|
| |
|
|
|
|
||||
| Home Help Feedback Subscriptions Archive Search Table of Contents | ||||
First published online November 17, 2006
Journal of Experimental Biology 209, 4607-4621 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.02539
Jumping performance of froghopper insects
Department of Zoology, University of Cambridge, Cambridge CB2 3EJ, UK
e-mail: mb135{at}hermes.cam.ac.uk
Accepted 6 September 2006
 |
Summary |
|---|
 TOP Summary IntroductionMaterials and methodsResultsDiscussionReferences |
|---|
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.
Key words: locomotion, kinematics, Hemiptera, Auchenorrhyncha
|
Introduction |
|---|
|
TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
|---|
) 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 |
|---|
|
TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
|---|
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.
|
). 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 |
|---|
|
TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
|---|
|
|
|
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.
|
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.
|
|
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).
|
|
|
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.
|
|
|
The energy required to achieve this performance depends on body mass. In the heavier species such as Cercopis the best jumps required 238 µJ 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.
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 |
|---|
|
TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
|---|
). 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.
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 Philaenus and 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 Neophilaenus to 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.
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.
|
Acknowledgments |
|---|
|
References |
|---|
|
TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
|---|
Alexander, R. M. (1995). Leg design and jumping technique for humans, other vertebrates and insects. Philos. Trans. R. Soc. Lond. B Biol. Sci. 347,235 -248.[Medline]
Baroni, U. C., Boyan, G. S., Blarer, A., Billen, J. and Musthak, A. T. M. (1994). A novel mechanism for jumping in the Indian ant Harpegnathos saltator (Jerdon) (Formicidae, Ponerinae). Experientia 50,63 -71.[CrossRef]
Bennet-Clark, H. C. (1975). The energetics of
the jump of the locust Schistocerca gregaria. J. Exp.
Biol. 63,53
-83.
Bennet-Clark, H. C. and Alder, G. M. (1979).
The effect of air resistance on the jumping performance of insects.
J. Exp. Biol. 82,105
-121.
Bennet-Clark, H. C. and Lucey, E. C. A. (1967).
The jump of the flea: a study of the energetics and a model of the mechanism.
J. Exp. Biol. 47,59
-76.
Brackenbury, J. and Hunt, H. (1993). Jumping in springtails: mechanism and dynamics. J. Zool. Lond. 229,217 -236.
Brown, R. H. J. (1967). The mechanism of locust jumping. Nature 214,939 .[Medline]
Burrows, M. (1996). The Neurobiology of an Insect Brain. Oxford: Oxford University Press.
Burrows, M. (2003). Froghopper insects leap to new heights. Nature 424,509 .[CrossRef][Medline]
Burrows, M. (2006). Morphology and action of
the hind leg joints controlling jumping in froghopper insects. J.
Exp. Biol. 209,4622
-4637.
Burrows, M. (2007). Neural control and co-ordination of jumping in froghopper insects. J. Neurophysiol. In press.
Burrows, M. and Morris, O. (2002). Jumping in a
winged stick insect. J. Exp. Biol.
205,2399
-2412.
Burrows, M. and Morris, O. (2003). Jumping and
kicking in bush crickets. J. Exp. Biol.
206,1035
-1049.
Burrows, M. and Wolf, H. (2002). Jumping and
kicking in the false stick insect Prosarthria: kinematics and neural
control. J. Exp. Biol.
205,1519
-1530.
Claridge, M. F. (1985). Acoustic signals in the Homoptera: behavior, taxonomy, and evolution. Annu. Rev. Entomol. 30,297 -317.[CrossRef]
Cocroft, R. B., Tieu, T. D., Hoy, R. R. and Miles, R. N. (2000). Directionality in the mechanical response to substrate vibration in a treehopper (Hemiptera: Membracidae: Umbonia crassicornis). J. Comp. Physiol. A 186,695 -705.[CrossRef][Medline]
Cokl, A. and Virant-Doberlet, M. (2003). Communication with substrateborne signals in small plant-dwelling insects. Annu. Rev. Entomol. 48,29 -50.[CrossRef][Medline]
Dowling, J. J. and Vamos, L. (1993). Identification of kinetic and temporal factors related to vertical jump performance. J. Appl. Biomech. 9, 95-110.
Evans, M. E. G. (1972). The jump of the click beetle (Coleoptera: Elateridae) - a preliminary study. J. Zool. Lond. 167,319 -336.
