High-speed video analyses of the natural behaviour of parasitoid wasps revealed three strategies used to launch the insects into the air. Which strategy is the most energy efficient? In Pteromalus puparum, 92% of take-offs by were propelled entirely by movements of the middle and hind legs, which were depressed at their coxo-trochanteral and extended at their femoro-tibial joints. The front legs left the ground first, followed by the hind legs, so that the middle legs provided the final propulsion. Second, in other species of a similar mass, Cotesia glomerata and Leptopilina boulardi, all take-offs were propelled by a mean of 2.8 and 3.8 wingbeats, respectively, with little or no contribution from the legs. The first strategy resulted in take-off times that were four times shorter (5 versus 22.8 ms) and take-off velocities that were four times faster (0.8 versus 0.2 m s−1). Calculations from the kinematics indicate that propulsion by the legs was the most energy-efficient strategy, because more energy is put into propulsion of the body, whereas in take-off propelled by repetitive wing movements energy is lost to generating these movements and moving the air. In heavier species such as Netelia testacea and Amblyteles armatorius, take-off was propelled by the combined movements of the middle and hind legs and wingbeats. In A. armatorius, this resulted in the longest mean take-off time of 33.8 ms but an intermediate take-off velocity of 0.4 m s−1. In all three strategies the performance could be explained without invoking energy storage and power amplification mechanisms.

Three different strategies are used by a wide diversity of insects to launch a take-off from the ground and into the air. First, rapid movements of the legs propel jumping to achieve take-off, without any contribution from the wings. Second, repeated movements of the wings generate take-off with no obvious thrust contributed by the legs. And third, propulsive movements of both the legs and the wings are combined. This paper analyses the dynamics of these different strategies for take-off and compares their energy efficiencies. We propose that generating take-off by a rapid jump propelled by the legs is more energy efficient than a take-off generated by repetitive flapping movements of the wings, and this could provide the basis of an explanation as to why so many winged insects jump to take-off. This hypothesis is tested by analysing the take-off mechanisms and performance of a five species of parasitoid wasp (Hymenoptera).

The most well-documented species of the Hymenoptera that jump are wingless ants. Trap jaw ants, Odontomachus bauri, use rapid closing movements of the mandibles to strike a hard substrate and propel a backwards escape jump (Patek et al., 2006) that increases the chance of surviving encounters with predatory insects such as antlions (Neuroptera) (Larabee and Suarez, 2015). They also use leg movements to jump forwards (Sorger, 2015). Ants such as Polyrhachis laboriosa that live in trees can jump downwards to escape predators or find new foraging sites (Mercier and Lenoir, 1999). Others such as the wingless workers of Cephalotes atratus live higher in the canopy and either jump or fall, but adjust their glide path by asymmetric movements of the hind legs and gaster to regain contact with the trunk of the same tree lower down (Yanoviak et al., 2005, 2010). Other ants such as the Indian ant Harpegnathos saltator jump by more conventional propulsive movements of the legs to escape predators, to catch prey in flight and to perform group movements that may aid in prey detection or predator avoidance (Musthak Ali et al., 1992). The jumping mechanism used is unclear. In one description, the hind legs push first and then the rapid movements of the middle legs generate the final propulsion to modest take-off velocities of 0.7 m s−1 (Tautz et al., 1994). A second description indicates that propulsive movements of the middle and hind legs are synchronous, a conclusion that is said to be supported by the electrical activity of muscles in the middle and hind legs also being synchronous during ‘fictive’ jumping movements (Baroni Urbani et al., 1994). Another species, Myrmecia nigrocincta, is also reported to move its middle and hind legs synchronously to propel jumping (Tautz et al., 1994). Gigantiops destructor combines movements of the middle and hind legs with a forward rotation of the gaster that shifts the centre of mass of the body and could reduce body spin once airborne (Tautz et al., 1994).

Some larval wasps have abrupt movements that resemble jumping. The larvae of Neuroterus saltatorius (Cynipidae) develop in small galls on the leaves of oak trees. When these galls fall to the ground, rapid contractions of the U-shaped larva within make the gall bounce 10 mm high (Manier and Deamer, 2014). Similarly, a larva of Bathyplectes anurus (Ichneumonidae) spins a cocoon within that of its larval weevil host and its twitch-like movements propel jumps some 50 mm high (Saeki et al., 2016).

