SUMMARY

The kinematics of jumping in froghopper insects were analysed from high speed sequences of images captured at rates up to 8000 s-1. In a jump, the attitude of the body is set by the front and middle legs, and the propulsion is delivered by rapid and synchronous movements of the hind legs that are 1.5 times longer than the other legs, but are only about half the length of the body and represent just 2% of the body mass. The wings are not moved and the front and middle legs may be raised off the ground before take-off. The hind legs are first cocked by a slow levation of the trochantera about the coxae so that the femora are pressed against the ventral, indented wall of the thorax, with the femoro-tibial joints tucked between the middle legs and body. Only the tips of the hind tarsi are in contact with the ground. In this position, the hind legs stay motionless for 1-2 s. Both trochantera are then synchronously and rapidly depressed about the coxae at rotational velocities of 75 500 deg. s-1 and the tibiae extended, to launch a jump that in Philaenus reaches a height of 700 mm, or 115 body lengths.

In the best jumps by Philaenus, take-off occurs within 0.875 ms of the start of movements of the hind legs at a peak velocity of 4.7 m s-1 and involves an acceleration of 5400 m s-2,equivalent to 550 times gravity. This jumping performance requires an energy output of 136 μJ, a power output of 155 mW and exerts a force of 66 mN.

Introduction

Insects have evolved many different mechanisms for jumping so that they may increase the speed of their locomotion, launch themselves into flight, or escape rapidly from a potential predator. The repeatable nature of these movements has enabled detailed analyses of the underlying neuronal mechanisms(Burrows, 1996) and determination of the mechanical and muscular solutions to these extreme locomotory demands. Click beetles (Elateridae) jack-knife a joint in their thorax (Evans, 1972; Evans, 1973), bristletails(Archaeognatha) (Evans, 1975),springtails (Collembola) (Brackenbury and Hunt, 1993) and the larvae of some flies(Maitland, 1992) use movements of their abdomens. Particular ants (Baroni et al., 1994; Tautz et al.,1994) and the stick insect Sipyloidea sp.(Burrows and Morris, 2002)combine forward movements of their abdomens with movements of their legs.

In many other insects simultaneous movements of specialised hind legs power jumping movements, though muscles of different leg segments may be used in different species. Fleas, for example, use the trochanteral depressor muscles to generate the necessary force whereas locusts and bush crickets use the tibial extensor muscles. Two design principles emerge as different ways to overcome the need to produce leg movements that are both rapid and powerful(Alexander, 1995). First, some insects have long hind legs allowing force to be delivered over a long period and over a long distance. Bush crickets with very long hind legs(Burrows and Morris, 2003)have therefore adopted the same strategy as frogs, kangaroos and bush babies in using direct muscle contractions to move long levers. Second, insects with short legs such as fleas use a catapult mechanism in which muscles are assumed to contract slowly and the force they generate is stored in elastic elements of the skeleton and then suddenly released(Bennet-Clark and Lucey, 1967; Rothschild and Schlein, 1975). Some insects, such as locusts, combine energy storage and long legs(Bennet-Clark, 1975).

A largely unexplored group of jumping insects are the abundant and diverse plant sucking Hemipteran bugs, belonging to the sub-order Auchenorrhyncha. One family of this group are the froghoppers (Cercopidae), which are common insects in many parts of the world. Their larvae develop on plants, some species below and some above ground. The latter secrete a froth, known colloquially in different countries as `cuckoo-', `witches-' or `frog-spit',which may afford protection from desiccation and predation. Both larvae and adults feed on xylem sap, as a result often transmitting viruses between crop plants, but only the adults jump from plant to plant. Their name derives from the resemblance of their body shape to that of a frog and their prodigious jumping ability that is the focus of this paper.

A brief report on the kinematics of the jumping movements of a froghopper, Philaenus spumarius (Burrows,2003), has demonstrated its jumping prowess, and a mechanism for jumping has been proposed for Cercopis vulnerata(Gorb, 2004). This paper analyses the detailed jumping performance of froghoppers and shows that in a jump they are airborne in less than 1 ms from the first propulsive movement of the hind legs. The enormous acceleration needed to achieve take-off velocities of over 4.7 m s-1 in this short time is equivalent to 550 g.

Materials and methods

Five species of froghoppers were analysed: Aphrophora alni(Fallén 1805), Cercopis vulnerata (Rossi 1807), Lepyronia coleoptrata (Linnaeus 1758), Philaenus spumarius (Linnaeus 1758), and Neophilaenus exclamationis (Thunberg 1784). Neophilaenus were collected near Wells-next-the-sea in Norfolk, UK and Lepyronia from the Nanus region of Slovenia and near Ljubljana. The other species were collected near Wells-next-the-sea and around Cambridge,UK. Observations on live insects were made on the same day of collection, or after they had been in the laboratory for no more than a few days feeding on live Chrysanthemum plants.

Sequential images of jumps were captured at rates of 1000 or 2000 s-1 with a high speed camera (Redlake Imaging, San Diego, CA, USA)and associated computer, or at 4000-8000 s-1 with a Photron Fastcam 512 or 1024PCI camera [Photron (Europe) Ltd, Marlow, Bucks., UK] and with exposure times of 0.05-0.25 ms. Spontaneous jumps, or jumps encouraged by delicate mechanical stimulation with a fine paintbrush or a 100 μm silver wire, were performed in a chamber of optical quality glass 80 mm wide, 80 mm tall and 25 mm deep with a floor of high density foam. Selected image files were analysed with Motionscope camera software (Redlake Imaging) or with Canvas (ACD Systems of America). Jumps were aligned by designating the point of take-off as time t=0 ms.

