Ballistics and Visual Targeting in Flea-Beetles (Alticinae)

Small leaping insects such as fleas (Bennet-Clark and Lucey, 1967), springtails (Christian, 1978, 1979; Brackenbury and Hunt, 1993) and the larvae of the tephritid fly Ceratitis capitata (Maitland, 1992) rely on a spring mechanism to achieve high accelerations over very short take-off distances. Catapult mechanisms are also used by click-beetles (Evans, 1972, 1973; Kaschek, 1984) and locusts (Bennet-Clark, 1975). Saltatorial Orthoptera exercise considerable control over the range and direction of jumping; locusts, grasshoppers and wood crickets, for example, estimate target distance using ‘peering’ movements of the head (Wallace, 1959; Collett, 1978; Eriksson, 1980; Goulet et al. 1981), and locusts match range to estimated target distance by altering take-off velocity (Sobel, 1990). Mantids frequently recruit the wings whilst jumping (Brackenbury, 1991), possibly to help in control. By contrast with these relatively large insects, little is known about the control of leaping in very small ‘explosive’ jumpers whose reliance on an ‘all-or-none’ catapult mechanism would be incompatible with a velocity control system. Springtails, click-beetles, tephritid fly larvae and bristle-tails (Evans, 1975) all spin through the air while jumping, and springtails show no statistical preference for landing on their heads or their tails (Christian, 1978).

The available evidence, therefore, might seem to suggest that leaping in small insects is little more than a high-speed escape reflex, with no time for controlled manoeuvre. Flea-beetles provide a test case for this hypothesis since, although their jumping is based on a metafemoral spring (Ker, 1977; Furth, 1982; Furth et al. 1983), most species are fully winged and hence are potentially capable of briefly recruiting the wings to influence jump kinematics. The objectives of the present investigation were threefold. First, to investigate the energetics and kinematics of flea-beetles. Second, to search for evidence of control over jump direction and/or landing capability. And third, to quantify such control in a way that provides information on the optokinetic capabilities of these insects.

The experiments were carried out on seven species of flea-beetle (Alticinae) which are listed, together with the host plants from which they were collected, in Table 1. Jumping behaviour was investigated with the help of a NAC 400 high-speed video (HSV) system, which was supplied with a manual frame-by-frame replay facility. Illumination was provided by a slave-driven stroboscope producing 400 synchronised flashes per second, each of 20 μs duration. To achieve maximum depth of focus, at the relatively high image magnifications that were necessary in the experiments, the iris diaphragm of the video camera lens was stopped down to f16 ½–f22 ½. This placed great demands on the light intensity requirement, so the insects were viewed in silhouette directly against the stroboscope face, after covering it with three layers of translucent tracing paper to disperse the light (Fig. 1A). At the start of each trial, the insect was introduced onto a slender twig held between the camera and the illuminated screen at an angle of approximately 45°. Normally the insect quickly began to climb towards the highest point of the twig, which was the terminal bud, and this provided time for the experimenter to align the body of the beetle with the centre of the screen and the optical axis of the lens (Fig. 1A). In specific cases described below, some beetles deliberately orientated towards the screen, in which case the smooth rounded surface of the terminal bud was important in facilitating these movements and in providing an exact footing for take-off. However, the individuals of most species jumped in a random direction once they had reached the terminal bud, either spontaneously or after gentle prompting by the tip of a second twig held by the experimenter.

The much more directed behaviour pattern of A. atrocaerulea and C. aurata provided an opportunity to measure the accuracy with which a specific target could be visually fixated and then struck by the body. In the case of C. aurata, the target consisted of a vertical grid of black and white stripes (Fig. 2A) painted directly onto the tracing paper covering the face of the stroboscope. The beetles were held at a distance of 8 cm from the screen, which is similar to the normal jumping range of this species. At this distance, the bars subtended an angle of 25° to the beetle’s eyes (spatial frequency = 0.04 cycles degree⁻¹).

