Flight metabolic rate of Locusta migratoria in relation to oxygen partial pressure in atmospheres of varying diffusivity and density

The high metabolic demands of insect flight are met by the tracheal system, which consists of air-filled, semi-rigid tubes, where respiratory gases (i.e. O₂ and CO₂) move rapidly in the gas phase between the atmosphere and the cells. The gas transport occurs by two mechanisms, diffusion (the passive net movement of a gas from a high concentration to a lower concentration as a result of molecular collisions) and convection (the usually active movement of gases by bulk flow in a medium from a high total pressure to a lower pressure, also called advection). Together, these mechanisms determine the conductance of the tracheal system, which is the ease of respiratory gas exchange in the system. Diffusion alone is thought to be sufficient to meet the flight metabolic rate (FMR) in very small insects (e.g. mosquitos); however, in larger insects (bees, dragonflies, locusts), ventilation creates convective flow in the lateral regions of the tracheal system, thereby reducing the diffusion distance and maintaining a pressure gradient for diffusion along the terminal parts of the tracheal system. Ventilation of the tracheal system occurs by abdominal pumping and thoracic autoventilation (Weis-Fogh, 1964a,b). Abdominal pumping affects haemolymph pressure, resulting in the compression and expansion of large tracheae and air sacs (large, modified tracheae), and the bulk movement of luminal air. Thoracic autoventilation occurs with deformation of the thorax by the wing muscles during flight, resulting in the pumping of air through the tracheal system at wingbeat frequency (Komai, 1998; Wasserthal, 2001, 2015; Weis-Fogh, 1964b, 1967). The degree to which these ventilation mechanisms are employed varies between species. For instance, ventilation in dragonflies, which have little capacity for abdominal movement, occurs almost exclusively by thoracic autoventilation (Weis-Fogh, 1967), while bees favour abdominal pumping (Komai, 2001). Locusts, in contrast, use both abdominal pumping and thoracic autoventilation to varying degrees (Harrison et al., 2013). Thoracic autoventilation services the flight muscles, pumping air at approximately 250 ml g⁻¹ h⁻¹, and it is supplemented by abdominal pumping, which delivers air at approximately 70 ml g⁻¹ h⁻¹ (Miller, 1960; Weis-Fogh, 1967).

Diffusion occurs throughout the tracheal system, but it is most important in the terminal regions, particularly the blind-ended tracheoles (Harrison et al., 2013). Oxygen diffuses down its concentration gradient, theoretically according to Fick's first law of diffusion. The rate of flux depends on the anatomy of the system (cross-sectional area and distance), the difference in O₂ partial pressure (P_O2) along a given distance, and Krogh's coefficient for O₂ diffusion in the gaseous medium (normally air). Krogh's coefficient for O₂ depends on temperature, barometric pressure and the nature of the background gases. For a given P_O2 differential, the O₂ diffusion rate should increase at low barometric pressure or in an artificial gas mixture where nitrogen (N₂), the background gas of normal air, is replaced with a gas of low molecular weight, such as helium (He). Conversely, the rate would decrease at high barometric pressure or in a gas mixture where N₂ is replaced with a gas of high molecular weight, such as sulfur hexafluoride (SF₆). These effects are in contrast to the convective mechanism of ventilation in which O₂ flux is largely independent of background gases, except for the added effort to move high-density gases compared with the reduced effort to move low-density gases.