Fig. 1.

Drawing of the anterior part of Philaenus, viewed from the side,to show the orientation of the proximal parts of its three pairs of legs. Each leg is shown in its most anterior position (black) and in its most posterior position (grey). The pivots of the coxae with the thorax are indicated by black dots and vertical arrows. The plane of movement is not orthogonal to the plane of the drawing.

Fig. 1.

Drawing of the anterior part of Philaenus, viewed from the side,to show the orientation of the proximal parts of its three pairs of legs. Each leg is shown in its most anterior position (black) and in its most posterior position (grey). The pivots of the coxae with the thorax are indicated by black dots and vertical arrows. The plane of movement is not orthogonal to the plane of the drawing.

Higher temporal resolution of the movements of a hind leg of a restrained Aphrophora was obtained by gluing a 0.2 mm disc of reflective tape to a hind femur close to the femoro-tibial joint. A modified single lens reflex camera with a concentric light around the lens was focussed on the disc and the light it reflected was captured by a photocell in the film plane of the camera (Hedwig, 2000). This method recorded the movement of the femur and was combined with sequential images of the hind legs captured by a high speed camera.

Seventy nine jumps by 19 Aphrophora, 92 jumps by 19 Philaenus, 47 jumps by 13 Cercopis, 8 jumps by 5 Neophilaenus and 16 jumps by 4 Lepyronia were captured and analysed. Data are given as means ± standard error of the mean(s.e.m.). Temperatures ranged from 24-30°C.

Results

Body form

The head of froghoppers is flattened dorso-ventrally and has short antennae. Its dorsal cuticle, and that of the prothorax, has many small indentations and its ventral cuticle is ribbed. The mouthparts point backwards and in Aphrophora extend to the coxae of the hind legs. The folded fore wings cover the body, extend beyond the abdomen posteriorly and cover most of the hind legs when viewed from the side. The five species of froghopper analysed have a tenfold range of body mass, from 3.2±0.08 mg(N=7) in Neophilaenus to 32.9±1.0 mg (N=16)in Cercopis (Table 1). Their body lengths have a 2.5 fold range from 4.0±0.03 mm(N=7) in Neophilaenus to 9.8±0.24 mm (N=23)in Aphrophora. Philaenus is toward the middle of this range with a body mass of 12.3±0.41 mg (N=34) and a body length of 6.1±0.08 mm.

Table 1.

Body form in froghoppers

Length (mm)
Ratio of leg lengths
Length (% of body length)
InsectNBody mass (mg)BodyHind leg, tibiaHind leg, femurFrontMiddleHindFrontMiddleHind
Neophilaenus 3.2±0.08 4.0±0.03 1.2±0.01 0.8±0.02 1.5 43 42 66 
Philaenus 34 12.3±0.74 6.1±0.08 1.8±0.07 1.1±0.03 1.5 46 46 66 
Lepyronia 17.6±0.18 7.2±0.18 2.0±0.06 1.3±0.03 1.4 44 46 61 
Aphrophora 23 28.3±1.1 9.8±0.24 2.5±0.09 1.3±0.04 1.5 36 36 52 
Cercopis 16 32.9±1.0 9.5±0.13 2.9±0.04 1.6±0.03 1.6 43 44 63 
Length (mm)
Ratio of leg lengths
Length (% of body length)
InsectNBody mass (mg)BodyHind leg, tibiaHind leg, femurFrontMiddleHindFrontMiddleHind
Neophilaenus 3.2±0.08 4.0±0.03 1.2±0.01 0.8±0.02 1.5 43 42 66 
Philaenus 34 12.3±0.74 6.1±0.08 1.8±0.07 1.1±0.03 1.5 46 46 66 
Lepyronia 17.6±0.18 7.2±0.18 2.0±0.06 1.3±0.03 1.4 44 46 61 
Aphrophora 23 28.3±1.1 9.8±0.24 2.5±0.09 1.3±0.04 1.5 36 36 52 
Cercopis 16 32.9±1.0 9.5±0.13 2.9±0.04 1.6±0.03 1.6 43 44 63 
Fig. 2.

Sequential images of a jump by Philaenus captured at 7500 s-1 and with an exposure time for each of 0.05 ms. The images are arranged vertically in two columns and are timed from the image at take-off (0 ms). The first movements of the right hind leg (white arrow) occurred 1.04 ms before take-off.

Fig. 2.

Sequential images of a jump by Philaenus captured at 7500 s-1 and with an exposure time for each of 0.05 ms. The images are arranged vertically in two columns and are timed from the image at take-off (0 ms). The first movements of the right hind leg (white arrow) occurred 1.04 ms before take-off.

The hind legs are only just over half the length of the body, ranging from 52.3±1.24% (N=23) of body length in Aphrophora to 66%in Philaenus and Neophilaenus(Table 1). In all species the front and middle legs are of similar length, but the hind legs are about one and half times longer so that the ratio of leg lengths ranges from 1 (front):1(middle):1.4-1.6 (hind legs) in the different species. The increased length of a hind leg is due to its longer tibia. By contrast, the femur of a hind leg is the same length and shape as those of the other legs. The mass of the two hind legs of Aphrophora, including the trochanter and all the more distal segments, represents only 2.0±0.11% (N=7) of the total body mass.