A. atrocaerulea had a much greater jumping range (up to 21 cm horizontally, 15–16 cm vertically) and could vary its take-off angle to intercept targets placed at any inclination between 0 and 90°. This made it possible to monitor target accuracy in this particular species as a function of distance and inclination. In exploratory experiments, the response of A. atrocaerulea to a variety of targets of different shapes and angular sizes was examined in order to arrive at a design that would be small enough to elicit maximum jump accuracy from the beetle whilst retaining enough total luminosity to keep its attention fixed towards the target. This optimisation process resulted in the target design shown in Fig. 1A, consisting of a cross cut out of black card and mounted directly onto the stroboscope screen. Four targets of different sizes were placed in separate experiments at horizontal distances of 8, 12, 16 or 21 cm from the launch point. Target size was matched to distance so that all the targets subtended the same angle to the launch point: the angular subtense of the central square of the cross was 14°. In two further series of experiments, the performance of the insects was also tested against oblique targets held at an angle of 60° to the horizontal and vertical targets placed directly above the body.

In order to analyse the target hit data, the cross was divided into equal-sized zones along the horizontal (x-axis) and vertical (y-axis) arms (Fig. 1B). Zonal scoring was carried out independently along the x-and y-axes in order to compare horizontal and vertical target accuracies.

Morphometric and kinematic data for all seven species of beetle are listed in Table 1. The measured values of take-off angle and take-off velocity obtained in A. atrocaerulea using the indirect method (column 1, Table 1) were not significantly different from those resulting from the direct method (take-off angle 16±1°, N=20; take-off velocity 1.8±0.1 m s⁻¹, N=28). Take-off distance was assumed to be equal to the combined length of the femur plus the tibia, since videographic data showed that the hind-leg was almost fully extended at take-off, but that the tarsus remained in contact with the ground throughout its length and therefore made no contribution to take-off distance (Fig. 3). The role of the tarsus appears to be to prevent slippage, rather than to add to the lever arm of the elongating leg. Take-off time was calculated as twice the take-off distance divided by take-off velocity. Take-off acceleration was calculated as take-off velocity divided by take-off time. A distinction can be made on the basis of take-off time, acceleration and velocity between the four flea-beetles on the left-hand side of Table 1, which may be described as ‘high-speed’ jumpers, and the remaining three on the right-hand side, which are ‘low-speed’ jumpers. The chosen morphometric indicators (femur width/femur length) and (femur width/body width) also divide along this line. Insufficient species are available to justify any attempt at a rigorous statistical correlation, but the available data suggest a clear link between femur width and power capability.

All species rotated during the leap, almost always in a backward or ‘head-over-heels’ direction. The highest rotation rate of 187 cycles s⁻¹ (Hz) coincided with the highest take-off acceleration and velocity, and the shortest take-off time, in Psylliodes affinis. Rapid rotation did not always imply high energy wastage. With the exception of P. affinis, the high-speed jumpers, despite their faster rotation rates, expended relatively less kinetic energy in this form than the low-speed jumpers.

C. aurata exhibited two different modes of jumping when confronted with the optical grid. In jump mode 1, which was wingless, the body spun through the air towards the target at 35 Hz. Wingless jumping was also characteristic of all the other beetles except A. atrocaerulea. In the second jump mode, the wings were opened approximately 50 ms before take-off and within this period performed two or three strokes of gradually increasing amplitude. Immediately prior to wing activity, the legs were shuffled in a very deliberate attempt to obtain proper balance and orientation. The take-off sequence would only be attempted once the prothoracic legs had been finally raised above the ground and extended forward into the air (Fig. 3). In 21 out of 24 cases examined in detail, final extension of the hind-legs coincided with the downstroke rather than with the upstroke phase of the wing beat.

Take-off angle during mode 2 jumping (50.7±1.6°, N=12) was marginally greater than during mode 1 jumping (46.7±0.8°, N=47) but take-off velocity was not significantly different (0.89±0.02 m s⁻¹, N=32, mode 2; 0.83±0.04 m s⁻¹, N=9, mode 1).

Wing recruitment had clear repercussions on jump kinematics. First, the wings had the effect of counteracting the pitching instability that was present from the moment of take-off in wingless jumping and, as a result, the jump became rotation-free. Second, the jump trajectory was altered so that the body gained a height of 0.078 m over the target distance compared with wingless jumping (Fig. 2A). The travel time to the target was 0.176±0.01 s (N=198), so the rate of potential energy gain by the body was equivalent to 0.078mg/ 0.176 J s⁻¹. The take-off time was 0.0036 s; therefore, the take-off power was equivalent to 0.5mV²/0.0036. The ratio of the potential energy gain to the take-off power gives an estimate of the relative contribution of the wings and the legs to the take-off effort: the resultant figure is less than 5 %. Although the calculation takes no account of possible changes in forward velocity due to wing activity, the contribution of these changes to the mechanical energy of the body during flight-assisted jumping is negligible compared with the gain in potential energy by increased height. It is therefore reasonable to conclude that wing effort contributes little or nothing to take-off momentum. This result is also compatible with the observation that take-off velocity is unaffected by wing recruitment.

