Measuring power input, power output and energy conversion efficiency in un-instrumented flying birds Free

The power required for birds to fly can be predicted from flight mechanical models (Klein Heerenbrink et al., 2015; Pennycuick, 1968, 2008), which in combination with optimality models can be used to predict adaptive flight behaviours in different ecological contexts (e.g. Pennycuick, 1969; Hedenstrom and Alerstam, 1995). These flight mechanical models describe the mechanical rate of work performed by the bird to propel itself through the air and maintain altitude, which follows a U-shaped relationship with flight speed (Fig. 1). To obtain the metabolic power during flight, which is a more relevant property for ecological decisions made by the bird, an energy conversion factor is required, representing the efficiency of generating mechanical output from the metabolic input. Ideally, the energy conversion efficiency should be determined by simultaneous measurements of flight metabolic rate (chemical power input, P_met) and mechanical power output (P_mech), but these measurements are logistically challenging to take in free-flying birds. In an attempt to overcome this challenge, Tucker (1972) introduced a method to estimate the partial efficiency (Kleiber, 1961), which involves measuring the flight metabolic rate of a bird flying with a respirometry mask at various angles of tilt in a wind tunnel. In this method, the partial conversion efficiency is estimated from the known change in mechanical power due to ascent/descent (±mgU_z, where m is mass, g is acceleration due to gravity and U_z is vertical speed). Based on Tucker's (1972) study and a subsequent, similar study (Bernstein et al., 1973), the partial energy conversion was estimated as 23% (with some variation), which has since been used as the default value for the energy conversion efficiency in models of bird flight (Klein Heerenbrink et al., 2015; Pennycuick, 1975, 2008). More recent attempts to determine the energy conversion efficiency in birds have been based on metabolic measurements compared with calculated P_mech from aerodynamic models (Chai and Dudley, 1995; Ward et al., 2001). The only effort to measure P_mech and P_met on the same birds is for cockatiels (Nymphicus hollandicus), where in vivo sonomicrometry and EMG measurements paired with in vitro measurements of muscle contractions produced work-loop estimates of P_mech (Morris and Askew, 2010), and mask respirometry was used to measure P_met (Morris et al., 2010). These studies yielded energy conversion efficiencies ranging from 7% to 11% (Morris et al., 2010). Hence, estimated conversion efficiency seems to vary substantially depending on the method and/or species. In addition to methodological issues, conversion efficiency is likely to vary with body mass and/or flight speed (Bernstein et al., 1973; Guigueno et al., 2019; Morris et al., 2010). Consequently, for model-derived flight metabolic rates to be useful, there is a need to further develop methods to empirically determine the energy conversion efficiency of bird flight by measuring both P_met and P_mech.

Previous methods to estimate flight efficiency by measuring both P_mech and P_met (sensu Morris et al., 2010) have two major drawbacks. First, using mask respirometry requires an animal to be connected to the flow respirometer with tubing while flying, which may affect natural flight behaviour and increase drag (Bundle et al., 2007; Morris et al., 2010; Tucker, 1972). Second, in vivo measurements of muscle work through sonomicrometry and/or EMG measurements are intrusive, and also require the carrying of instrumentation or trailing wires that may load the animals and impede natural flight. The ¹³C-labelled sodium bicarbonate method (hereafter ‘NaBi’), has been adapted to estimate P_met in flight studies (Hambly et al., 2002; Hambly and Voigt, 2011). Similar to the doubly labelled water (DLW) technique, it makes use of isotopic elimination rates, but instead of measuring elimination of ¹⁸O and ²H (deuterium) in a relatively large water pool, the NaBi method measures the elimination of ¹³C in a much smaller bicarbonate pool (Hambly and Voigt, 2011; Speakman and Hambly, 2016). This dynamic allows for measurements over much shorter time periods (of the order of minutes) and is therefore more suitable to estimate P_met in flying birds within a controlled environment (Hambly et al., 2002). So far the method has been successfully used for short flights in a few bird species performing bouts of flight between perches (Hambly et al., 2002, 2004), for two bat species flying at different speeds in a wind tunnel (Troxell and Holderied, 2019; von Busse et al., 2013) and for bats in the field (Voigt et al., 2010a, 2011). Another method that has recently become available is quantitative magnetic resonance (QMR), which measures fat and wet lean tissue non-invasively within minutes (Guglielmo et al., 2011). Two consecutive measurements flanking a flight period can thus be used to estimate P_met due to consumption of fat and lean mass. Although this method requires relatively long flights at a single speed, it is precise and can generate reliable estimates of metabolic power input (Gerson and Guglielmo, 2011; Guglielmo et al., 2017). To estimate P_mech without hampering natural flight (apart from being confined by space in a wind tunnel), the use of direct measurements of the mechanical power from air flow induced by the animal has become feasible as a result of the technical developments in particle image velocimetry (PIV) (Raffel et al., 2007). The kinetic energy added to the air behind the animal by the flapping wings can be estimated from the resulting flow fields, which can be directly related to P_mech of flight (von Busse et al., 2013; Warfvinge et al., 2017; Johansson et al., 2018a).