Fig. 3.

Graphs of leg and body movements during a jump by Philaenuscaptured at 8000 s-1. (A) Five points on the body (see cartoon inset) are plotted against time. Take-off is indicated by the right arrow and vertical yellow bar. The first movement of a hind leg occurred 0.875 ms before take-off (left arrow and yellow bar). The tarsi of the front and middle legs left the ground 0.5 ms before take-off (middle arrow and yellow bar). Velocity, measured as the movement of the centre of an ellipse representing the overall shape of the body, is plotted as a two-point average of successive frames (blue line). (B) Sequential movements of the five points on the body as the insect moved through the field of view of the stationary camera,superimposed on an image of the froghopper in its starting position. The black arrowheads and the linking black lines show the position of these five points at take-off. The corresponding positions of these points at different times during the jump can be read frame-by-frame from these positions at take-off.

Fig. 3.

Graphs of leg and body movements during a jump by Philaenuscaptured at 8000 s-1. (A) Five points on the body (see cartoon inset) are plotted against time. Take-off is indicated by the right arrow and vertical yellow bar. The first movement of a hind leg occurred 0.875 ms before take-off (left arrow and yellow bar). The tarsi of the front and middle legs left the ground 0.5 ms before take-off (middle arrow and yellow bar). Velocity, measured as the movement of the centre of an ellipse representing the overall shape of the body, is plotted as a two-point average of successive frames (blue line). (B) Sequential movements of the five points on the body as the insect moved through the field of view of the stationary camera,superimposed on an image of the froghopper in its starting position. The black arrowheads and the linking black lines show the position of these five points at take-off. The corresponding positions of these points at different times during the jump can be read frame-by-frame from these positions at take-off.

The coxae of the three pairs of legs articulate with the thorax at different angles (Fig. 1). In its most forward position the coxa of a hind leg subtends an angle of 155°to the longitudinal axis of the body and rotates, as determined by imposed movements, backwards and upwards in one plane about its paired pivots by only a further 20-25°. Movements of segments distal to the coxa are in this plane. By contrast, in their most forward positions the coxae of the front and middle legs subtend angles of 80-90° and can rotate backwards through an angle of about 40°, or almost twice the range of a hind leg.

Kinematics of the jump

The same rapid movements of the hind legs propelled jumping by all species but the following analysis focuses on Philaenus, with information from other species illustrating particular features.

In preparation for a jump from a horizontal surface, the front of the body was raised or lowered by movements of the front and middle legs to give a mean attitude of the body relative to the ground at take-off of 28±1.9°(N=20). After adjustment of the body attitude was complete, the hind legs then remained still for 1-2 s with only the distal tips of their tarsi in contact with the ground. A rapid and simultaneous depression of both hind legs then powered an explosive take-off. No differences could be detected in the timing of the movements of the two hind legs and both left the ground at the same time.

The first movement of a hind leg in a jump was a downward and backward thrust of the trochanter and femur (their individual movements cannot be distinguished in these images viewed from the side) which, as transmitted through the tibia, forced the whole ventral surface of the tarsus to the ground (Fig. 2, Fig. 3A). Images captured at 8000 s-1 showed that this first movement of a hind leg occurred only 0.875 ms (7 frames) before the insect became airborne. The force from the continuing backwards movement of the hind legs began to lift the body because their tarsi were now directly applied to the ground(Fig. 2, Fig. 3A,B). The body continued to be raised as the hind femora were further depressed and the hind tibiae were extended so that the tarsi of the front and middle legs were raised from the ground before take-off. The velocity of the insect followed these movements of the legs. The first surge in velocity corresponded to the initial movement of the femur (Fig. 3A)and after a short pause of 0.25 ms was followed by a rapid acceleration to a peak velocity of 4.7 m s-1 at take-off.

To resolve the movements of particular joints of the hind legs during jumping, images of Aphrophora jumping were captured from a ventral view (Fig. 4). Inevitably this meant allowing it to jump from a transparent glass surface, with the result that the hind legs gained little purchase and the whole movement was completed in 0.4 ms or 2 frames at 5000 s-1. In preparation for a jump, the hind legs were levated at the coxo-trochanteral joints so that they were tucked between the femora of the middle legs and the thorax(Fig. 4A,B). The tibiae were also flexed about the femora so that they lay ventral to the abdomen along its lateral edges. The legs then remained stationary in this cocked position for a few seconds. The first movements of the hind legs in a jump were the sudden depression of the trochantera about the coxae, most notable as a closure of the gap between the trochantera at the midline(Fig. 4A). This resulted in the femora moving posteriorly, without an apparent change in the angle of trochantero-femoral joints and the tibiae extended about the femora. This combination of joint movements continued and resulted in a full depression of the trochantera about the coxae and a full extension of the tibiae about the femora. After these movements were completed at take-off, the trochantera then levated and the tibiae flexed again to move the hind legs back into their cocked position.

Fig. 4.

Jump by Aphrophora viewed ventrally and captured at 5000 s-1 with an exposure time of 0.05 ms. (A) Sequence of four images from the jump. (B) Drawings to show the joint positions of the hind legs before (-0.4 ms, fully levated) and after (0 ms, fully depressed) their rapid movements.

