no visual feed-back from its turn.

Forward running often occurred spontaneously, or could sometimes be evoked by holding a suitably interesting object (such as another spider) directly in front of the fixed animal. Backward walking could be produced by waving a threatening object (e.g. a pencil) a few mm from the spider.

Leg movements were filmed from above, using an Arriflex 16 mm ciné camera operating at either 25 or 50 f/s, and the leg movements were examined frame by frame using a stop-motion projector (Specto).

Although the situation in which the spider is placed, i.e. it can move its substrate but not itself, is obviously artificial, it can be justified as being not importantly different from the ‘real world’ on the following grounds. First, these spiders are arboreal and the twigs and leaflets of redwood trees are their normal habitat, so that manipulation of a card ring of the spider’s weight is little different gravitationally from the situation of the spider walking or turning on the underside of a twig, which they often do in nature. The principal difference here is that the ring has a greater moment of inertia than the spider (by a factor of roughly 27 times) and this might be expected to affect turning behaviour. However, as will be shown, increasing this moment of inertia to 400 times that of the spider has no effect on the accuracy of turning and no obvious effect on the pattern of leg movements. It is therefore almost certain that the spider’s motor behaviour in manipulating the small ring used here is very similar to its normal unrestrained behaviour. Secondly, the movements made during turning and walking around the ring look no different from those made with the animal unrestrained when both are studied on film. Unfortunately it has not been possible to obtain sufficient photographic resolution to make accurate records of the leg movements of freely moving spiders, but the qualitative appearances of the leg movements of free spiders are not in any obvious way different from those made of restrained animals.

A series of nine 100 ft films were made using a total of four spiders (all female) turning the small ring, and another series of nine films using three other spiders turning larger rings. In each film stimuli were presented once at each of the 72 positions around the animal (5° apart), and each such ‘run’ usually resulted in from 20 to 40 turns.

Jumping spiders can move in six distinct ways. They can walk forwards, backwards and sideways, turn left and right, and jump. This paper is principally concerned with turning, but since stepping during turning is closely related to forward and backward locomotion, these will be described briefly. Wilson (1967) studied walking in tarantulas, and concluded that at all speeds the basic stepping pattern was one of alternating tetrapods, with adjacent legs on each side stepping alternately and corresponding legs on opposite sides also alternating, so that the resulting pattern was one in which L₁, R₂, L₃ and R₄ tended to step together, followed by R₁, L₂, R₃ and L₄, and so on. The stepping pattern in jumping spiders seems to be very similar (Fig. 2). During forward walking each leg is engaged in its powerstroke for approximately 70 % of the duration of the complete step, independent of the rate of stepping. Returnstrokes (protraction) of adjacent legs tend to alternate, and those of adjacent-but-one legs tend to occur together. The result is that the legs appear to step in a metachronal rhythm beginning either at the front or the rear (dashed lines). In spite of a great deal of variability of the timing of individual steps, the reader can convince himself that this pattern exists throughout most of the records in Fig. 2. If one plots the time of occurrence of the onset of the returnstroke of one leg, as a fraction of the time interval between the onset of returnstrokes in another leg, the relations between the timing of leg movements can be expressed succinctly as phase histograms (Fig. 5). The position of the peak of the histogram indicates the phase, or relative timing of one leg movement with respect to another, and the spread around the peak can be taken as a measure of the degree of interaction between legs, i.e. a wide spread indicates a weak coupling. The histograms given in Fig. 5, derived from Fig. 2, confirm that interactions between adjacent ipsilateral legs are strongly negative (peak around 0·5), and that the interaction between opposite legs of the same segment is also negative, but the peak is broader and hence the coupling looser (see also ‘similarity of turning to walking’ below).

Backward walking (of which Fig. 2d is one example) is very similar to forward walking except that the powerstroke, in which the leg is in contact with the substrate, is a protraction movement rather than a retraction. Otherwise, the relative duration of powerstrokes and returnstrokes, and the ‘alternating tetrapod’ pattern of stepping is the same as in forward locomotion. Very often in backward locomotion, and occasionally in forward locomotion the first pair of legs are not used but are held off the ground (Fig. 2 c and d) so that the normal tetrapod gait becomes, without any other change, a tripod gait (L₂, R₃, L₄/R₂, L₃, R₄). Backward walking, which the spiders appear to be able to perform as easily as forward walking over a similar range of speeds, is most commonly seen when the animal is suddenly presented with a threatening object in front of it.

Sideways walking occurs principally during courtship displays by the male, in which he approaches the female in a zig-zag series of arcs (Crane, 1949; Drees, 1952). The leg movements consist of alternating flexions and extensions of the limb joints, very much like crab walking; however, the timing and coordination of the legs during sideways walking has not been studied.

Jumping is peculiar in that the sudden extension of the 3rd and 4th legs which causes the jump is not the result of the action of the leg muscles themselves, but of muscles in the prosoma which raise the hydrostatic pressure of the body fluid; this causes a sudden inflation of the legs resulting in their rapid extension (Parry & Brown, 1959). Salticids may jump 1 or 2 cm when leaping on prey, or much larger distances when pursued.