Adult winged wasps of a few species within the family Eupelmidae are more conventional but able jumpers propelled by movements of the legs (Gibson, 1986). No measurements of their performance have been reported, and mechanisms have instead been inferred from their thoracic morphology and musculature. The middle legs are thought to propel jumping and the necessary power is suggested to be generated by different mesothoracic muscles in males and females, although jumping appears to be similar in both sexes (Gibson, 1986). A pad of material onto which one of these muscles attaches has some of the properties of the elastic protein resilin, leading to the inference that the jumping mechanism must involve the storage of energy (Gibson, 1986). A mechanism, however, has not been demonstrated that would explain how energy is stored. These wasps, unlike the wingless ants, but like many other insects such as moths (Burrows and Dorosenko, 2015a) and butterflies (Bimbard et al., 2013; Sunada et al., 1993), may use jumping as a means of launching into flight. This take-off objective might also be met by repetitive beating of the wings acting alone, or in concert with propulsive legs movements as in whiteflies (Ribak et al., 2016).

Why take-off with a jump powered by rapid leg movements rather than simply flapping the wings? To address this question, we used high-speed videos to analyse the take-off strategies and mechanisms of parasitoid wasps, selected for two reasons. First, these species fall into two groups based on their mass: three have masses of 1 mg or less, while the others have masses that are 50 times greater. We ask in all these species whether take-off is propelled by leg movements and, if so, which legs are used. Alternatively, is take-off propelled by wing movements or by a combination of legs and wing movements? From these analyses, we calculate which mechanisms are the most energy efficient and whether energy storage with concomitant power amplification has to be invoked to explain the observed take-off times and velocities.

Five species of parasitoid wasps were analysed. Pteromalus puparum (Linnaeus 1758) (Pteromalidae) (Fig. 1A) and Cotesia glomerata (Linnaeus 1758), formerly Apanteles glomeratus (Braconidae) (Fig. 1B), were found parasitizing a culture of the cabbage white butterfly. Leptopilina boulardi (Barbotin, Carton & Kelner-Pillault 1979) (Figitidae) (Fig. 1C,D) was found in a Drosophila culture. Amblyteles armatorius (Forster 1771) (Fig. 1E) and Netelia testacea (Gravenhorst 1829) (Ichneumonidae) were caught amongst garden plants in Girton, Cambridge, UK. The phylogenies of these wasps within the Hymenoptera have recently been analysed (Branstetter et al., 2017; Quicke et al., 2012).

Live wasps were photographed with a Nikon D7200 camera fitted with a 100 mm Nikon macro lens. The anatomy of the legs was examined in intact wasps, and in those fixed and stored in 70% alcohol or 50% glycerol. Leg lengths were measured to an accuracy of 0.1 mm from images taken with a GX CAM 5-C camera (GT Vision Ltd, Stansfield, UK) attached to a Leica MZ16 microscope (Wetzlar, Germany) and projected onto a monitor (Table 1). Body masses were determined to an accuracy of 0.1 mg with a Mettler Toledo AB104 balance (Beaumont Leys, Leicester, UK).

Sequential images of take-offs were captured with a single Photron Fastcam SA3 camera (Photron Europe Ltd, High Wycombe, UK) fitted with a 100 mm micro Tokina lens. Frame rates of 1000 s−1 with an exposure time of 0.2 ms and 5000 s−1 with an exposure time of 0.1 ms were used. Several of the three smaller species were placed at the same time in a chamber made of optical quality glass that was 25 mm wide, 25 mm tall and 12 mm deep. The two larger species were placed individually in a larger chamber measuring 80 mm wide, 80 mm tall and 25 mm deep. The camera pointed directly at the middle of these chambers and focused on an individual wasp. The floor, side walls and ceiling of each chamber were made of 12-mm-thick, closed-cell foam (Plastazote, Watkins and Doncaster, Cranbrook, UK) from which the wasps would take off spontaneously. Tracks of the movements of specific body parts were made manually frame by frame with Tracker software (http://physlets.org/tracker/); auto-tracking failed to follow the movements of small body parts reliably. The frame at which a particular leg lost contact with the ground was determined by playing the video backwards and forwards frame by frame. An abrupt shift in position of a tarsus indicated that it was no longer load bearing and had lost contact with the ground. Take-off was indicated by the last leg losing contact with the ground so that the insect was airborne; it was designated as time t=0 ms. The acceleration time was defined as the period from the first detectable movement of the propulsive legs or wings until take-off. Peak velocity was calculated as the distance moved in a rolling three-point average of successive images before take-off. A point on the body that could be recognized in successive frames and was close to the centre of mass was selected for measurements of the trajectory. The angle subtended by a line joining these positions after take-off, relative to the natural horizontal, gave the trajectory angle. The body angle was defined as the angle subtended by the longitudinal axis of the wasp relative to the natural horizontal at take-off. The results are based on high-speed videos of 292 take-offs by 35 wasps at temperatures of 23–25°C. At least three jumps were analysed in detail for each individual wasp. The number of specimens of N. testacea was small, so that no quantitative analysis was performed. Data are presented as means±s.e.m. for an individual insect and as grand means (mean of means) for all individuals of a particular species.