The low metabolic rate of resting insects is satisfied easily by a tracheal system capable of achieving metabolic rates during flight that are 20–100 times higher than at rest (Ellington, 1985). The conductance of the O₂ supply pathway is often revealed by measuring metabolic rate over a range of ambient P_O2 and defining a point, called the critical P_O2 (P_C), below which metabolic rate declines. Resting adult insects tolerate severe hypoxia as low as 1–5 kPa without exhibiting a decline in metabolic rate (Greenlee and Harrison, 2004a,b; Greenlee et al., 2007; Harrison et al., 2006; Joos et al., 1997; Klok et al., 2010; Rascón and Harrison, 2005; Van Voorhies, 2009). During flight, this apparently large reserve capacity or ‘safety margin’ for O₂ delivery decreases significantly (Harrison et al., 2006). The P_C is approximately 10 kPa in hovering honeybees, Apis mellifera (Joos et al., 1997), and between 10 and 21 kPa in tethered flying locusts Schistocerca americana (Rascón and Harrison, 2005). The P_C values for 11 species of flying dragonfly appear to be about 10–15 kPa (Henry and Harrison, 2014), but P_C is difficult to define in one dragonfly species, Erythemis simplicicollis, because only a slight change in metabolic rate occurs between 5 and 50 kPa, and the rate at 5 kPa is only 18% below that at 21 kPa (Harrison and Lighton, 1998). In most studies, the relationship between metabolic rate and P_O2 is curved, rather than an ideal independence above the P_C and proportional dependence below it. This curved relationship introduces uncertainties in determining P_C, and calls into question whether a single definitive P_C even exists. Instead of calculating P_C from broken stick regression models, the dependence of metabolic rate on P_O2 can be evaluated with a new metric, the Regulation Index, which is a value that has clearly defined limits, from perfect oxy-conformity (0) to perfect oxy-independence (1), but does not force the data to follow any particular pattern (Mueller and Seymour, 2011).

An important question in insect respiration concerns how the structure and function of the respiratory system are matched to the gas exchange requirements of the animal. One working hypothesis, called symmorphosis, predicts that the respiratory system should be constructed according to economic design principles (Weibel et al., 1998). Symmorphosis posits that every step of the O₂ cascade should be equal in its capacity to transport O₂ from the atmosphere towards the mitochondria that use it (Weibel et al., 1991). Flying insects are arguably the most appropriate group to study, because their mass-specific metabolic rates are the highest of all animals (Schippers et al., 2010; Suarez, 2000). Symmorphosis is evident in the hopping muscle of Locusta migratoria by the parallel scaling of maximum muscle metabolic rate, tracheolar radial diffusing capacity, mitochondrial volume and inner mitochondrial membrane surface area (Snelling et al., 2011b). Symmorphosis also holds for the locust flight muscle, except for an apparent mitochondrial oversupply (Snelling et al., 2012b). Other studies indirectly show parallel development of tracheal capacity and metabolic rate (Greenlee and Harrison, 2004a; Harrison et al., 2005; Hartung et al., 2004; Kaiser et al., 2007). One test for symmorphosis is to assess the matching of tracheal O₂ transport capacity with maximum O₂ consumption rate by the mitochondria. This can be achieved by analysing the response of maximum metabolic rate to varying ambient P_O2 levels. An increase in maximum O₂ consumption rate under hyperoxia would indicate that the maximum rate is normally limited by the conductance of the tracheal system. Conversely, the maintenance of maximum O₂ consumption rate under hypoxia would indicate a conductance oversupply of the tracheal system, possibly to maintain a reserve capacity for carrying added loads or for bouts of energy-intensive acrobatic flight not normally performed.

Another experimental approach to test for matching between maximum O₂ transport and maximum O₂ consumption is to vary the O₂ diffusivity of the gaseous medium. The diffusion rate of O₂ in the tracheal system is dependent, in part, upon the molecular weights of all gas species present. The diffusivity of a gas increases with decreasing molecular weight, according to Graham's law; however, it is also affected by a range of other factors, including temperature, pressure and the viscous properties of the other gas molecules through which the gas diffuses. If two gases are involved, then binary diffusion coefficients can be used to estimate the rate, but if three gases are involved, then ternary coefficients must be used (Cussler, 2009; Poling et al., 2001). Manipulating the molecular weights of gases also affects the density of the gas mixture, with density being directly proportional to molecular weight. This relationship is the opposite of the relationship between molecular weight and diffusivity and, as such, density is also inversely (though not linearly) proportional to diffusivity.

Given the inverse relationship between diffusivity and density parameters, it is difficult to determine conclusively which factor, or whether a combination of both factors, affects the metabolic rate of insects flying in artificial gas mixtures. It has been assumed that increased O₂ diffusivity does not have a significant effect on O₂ consumption rate during flight (Roberts et al., 2004); however, there are no data to support this idea. Previous studies measuring FMR of insects under variable barometric pressure (e.g. Withers, 1981) are inconclusive, because altering barometric pressure has three opposing influences on flight metabolism. For example, low barometric pressure reduces atmospheric density, which should increase the power required for flight and therefore increase FMR. Low barometric pressure decreases atmospheric P_O2, which should decrease the driving force for diffusion and therefore decrease FMR. Low total pressure increases O₂ diffusivity, which should increase FMR. No previous study has examined the effect of decreased molecular diffusivity in isolation. By selecting specific gas combinations, it is possible to separate the confounding effects of diffusivity and density through the creation of mixtures with normal atmospheric diffusivity and varying density, and vice versa, while holding the P_O2 at normal levels (normoxia).