It should be said that, with the exception of jumping which is always quite distinct, the various kinds of locomotion described above merge into one another somewhat during ordinary locomotion over a complex substrate. Walking on leaves and twigs may involve forward walking and some turning and sidestepping, and it is clear that the animal’s motor control system is in fact much more flexible than the above characterization would imply. However, certain activities such as turning can be reliably evoked in isolation, and it seems sensible initially to deal with these rather stereotyped mechanisms.

There are two kinds of question that arise when one asks how a turn is performed. First, what happens to the stepping pattern? Do the legs on one side walk faster or take longer strides than those on the other; or do the legs on the two sides walk in opposite directions, in which case, are step duration and step length the same or different on the two sides (imagine a rower turning a boat)? The answer appears in this case to be that the two sides do step in opposite directions, and that both step frequency and step length are the same on the two sides (fig. 3). The second question concerns what happens to the rhythm of leg movements at the end of a turn and during the interval between one turn and the next. Do the legs return to a resting position after each turn, or if not, what happens to the stepping rhythm when the next turn begins? The answer to this is that there is no rest position, and that the rhythm of stepping is resumed at the beginning of the next turn, as though there had been no temporal gap.

In Fig. 3 the pattern of stepping during eight consecutive right turns and thirteen consecutive left turns are shown. The terms ‘left’ and ‘right’ here indicate the direction the spider would have turned if it were free and the substrate fixed. The turns were evoked by moving a spot through an angle of 5° every 2 secs, from the animals’ right rear towards its front in Fig. 3,a, and from the front towards the left rear in Fig. 3 b. Since the spider does not respond to all stimulus movements, each vertical line across the record represents a temporal gap of 2 sec or a multiple of this.

The method of plotting the step pattern is the same as in Fig. 2 (retractions are shown as heavy lines and protractions as spaces) except that the abscissa in this case is not time, but the cumulative angle through which the spider turns its ring. The reasons for this change are, first, that the temporal gap between successive turns would obscure the basic regularity of the stepping pattern, which continues across the time interval, and secondly, that turns can be accomplished at a variety of speeds (see Figs. 9 and 10) and the most constant feature of the pattern is not the duration of a step, but the angle turned during it. The record shown in Fig. 3 is one of a total of nine such records filmed with four animals, and was selected for analysis because it contained the greatest number of large turns. The record also shows a typical relationship between the sizes of the turns made and the angular positions of the stimuli eliciting them (Fig. 4); most of the turns approximate closely to the stimulus angle (‘complete’ turns), except four, nos. 29, 30, 33 and 38, which are of small magnitude and unrelated to the stimulus angle (‘partial’ turns). The functions of the two kinds of turn have been considered in an earlier paper (Land, 1971). The unnumbered dots in Fig. 4 are the turns from the same stimulus run as those shown in Fig. 3, but which are not illustrated.

During turning the legs on the side towards which the animal is turning walk backwards, while those on the side turned away from walk forwards. The result is that the animal spins about a vertical axis through the prosoma ; this is true not only in the experimental situation here where it is more or less forced to turn in this way, but also when the spider is freely moving on the ground.

A comparison of Fig. 3 with Fig. 2 shows the following.

• The pattern of stepping of the legs on each side is the same in turning as in walking. The dashed lines in Fig. 3 show the same apparent metachronal rhythm (1 – 2 – 3 – 4 or 4 – 3 – 2 – 1), or alternation of ipsilateral leg-pairs (1 and 3, 2 and 4) as occurs in walking. This is illustrated statistically in Fig. 5, in which the phase relations of various combinations of legs are compared during walking and turning. Because of the fact that steps run across the temporal gaps between turns, ‘phase’ is measured here not in terms of relative timing but as the angle of the ring at which a particular leg steps, within the angle turned during a step by another leg. The condition for the validity of a comparison between phase relationships determined by these two methods is that the timing of the movements of an individual leg is determined by the position of that leg and its neighbours, and not the converse. This point is very important when considering the mechanism of co-ordination of leg movements, and will be considered further in the discussion; for the moment we will justify the comparison on the grounds that if the appropriate 2 sec gaps were inserted into Fig. 3, plotted with time as the abscissa, phase relationships would become totally meaningless. Fig. 5 shows that adjacent ipsilateral leg pairs have a strong tendency to step out of phase with each other, during both turning and walking, that adjacent-but-one pairs tend to step together but the strength of this interaction is much less than that between adjacent legs, and that contralateral leg pairs show a weak tendency to step out of phase. The numbers above each histogram are an attempt to quantify the extent of phase-locking, and represent:

  

  This index, which is similar to the physical definition of contrast, is negative when legs tend to step out-of-phase and positive when in-phase, and its magnitude is a useful measure of the strength of this tendency, provided the histograms do tend to clump around 0·5, or 0 and 1, and do not for example show two obvious peaks at 0·25 and 0·75. The values given in Fig. 5 support in sign and generally in magnitude the conclusion that the mechanism underlying the coupling of the leg-movements during turning is the same as that during walking.

  It is interesting to compare the extent of phase coupling in Wilson’s study of tarantula walking with that given here for salticids. From the data given in Wilson (1967) Figs. 2 and 3, the corresponding indices for adjacent legs, next-but-one legs and opposite legs are −0·89, +0·61 and −0·49; these are rather greater than those obtained here for forward walking, −0·53, +0·42 and −0·25, implying that although the pattern of coupling is the same, it is looser in salticids than in tarantulas.