Body form

The parasitoid wasps fell into two distinct groups on the basis of their mass and size. First were three small species, L. boulardi, P. puparum and C. glomerata, with body masses of, respectively, 0.4±0.03, 1.0±0.1 and 1.0±0.07 mg and body lengths of 1.8±0.06, 2.7±0.01 and 3.1±0.05 mm (N=7 for each species) (Table 1). By contrast, the second group contained two heavier and larger species, A. armatorius and N. testacea, with A. armatorius having a mass of 56.9±0.83 mg and a body length of 19.5±0.5 mm (N=7).

In all species the middle legs were either the same length as the front legs (as in L. boulardi), or they were just 20% longer. The middle legs were also short relative to the body length, ranging from 46% in A. armatorius to 68% in P. puparum (Table 1). The hind legs in L. boulardi and P. puparum were 40% longer than the front legs, in C. glomerata they were 70% longer and in A. armatorius they were 80% longer. Relative to body length, the hind legs were longest at 87% in C. glomerata and shortest at 70% in A. armatorius (Table 1). The middle femora were 12% wider than those of the front legs in C. glomerata but in A. armatorius they were only 3% wider (Fig. 1F,G). By contrast, the hind femora of these two species were 74–75% wider than those of the front legs.

Kinematics of jumping and take-off

Pteromalus puparum

In P. puparum, 65 of 71 jumps (91.55%) performed by 11 individuals were propelled by movements of the middle legs alone (Figs 2 and 3, Movie 1). The wings remained closed so that the forward and upward trajectories were determined solely by the forces generated by the legs during the jump. In some jumps, the wings opened after take-off and flapping flight ensued, but this rarely occurred under the experimental conditions.

In a selected jump of P. puparum viewed from the side (Fig. 2), the hind legs were the first to move some 4 ms before take-off, and their contribution to propulsion was brief because they were the first pair of legs to lose contact with the ground 0.6 ms later followed by the front legs 2 ms before take-off (Fig. 2A). During this time the two middle legs moved symmetrically by depressing about their coxo-trochanteral joints and extending about their femoro-tibial joints. These movements continued until take-off so that the middle legs alone were then responsible for propulsion. After take-off, the left and right middle legs crossed because the forces they generated now acted only against the air. Clear differences in when the three pairs of legs lost contact with the ground were revealed by plotting their movements against time (Fig. 2B). However, the sequence in which the legs moved and lost contact with the ground varied, both between successive jumps of an individual and between jumps of different individuals; the hind legs were usually the first to lose contact with the ground, but sometimes the front legs were the first. Different sequences did not correlate with the angle of the body relative to the ground, or with the angle of the jump trajectory after take-off. The action of the middle legs was a constant feature in all jumps; their joints depressed and extended progressively to provide upwards and forwards propulsion, and their tarsi were always the last to lose contact with the ground.

Six jumps by P. puparum (8.45% of the total jumps by this species) were propelled by the same leg movements but were also accompanied before take-off by a single depression of the wings (Fig. 3, Movie 2). The wings opened 30 ms before take-off and reached their fully open and elevated position before the first leg movement occurred. The wings then began to depress while the front legs were the first to lose contact with the ground, followed by the hind legs. At take-off, the wings were completing their first depression movement. After take-off, the wings began to beat so that there was a seamless transition to powered flight. The mean wingbeat frequency in these wasps once airborne was 185.4±3.2 Hz so that the period from one full elevation to the next was 5.4±0.1 ms (N=10 individuals; Table 2).