Fig. 2B shows the wing-beat characteristics during mode 2 jumping. The most noticeable feature was that the elytra beat in phase with the hind-wings, with a stroke angle of nearly 90°.

The choice of jump mode also affected targeting and landing (Table 2). As a result of rotation, only 10 % of all wingless jumps terminated in a feet-first landing on target. This figure rose to 95 % during flight-assisted jumping. Wingless jumping was also significantly less discriminating: black and white stripes were struck with equal likelihood. In contrast, beetles leaping towards the optical grid after wing recruitment showed a significant preference for landing on the black stripes.

Hit density distributions for targets placed horizontally, vertically or obliquely with respect to the body are shown in Fig. 4A–C respectively. Each of these graphs shows the hit scores that were measured independently along the x-and y-axes of the target. The results for horizontal and vertical jumping are almost identical: regardless of jump distance, the hit density distribution is the same along the vertical and the horizontal axes. Fig. 4 also shows the mean x,y-coordinates for all recorded hits against each target. This gives an independent estimate of the ‘perceived’ or ‘apparent’ target centre, since it is the point towards which the jumps appear to be directed. If the jumps were perfectly distributed about the geometric target centre, the mean coordinates would be zero along both the x-and the y-axes. In all cases, the perceived target centre lay within 5° of the true geometric centre.

The data in Fig. 4A,B suggest that a target is struck with the same accuracy regardless of its distance (so long as it is within range) or whether it is located directly above or in front of the flea-beetle. Moreover, accuracy is the same whether it is measured along the vertical or horizontal axis of the target. In view of the similarities between the hit density distributions shown in Fig. 4A,B and in order to obtain a more precise quantification of ‘target accuracy’, the data from all seven series of experiments are aggregated in Fig. 5. The summed data confirm that there is no significant difference in the distribution of hits along the horizontal and vertical axes. Furthermore, the average value of all the recorded hits lies within a solid angle of 1° of the geometric target centre (Fig. 1B).

Fig. 5 shows two further measures of target hit distribution. The first (‘concentric hits’) is the distribution of hits within individual concentric, 1° wide circular bands of the target. These are the equivalent of the successive black and white circles of an archery target. The concentric hit frequency values were obtained by multiplying each axial value (hits per degree) by its angular distance from the centre (ϕ). Finally, the cumulative hit frequency distribution, also shown in Fig. 5, measures the proportion of total hits lying within any solid angle ϕ of the target centre. This was obtained by graphical integration of the concentric hit frequency distribution curve, from the centre to the edge of the target area.

The axial hit density curve and the cumulative hit frequency curve were used to quantify target accuracy as the angle, measured with respect to the target centre, within which 50 % of the recorded hits were located. If the angle is measured along an axis (x or y), its value is equal to the angle that encloses the central 50 % of the area lying beneath the axial hit density curve. From Fig. 5, the axial target accuracy measured in this way is ±6°. The advantage of this method of measuring target accuracy is that it directly reflects the precision with which the target is perceived by the eye, as will be seen in the Discussion. However, a more precise gauge of the accuracy with which the task of hitting the target is carried out by the beetle is based on the two-dimensional distribution of hits across the target area. In these terms, accuracy can be defined as the solid angle enclosing the central 50 % of all recorded hits. This is obtained by downward projection from the cumulative hit frequency curve in Fig. 5, and its value is ±11°.

When jumping towards the target inclined at 60° to the horizontal, accuracy noticeably deteriorated. In particular, the distribution of hits along the vertical axis was skewed downwards (Fig. 4C), implying that, although the beetles were still aiming towards the centre of the target, they were falling short of it. The achievement of both height and range was evidently incompatible with the mechanical energy available at take-off.