The main objective of this study was to determine the metabolic limitations of tethered flight in the migratory locust Locusta migratoria. Conductance limitations of the tracheal system during flight were tested four ways. Firstly, maximum FMR was measured across a range of ambient P_O2 to evaluate the influence of O₂-supply limitation with N₂ as the sole background gas. Secondly, FMR was measured across a range of ambient P_O2 with SF₆ as the sole background gas to decrease O₂ diffusivity in the tracheal system. In theory, the effects of low diffusivity due to the presence of SF₆ can be offset by an adequate increase in ambient P_O2. Thirdly, FMR was measured across ambient P_O2 with He as the sole background gas to increase O₂ diffusivity in the tracheal system. Fourthly, to distinguish between the O₂ diffusivity and density effects of the background gas, ternary gas mixtures of O₂, He and SF₆ were used to adjust these properties independently while holding P_O2 constant at normoxia.

Gregarious-phase migratory locusts Locusta migratoria (Linnaeus 1758) were reared from egg to adulthood at the University of Adelaide, under a regulated temperature (33±2°C) and photoperiod regime (12 h:12 h light–dark cycle), and with ad libitum access to wheatgrass and wheat germ, as previously described (Snelling et al., 2011a). Only adult males 2–5 weeks post-final moult were used, as by this age the flight muscles are fully developed (Mizisin and Ready, 1986).

Flow-through respirometry was used to measure metabolic rate during tethered flight exercise in a constant-temperature cabinet set to 35±2°C, the upper-preferred temperature of locust flight (Weis-Fogh, 1967). The respirometer consisted of a clear cylindrical acrylic flight chamber (93×100 mm, inner diameter×length) through which artificial gas mixtures were pushed at a rate of 1000 ml min⁻¹. Gas exiting the chamber passed through a small column of desiccant (Drierite; W. A. Hammond Drierite Co. Ltd, Xenia, OH, USA) prior to entering a CO₂ gas analyser (LI-820; Li-COR Biosciences, Lincoln, NE, USA) and then an O₂ gas analyser (FC-2 Oxzilla; Sable Systems, Las Vegas, NV, USA). The analog outputs of both gas analysers were recorded with a PowerLab data acquisition system running LabChart software (ADInstruments, Bella Vista, NSW, Australia). Analyser baselines were set using a bypass around the chamber before and after flight measurements.

A tether descending from the roof of the flight chamber was used to position the locust centrally and toward the incoming stream. A small magnetic disk (3 mm diameter) was affixed to the pronotum of each locust to allow temporary, but firm, attachment to the tether head. The disk was affixed using melted depilatory wax (Klorane, Boulogne, France) and care was taken to ensure the wax was not excessively hot upon application (locusts seemed unperturbed). Once tethered within the flight chamber, individual locusts were placed in the constant-temperature cabinet for at least 10 min before each experiment to acclimate. Then, flight was initiated through rapid removal of a flexible perch beneath the locust, which elicited a tarsal flight response (Weis-Fogh, 1956). Flight bouts typically lasted 5–10 min, including an initial washout period before the perch was removed. No more than four flights per locust per day were conducted as there was an apparent decrease in flight effort thereafter. At least 1 h recovery was given to each locust between flight bouts. After each flight, locusts were weighed to the nearest 0.01 mg on a digital balance (AE163; Mettler, Greifensee, Switzerland) and adjusted later to account for the weight of the magnetic disk and wax.