• The proportion of time spent in powerstrokes and returnstrokes is the same in turning as in walking. It was mentioned above that during walking the relative amounts of time spent by a leg in returnstrokes is approximately 30% of the total, over at least a six-fold range of speeds. This is also the case during turning (Fig. 6) both for those legs whose powerstroke is a protraction (side turned towards) and for the opposite side which is walking forwards. This is less true for the first pair of legs, which spend a greater proportion of time in the air (up to 60%) and it is often not clear whether they are participating in the turn at all.

There are certain details of the movements of legs during turning which differ from those in walking. The tip of each leg describes an arc during a turn, but a line during walking, and because the position of the ring with respect to the body axis varies from one part of a turn to another, the positions in which a depressed limb begins its powerstroke vary from step to step. However, these can probably be regarded simply as mechanical consequences of the different situations, and the similarities between the timing and pattern of stepping during walking and turning imply the existence of a common mechanism in which the limbs of each side can give motion forwards or backwards, together in the case of walking, and in opposite directions in turning.

At the end of a turn each leg simply stops in whatever stage of its cycle it has then reached (drawings on Fig. 3). The legs are not ‘reset’ to a standard rest position, and the next turn begins with the legs in the positions they reached when they stopped. Provided the succeeding turn is in the same direction as the preceding, legs which are engaged in a powerstroke at the end of one turn, stop, and then resume the powerstroke at the beginning of the next. More interestingly, legs engaged in a returnstroke resume their returnstroke at the beginning of the next turn ; they are depressed to make contact with the substrate during the interval but do not complete the stroke until the next turn begins. The significance of this observation is that returnstrokes are not inviolable, as they would be if the model adopted for their cause were a relaxation oscillator -as in the flyback of an oscilloscope trace-but are subject to the same kind of controls that operate to start and stop powerstrokes at the appropriate moment. There are several examples of this shown in Fig. 3 (e.g. R₂ at the beginning of turn 2, L₂ at turn 3, etc.), and the detail of one such step is shown in Fig. 7. At the end of the ‘partial’ turn No. 30, leg R₃ begins a returnstroke, the leg makes contact with the ring at the end of the turn and remains stationary for 2 sec before completing its returnstroke during the first two frames of turn 31.

The actual positions of the legs that are adopted at the ends of turns depend principally on the phase of each leg’s stepping cycle that has been reached, but the exact details of the stance do also depend on the angle the ring makes with the body axis. However, it is important to point out that the position of the ring only modifies the details of the leg positions, it does not determine the rhythm itself. Clearly, if the average angle turned during a step was 180°, the spider would always encounter the ring with a particular foot at the same stage in that leg’s cycle, and the instantaneous position of the legs both during and at the end of turns would depend only on the ring position. However, this is not so. The average angle turned in the course of a single step by one leg is 65° (S.D. 28°) for the series of turns shown in Fig. 3. If one excludes obvious examples of double stepping-such as that of R₄ near the end of turn 2, or L₃ at the end of turn 7-this figure becomes approximately 75°. Further, because of the symmetry of the basic stepping pattern, this ‘repeat angle’ for each leg is the repeat angle for all legs. The result is that the legs virtually never encounter the ring in the same position at the same stage of their stepping cycle. This observation proves that it is the movements of the legs that determine the position of the ring, and not that the ring position determines the rhythm of the legs.

The effect that ring position does have is to determine the point at which each leg encounters the substrate when beginning a step. For example, in Fig. 7 leg R₂ makes two returnstrokes, one towards the end of turn 28, and another during turn 31, and the pre-and post-returnstroke positions of the legs are different in the two instances. It is obvious in this example that the position of the edge of the ring determines the starting position of the new stroke, although it is less clear why the leg is protracted at the particular time (or position) that the returnstroke begins. One would expect that a spider turning on a uniform flat substrate would show much more uniformity of individual leg movements than when turning a ring. Unfortunately, no satisfactory films of this have yet been made because of the difficulty of restraining the animal while permitting it to walk; a problem which can only be solved using a globe and a feedback arrangement to keep the animal still, or by presenting it with the more difficult problem of dealing with a ring, as in this paper.

If a stimulus on the animal’s left is followed by one to the animal’s right, the spider may make a left turn followed by a right turn (Fig. 8). During consecutive turns in the same direction legs engaged in a powerstroke continue in powerstroke, whether this is a protraction or retraction. When consecutive turns are in different directions one of two things might occur. Legs in powerstrokes might continue in powerstrokes, but change direction (i.e. a leg formerly in contact with the substrate and retracting would remain in contact but protract) or alternatively, a leg engaged in a powerstroke might continue in the same direction but change from a powerstroke (depressed) to a returnstroke (elevated). The example in Fig. 8, and three similar instances filmed, show conclusively that the former is the case-the legs change the direction of their movement, but powerstrokes do not become returnstrokes. The spider appears literally to retrace its steps.