Fig. 4.

Jump by Aphrophora viewed ventrally and captured at 5000 s-1 with an exposure time of 0.05 ms. (A) Sequence of four images from the jump. (B) Drawings to show the joint positions of the hind legs before (-0.4 ms, fully levated) and after (0 ms, fully depressed) their rapid movements.

The same sequence of movements of the joints of a hind leg were also seen in Philaenus jumping from a horizontal position toward the camera and therefore moving out of its focal plane.(Fig. 5A-C). The first movement of a hind leg was a downward movement of the femur resulting from a depression of the trochanter about the coxa, accompanied by an extension of the tibia. With the tarsus pushed fully to the ground, further depression of the femur and extension of the tibia resulted in an upward movement of the body. At take-off the coxo-trochanteral joint had been depressed through its full range at angular velocities of 75 500 deg. s-1 and the femoro-tibial joint extended at an angular velocity of 105 000 deg. s-1.

Fig. 5.

(A) Sequential images captured at 5000 s-1 and with an exposure of 0.05 ms of Philaenus jumping toward and to the right of the camera to show the leg movements. Movements of the right hind femur are indicated by the arrows. (B) Graphs of changes in the angle between the femur and the longitudinal axis of the body and of the femoro-tibial joint (see inset drawings) in a jump by another Philaenus captured at 4000 s-1. (C) Movements of four points on the body (see cartoon) and of the angular changes of the femur and tibia (coloured lines). The changes in the femoro-tibial angle at the times indicated (ms) are shown in detail on the right.

Fig. 5.

(A) Sequential images captured at 5000 s-1 and with an exposure of 0.05 ms of Philaenus jumping toward and to the right of the camera to show the leg movements. Movements of the right hind femur are indicated by the arrows. (B) Graphs of changes in the angle between the femur and the longitudinal axis of the body and of the femoro-tibial joint (see inset drawings) in a jump by another Philaenus captured at 4000 s-1. (C) Movements of four points on the body (see cartoon) and of the angular changes of the femur and tibia (coloured lines). The changes in the femoro-tibial angle at the times indicated (ms) are shown in detail on the right.

Fig. 6.

Hind leg movements of a restrained Aphrophora recorded simultaneously by a camera capturing images at 1000 s-1 and with an exposure of 0.25 ms and by a photoelectric device (see Materials and methods).(A) Two sequential images, the first showing the hind legs fully levated before the attempted jump and the second after the rapid movement. The inset drawings show the position of the hind legs in these two frames. Note the small piece of reflective tape on the hind femur. The outputs of the photoelectric device during six jumps were captured at a sampling rate of 45 kHz and low-pass filtered at 2 kHz. One trace in blue shows the unfiltered recording. The leg movements were complete in 0.3 ms. (B) Seven attempted jumps by a second Aphrophora show that the movement was again complete in 0.3 ms.

Fig. 6.

Hind leg movements of a restrained Aphrophora recorded simultaneously by a camera capturing images at 1000 s-1 and with an exposure of 0.25 ms and by a photoelectric device (see Materials and methods).(A) Two sequential images, the first showing the hind legs fully levated before the attempted jump and the second after the rapid movement. The inset drawings show the position of the hind legs in these two frames. Note the small piece of reflective tape on the hind femur. The outputs of the photoelectric device during six jumps were captured at a sampling rate of 45 kHz and low-pass filtered at 2 kHz. One trace in blue shows the unfiltered recording. The leg movements were complete in 0.3 ms. (B) Seven attempted jumps by a second Aphrophora show that the movement was again complete in 0.3 ms.

Further detail of the joint movements was obtained by fixing Aphrophora ventral surface uppermost in Plasticene™ with the hind legs free to move (Fig. 6). Rapid and simultaneous movements of both hind legs occasionally occurred spontaneously or could be evoked by gently tickling hairs on the abdomen with a fine paintbrush. No differences in the form of these attempted jump movements could be discerned compared with those in free jumping. They were, however, much faster and were completed in 0.3 ms because they did not lift the mass of the body. The key movement was again a simultaneous depression of both trochantera about the coxae which occurred at 267 000 deg. s-1, almost three times faster than in a real jump. The speed of these movements was consistent in 6 attempted jumps by one Aphrophora and in 7 by a second(Fig. 6A,B).

Kinematics of the jump in other froghoppers

In the smallest of the froghoppers, Neophilaenus, take-off was also achieved within 1 ms of the first movements of the hind legs(Fig. 7A,B). The first and key movements of the hind legs were again a rapid depression of the trochanter,with an accompanying extension of the tibia. Before take-off in some jumps,the tarsi of the front and middle legs had already lost contact with the ground (Fig. 7B).

In the heaviest of the froghoppers, Cercopis, the body was accelerated for a longer period to achieve take-off, with the movements of the hind legs beginning 1.5 ms before take-off(Fig. 8A,B). The whole jumping sequence began with the front and middle legs adjusting the attitude of the body, which, in this example was only 16°. Both front and middle pairs of legs were again off the ground before take-off(Fig. 8B,C). Movements of the hind legs led to the head being raised while the posterior of the body was lowered, giving a take-off angle of 45° despite the initial shallow body attitude.