In this study, we present an approach to measure P_met using the NaBi method, and P_mech using PIV to obtain energy conversion efficiency of birds flying in a wind tunnel. We used QMR to quantitatively cross-validate the NaBi method; for logistical reasons (availability of a QMR), these measurements were made on different species at two wind tunnel facilities. The main aim of this paper was to evaluate the use of NaBi combined with PIV as a viable method to quantify energy conversion efficiency in birds and to discuss pitfalls and opportunities based on our experiences.

Twelve blackcaps, Sylvia atricapilla (L. 1758), were caught at Lund University ecological field station at Stensoffa (N55.7, E13.4) in October 2017. The birds were held in an aviary (W×H×D: 1.5×2×1.5 m) with a photoperiod of 10 h light:14 h dark and trained for 2 weeks in the Lund University wind tunnel prior to the experiment. The blackcap is a small (15 g) passerine bird that exhibits a large variation in migratory propensity among populations in Europe, which makes it a suitable and relevant candidate for studying flight energetics. Furthermore, the species has been studied extensively in captivity and performs well under laboratory conditions (e.g. Berthold and Querner, 1983), including during PIV measurements (Johansson and Hedenström, 2009). Water and mealworms (Tenebrio molitor) were provided ad libitum. All birds were habituated to the wind tunnel for 2 weeks and four that could reliably sustain steady flight for approximately 20 min were selected for the experiments so that replicate measurements of each individual at multiple speeds could be attempted. Birds were transferred to individual cages (W×H×D: 0.7×0.6×0.7 m) before NaBi and PIV experiments to facilitate food removal and capture. Each bird was photographed with the wing outstretched together with a reference length, from which wing span and area were measured using ImageJ (v.1.50i) following Pennycuick (1989). The mean wing metric values along with mean body mass measured prior to flight were used to parameterize an aerodynamic model (Klein Heerenbrink et al., 2015) to calculate P_mech. All experiments were performed in accordance with approved experimental guidelines and by the Malmö-Lund animal ethics committee (M 33-13) and birds were released in a healthy condition after completion of the study.

Cross-validation of the NaBi method using QMR was done on yellow-rumped warblers, Setophaga coronata coronata (L. 1766) captured near Long Point, ON, Canada (42.6N, 80.4W) in October 2017. The birds were kept in an indoor aviary (W×H×L: 2.3×2.4×3.5 m) at the Advanced Facility for Avian Research (AFAR) at the University of Western Ontario, at a room temperature of approximately 21°C and with a photoperiod of 12 h light:12 h dark. Until mid-December 2017, the birds were used for unrelated wind tunnel experiments where they flew reliably non-stop for as long as 12 h, and were thereafter exposed to a short-day winter photoperiod (8 h light:16 h dark). On 15 March 2018, they were switched to a long-day spring photoperiod (16 h light:8 h dark) to elicit migratory behaviour and associated physiology (Guglielmo et al., 2017). We fed the warblers a synthetic agar-based high-carbohydrate diet ad libitum (Guglielmo et al., 2017) supplemented with mealworms, and water was freely available. Twelve birds known to be excellent fliers from the previous study were trialled, and five birds were selected for their reliable and steady flights. Training consisted of several short habituation flights (10–20 min) before QMR experiments commenced where they repeatedly flew for up to 3 h non-stop. Thus, the birds were highly trained before NaBi experiments commenced. Warblers were released following the study. All experiments were approved by the University of Western Ontario Animal Care Committee (Protocol 2010-216) and birds were captured under a Canadian Wildlife Service Scientific Collection Permit (CA-0256).