Fig. 9 is a plot of the angular position of the ring as a function of time for six turns made by two spiders. In each case the stimulus is behind the animal (170 ° to the left or right). The records have been selected to illustrate both the range of angular velocities over which the spiders can make turns of a given magnitude (110 – 1200 ° /sec), and also the variations in the rate of turning that can occur in the course of individual turns. The fourth turn, for example, begins fast and finishes slowly, which is the most commonly seen condition, but in others like turn 3 the reverse is true. In turns 5 and 6 there are several changes in velocity in the course of execution of the turns.

Examination of turns of different magnitude showed no correlation between the size of a turn and the rate of its execution; large and small turns could both be performed fast or slowly. Similarly, successive turns made by the same animal could be performed at quite different rates. The principal conclusion is that the rate at which a turn is performed is quite unrelated to the accuracy of its execution.

There are three possible ways in which the spider could alter its rate of turning: (i) by increasing the length of each step, keeping the rate of stepping constant; (ii) by increasing the rate of stepping while maintaining step length ; (iii) by some combination of the two.

In Fig. 10 four turns are illustrated (retracting legs only); they cover a five-fold range of turning velocities, and the leg movements are plotted first with time as the abscissa, and secondly, with angle turned. It is immediately clear that while the duration of individual steps varies inversely with the velocity of turning, the length of each step (i.e. the angle turned by the spider during that step) remains approximately constant.

This relation is shown for eleven turns in Fig. 11 (closed circles). Because in the course of a single turn of say 150 ° each leg steps only once or twice, the points are averages obtained from between five and ten steps-i.e. all the steps made during that turn -and are necessarily confined to turns of greater than 120 °. In the nine films there were another thirteen turns in this range at low velocities, but these all fell within the range of those illustrated and have been omitted for clarity. All the turns made at velocities greater than 250 ° /sec have been included. Fig. 11 shows clearly that while the rate of stepping is a linear function of velocity (causally of course this must be the other way round) the angle turned per step stays virtually constant over the ten-fold velocity range included. The lines on the graph are not attempts to fit the points, but both represent the hypothesis that in each step the animal turns 75 °. This fits the data fairly well ; in fact the points in (a) suggest a value closer to 70 ° and those in (b) to 80 °, but this small discrepancy probably reflects the difficulty of obtaining sufficient time resolution when filming at 25 frames/sec. It is concluded that hypothesis (ii) is correct: stepping rate changes but not step length.

By giving the spider rings of different sizes to turn it is possible to examine the ways in which the animal deals with inertial loads that are very much greater than that of its own body. If no compensation is made for the increased moment of inertia of the ring in terms of the pattern of energy output during the turn, one would expect the accuracy of turning to be greatly impaired-turns will be much smaller than they ought to be -and that there will be a marked decrease in the rate at which they are executed.

The spider’s moment of inertia can be estimated approximately by assuming that it is going to lie somewere between that of a sphere of density 1 with the same mass as the spider (average 15 mg), and that of a flat rectangle of roughly the same dimensions as the spider’s body (1 × 5 mm) also with a mass of 15 mg. For the sphere, the moment of inertia, I, is given by ⁠, and for the rectangle ⁠. These give values of 14·0 and 32·5 mg mm² respectively and, since the moment of inertia is certain to lie between these two, we shall assume for convenience that it is 20 mg mm².

In the series of experiments to be described the spider held rings of the same weight (25 mg) but different diameters; this was achieved by changing the material of the rings from stiff card to light tissue paper. The moment of inertia of a ring about its diameter is given by ⁠, and the smallest ring (A) had a radius of 6·5 mm and moment of inertia of 530 mg mm², for the second (B) the corresponding figures were 24·5 mm and 7500 mg mm², and the largest (C) 38 mm and 18,000 mg mm². The three rings just described thus had moments of inertia approximately 26·5, 375, and 900 times that of the spider.

The work done by the spider in accelerating its ring to a particular angular velocity (ω) is equal to ⁠, the kinetic energy of the ring, which is also the work done in decelerating the ring to rest. This means, for example, that if the spider performs two turns of the same size at the same overall velocity, one with ring A and another with ring C, it must do 38 times more work in the second case, or 900 times as much work in turning ring C as it would in simply turning itself at the same speed.

The most remarkable finding was that the spider was able to turn the largest ring, with very little apparent difficulty. To the observer, the activities of the 5 mm animal turning a 76 mm ring appear ludicrous, but, nevertheless, the animal turns at speeds within the same range of angular velocities that it turns the smaller rings, and with very little difference in the accuracy with which the turns are completed. The results are summarized in Tables i and 2.

Accuracy of turning, expressed as the difference between the angle turned and the stimulus position, is the same for rings A and B, and is very similar to that obtained a year earlier on another animal turning a small ring (negligible mean error −0·5°, standard deviation of errors 16·2°, Land, 1971). With the largest ring there is an increase both in the average error-interestingly the spider tends to overshoot by 10° – and in the variability of the error (Fig. 12). However, this error is still small compared with the size of the turns themselves, and one can conclude that whatever other compensations the spider has to make in coping with the problem of dealing wth large moments of inertia, they do not involve a serious decrease in the accuracy with which turns are made, and in fact may well serve to maintain this accuracy.