In some jumps when Lepyronia took off almost vertically the middle legs were already off the ground and the front legs were fully depressed and extended even before the first movements of the hind legs began(Fig. 9). At 1 ms before take-off, the front and middle legs were clear of the ground but the take-off velocity of 4.0 m s-1 was, nevertheless, as great as that achieved at take-off angles closer to the mean of 45° when the front and middle legs remained in contact with the ground for a longer period.

Fig. 7.

Images from two jumps by Neophilaenus captured at 2000 s-1 with an exposure of 0.25 s. (A) A jump in which the take-off occurred within 1 ms of the first movements of the hind legs: body angle,36°; take-off angle, 55°; take-off velocity, 4.2m s-1. (B)A jump toward and to the right of the camera in which the body was raised by the front and middle legs to assume a higher take-off angle: body angle,50°; take-off angle, 72°; take-off velocity, 4.0 m s-1;body mass, 3.2 mg.

Fig. 7.

Images from two jumps by Neophilaenus captured at 2000 s-1 with an exposure of 0.25 s. (A) A jump in which the take-off occurred within 1 ms of the first movements of the hind legs: body angle,36°; take-off angle, 55°; take-off velocity, 4.2m s-1. (B)A jump toward and to the right of the camera in which the body was raised by the front and middle legs to assume a higher take-off angle: body angle,50°; take-off angle, 72°; take-off velocity, 4.0 m s-1;body mass, 3.2 mg.

Trajectories

Philaenus had a mean take-off angle of 46.8±2.0° (range 18° to 90°, N=50) and a mode of 45°(Fig. 10A). In the first few milliseconds after take-off the insect typically maintained a stable orientation, and in many jumps this continued until a landing feet-first on a vertical or horizontal surface. In other jumps, however, the body rotated about its long or transverse axes and occasionally about both axes(Fig. 10B). In the example shown, Philaenus spun through four complete cycles during the first 50 ms after take-off. In a second jump, the abdomen started to rotate forward about the transverse axis 10 ms after take-off so that it rather than the head pointed forwards. In a third jump, the body began to rotate about its long axis after 10 ms and after 19 ms had rotated by 180° so that the legs were pointed upwards. The rotation was completed 28 ms after take-off and then the next cycle of rotation began. In a fourth jump, the body first started to rotate about its long axis and then some 5 ms later also began to rotate about its transverse axis.

In all species the wings remained folded during take-off, so that the movement was a pure jump powered by the hind legs and not assisted by active wing movements. Occasionally, however, the wings were opened after take-off,and flapping flight was assumed though this did not always lead to sustained flight or even to maintaining the height attained by the initial jump(Fig. 11).

Jumping performance

The jumping performance of these insects was calculated from the kinematic analysis of the jumping movements (Table 2). The take-off velocity was calculated as the mean velocity over the first 3 ms when airborne. This will underestimate performance as peak velocity occurs just before take-off and gradually declines thereafter(Fig. 3A). Such a calculation was necessary because images of most jumps were captured at either 1000 or 2000 s-1, which did not record the accelerations before take-off with sufficient resolution. In ten jumps by Philaenus the mean take-off velocity was 2.8±0.1 m s-1 with the best jumps captured at 8000 s-1, achieving a take-off velocity of 4.7 m s-1. In the other species, the take-off velocity in the best jumps when measured with the same image capture rates ranged from 4.6 m s-1 in Lepyronia to 3.4 m s-1 in Aphrophora. The heavier insects generated the lower take-off velocities. The time over which the body was accelerated was measured from the first visible movement of the hind legs until the insect became airborne. In Philaenus this acceleration period was only 0.875 ms and in Neophilaenus no more than 1 ms, but in Lepyronia, Aphrophoraand Cercopis it was 1.5 ms. For the best jumps this meant that the applied acceleration ranged from 2267-5400 m s-2.

Table 2.

Jumping performance of froghoppers

Body mass, Mb (mg)Body length (mm)Time to take-off (ms)Take-off velocity, v (m s−1)Acceleration (m s−2)g forceEnergy (μJ)Power (mW)Force (mN)
Neophilaenus          
Best 3.2 4.0 4.2 4200 428 28 28 13 
Philaenus          
Averagea 12.3 6.1 2.8 2800 286 48 48 34 
Best   0.875 4.7 5400 550 136 155 66 
Lepyronia          
Averageb 17.6 7.2 1.5 2667 272 141 94 .47 
Best    4.6 3067 313 190 127 54 
Aphrophora          
Averageb 28.3 9.6 1.5 2.5 1667 170 88 59 47 
Best    3.4 2267 231 164 109 64 
Cercopis          
Best 32.9 9.5 1.5 3.8 2533 258 238 158 83 
Body mass, Mb (mg)Body length (mm)Time to take-off (ms)Take-off velocity, v (m s−1)Acceleration (m s−2)g forceEnergy (μJ)Power (mW)Force (mN)
Neophilaenus          
Best 3.2 4.0 4.2 4200 428 28 28 13 
Philaenus          
Averagea 12.3 6.1 2.8 2800 286 48 48 34 
Best   0.875 4.7 5400 550 136 155 66 
Lepyronia          
Averageb 17.6 7.2 1.5 2667 272 141 94 .47 
Best    4.6 3067 313 190 127 54 
Aphrophora          
Averageb 28.3 9.6 1.5 2.5 1667 170 88 59 47 
Best    3.4 2267 231 164 109 64 
Cercopis          
Best 32.9 9.5 1.5 3.8 2533 258 238 158 83 

a(N=10 jumps by 5 insects); b(N=10 jumps by 4 insects). N, number of jumps used to determine time to take-off and take-off velocity.