The raw recordings of CO₂ production were instantaneously corrected by applying an empirically derived washout constant for the chamber using previously described principles (Seymour et al., 1998). Instantaneous CO₂ production rates (µmol s⁻¹) were calculated as the product of incurrent flow rate and the fraction of CO₂ added to the excurrent air (Lighton, 2008), and then converted to instantaneous metabolic rate (mW) assuming a respiratory exchange ratio of 0.86, as determined in pilot experiments, and a conversion factor of 0.54 J µmol⁻¹ (Withers, 1992). Finally, the mean maximum FMR for each locust was calculated by averaging the highest instantaneous metabolic rate over 30 s of flight exercise, consistent with earlier studies (Kirkton et al., 2005; Snelling et al., 2012a). Because mass-specific data do not eliminate the effect of body mass, the data are presented in mass-independent units (mW g^−0.75) to standardise the values. The exponent of 0.75 comes from a previous study of locusts in which the maximum metabolic rate during tethered flight (FMR, µmol⁻¹ O₂ h⁻¹) scales with body mass (M_b, g) according to the equation FMR=994 M_b^0.75 (Snelling et al., 2012a). As the mean body mass of locusts used in this study was 1.01 g, the mass-specific, mass-independent and absolute metabolic rates are all approximately equal.

The artificial gas mixtures that were pushed through the flight chamber were generated using a combination of mass flow controllers (10, 100, 500, 1000 and 10,000 ml min⁻¹; Aalborg Instruments and Controls, Orangeburg, NY, USA), calibrated for each gas with a bubble flow meter (Gilibrator; Sensidyne, Clearwater, FL, USA), and regulated by a spreadsheet-controlled 16-bit analog output board (PowerDAQ PD2-AO and Professor DAQ software; United Electronic Industries, Watertown, MA, USA). The gases were mixed at an elevation of ∼50 m and a barometric pressure of ∼101 kPa (Adelaide, Australia) and so the oxygen percentage (% O₂) is approximately numerically equivalent to the P_O2 expressed in kPa.

Binary gas mixtures consisting of selected levels of O₂ balanced with N₂, He or SF₆ were used to test the dependency of locust FMR on P_O2 in the various background gases. The chosen nominal compositions (±1%) were as follows: 5, 8, 10, 12, 15, 17, 19, 21, 32, 43% O₂ balanced in N₂; 5, 10, 15, 21, 44% O₂ balanced in He; and 5, 10, 15, 21, 26, 30, 37, 44% O₂ balanced in SF₆. Ternary gas mixtures consisting of 21% O₂ in varying levels of both He and SF₆ allowed independent manipulation of the O₂ diffusivity and density parameters of the gas mix while holding P_O2 constant. Determination of the desired gas compositions required the calculation of both binary (D_A,B; Eqn 1) and ternary (D_A,mix Eqn 2) diffusion coefficients.

Wingbeat frequency and wing stroke amplitude were measured in a second cohort of similarly aged adult male locusts, also at 35±2°C. These individuals were flown in binary gas mixtures of 21% O₂ balanced with either N₂ or SF₆ background gases, using the same respirometry apparatus, and under the same conditions, as described previously. A high-speed digital video camera (Xacti VPC-FH1; Sanyo Electric Co., Osaka, Japan) was positioned lateral to the tethered locust in the chamber, and flight bouts were recorded at 600 frames s⁻¹. Tracking the tips of the forewing and hindwing during slow-motion playback was facilitated by bright lighting, the application of small black dots on the wing tips (marked with felt pen), and a white background behind the flight chamber.

Videos were analysed early in the flight bouts corresponding to periods of FMR measured at the same time. Mean wingbeat frequency (f, Hz) was calculated over five complete wing cycles as f=(600×5)/N, where 600 is the frame rate (Hz), 5 is the number of complete wing cycles analysed, and N is the number of frames taken over the five complete wing cycles. Mean wing stroke amplitude of the forewing and hindwing was determined as the angle (degrees) between the upper and lower reversal points of the wings. This angle was not measured directly, but calculated from the distance between the upper and lower reversal points of the wing tips as a cosine function of wing length (Fischer et al., 2002; Snelling et al., 2012a). The distance between the reversal points was measured from superimposed images of the wings in these extreme positions captured from the high-speed video footage, and corrected to scale using a high-definition photograph of a 1 mm incremented ruler positioned in the same plane. Because mean wing stroke amplitude did not differ significantly between the forewings and hindwings measured in air, the angles from five dual measurements were averaged for each locust.