By observation alone it quickly becomes apparent that turns made with the largest ring cannot be made as rapidly as those made with the smaller rings. This is illustrated in Table 2, where velocities were measured from films. The effect of inertial load is to restrict the range of velocities over which turns are made. The lowest velocity with all three rings is about the same (164–2oo°/sec), but the highest velocity decreases by a factor of nearly three for ring C, and the mean decreases accordingly by a factor of rather less than two. Notice that if the same work were done in all three cases in moving the ring one would expect the mean velocity for ring B to be the square root of I(A)/I(B) times that for ring A, i.e. 3·8 times less, and for ring C, 5·8 times less. The figures are in fact roughly 1·3 and 1·8 times, meaning that the spider is adjusting both the speed of turning, and the work done, in dealing with increased inertial load.

Analysis of the rates of stepping, and sizes of step, that are made during turns with rings B and C showed that the generalizations made earlier for changes in velocity of turning are still valid under conditions of inertial loading. The angle turned during a step remains approximately constant, and the rate of stepping is proportional to the rate of turning. For those turns that were large enough to permit step length and duration to be measured, their values are included in Fig. 11 (triangles, ring B; squares, ring C). Their mean values are a little higher than those obtained with the smaller ring (85°and 87° on Fig. 11 b, as opposed to 78°), but the difference is not significant.

What happens when the spider attempts to stop a ring which is moving with a large angular momentum, as it must in order to turn through the correct angle? If it simply ceased all motoneurone firing, one would expect that the momentum of the ring would carry it well past its ‘intended’ final position. That this is not the case can be seen from Fig. 13, which shows the time courses of four large turns made with each of the three rings.

In the case of turns made with ring A, acceleration and deceleration are apparently instantaneous ; at least they occur within the 40 msec, between frames of film. With ring B there is a slight indication that it takes a frame or two for the ring to reach its maximum velocity, but more interesting is the fact that the ring clearly overshoots its final position by about 10°, and then returns to its final resting position in 40–80 msec. In C, both the initial acceleration time, and the overshoot at the end of the turn become more obvious. The overshoot may be as great as 20°, followed by a return lasting 200 ms, and itself followed by an overswing in the opposite direction. The ring is thus not simply allowed to stop, or even actively ‘braked’ when the final position is attained. Instead, the turn is terminated by a system which ‘clamps’ the position of each limb such that if the limb departs from that position it is brought back. The system, which clearly comes into the category of a ‘resistance reflex’, responds to the momentum of the ring as though it were a damped spring, and the result is a damped oscillation. It is interesting that this system does not appear to come into operation until the moment the final position of the ring is attained; the evidence for this is that no deceleration apparently occurs before the final, stable position of the ring is reached (dotted lines). In other words, there is no indication that the legs know when to end the turn until they have actually got there. Under more normal circumstances, where the spider has only its own momentum to oppose, there is of course no overshoot, and since the animal possesses a system capable of coping with several hundred times the load it could reasonably be expected to encounter, stopping its turns in the correct position presents no problems.

It can be shown, by placing a spider on a turntable and measuring the torque with which the spider opposes forced rotation, that a resistance reflex operates after the end of the turn when the animal is perfectly stationary. It can also be shown (Land, unpublished data) that the strength of this reflex, measured as the counter-torque produced per degree of forced rotation, lies within a factor of two of the equivalent measurement calculated from the size of the overshoot produced at the end of a turn. It seems likely from this that the reflex that stops the turn continues to operate through the intervals between turns.

It has been shown that jumping spiders can walk forwards or backwards, and that in most respects the two forms of locomotion are mirror images of each other. In forward walking depression is coupled to retraction (powerstroke) and elevation to protraction (returnstroke): in backward walking the converse is true. The proportion of time spent in powerstrokes and returnstrokes is the same in both forward and backward walking (about 70 and 30%), and the pattern of phase relations of the legs during stepping (adjacent legs strongly out of phase and opposite legs weakly so) is also the same.

During turning the same observations hold, with respect to coupling (Fig. 3), powerstroke and returnstroke timing (Fig. 6), and stepping pattern (Figs. 3 and 5). The major difference, of course, is that in turning, the legs on the two sides walk in opposite directions: those on the side contralateral to the direction of turning walk forwards, and those on the ipsilateral side backwards. An observation that further strengthens the analogy between walking and turning is that the most anterior and posterior positions attained by a leg during a step tend, on the average, to be more posteriorly directed in forward than in backward walking; in other words the powerstroke retractions of forward walking take the leg farther backwards than the returnstroke retractions of backward walking. The same is also true of turning; the legs contralateral to the direction of turning in general occupy positions that are farther backward than those of the ipsilateral (backward walking) legs. This can be seen in the drawings on Fig. 3.

On the basis of these observations, and in the absence of any evidence to the contrary, we shall assume in the rest of the discussion that turning and walking are mediated by the same two neural mechanisms: one command arrangement (not necessarily a single fibre!) that evokes forward stepping and another that evokes backward stepping on each side of the body. The two forward or the two backward commands would be active in walking, whereas in turning opposite commands would operate on the two sides of the body.