The landing success of A. atrocaerulea like that of C. aurata was strongly influenced by the behaviour of the wings. A. atrocaerulea invariably took off in a wingless mode and for the first 40 ms or so of travel time it rotated through the air at a rate of 66 Hz. This was, coincidentally, roughly the same amount of time that was needed to cover the distance to the nearest (8 cm) target. From this point, the wings began to open, the exact timing varying from jump to jump. By 100 ms of travel time, close to the end of a normal full-length jump, virtually all the beetles had opened their wings. There was a direct correlation between the timing of wing opening and the ability to make a feet-first landing on target (Fig. 6). Whereas none of the beetles made a feet-first landing on the 8 cm horizontal target, virtually all landed feet-first on the 16 cm horizontal target. The time lag between the landing success curve and the wing-opening curve in Fig. 6A is approximately 10 ms. This implies that, within 10 ms of beginning to open its wings, the chances of any individual making a feet-first landing increase from 0 to 100 %. This deduction was confirmed by the visible events recorded by the HSV. As soon as the wings were extended, rotation was abolished and the body became stabilised with its ventral side, including the feet, pointing in the direction of the target. The same mechanical events occurred during vertical jumping, with the result that the beetle approached and landed on the target in an upside-down position.

The wings took approximately 9.5 ms to open (mean of eight measurements) but a further 11.5 ms (N=70) was needed before they began to beat. Since the abolition of spin required only 10 ms, it must be concluded that the extension of the hind-wings and elytra in itself was sufficient to counteract rotation.

In confirmation of this, many of the feet-first landings recorded during vertical jumping were achieved whilst the wings were extended, but had not yet begun to beat (Fig. 6B).

Landing success during vertical jumping never quite achieved the 100 % level. Approximately 20 % of the jumps fell short of the 16 cm target and, although the wings were open by this stage, the beetles either fell to the ground or else became propelled in a random direction by the wings.

The high take-off acceleration and velocity and the short take-off time observed in the four high-speed species are compatible with jumping based on a spring-driven mechanism. A scroll-like spring has been identified in the flea-beetle metafemur (Ker, 1977; Furth, 1980, 1982), connected to an apodeme into which the primary and secondary extensor muscles insert. The muscles dilate the spring, accumulating tensional energy. According to Furth et al. (1983), the elastic material of the spring is not resilin. Springs have been described in fleas (Bennet-Clark and Lucey, 1967) and locusts (Bennet-Clark, 1975). They are also employed for legless jumping in click-beetles (Evans, 1972, 1973; Kaschek, 1984), tephritid fly larvae (Maitland, 1992; Suenaaga et al. 1992), springtails (Christian, 1978, 1979; Brackenbury and Hunt, 1993) and bristle-tails (Evans, 1975).

The spring used by soft-bodied springtails and fly larvae is hydroelastic and is therefore probably subjected to considerable damping as fluid is translocated within the body cavity. This may account for the relatively low (<100 g, where g=9.81 m s⁻²) accelerations relative to gravity encountered in these insects. Click-beetles use a much stiffer spring, to judge by the very large accelerations (up to 450 g) reported in some species (Kaschek, 1984). The maximum acceleration measured in the present study, 270 g in the flea-beetle Psylliodes affinis, is comparable to that of the flea (245 g). In contrast, the accelerations found in the low-speed species shown in Table 1 must be viewed as being amongst the lowest of any small jumping insect. Their femora show no obvious adaptation for saltation and, if a metafemoral spring is present, it appears to be very weak. Metafemoral springs are found in non-alticid beetles, such as the curculionid Rhynchaenus fagi described by Ker (1977). The take-off times of the three low-speed flea-beetles, though lengthy compared with those of the others, were nonetheless well below 10 ms, a period not incompatible with spring assistance. A final note in this context: femoral thickness is not always a reliable indicator of leaping prowess. Females of the European flower beetle Oedomera nobilis have notably enlarged hind femora but, at least in the experience of one of the authors (J.B.), they do not leap.