Significance between means, tests for normality and equal variance, and curve fitting of the data were undertaken using graphing and statistical software (Prism 5; GraphPad Software, La Jolla, CA, USA). The Regulation Index (RI) was calculated as the ratio A/B, where A is the area bounded by the regression curve of FMR below P_O2 of 21 kPa and a diagonal line between FMR at 21 kPa and the origin, and B is the triangular area above the diagonal line and below a horizontal line intersecting FMR at 21 kPa (Mueller and Seymour, 2011). Thus, RI varies between 0 representing no regulation (i.e. linear dependence of FMR on P_O2 below 21 kPa), and 1 representing perfect regulation (i.e. ideal independence of FMR down to P_O2 of 0 kPa).

The mean body mass (M_b) of the 42 locusts used for flights in the binary gas mixtures of variable P_O2 balanced with either N₂ or SF₆ was 1.01±0.08 g (mean±95% confidence interval, CI). For comparison with other studies, the mean mass-specific FMR measured in normal air at normoxia (P_O2=21 kPa) from 12 locusts (M_b=1.08 g) was 1009±138 µmol O₂ g⁻¹ h⁻¹ and 847±131 µmol CO₂ g⁻¹ h⁻¹, giving a respiratory exchange ratio of 0.84±0.03.

The mean mass-independent FMR measured over a range of P_O2 revealed curves that plateaued above normoxia in both N₂ and SF₆ as the sole background gas (Fig. 1). With N₂ as the sole background gas, FMR did not increase significantly above 21 kPa, but dropped precipitously below it, decreasing 25% from 132 to 99 mW g^−0.75 between P_O2 of 21 and 15 kPa. Regressions involving sigmoid curves fitted the data better than one-phase associations and allowed the dependence of FMR on P_O2 to be evaluated with the RI. The RI value was 0.19 with N₂ as the sole background gas and 0.18 with SF₆ as the sole background gas, both of which indicate very low regulatory ability.

The general trend showed that FMR tended to be lower in SF₆ than in N₂ background gases at P_O2 levels above approximately 10 kPa (Fig. 1). At 21 kPa, FMR was 24% lower in SF₆ (100 mW g^−0.75, N=18) than in N₂ (132 mW g^−0.75, N=12) (t-test, two-tailed, unpaired: t_1,28=3.03, P=0.0052). Only eight successful flight bouts were obtained with He as the sole background gas because, for some reason, the locusts were reluctant to fly. Mean FMR data from three insects flown in five treatments of varying P_O2 with He as the background gas are superimposed in Fig. 1. Although not statistically adequate, these points suggest that the He background did not enhance FMR, except possibly at 5 kPa.

Comparisons of FMR measured in normoxia (P_O2=21 kPa) and balanced in four different background gases, or gas mixtures, are shown in Table 2. FMR with N₂ as the sole background gas was significantly higher than that with SF₆ as the sole background gas (ANOVA: F_3,42=3.99, P=0.014; Tukey's post hoc test: P<0.05). FMR with N₂ was also significantly higher than that with the SF₆-He background mixture (P<0.05), but it was not significantly different from that of flights in the He-SF₆ background mixture (P>0.05; Table 2).

There were marked differences in the measured kinematics of locusts flying in normoxia with N₂ as the sole background gas compared with SF₆ as the sole background gas (Table 3). In SF₆, wingbeat frequency decreased by 15% and wing stroke amplitude by 12% (t-tests, two-tailed, unpaired: P<0.01).

The aim of this study was to determine how the gaseous environment affects O₂ delivery to the flight muscles of locusts under conditions of maximum O₂ demand. To achieve this aim, it was first necessary to establish that flight efforts were maximal. Tethering is thought to underestimate the FMR of free flight, because it removes the requirement of insects to support their own body weight, alters flight kinematics and interrupts sensory feedback loops (Dudley and Ellington, 1990). Past comparisons of the flight mechanics of locusts undertaking tethered flight versus free flight suggested significant tethering effects, including lower wingbeat frequencies (Baker et al., 1981; Gewecke, 1975; Gewecke and Kutsch, 1979) and measured lift that was less than body mass (Gee and Robertson, 1998; Kutsch and Gewecke, 1979; Rascón and Harrison, 2005; Robertson and Johnson, 1993; Wolf, 1993). Furthermore, the FMR of hovering species of insect (bees and moths) is approximately 3-fold higher than that of tethered locusts (Snelling et al., 2012a).