Most recent theories of locomotory activity in arthropods postulate some sort of oscillatory pacemaker in the C.N.S., driven by a central ‘command’ but largely independent of peripheral feed-back. There is a considerable body of evidence which supports the existence of such endogenous pacemakers; examples are cicada tymbal activity (Hagiwara & Watanabe, 1956), locust flight (Wilson, 1961), crayfish and lobster swimmeret beating (Hughes & Wiersma, 1960; Davis, 1969a), cricket chirping (Bentley, 1969) and cockroach walking (Pearson & Iles, 1970). In all these systems the rhythm of the particular activity is observed to continue after the removal of peripheral feed-back demonstrating that the source of the rhythm is endogenous to the C.N.S., and in those cases in which proprioceptive feed-back has been shown to have a modifying role, this has been either the tonic (Wilson & Gettrup, 1963) or phasic (Davis, 1969b) reinforcement of the endogenous rhythm.

Two of the observations reported here indicate that proprioception plays a very much larger role in the turning behaviour of spiders than has been postulated for other systems. The first is that the aspect of the stepping rhythm during turning that varies least is the average amplitude of a step (i.e. the angle through which the animal turns during a step). Fig. 11 shows that this is virtually constant over a ten-fold range of stepping speeds, and over an even greater range of inertial loading. It is difficult to imagine how this could come about unless the oscillator (s) responsible for stepping were very directly influenced by proprioceptive information, since maintaining a constant step amplitude at different speeds requires a compensatory increase in power, and keeping a constant amplitude under different conditions of loading requires a change in both rate of stepping and power output (see RESULTS: effect of varying inertial load). The information required for these compensations cannot be entirely ‘built into’ the oscillator, and must originate in the legs that are doing the turning.

The second observation has more profound consequences for existing models of how neural oscillators function. This is the finding that at the end of a turn the entire stepping rhythm is ‘frozen’ with each leg simply stopping in whatever phase of protraction or retraction it has reached (Figs. 3 and 7), and that after an indefinite period of time the legs recommence the stepping rhythm from where they left it, when a new turn is initiated. For this to occur, the oscillator that drives each leg must be capable of being stopped and then restarted at a later time, while remaining in the same phase of its cycle. This requires that, during the period between turns, the oscillator ‘remembers’ what this phase is. This could in principle be done by an internal memory, although the sudden activation of a memory lasting at least several seconds and probably indefinitely (as long as the spider stays in the same position) seems unlikely. Much more plausible is the idea that the ‘memory’ is the actual position of the limb, as indicated continuously by position-sensitive proprioceptors in the limb.

The models that have so far been advanced to account for rhythmic activity in arthropods are not able to accommodate this property of being startable and stoppable at any phase of their cyclic activity. Wilson’s (1966) models of neural oscillators based on excitatorily or inhibitorily coupled groups of neurones, Pearson & Iles’s (1970) and Delcomyn’s (1971) models of cockroach stepping involving a ‘burster’ neurone or its logical equivalent as the source of the rhythm, and Davis’s (1969) postulation of travelling waves of excitation in the neuropile containing the lobster’s swimmeret motoneurones, are all essentially ‘free-running’ oscillators, working faster or slower depending on the rate of activity in the command fibres driving them. When they stop, as a result of cessation of command fibre drive, they presumably do so at some stable point in their cycle, for example, at the end of a power or returnstroke movement. For the spider, however, cessation of activity, and its subsequent re-initiation, can occur at any stage of the cycle of the oscillator, and this requires a different kind of oscillator in which the knowledge of its phase is stored.

It seems unlikely that the nervous system of jumping spiders is particularly different from that of other terrestrial arthropods-certainly not from that of the tarantulas studied by Wilson (1967). Rather, because the models that have been developed to account for arthropod locomotion have been concerned principally with ongoing activity, the questions of when and how this activity is terminated appear to have been ignored. In the case of the spider these are crucial, since the animals’ nervous system must be organized in such a way that brief turns can be executed accurately without visual feed-back (Land, 1971), which means that rhythmic stepping must be started and, more importantly, stopped after only one or two, or a fractional number of cycles of the rhythm of each leg. This is not an easy property to build into an ‘oscillator’, but it may be of importance not only for animals that make accurate turns as jumping spiders do, but for any arthropod that either turns or runs short distances.

There seems no reason at present to abandon the idea of an ‘oscillator’ as the producer of rhythmic stepping-indeed this is no more than a tautology-the problem is the extent of proprioceptive involvement in the way the oscillator is driven. I agree with Wilson’s cautious assumption, in discussing tarantula walking, that ‘each leg and the control mechanism of its half-ganglion comprise some sort of an oscillator’.

Any neural model that attempts to account for the leg movements observed during turning must be compatible with the following observations.

• The stage (or phase) of its stepping cycle in which a leg begins a turn is the same as that at which it ended the preceding turn. The intervening time interval does not affect the continuity of the rhythm of stepping (Fig. 3), and the legs do not come to a standard rest position between turns.

• This is true for returnstrokes, which survive temporal interruption in the same way as powerstrokes (Figs. 3 and 7).

• The phase of the stepping rhythm of a particular leg at an instant during a turn is determined in part by that of its neighbours: in particular by the adjacent ipsilateral legs and to a lesser extent by its contralateral homologue (Fig. 5).