Cotesia glomerata

Take-off by C. glomerata was propelled by a series of wingbeats with only small movements of the middle and hind legs occurring (Fig. 4, Movie 3). Preparation for take-off was marked by the adoption of a steep angle of the body relative to the ground (69.1±8.0 deg; Table 3) so that the front legs were lifted from the ground. The wings then opened and executed 2.8±0.3 wingbeats before take-off (21 take-offs, N=3 individuals; Fig. 4A). The mean wingbeat frequency was 126.1±6.7 Hz (period 8.2±0.3 ms; Table 3). The first wingbeat before take-off was often of small amplitude but thereafter all wingbeats were of a full amplitude both during the acceleration phase of take-off and once airborne (Fig. 4B–D). At the start of the first wing movement the middle and hind legs began to show small changes in the angles between the body and the femora and between the femora and tibiae (Fig. 4A,D). These changes continued after take-off as the legs sagged beneath the body under the influence of gravity, suggesting that the initial small changes observed before take-off might be due to the lift generated by the wings rather than to active propulsion by the legs. The hind legs were the next to lose contact with the ground so that as in P. puparum, it was the middle legs that finally lost contact at take-off while the wings were being depressed (Fig. 4D).

Leptopilina boulardi

In L. boulardi, the lightest of all the species analysed, propulsion for take-off shifted further towards a greater reliance on the wings. Preparation for take-off was initiated by tilting of the front of the body upwards so that the front legs lost contact with the ground and thus made no further contribution. The wings then opened and executed 3.8±0.1 wingbeats (28 take-offs, N=4 individuals), with take-off again being accomplished during wing depression (Figs 5 and 6). The mean wingbeat frequency was the highest at 198.9±5.4 Hz (mean period 5.0±0.1 ms, N=4 individuals; Table 2). No contribution to propulsion could be discerned by the middle and hind legs as viewed from directly in front (Fig. 5A) or from the side (Fig. 6, Movie 4). The angles between the body and femora and between the femora and tibiae in both pairs of these legs did not change before take-off, but once airborne they increased as the legs sagged beneath the body (Fig. 5B,C). The wing movements described symmetrical paths leading to take-off while the movements of the body described an upward trajectory with a mean angle of 91.2±31.8 deg but with much variation (Fig. 5B, Table 3). The rhythmic wing movements continued after take-off so that there was a smooth transition to powered flight.

Ichneumonidae

Amblytelesarmatorius and N. testacea were the largest wasps analysed and both used a combination of leg and wing movements to propel take-off (Figs 7 and 8). However, the legs were used in a different sequence to that described for the preceding wasps. The wings opened first and then before they started to beat (Fig. 7A, Movie 5), or during their first depression (Fig. 8A), the hind legs began their propulsive movements. The front legs were the first to leave the ground, followed by the middle legs (Figs 7B and 8B). The hind legs were thus the only legs adding to the forces during the latter part of the propulsive phase of the take-off. The wings generated a mean of 2.6±0.2 wingbeats (27 take-offs) before take-off and the lowest mean frequency for any of the wasps recorded here of 80±3.7 Hz (mean period 13.1±0.5 ms, N=9 individuals; Table 2). The angle between both the body and the hind femora and the femora and the tibiae changed progressively to depress and extend the hind legs to take-off while the wings were beating (Fig. 7B). For N. testacea, plotting the trajectories described by the tip of the right front wing before take-off together with the movements of the tarsi of the right middle and hind legs showed that take-off occurred during the depression phase of a wingbeat and that the middle legs lost contact with the ground well before the hind legs (Fig. 8B).

Jumping and take-off performance

Jumping and take-off performance were derived from measurements taken from the high-speed videos and from subsequent calculations (Table 3). The time taken to accelerate to take-off varied by a factor of six between the different species. It was shortest at 5.0±0.3 ms (three jumps by each of 11 wasps) in P. puparum, which was propelled by leg movements. The acceleration times of take-offs by this species that were assisted by a single depression of the wings all fell within the range of times shown in jumps propelled only by the legs, suggesting only a small contribution of the wings to lift. In other species where take-off was propelled by a few wingbeats, the take-off time was longer at 19.3±1.1 ms (N=4 individuals) in L. boulardi and 22.8±2.8 ms (N=3 individuals) in C. glomerata. It was longest at 33.8±1.9 ms (N=9 individuals) in the heaviest wasp, A. armatorius, which was propelled by combined leg and wing movements.