Evans, M. E. G. (1973). The jump of the click beetle (Coleoptera, Elateridae)-energetics and mechanics. J. Zool. Lond. 169,181 -194.
Evans, M. E. G. (1975). The jump of Petrobius (Thysanura, Machilidae). J. Zool. Lond. 176,49 -65.
Gorb, S. N. (2004). The jumping mechanism of the cicada Cercopis vulnerata (Auchenorrhyncha, Cercopidae): skeleton-muscle organisation, frictional surfaces, and inverse-kinematic model of leg movements. Arthropod Struct. Dev. 33,210 -220.
Hedwig, B. (2000). A highly sensitive opto-electronic system for the measurement of movements. J. Neurosci. Methods 100,165 -171.[CrossRef][Medline]
Kehlmaier, C. (2000). Zu Verbreitung, Lebenszyklus und Gesang der Blutzikade Cercopis vulnerata ROSSI, 1807 (Auchenorrhyncha: Cercopidae) am Lüneburger Schildstein (Niedersachsen). Braunschw. Naturkdl. Schr. 6, 69-84.
Maitland, D. P. (1992). Locomotion by jumping in the Mediterranean fruit-fly larva Ceratitis capitata.Nature 355,159 -161.[CrossRef]
Rothschild, M. and Schlein, J. (1975). The jumping mechanism of Xenopsylla cheopis. Exoskeletal structures and musculature. Philos. Trans. R. Soc. Lond. B Biol. Sci. 271,457 -490.[Medline]
Rothschild, M., Schlein, Y., Parker, K. and Sternberg, S. (1972). Jump of the Oriental Rat Flea Xenopsylla cheopis (Roths.). Nature 239,45 -47.[CrossRef]
Rothschild, M., Schlein, J., Parker, K., Neville, C. and Sternberg, S. (1975). The jumping mechanism of Xenopsylla cheopis. III. Execution of the jump and activity. Philos. Trans. R. Soc. Lond. B Biol. Sci. 271,499 -515.[Medline]
Tautz, J., Holldobler, B. and Danker, T. (1994). The ants that jump: different techniques to take off. Zoology 98,1 -6.
Vogel, S. (2005). Living in a physical world. II. The bio-ballistics of small projectiles. J. Biosci. 30,167 -175.[Medline]
CiteULike 
Complore 
Connotea 
Del.icio.us 
Digg 
Reddit 
Technorati 
Twitter What's this?
This article has been cited by other articles:
|
|
 |
|
  S. B. Williams, H. Tan, J. R. Usherwood, and A. M. Wilson Pitch then power: limitations to acceleration in quadrupeds Biol Lett, October 23, 2009; 5(5): 610 - 613. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 X. Noblin, S. Yang, and J. Dumais Surface tension propulsion of fungal spores J. Exp. Biol., September 1, 2009; 212(17): 2835 - 2843. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
M. Burrows Jumping performance of planthoppers (Hemiptera, Issidae) J. Exp. Biol., September 1, 2009; 212(17): 2844 - 2855. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
M. Burrows Jumping strategies and performance in shore bugs (Hemiptera, Heteroptera, Saldidae) J. Exp. Biol., January 1, 2009; 212(1): 106 - 115. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
M. Burrows and G. P. Sutton The effect of leg length on jumping performance of short- and long-legged leafhopper insects J. Exp. Biol., April 15, 2008; 211(8): 1317 - 1325. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
M. Burrows Jumping in a wingless stick insect, Timema chumash (Phasmatodea, Timematodea, Timematidae) J. Exp. Biol., April 1, 2008; 211(7): 1021 - 1028. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
M. Burrows Kinematics of jumping in leafhopper insects (Hemiptera, Auchenorrhyncha, Cicadellidae) J. Exp. Biol., October 15, 2007; 210(20): 3579 - 3589. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
M. Burrows Anatomy of the hind legs and actions of their muscles during jumping in leafhopper insects J. Exp. Biol., October 15, 2007; 210(20): 3590 - 3600. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
M. Burrows, V. Hartung, and H. Hoch Jumping behaviour in a Gondwanan relict insect (Hemiptera: Coleorrhyncha: Peloridiidae) J. Exp. Biol., September 15, 2007; 210(18): 3311 - 3318. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 M. Burrows Neural Control and Coordination of Jumping in Froghopper Insects J Neurophysiol, January 1, 2007; 97(1): 320 - 330. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
M. Burrows Morphology and action of the hind leg joints controlling jumping in froghopper insects J. Exp. Biol., December 1, 2006; 209(23): 4622 - 4637. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