• The rate at which turns are executed, with the same load, may vary by a factor of at least ten. The rate of turning and stepping must therefore depend on internal factors, i.e. the rate of central ‘driving’ (Figs. 9, 10 and 11).

• The rate of turning is altered by the inertial load against which the spider turns; a greater load decreases the upper limit of the range of turning velocities. Nevertheless, the spider still does more external work, and thus load affects both the velocity of turning and the power supplied to the legs (Table 1).

• Neither the rate at which a turn is executed, nor the load against which the spider turns has more than a minimal effect on the average amplitude of the steps the legs make (Figs. 10 and 11). This is about 75 ° per step.

• The accuracy of turning is not affected by a ten-fold change in the rate of turning, nor by at least 100-fold difference in the magnitude of the spider’s inertial load (Figs. 4, 12 and additional observations).

• When turns are made in opposite directions the coupling of retraction to depression and protraction to elevation (as in forward walking) changes to the converse (as in backward walking) for the legs on one side, while those on the other side change from the backward to the forward walking coupling pattern (Figs. 3 and 8).

• When successive turns are made in opposite directions, each leg stays in the same stroke (power or return) as previously, but changes direction.

The model presented in Fig. 14 is an attempt to design an arrangement that would work under the constraints outlined above. It makes no claim to be more than a mnemonic device consistent with these constraints, and the ‘neurones’ of which it is constructed are intended as logical elements rather than as real cells. The symbols used in the model are explained in the figure legend, and the following section will be used to indicate the important features of the model, and explain its mode of operation.

The principal difference between this model and those of Wilson, Pearson & Iles, Delcomyn, and Davis, is that the ‘oscillator’ that determines the pattern of the instantaneous output of the motoneurones is functionally independent of the rate at which these motoneurones are driven. This is made necessary by conditions (i) to (iii) above which demand that a leg’s phase is determined by its own position and that of its neighbours, and (vi) which requires that the amplitude of each step is independent of the rate at which the rhythm is driven. In the model this is achieved as follows. Length-sensitive proprioceptors, functionally in parallel with the retractor and protractor muscles, drive two pairs of cells (R ′ and R ″, P ′ and P ″) which are coupled by reciprocal inhibition in such a way that only one of each pair (R ′ or P ′, R ″ or P ″) is active at any one moment. These four cells constitute the two oscillators that drive the retractor and protractor motoneurones during locomotion. The degree of excitation that each member of the R ′ R ″ pair and the P ′ P ″ pair receives from the proprioceptors (R_p and P_p) driving them is different, so that R ′ will be active right up to the end of the retraction stroke, when P ′ with its much weaker input takes over. Similarly, P ″ is the active member of its pair, except at the very end of protraction when the weak input to R” becomes relatively greater. In addition to the proprioceptive input from their own segment, the oscillator cells receive inputs from adjacent and opposite legs, so that the determination of which member of each pair is active is influenced by the activity of neighbouring limbs (condition (iii)). The reason for having two differently biased oscillators rather than one will become apparent after the role of command fibre drive has been discussed.

The oscillators R ′ P ′ and R ″ P ″ are active all the time whether or not the limb is moving, and their activity constitutes the ‘memory’ of what phase the limb is supposed to be in that persists between turns. However, which oscillator cell drives a particular motoneurone (R_m, P_m) and how fast the driving is, are determined by which command fibre (forward F, or backward B) is active, and on the rate of this activity. The model assumes that the effect of command fibre input is to selectively facilitate the synapses via which the oscillator cells drive the motoneurones. Thus when F is active, the synapses of the R ′ P ′ oscillator are facilitated and stepping is weighted in the direction of retraction: when B is active R ″ P ″ controls the step. Facilitation is graded according to the tonic frequency of command-fibre activity, so that this frequency determines the amount of synaptic driving that the motoneurones receive and hence, ultimately, how fast the stepping cycle is driven. The importance of this arrangement is that command-fibre activity determines only the rate and direction of stepping. The phase of its cycle that a leg is in, during a turn or between turns, depends only on the ongoing activity of the oscillators. Similarly, step length will remain constant under different conditions, since this depends only on the threshold levels of proprioceptive input that P ′, and R ′ and P ″, and R ″ use in establishing which member of each pair shall be active. This meets condition (vi) above.

Two oscillators are necessary rather than one because of condition (ix). This requires that when the command changes from forward to backward the apparent phase of the leg also changes; a leg near the end of a retracting powerstroke now finds itself at the beginning of a protracting powerstroke. In models based on single oscillators-at least ones that the author could devise-a change from one command to the other could be made to cause a switch from powerstroke to returnstroke, but not a change in direction and the implied change of phase. Having two oscillators, one biased in favour of retraction (P ′ R ′) and the other protraction (P ″ R ″) gets round this difficulty. It can also, incidentally, be used to explain the observation in Part 1 of the discussion that retracting powerstrokes retract the leg further than retracting returnstrokes (and vice versa), since the relative strengths of the inputs to R ′ and R ″ require that the legs attain different positions (more retracted for R ′) before P ′ or P ″ are allowed to become active.

The appropriate coupling of retraction to depression and protraction to elevation, or vice versa, is managed here by making the R_m and P_m motoneurones drive both the depressor and levator motoneurones (D_m and L_m) directly. The appropriate synaptic connexions are ‘gated’ by the command fibres by a facilitation mechanism similar to that by means of which they drive R_m and P_m. This meets condition (viii).