Spinning seems to be almost unavoidable in small leaping insects, to judge by its occurrence in almost all the groups that have been studied to date. In energetic terms, it is not necessarily wasteful since it normally accounts for less than 10 % of the total kinetic energy of the body. There are exceptions: the globular springtail Sminthurus viridis rotates at 480 Hz and this consumes nearly 60 % of the take-off energy (Christian, 1979). Amongst jumping beetles, rotational energy (as a proportion of the total kinetic energy) was greatest in the more slowly spinning species (Table 1). This is not paradoxical: equation 4 shows that rotational energy (per unit body mass) scales to the square of the linear dimensions of the body, and the slowly spinning species were also the biggest. A spherical insect with a diameter of 1 mm would need to spin four times as fast as one with a diameter of 2 mm to dissipate the same proportion of its kinetic energy.

The present study demonstrates that, at least in two species, jumping in flea-beetles is a directed behaviour pattern and not just a randomised high-speed escape reaction. To elicit this behaviour, the insect seems to need a stimulus that it can perceive and to which it is attracted. It is beyond the scope of the present study to try to explain which particular attributes of target design proved effective in this respect and how they were perceived by the flea-beetles, except on a very general basis, as will be seen below. One of the objectives was to investigate any link that might exist between biomechanical performance and steering behaviour, and in this area evidence has been forthcoming. The ability of C. aurata to discriminate in its locomotory behaviour between the black and white stripes of an optical grid was predicated upon the adoption of a jumping mode that specifically excluded spinning and maximised landing probability. But this mode also imposes a delay in take-off of at least 50 ms: increased control, and landing certainty, is only achieved at a cost in response time. Wingless jumping may be more expeditious, increasing the chances of escape but sacrificing landing certainty.

Flight-assisted leaping has previously been described in mantids (Brackenbury, 1991) where, as in C. aurata, the downward sweep of the wings was found to be exactly synchronised with hind-leg extension at take-off. This led to the suggestion that the wings might be used to augment the thrust developed by the legs at take-off. In C. aurata at least, this was not the case: the contribution of the wings to take-off energy was negligible compared with that released from the spring. C. aurata uses its wings primarily to increase control and possibly also to gain additional height or range in its jumping. It is important to note that flight-assisted leaping in flea-beetles is not the same phenomenon as taking off into sustained flight. The opening and subsequent beating of the wings in A. atrocaerulea, for instance, had little if any apparent effects on the geometry of the path through the air. However, it is also likely that C. aurata uses winged jumping in order to initiate extended flight. This not only abolishes pitching instability, but also, as in the locust take-off jump (Pond, 1972), enables flight speed to be attained within one body length.

The elimination of pitching instability in the body is dependent on an extended wing, but not necessarily a beating wing. Evidently the sudden increase in drag on the wings as they are extended, due to the motion of the body through the air, is sufficient to align the body in the ‘feet-forward’ position. The mechanism is similar to that operating on the feathers of a ‘shuttlecock’ or the fins of a dart. Any further increase in drag due to the motion of the wings themselves is, in these particular circumstances, relatively small.

C. aurata took off either on the second (13 of 24 observations) or third (8 out of 24 observations) wing-beat. A brief, pre-flight ‘burst’ of the flight motor in this way may not be unusual in insects. The milkweed bug Oncopeltus completes two or three wing cycles before launching into flight (Govind and Dandy, 1972).

The pattern of hits made by A. atrocaerulea upon the target (Figs 4, 5) demonstrates that the insect was aiming specifically at the target centre and not at its highly contrasted edges. In this respect, A. atrocaerulea resembles the mantid Tenodera australasiae, which also specifically directs its strike towards the middle of a symmetrical target (Rossel, 1980). The scatter of hits around the target centre results from two sources of error: the first is due to target perception (sensor error); the second is due to the locomotory machinery (motor error). It is not possible to disentangle these two sources of error with the data available. However, a ‘worst-case’ estimate of the accuracy of visual resolution of the target can be arrived at by assuming a motor error of zero. In this case, visual resolution can be equated to whatever value has been arrived at for target accuracy. Two definitions of target accuracy were used in this study, based on the distribution of hits along an axis (axial resolution) or upon an area (solid angle resolution). It is the former that reflects more explicitly the performance of the sensory mechanism. The axial hit density distribution (Fig. 5) is Gaussian in shape and, moreover, since it is identical along the horizontal and vertical axes it can be concluded that targeting is radially symmetrical. This is what would be expected of a visual system that had the same spatial discrimination in the horizontal and vertical directions. According to the 50 % criterion that we adopted, A. atrocaerulea can hit the target centre with an accuracy of ±6°. This is also the ‘worst case’ visual resolution of the target centre. 50 % of all the ‘lines of sight’ prescribed by the eye in preparation for jumping will fall within an angle of ±6° along the horizontal axis or along the vertical axis. The horizontal and vertical errors of estimation, however, are independent and multiplicative. Consequently, although A. atrocaerulea can resolve a target with a minimum linear accuracy of ±6°, only 25 % (50 %X50 %) of its prescribed lines of sight will actually fall within a two-dimensional square measuring 12°X12°. This explains why the ‘solid angle’ target resolution estimated from the data given in Fig. 5 was not ±6°, but much larger at ±11°.