Despite the possibility of significant tethering effects, the results of our study indicate that FMR during tethered flight of locusts was indeed maximal, at least during the initial period of intense exercise. If the locusts had the potential to increase FMR further for free flight, then we would expect that the tethered individuals would maintain the same FMR in mild hypoxia as in normoxia. However, FMR began to decrease immediately as P_O2 was reduced (Fig. 1). Several lines of recent evidence support this conclusion for locusts (Snelling et al., 2012a). Firstly, locusts tethered to a vertical force transducer with air flowing over them at velocities comparable to those of forward flight (ca. 4 to 5 m s⁻¹) can create average lift that is equivalent to body mass (previous work on locusts in stagnant air may have prevented the lift generated by aerofoils in forward flight). Secondly, during these periods of peak lift, wingbeat frequencies and wing stroke amplitudes are similar to those in free flight. Thirdly, locust FMR does not increase with the addition of weights to the wings. And lastly, the approximately 3-fold higher FMR of hovering bees and moths compared with tethered locusts can be largely accounted for by the ∼4-fold greater mitochondrial investment in the flight muscles of the hovering insects compared with those of the locusts (Snelling et al., 2012a).

FMR during tethered flight in the locusts measured under a range of P_O2 with N₂ as the sole background gas shows a pattern of independence above 21 kPa and steeply declining rates below it (Fig. 1). The steepness of the decline suggests a P_C near normal atmospheric levels, and the low RI value of 0.19 reveals high dependence of FMR under hypoxia. These results indicate that the conductance of the tracheal system is matched to peak O₂ demand under normal atmospheric conditions, neither being limited by convection or diffusion nor having excess supply. Such results are expected according to the economical design hypothesis of symmorphosis.

The pattern of O₂ dependence of FMR in our locusts is similar to that in the American locust S. americana, but quite different from that of hovering bees and dragonflies (Fig. 2). The locusts have very low RI values and show immediate oxy-conforming metabolism, while the bees and dragonflies have moderate to high RI values that indicate a considerable reserve capacity or ‘safety margin’. The results may be related to the fact that locusts do not carry significant extra weight during flight, while the predatory dragonflies and foraging bees commonly do (Marden, 2000).

FMR was 24% lower during normoxic flights with O₂-SF₆ compared with O₂-N₂ (Fig. 1). The reduction does not appear to be related strictly to the lower O₂ diffusivity in the dense SF₆, because hyperoxia in SF₆ did not result in higher FMR. Hyperoxia not only increases the P_O2 differential but also decreases the SF₆ concentration, decreasing the density of the mixture and increasing O₂ diffusivity, all of which would augment the rate of O₂ diffusion. Instead of increasing, however, FMR in all O₂-SF₆ treatments appeared lower than in O₂-N₂ treatments. The curves fitted to the data are similar in shape, with virtually identical RI values of 0.18 and 0.19, respectively. The few successful runs with the hyperdiffusive–hypodense O₂-He mixtures were largely coincident with those for O₂-N₂ (Fig. 1), tentatively suggesting that increased O₂ diffusivity does not augment FMR above the maximum measured in air.

In an attempt to separate the effects of O₂ diffusivity and density on FMR, and to determine why there is a significant difference between normoxic flights with SF₆ as the sole background gas compared with N₂ as the sole background gas, we created normoxic hyperdiffusive–normodense and normoxic normodiffusive–hyperdense ternary gas mixtures with O₂, He and SF₆. Our results indicate that gas mixture density has a greater impact on FMR than O₂ diffusivity (Table 2). FMR in SF₆ (hypodiffusive-hyperdense) and in SF₆-He (normodiffusive–hyperdense) was significantly lower than that in N₂ (normodiffusive–normodense). There was no significant difference between FMR in He-SF₆ (hyperdiffusive–normodense) background gases compared with that in N₂, and, rather than augmenting FMR, the He-SF₆ data were nearly significantly lower (P=0.093). We conclude that O₂ diffusivity has very little effect on tracheal conductance in flying locust. These experiments may be improved upon, because the calculation of the diffusivity of ternary gas mixtures (Eqn 2) is not always confirmed by direct measurement, and may be better calculated as the summation of concentration-weighted reciprocal binary diffusion coefficients (Fairbanks and Wilke, 1950; Piiper and Worth, 1980; Worth and Piiper, 1978).