Finally, the motoneurones receive a second kind of proprioceptive input from the legs (P_p*, P_p*) proportional to the force exerted or cuticle deformation produced during the turn. This increases motoneurone output as the load against which movement is performed increases (condition (v)).

The model makes a number of predictions, for example, what effects de-afferentation or amputation should have, and these can be tested in due course. No attempt has been made here to incorporate an explanation of the way in which turns are stopped. It is clear from Fig. 13 that this involves not only the cessation of the turning command, but the imposition of an active resistance reflex clamping the legs in their final positions. However, the nature of this reflex, and those that operate in stationary animals are a separate matter, and will be discussed elsewhere.

In the introduction the problem was raised as to how the spider manages to turn through an angle specified by the position on the retina at which a stimulus was detected. We are now in a position to narrow down the choice of mechanism by which this might be done. There are five possibilities.

This possibility was dismissed in an earlier paper (Land, 1971) on the grounds that turns were executed accurately whether or not the stimulus moved relative to the spider as a result of the turn. Furthermore, the previously reported finding that the spider accurately completes turns even when the light is extinguished before or during the turn shows that the animal does not use vision at all in the execution of the turn, once the stimulus has been detected.

This hypothesis supposes that each retinal position connects with the legs in a genetically programmed way so that a stimulus at each such position causes a unique set of spatio-temporal muscular activities to be performed, resulting in a turn of a predetermined magnitude. This is clearly not the case because the positions of the legs at the beginning of a turn differ from turn to turn. During a succession of turns like those shown in Fig. 3 a and b, the positions of the legs at the beginning of any one turn are determined by the stage of the stepping cycle reached by the spider as a result of an unpredictable historic accident-the magnitude of the previous turn. Thus all turns of a given angle, say 120°, do not begin with the legs in the same positions, nor do they end with the legs in similar positions, and neither is the temporal pattern of leg movements during two such turns the same. The retinal position, therefore, specifies something other than the precise movements the legs must make. To put this another way: there is no single ‘motor tape’ corresponding to a particular retinal position.

Here it is assumed that the spider always turns at a constant velocity. The eye could then specify the angle to be turned by ‘gating’ the machinery responsible for turning, permitting it to operate for longer or shorter periods of time. That this is not the case is indicated by Figs. 9 and 10, which show several accurately executed 170° turns, performed at angular velocities differing by a factor of up to ten. Velocity of turningis not constant between or within turns, and this hypothesis is wrong.

The principal difficulty with this suggestion, apart from the complexity of the task it expects the nervous system to perform, is that it contains the possibility of ambiguous execution of turns. Since the average angle turned during a complete cycle of stepping by all eight legs is about 75°, closely similar patterns of leg positions will recur at the end of a 75° turn, and also a 150° turn. Similarly, after a 25° turn, a 100° turn and a 175° turn. Confusions of this kind are not observed; the spider does not make 75° turns when it should be making 150° turns, and so it is very unlikely that such a mechanism is present.

There are two alternative formulations of this hypothesis. The first is that the eye specifies the number of cycles of the whole stepping pattern that are to be made-clearly this will not be a whole number since the angle turned in one complete cycle is about 75°, and the spider can make turns with much greater precision than ‘the nearest 75°’. The second is that the eye specifies the total number of steps to be made by all legs : since there are eight legs there will be a step completed by one of the legs on the average every ⁠. This figure is well within the observed accuracy of turning (the standard deviation of the spider’s errors in turning is about 16° for ‘complete’ turns: Land, 1971) so a ‘quantum’ of turning of 9° is not unrealistic. Because the stepping pattern is not perfectly regular, the beginnings of steps made by different legs are very nearly randomly distributed with respect to the angle turned, as opposed to being clumped at roughly 38° intervals (average step amplitude÷2) as they would be if adjacent and contralateral phase coupling was perfect. Thus a step does occur on the average after every 9° turned, with variations in this interval that follow a binomial distribution.

A mechanism for specifying turn size based on step counting requires for its accuracy that the angle turned per step stays constant under all conditions. So far this seems to be very nearly true, for different animals, different rates of turning, and different conditions of loading (Fig. 11). A test of this hypothesis would be to find a situation which caused step size to alter, and to see whether this causes a proportional change in the sizes of turns made to stimuli at constant locations. So far, however, the spiders have defied all attempts to alter their step size sufficiently for this to be done. If circumstances can be found under which turn accuracy and step size do not co-vary, then the counting hypothesis must be Wrong, and a more complex form of integration must be responsible. For the moment, however, it remains the most plausible hypothesis.

I am very grateful to Paul Benjamin and Thomas Collett of the University of Sussex, and Peter Miller of the University of Oxford, for helpful criticisms of the manuscript, and to Hugh Rowell and Gerald Westheimer of the University of California, Berkeley, for useful discussions. The author was discussing the results with the late Donald Wilson shortly before his tragic death in 1970, and wishes to dedicate this paper to the memory of an extremely stimulating biologist. The work was performed with the aid of a grant from the U.S. Public Health Service (EY-00044).