Target resolution is used here as a non-specific term and it is not meant to be synonymous with visual acuity (spatial acuity), which measures the ability of the visual system to discriminate adjacent points in space. There may be methods of visual resolution of the target available to flea-beetles which are not directly based on visual acuity; for example, orientating the body towards the target so that each eye receives the same level of illumination. In this case, the ‘line of sight’ accuracy prescribed by the visual system would depend on the accuracy with which variations in light intensity could be mapped across the target.

Spatial acuity has been measured in one species of beetle, the dung beetle Onitis aygulus (Warrant et al. 1990). Dung beetles have a relatively complex eye and the value for spatial acuity given by these authors (0.25 cycles degree⁻¹) is likely to be much greater than that of the much simpler eye of flea-beetles. Tiny beetles in general possess acone eyes with very small facets: both of these are features that limit spatial resolution and light-collecting capability (Caveney, 1986). The paucity of ommatidia in the flea-beetle eye (Fig. 7) suggests that the spatial acuity of its visual system may be less than the measured value of target resolution (±6°). An optical system is capable of separately resolving two points in space when:

Spatial acuity has also been measured indirectly in freely flying bees (Srinivasan and Lehrer, 1988). The bees were trained to distinguish between horizontal and vertical optical gratings placed at the end of a tunnel, towards the entrance of which the bees flew. The minimum spatial acuity measured in this fashion agreed with estimates based on the optical characteristics of bee eyes. The grid used in the present study in connection with C. aurata was designed simply to demonstrate the presence of optokinetic behaviour, rather than accurately to quantify such behaviour. We would expect the spatial frequency of the grid used (0.04 cycles degree⁻¹) to be considerably less than the actual visual acuity of this insect. Indeed, 0.04 cycles degree⁻¹ is only 10 % of the spatial acuity found in flying bees.

In order to arrive at a minimal estimate of visual resolution, we assumed a motor error of zero, but in reality this is not likely to be the case. The accuracy of the delivery system during leaping depends on the precision with which an actual trajectory can be matched to the line of sight prescribed by the eye. This matching process, in turn, must depend critically on take-off angle and therefore any small inaccuracies in the placing of the feet, for example, would have a large effect on targeting performance. Although A. atrocaerulea is probably incapable of varying take-off velocity, it is clearly highly flexible in its choice of take-off angle. In fact, its measured accuracy during ‘straight upward’ jumping was undiminished compared with forward jumping (Fig. 4A,B). A. atrocaerulea benefits in its targeting behaviour from the possession of an almost linear trajectory: the vertex/height ratio of its parabola during horizontal jumping is only 7 %. It is arguable that only such a high-speed, quasi-linear trajectory can supply the accuracy needed for targeting, in the same way that only a high-velocity bullet can faithfully follow the line-of-sight prescribed by a marksman’s eye.

For similar reasons, the invariance of target accuracy with distance (Fig. 4A,B) may be an automatic consequence of the execution of an almost straight trajectory. Although large jumping orthopterans such as locusts, grasshoppers and wood crickets are known to estimate distance before leaping, using parallax information gleaned from ‘peering’ movements of the head (Wallace, 1959; Collett, 1978; Eriksson, 1980; Goulet et al. 1981), it does not seem to be necessary to invoke such refinements in the case of targeted leaping in flea-beetles.

This work was supported by a grant from the BBSRC. We are grateful for the loan of high-speed video equipment from the Rutherford-Appleton Laboratories, Oxfordshire, and Cambridge Consultants of Cambridge. Sharon Shute of the Natural History Museum, London, carried out some of the species identifications.