Formulae: acceleration f=vlt; g=fl9.86; energy e=0.5Mbv2;power=elt; force=Mbf.

Fig. 8.

Jump by Cercopis. (A) Sequential frames from the jump viewed from the side and captured at 2000 s-1 with an exposure of 0.25 ms. (B)Graph of the movements of six points on the body (see cartoon inset) during this jump. (C) Sequential movements of the same six points superimposed on an image of Cercopis in its starting position to show their vertical and horizontal displacement. The yellow arrows show the direction of the initial movements of the femoro-tibial joint. Body angle at take-off, 16°;take-off angle, 45°; take-off velocity, 3.8m s-1; body mass,41.9 mg.

Fig. 8.

Jump by Cercopis. (A) Sequential frames from the jump viewed from the side and captured at 2000 s-1 with an exposure of 0.25 ms. (B)Graph of the movements of six points on the body (see cartoon inset) during this jump. (C) Sequential movements of the same six points superimposed on an image of Cercopis in its starting position to show their vertical and horizontal displacement. The yellow arrows show the direction of the initial movements of the femoro-tibial joint. Body angle at take-off, 16°;take-off angle, 45°; take-off velocity, 3.8m s-1; body mass,41.9 mg.

The energy required to achieve this performance depends on body mass. In the heavier species such as Cercopis the best jumps required 238μJ but in the much lighter Neophilaenus this fell to 28 μJ; Philaenus required 136 μJ. The power output in a jump depends on the time during which the energy is expended. In the 0.875 ms that Philaenus took to accelerate its body the power output was thus 155 mW. The force exerted during the best jumps by Philaenus was 66 mN. For the heavier Cercopis the force was highest at 83 mN and for the lighter Neophilaenus was lowest at 13 mN.

Fig. 9.

Jump by Lepyronia. (A) Two columns of sequential images from a jump captured at 4000 s-1 and with an exposure of 0.25 ms. At the start, the body was raised at an angle of 61° to the ground so that only the tips of the tarsi of the front and middle legs were in contact with the ground. (B) Movements of five points on the body (see image in C) against time. (C) Movements of the same body points to show their vertical and horizontal displacement. The black curved arrows show the direction of the initial movements of the femoro-tibial joint. Body angle at take-off, 61°;take-off angle, 90°; take-off velocity, 4.0 m s-1; body mass,17 mg; temperature, 36°C.

Fig. 9.

Jump by Lepyronia. (A) Two columns of sequential images from a jump captured at 4000 s-1 and with an exposure of 0.25 ms. At the start, the body was raised at an angle of 61° to the ground so that only the tips of the tarsi of the front and middle legs were in contact with the ground. (B) Movements of five points on the body (see image in C) against time. (C) Movements of the same body points to show their vertical and horizontal displacement. The black curved arrows show the direction of the initial movements of the femoro-tibial joint. Body angle at take-off, 61°;take-off angle, 90°; take-off velocity, 4.0 m s-1; body mass,17 mg; temperature, 36°C.

In a laboratory chamber at a temperature of 25°C and in still air, the average height jumped by Philaenus was 428±26 mm(N=17 insects) with the highest jumps reaching 700 mm, or 115 times its body length. None of the other species bettered these performances; for example, in the same conditions Aphrophora reached an average height of 263±20 mm (N=13). In a particular individual, jumping performance declined with increasing attempts to encourage jumping with the consequence that averaged values are likely to have underestimated the true jumping performance of these insects. The best indication of ability came by taking the maximal performance of particular individuals, which under laboratory conditions and temperatures may still be an underestimate.

Walking

The orientation of the hind legs, and their key role in powering jumping,raised the question of whether this compromised their ability to contribute to walking. The striking feature of horizontal walking was that the hind legs did not show rhythmic movements in the walking pattern and were not sequentially placed on the ground and then lifted (Fig. 12A). Instead they were held in the cocked position with the trochantera fully levated about the coxae so that the tarsi did not contact the ground. The hind legs were, however, used when climbing on a vertical surface on which there was limited traction(Fig. 12B). They moved rhythmically and were placed on the ground in time with the walking pattern so that they might therefore be expected to contribute thrust to the movement.

Discussion

Body structure

The hind legs of froghoppers are short relative to the body, ranging from only 52-66% of body length, and are only 1.4-1.6 times longer, by virtue of longer tibiae, than the front or middle legs in the different species. This contrasts with other prodigious jumping insects such as locusts, in which the hind legs are equal to body length, and most strongly with bush crickets, in which the hind legs are longer than the body and several times the length of the front legs (Burrows and Morris,2003). This implies that the hind legs of froghoppers can provide much less leverage, a design that they share with fleas(Bennet-Clark and Lucey, 1967). The mass of the hind legs is also only a small (2%) proportion of body mass,contrasting again with locusts where it is 14%(Bennet-Clark, 1975). The hind femur is not enlarged to contain a powerful extensor tibiae muscle as in jumping insects such as grasshoppers, bush crickets (Tettigonidae) and flea beetles (Chrysomelidae, Halticinae). The overall design is therefore of a body that can be accelerated rapidly and which is able to transmit power to the ground through short but light hind legs.

Fig. 10.