Take-off velocity varied by a factor of four between the different species. The fastest velocities, mean (0.8±0.1 m s−1) and best (0.99 m s−1), were achieved by P. puparum. Both L. boulardi and C. glomerata which have a similar mass but were propelled by wing movements, could only achieve mean take-off velocities that were a quarter of this at 0.2 m s−1 (Table 3). The heaviest wasp, A. armatorius, which used leg and wing movements, had an intermediate take-off velocity with a mean of 0.4±0.03 m s−1 and best value of 0.6 m s−1.

The trajectory of the take-off and the angle of the body relative to the horizontal were correlated with the propulsive strategy that was used. Where the legs provided the sole or main propulsion, as in P. puparum, the mean trajectory angle was 65.8±7.8 deg, and where leg movements were combined with wing movements, as in the much heavier A. armatorius, the angle was shallower at 54.4±4.9 deg (Table 3). The body angle relative to the ground was also low at 35.1±4.6 and 25.4±2.6 deg, respectively. In contrast, where wing movements were the sole or dominant propulsive force, the trajectories were much steeper; in L. boulardi they were almost vertical (mean 91.2±5.4 deg), and in C. glomerata they were backwards (mean 110.7±14.6 deg). The angle of the body at take-off was also steeper at 63.3±10.2 and 69.1±8.0 deg, respectively.

The acceleration experienced at take-off was highest at 17 g in P. puparum, which had the fastest take-off velocity and shortest acceleration time (Table 3). By contrast, in species with both slower take-off velocities and longer acceleration times, the values ranged only between 1 and 2 g.

The energy for take-off (E) was calculated in the same way (Eqn 1) for each of the three strategies used by these parasitoid wasps:
formula
(1)

where m is mass (kg) and v is velocity (m s−1).

In P. puparum, the mean energy required for a jump propelled by leg movements was 0.3 µJ and the mean power was 0.06 mW. In the two other species of similar mass, but in which take-off was propelled by wing movements, the mean energy required was only 0.01–0.02 µJ and the mean power 0.0003–0.001 mW. In the much heavier A. armatorius, these values were 10.9 µJ and 0.15 mW in its best jumps.

The power requirements for take-off in its best jumps by P. puparum were 766 W kg−1 muscle, whereas in the remaining three species they were dramatically lower at 13–24 W kg−1 muscle in their best jumps. This calculation assumes that the muscles used to propel take-off comprised 10% of body mass.

Consequences of different strategies for take-off

This paper has shown that different species of parasitoid wasps use different strategies to generate take-off. In three species of similar mass (0.4–1.0 mg), two distinct strategies were found even in species that parasitise the same host. Pteromaluspuparum propelled 92% of its jumps by rapid leg movements alone with no accompanying movements of the wings. In the small number of their remaining jumps, the wings executed just one depression movement of the wings before take-off, which did not increase take-off velocity above that achieved by the propulsive leg movements alone. By contrast, in C. glomerata and L. boulardi wings movements were, respectively, either the main or the only contributors of force to take-off. In the much heavier A. armatorius (mass 50 times greater), a combination of propulsive leg movements and wing beating generated take-off. Only one species showed evidence of being able to change strategies. In a few take-offs, P. puparum added one cycle of wing depression to the same sequence of leg movements. The measurements were made in a limited behavioural context in which the take-offs could not be related directly to a particular sensory stimulus. Some take-offs appeared to be ‘spontaneous’ but the possibility remains that others might have been triggered by the presence of members of the same species in the chamber at the same time. In insects such as Drosophila, different take-off strategies are clearly used in different behavioural contexts (Card and Dickinson, 2008; Trimarchi and Schneiderman, 1995a,b; von Reyn et al., 2014).