Our conclusion that diffusivity is having a negligible effect on the locusts during normoxic flight is consistent with gas mixing experiments on dogs which show that molecular diffusivity plays only a minor role under conditions of high ventilation (Klocke et al., 1990). Another factor to consider is the effect of high-frequency vibrations during flight on the overall effective diffusivity of the system. Vibrations occurring in the tracheal system during locust flight could produce ‘facilitated diffusion’ whereby high-frequency, small-volume, non-directional oscillations enhance gas diffusivity, as has been shown in the lungs of dogs (Bohn et al., 1980). The high ventilation rates and thoracic vibrations of locusts during flight apparently overwhelm any limitations in molecular diffusivity of O₂.

The effect of dense background gases on FMR is probably related to changes in flight kinematics affecting the work rate of the flight muscles. Locust flight in normoxia revealed significantly decreased wingbeat frequency and wing stroke amplitude in SF₆ compared with N₂ background gases (Table 3). The mean wingbeat frequency of locusts flown in normal air is 24.6±1.5 Hz. This is comparable to 23.7 Hz recorded in a similar study using tethered locusts (Snelling et al., 2012a) and 22.9 Hz recorded from locusts in free flight (Baker et al., 1981). By comparison, the wingbeat frequency in SF₆ is 21.0±1.3 Hz. The mean wing stroke amplitude of the forewings and hindwings in normal air is 100±5 deg. Once again, this compares well with previous estimates of 105 deg for forewings and 96 deg for hindwings in the same species during tethered flight in normal air (Snelling et al., 2012a). In contrast, mean wing stroke amplitude is 88±4 deg in SF₆.

Changing the density of the flight medium consequently alters flight kinematics. Decreasing density appears to increase the level of mechanical work required of the wings to produce enough lift to offset body mass and maintain flight, while increasing density appears to have the opposite effect (Chai and Dudley, 1999; Dudley, 1998). These changes in mechanical work often exhibit as respective changes in wingbeat frequency and/or wing stroke amplitude. For instance, low density flight experiments (e.g. heliox, 21% O₂ and 79% He) show increases in metabolic rate and wing stroke amplitude in both carpenter bees (Roberts et al., 2004) and hummingbirds (Chai and Dudley, 1996, 1999). In contrast, insects flown in high density atmospheres (e.g. high barometric pressures) can produce the same amount of lift as they would in normodense air by changing a range of wing mechanics, including angle of attack, wingbeat frequency and wing stroke amplitude (Withers, 1981). For example, wingbeat frequency of Drosophila decreases with experimental increases in barometric pressure (Chadwick and Williams, 1949), and the O₂ consumption rate of honeybees decreases linearly with increasing barometric pressure (Withers, 1981). Certainly, it would seem that the 24% decrease in locust FMR measured here in SF₆ relative to that in normal air must be related to the 15% decrease in wingbeat frequency (Ellington, 1985; Pennycuick and Rezende, 1984) and the 12% decrease in wing stroke amplitude.

Changing the density of the flight medium also affects the mechanical work of ventilation, with ventilation becoming easier at lower densities, and more difficult at higher densities (Dudley, 2000). The decrease in flight performance in SF₆ could be related to a decrease in active ventilation, autoventilation and facilitated diffusion, consequently impairing O₂ transport through the tracheal system. Thus, the effects of density can be multiple and complex. The effect on ventilation could be explored further by creating variable P_O2 in ternary gas mixtures of different densities.

The flight muscles of the locust are supplied by the diffusion and convection of O₂ along the tracheal system. At maximum FMR, O₂ delivery does not appear to be limited at normal atmospheric P_O2, but it does become limited at slightly hypoxic P_O2, consonant with the data from the American locust S. americana. This suggests that the conductance of the tracheal system is matched to maximum functional requirements, in line with the hypothesis of symmorphosis. Locusts therefore have little reserve capacity to deliver O₂, compared with bees and dragonflies, which is possibly related to their modest ability to carry additional loads. Exposure to normoxia in background gas mixtures involving different O₂ diffusivities and densities reveals that O₂ supply to the flight muscles is primarily by convection rather than diffusion.

The authors thank Jon Harrison of Arizona State University who provided valuable suggestions on an earlier draft of this manuscript.