(A) Trajectories of five jumps by the same Philaenus. Take-off angles are the average over the first 10 ms after take-off. (B) Rotation of the body during a single jump by Philaenus. A fixed point on the head in the vertical or in the horizontal plane was plotted against time. The body spins about its longitudinal (y axis) and transverse (x)axis undergoing five cycles of rotation in the first 70 ms that it is airborne. Images were captured at 1000 s-1; body mass, 12 mg.

Fig. 10.

(A) Trajectories of five jumps by the same Philaenus. Take-off angles are the average over the first 10 ms after take-off. (B) Rotation of the body during a single jump by Philaenus. A fixed point on the head in the vertical or in the horizontal plane was plotted against time. The body spins about its longitudinal (y axis) and transverse (x)axis undergoing five cycles of rotation in the first 70 ms that it is airborne. Images were captured at 1000 s-1; body mass, 12 mg.

Fig. 11.

A jump in which Aphrophora flapped its wings after take-off. The selected images captured at 1000 s-1 and with an exposure of 0.25 ms are arranged in two columns. At take-off (time 0 ms) the wings were not opened. 5 ms later it started to lose height and 8 ms after take-off opened its hind wings and flapped them.

Fig. 11.

A jump in which Aphrophora flapped its wings after take-off. The selected images captured at 1000 s-1 and with an exposure of 0.25 ms are arranged in two columns. At take-off (time 0 ms) the wings were not opened. 5 ms later it started to lose height and 8 ms after take-off opened its hind wings and flapped them.

Jumping performance

The main thrust for jumping is provided by the hind legs. Any contribution from the front and middle legs is limited as they are often lifted from the ground before movements of the hind legs begin. Their primary responsibilities are therefore to provide a stable platform and to set the angle of the body and the take-off trajectory, by raising or lowering the anterior part of the body. The critical movement of the hind legs in generating the thrust for a jump is the depression of the trochantera about the coxae. Before take-off,the hind legs are levated forwards at the coxo-trochanteral joints so that that the femora are tucked between the thorax and the middle legs and are apposed to the lateral and ventral surfaces of the coxae. The tibiae are also flexed about the femora. By contrast, the front and middle tibiae are held in their most forward positions at angles of 80-90° to the longitudinal axis of the body. These critical actions of the hind legs in jumping are at the expense of their ability to contribute to the propulsion of the body in horizontal walking.

From the start of the first visible movements of the hind legs to a froghopper becoming airborne takes no more than 0.875 ms in Philaenusand a maximum of 1.5 ms in the heavier Cercopis or Aphrophora. In this short time, the body is accelerated to a take-off velocity of 4.7 m s-1 in the best jumps by Philaenus. In the best jumps by the different species, the applied acceleration ranged from 2267-5400 m s-2. Philaenus experiences the equivalent of 550 g at take-off and the others from 231-428 g. The best jumps by Philaenus require an energy output of 136 μJ, a power output of 155 mW and exert a force of 66 mN. These forces and accelerations generated in jumping could not be produced by direct contractions of the muscles and indicate that muscular force must be generated in advance of the movement, energy stored and then released rapidly.

None of the five species of froghoppers were captured opening their wings before take-off or flapping them to assist take-off. Indeed, the high accelerations and velocities at take-off may preclude opening the wings. Occasionally Aphrophora and more frequently Cercopis opened their wings when they were airborne and then flapped them in a flight pattern. Flapping the wings after take-off could presumably generate further lift or forward momentum, but could also act as an air brake to stabilise the movements and increase the likelihood of a soft landing. The hind legs were held fully extended after take-off so that adjustments of their posture could provide some ruddering control. The body may nevertheless still rotate about its longitudinal and transverse axes. These characteristics of a jump suggests that its overriding objective is to move a froghopper from one position to another as rapidly as possible at the expense of a controlled path through the air, or a controlled feet-first landing.

Which of the five species of froghoppers examined is the best jumper? The answer lies in which aspects of jumping performance are considered and how they are related to body mass and volume. The five species of froghopper analysed have a tenfold range of body masses (3.2 mg in Neophilaenusto 32.9 mg in Cercopis), and vary in length from 4.0 mm in Neophilaenus to 9.8 mm in Aphrophora.

In terms of the height jumped then Philaenus comes out on top. Its average height jumped was 428 mm with the best jumps attaining heights of 700 mm, or 115 times its body length. By contrast, in the same conditions Aphrophora reached an average height of only 263 mm, or 27 times its body length. Distance and height achieved will be determined by take-off velocity, take-off angle and by the drag. All the froghoppers achieve high take-off velocities ranging from 3.4 to 4.7 m s-1 and average take-off angles are close to 45°. Drag will, however, be different because of the different body sizes and masses(Bennet-Clark and Alder, 1979). The distance lost due to drag by Philaenus is estimated to be about 25% (Vogel, 2005) based on my data. The smaller Neophilaenus would be expected to experience greater drag while the larger froghoppers should experience less.

In terms of velocity, acceleration and force relative to body mass generated at take-off, then Philaenus again comes out on top. It accelerates its body in less than 1 ms to achieve an average velocity over the first 3 ms of the jump of 4.7 m s-1. Both Neophilaenus and Lepyronia approach but never better these velocities at take-off, but the heavier Aphrophora and Cercopis both take longer (1.5 ms) to accelerate their bodies and achieve lower velocities.

Fig. 12.