The following conclusions can be drawn about the effectiveness of the strategies for take-off, particularly by comparing the performance of the three species with similar, low masses. The shortest acceleration time of 5 ms and a mean take-off velocity of 0.8 m s−1, with the fastest take-off reaching almost 1 m s−1, was achieved by take-off propelled by movements of the legs in P. puparum. By contrast, in two other species of similar mass, take-off generated by beating the wings a mean of 2.8 times in C. glomerata and 3.8 times in L. boulardi resulted in acceleration times that were four times longer at 19–23 ms and take-off velocities that were four times slower at 0.2 m s−1. The take-off angles and the subsequent trajectories of these two species once airborne were also much steeper than those of P. puparum, which was propelled only by jumping movements of the legs. These three species of wasps had bodies of similar size, shape and mass. The legs of P. puparum and L. boulardi were also of similar proportions relative to each other and to body length. The exception was C. glomerata, the hind legs of which were 70% longer than the front legs and the longest relative to the body, but this increased leverage did not apparently contribute to take-off.

To calculate the energy expended in translation of the body, the same method was used for take-offs generated by both strategies. This method calculates the energy put into propelling the body into the air. Take-offs of P. puparum generated by leg movements resulted in 0.3 µJ of energy being put into achieving this goal, whereas in take-offs generated by flapping movements of the wings, this value fell by 15–30 times to 0.02 or 0.01 µJ. The reason for this dramatic difference is that in the latter strategy, energy is lost in generating repetitive movements of the wings and in moving air rather than in propelling the body upwards and forwards. These data therefore support the hypothesis of this paper that jumping as a mechanism to propel take-off is more energy efficient than propulsion generated by flapping movements of the wings. This energy efficiency is thus a further advantage conferred by jumping in addition to a shorter acceleration time to take-off and a faster take-off velocity.

This conclusion is even more striking when consideration is given to the mechanical power that is transmitted to the body during take-off. In all strategies, the relevant muscles must generate much power but the amount seen in the output kinematics is very different for the different strategies. In take-offs by P. puparum that are propelled by leg movements, this power is almost completely transferred to the final movement of the wasp (Table 3). The high power outputs of this species may also indicate a contribution from hind leg muscles to take-off. By contrast, in C. glomerata, L. boulardi and A. amartorius, in which take-offs are propelled by wing movements, less than 10% of the power generated by the muscles is transferred directly to the final movement of the wasp (Table 3). Most of the power is used in accelerating the wings and the air beneath the wings, and not into accelerating the wasp itself.

In the heavier species such as A. armatorius, both leg and wing movements were combined to propel take-off in the longest acceleration time of 34 ms and to a take-off with a velocity of 0.4 m s−1 that is half generated by P. puparum when jumping. Lifting the heavy body must contribute to this long acceleration time and lower take-off velocity and offers a possible explanation of why a combination of leg and wing movements are needed to effect take-off.

Take-off performance

How does the jumping performance of the wasps analysed here compare with other insects that also use a power generating mechanism that depends on direct contractions of leg muscles and four propulsive legs? The take-off velocity of P. puparum matched that of lacewings (Neuroptera; 0.5–0.6 m s−1; Burrows and Dorosenko, 2014) and moths (Lepidoptera; 0.6–0.9 m s−1; Burrows and Dorosenko, 2015a), overlapped with some caddis flies (Trichoptera; 0.7–1.0 m s−1; Burrows and Dorosenko, 2015b), but fell short of the velocities achieved by a praying mantis (Mantodea; 1.0 m s−1; Burrows et al., 2015) and the fly Hydrophorus alboflorens (Diptera; 1.6 m s−1; Burrows, 2013a). Two of the species of wasp analysed here, C. glomerata and L. boulardi, used the wings alone to propel take-off and reached low velocities of 0.2 m s−1. Their take-offs were almost vertical or sometimes slightly backwards so their trajectories were much steeper than those of wasps that are propelled by the legs alone or assisted by the wings. Caddis flies also differ in their take-off trajectory depending on the strategy they use (Burrows and Dorosenko, 2015b).