Contribution of the hind legs of Philaenus in walking. Images were captured at 1000 s-1 with an exposure of 0.5 ms. Selected images,viewed ventrally, are shown at the times indicated. (A) Horizontal walking. The middle and front legs were lifted in a sequence to perform a swing phase of similar duration (thick black bars) and contact the ground during a stance phase of variable duration (thin blue bars). The hind legs did not move. (B)Vertical walking in which the hind legs did contribute.

Fig. 12.

Contribution of the hind legs of Philaenus in walking. Images were captured at 1000 s-1 with an exposure of 0.5 ms. Selected images,viewed ventrally, are shown at the times indicated. (A) Horizontal walking. The middle and front legs were lifted in a sequence to perform a swing phase of similar duration (thick black bars) and contact the ground during a stance phase of variable duration (thin blue bars). The hind legs did not move. (B)Vertical walking in which the hind legs did contribute.

Jumping performance relative to other animals

Fleas have been considered the best jumpers amongst the insects,accelerating their body within 1 ms to a take-off velocity of 1 m s-1 (Bennet-Clark and Lucey,1967; Rothschild et al.,1975; Rothschild et al.,1972). Froghoppers produce a substantially better jumping performance. Philaenus accelerates its body to a take-off velocity that is more than 4.7 times faster than a flea despite having a body mass that is 27 times greater and a body that is four times longer. Once airborne,however, the flea is likely to have its jumping distance reduced by 80% due to drag compared to the 25% reduction experienced by Philaenus(Vogel, 2005). Heavier Orthopteran insects such as locusts (Schistocerca gregaria) with a mass of 1-2 g take 20-30 ms to extend their hind legs and accelerate their body (Brown, 1967) to a take-off velocity of 3 m s-1(Bennet-Clark, 1975) while Prosarthria teretrirostris with a mass of 280 mg takes 30 ms of acceleration to achieve a take-off velocity of 2.5 m s-1(Burrows and Wolf, 2002). The jumping distance of these larger insects is likely to be curtailed by only some 6% due to drag (Vogel,2005). If jumping performance is expressed as the force exerted relative to body mass, then froghoppers again outperform other insects and other jumping animals. The force that froghoppers exert at take-off is more than 400 times their body weight and is, therefore, much higher than in other jumpers such as the flea (∼135 times)(Bennet-Clark and Lucey, 1967),locust (∼8) (Bennet-Clark,1975) and humans (∼2-3)(Dowling and Vamos, 1993).

Biology of the jump

What do froghoppers gain by investing so much in their prodigious jumping performance? Is it simply a way of improving locomotion so that a froghopper can move quickly from one food plant to another without being spotted? Is it to avoid predation or being parasitized? Only the adults jump. The nymphs of Philaenus surround themselves with froth that is generated by blowing air into secretions from their Malpighian tubules. They do not jump if their frothy surroundings are removed. Jumping is thus associated with the free-living life style of adults, but very little is known of what determines movements from one host plant to another, and what dangers might be posed by other animals. The adults generally feed on the underside of leaves but the aposematically coloured Cercopis feeds more frequently on the more exposed stems of plants.

Potential predators of froghoppers are many and include birds, solitary wasps that provision their nests with froghoppers, and predatory social wasps or flies. Parasitoids such as Pipunculidae attack the pre-adult stages which are unable to jump. A further major danger may be unwitting predation by grazing mammals. They share this danger with all the other insects that live or feed on vegetation, but a rapid and long jump out of harm's way becomes advantageous. It may be that froghoppers are vulnerable while airborne and thus need to minimise exposure time in the air by jumping rapidly. This assessment of the value of jumping, however, poses further questions.

First, at what distance and with what sense does a froghopper detect an approaching predator? A vibratory sense could give advanced warning of an approaching danger by detecting footfalls or movements of the plant on which it is feeding. This would allow the necessary time for developing the forces needed to jump (Burrows,2007). Related families of Auchenorrhyncha use this sense to communicate with each other on the same plant(Claridge, 1985; Cocroft et al., 2000; Cokl and Virant-Doberlet,2003) and Cercopis appears to signal by vibrating its wings while remaining stationary on a plant(Kehlmaier, 2000).

Second, does a froghopper have to anticipate the possible need to jump and thus hold its hind legs in readiness? This would explain the cocked position adopted by the hind legs during walking.

Third, how quickly can a froghopper unplug its stylets? Are the stylets withdrawn before take-off or does the act of jumping merely rip them from the plant?

Fourth, does a froghopper orient itself out of the line of approach of a predator before it takes off, or is the direction of its jump determined by the way it was facing when feeding and had to unplug its stylets?

The structural specialisations of the joints and the sequence of muscle actions that enable this remarkable jumping performance is analysed in two subsequent papers (Burrows,2006; Burrows,2007) and further papers will explore the evolution of the particular jumping mechanisms in other families of these plant sucking bugs.

Acknowledgements

I thank my Cambridge colleagues for their help in collecting these bugs,for their constructive suggestions during the course of this work, and for their comments on the manuscript. This work was initiated at the Wells Field Study Centre, Wells-next-the-sea, Norfolk, England during an undergraduate field course, and I am most grateful to the warden Christine Marshall for the use of these facilities. Some experiments were also carried out at the Department of Entomology, National Institute of Biology, Ljubljana, Slovenia and I am most grateful to Dr Meta Virant and her colleagues for their support.

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