Use of two pairs of legs for take-off

A number of jumping solutions have evolved in insects, particularly when the legs are used for propulsion. When one pair of legs is used by true flies (Diptera) it is the middle legs (Hammond and O'Shea, 2007; Trimarchi and Schneiderman, 1995b), but in other insects it is more frequently the hind legs. In bush crickets, these legs are long relative to the body and allow jumps to be propelled by direct contractions of the muscles acting on these long levers (Burrows and Morris, 2003). Higher take-off velocities have been achieved by catapult mechanisms involving the hind legs in insects such as grasshoppers, fleas and froghoppers (Bennet-Clark, 1975; Bennet-Clark and Lucey, 1967; Burrows, 2003). In catapult mechanisms, energy can be stored in advance of a jump to enable power to be amplified with a concomitant reduction of the acceleration time. The stored energy is then released suddenly to generate fast leg movements that propel a jump. So rapid are the leg movements of froghoppers, planthoppers and treehoppers (Burrows, 2006, 2009, 2013b) using this mechanism that additional specialisations are needed to ensure that the leg movements are synchronised (Burrows, 2010; Burrows and Sutton, 2013) so as not to result in rotation of the body and the loss of energy for forward momentum.

In other insects, such as the wasps described here, both the middle and hind legs can potentially be used to propel jumping or assist in take-off. The front legs can be excluded as in none of the recorded take-offs do they move in ways that are consistent with generating propulsion. In snow fleas (Burrows, 2011), praying mantis (Burrows et al., 2015) and the dolichopodid fly Hydrophorus alboflorens (Burrows, 2013a), the middle and the hind legs leave the ground at the same time so both are able to contribute thrust during the last part of the acceleration phase of take-off. In caddis flies (Trichoptera) (Burrows and Dorosenko, 2015b) the middle legs are the last to leave the ground, but in moths (Lepidoptera) (Burrows and Dorosenko, 2015a), lacewings (Neuroptera) (Burrows and Dorosenko, 2014) and mirid bugs (Hemiptera) (Burrows and Dorosenko, 2017) it is the hind legs. In the wasp P. puparum, the middle legs are the last to leave the ground, so it is using the same strategy as caddis flies (Burrows and Dorosenko, 2015b). By contrast, the hind legs of A. armatorius are the last to lose contact with the ground, so it is using the same strategy as ants (Baroni Urbani et al., 1994; Tautz et al., 1994), moths (Burrows and Dorosenko, 2015a) and lacewings (Burrows and Dorosenko, 2014).

What advantages does the use of two propulsive pairs of legs confer? First, four propulsive legs ensure that forces needed for take-off are distributed over a larger surface area of the substrate. This could allow take-off from more compliant surfaces. Adding thrust from wing movements should further reduce the forces transmitted directly to the ground, while at the same time allowing a smooth transition into forward, powered flight.

Second, the muscles of both pairs of legs power the movement, effectively almost doubling the muscle mass available for take-off. Estimates that the jumping muscles represent approximately 10% of total body mass are based on measurements from insects using just one pair of propulsive legs. On this basis, the calculated energy requirements for take-off by the wasps studied here are low and only in P. puparum do they reach the high end of values shown for muscle from a range of animals (Askew and Marsh, 2002; Ellington, 1985; Josephson, 1993; Weis-Fogh and Alexander, 1977). Increasing the muscle mass used for jumping would thus reduce the expected energy demands to well within these limits and allow all the wasp jumps and take-offs to be explained by direct contractions of the muscles. Mechanisms involving energy storage have been invoked (Gibson, 1986) to explain the take-offs of some wasps, but the data presented here indicate that such mechanisms are not required for the performance of the parasitoid wasps studied here. A clear disadvantage of using four legs is that it precludes achieving the high take-off velocities that catapult mechanisms can generate, because no neural or mechanical mechanisms have been found that could synchronise all these legs with the necessary precision.

Many thanks to Roger Northfield for supplying C. glomerata and P. puparum from his culture of cabbage white butterflies and to Sophie Smith for supplying L. boulardi from Drosophila cultures. We thank William Foster for help with the identification and classification of these wasps and Peter Lawrence for many helpful suggestions during the experimental work.

Author contributions

Conceptualization: M.B.; Methodology: M.B.; Validation: M.B.; Formal analysis: M.B., M.D.; Investigation: M.B., M.D.; Writing - original draft: M.B.; Writing - review & editing: M.D.; Visualization: M.B.; Supervision: M.B.; Project administration: M.B.

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

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Competing interests

The authors declare no competing or financial interests.

Supplementary information