Prior to the experiment, the blackcaps were fasted for 2 h and then weighed (0.01 g). The NaBi vial septum was cleaned with an isopropyl alcohol wipe and approximately 150 µl of NaBi solution was withdrawn into a 1 ml insulin syringe (29 gauge needle, Becton Dickson, Franklin Lakes, NJ, USA). The syringe was weighed (0.0001 g) before and after injection to calculate injected mass of NaBi solution. A patch of skin beneath the feathers anterior to the thigh was exposed and disinfected with an alcohol wipe. The NaBi dose was then injected subcutaneously anterior to the thigh and the needle and dose could easily be visualized through the skin. Any leakage was noted and the fluid was collected back into the syringe if possible to estimate volume. The bird was quickly placed into an airtight 1.5 l stainless steel chamber at room temperature (approximately 20°C) for respirometry measurements (see below). While in the chamber, the bird was supplied with dry, CO₂-free breathing air (21% O₂, balance N₂) from a gas cylinder (Linde Gas AB, Solna, Sweden) regulated at 2.5 l min⁻¹ by a STP-corrected 0–5 SLPM mass flow meter/controller (Sierra Instruments 840-L, Monterey, CA, USA) connected to a mass flow controller (MF2, Sable Systems, Las Vegas, NV, USA). The δ¹³C value of the bird's breath was monitored continuously until it reached a plateau (usually within about 5 min), and then showed a visually linear or log-linear decline along with a stable excurrent [CO₂] for 5 min (usually within 15–20 min post-injection). The bird was quickly removed from the chamber, brought to the wind tunnel and flown for approximately 60–120 s at a pre-determined equivalent airspeed of 4, 6, 8, 10, 11 or 12 m s⁻¹. At the appropriate time, the bird was quickly captured with a nylon net and returned to the respirometry chamber for post-flight measurement of breath δ¹³C lasting an additional 15 min. The entire period from removal to return to the chamber was video recorded (Sony Handicam HDR-CX240) with the clock synchronized to the isotope analyser clock so that exact flight start and stop times could be determined. We noted in the first 12 experimental flights that the [CO₂] and δ¹³C of the chamber excurrent flow did not return to baseline, reaching about 80–100 ppm during the short time the bird was in the wind tunnel, and that in many runs there was evidence of a re-enrichment and overshoot of the post-flight enrichment curve with the pre-flight values. Thus, we initiated a practice to flush the chamber at 5 l min⁻¹ while the bird was flying (17 flights) that lowered [CO₂] to about 20 ppm. For the final 21 flights, we added a separate flush line to the respirometry chamber that we could switch on and off to deliver 10 l min⁻¹ of CO₂-free air while the bird flew, and this returned [CO₂] to background before the bird returned from flight. This improved the technique but did not eliminate the post-flight overshoot for all runs. Therefore, runs in which the chamber was not flushed were also included if the post-flight δ¹³C curve rose quickly with no signs of re-enrichment or overshoots (see ‘Criteria for successful flight experiments using NaBi’, below, for more details).

The flow exiting the respirometry chamber passed through a STP-corrected 0–20 SLPM mass flow meter (Sierra Instruments 824-S) to confirm that excurrent flow was close to incurrent flow rate, and then to a T-fitting so that it could be subsampled for measurement of [CO₂] and δ¹³C values. Part of the chamber excurrent flow was drawn from the T-connector through a HEPA disk filter (Whatman HEPA Vent 9825397), a Nafion drying system (Perma Pure PD200T-12MPS, with countercurrent flow dried by a 28.9×6.6 cm Drierite column), a STP-corrected 0–2 SLPM mass flow meter (Sierra Instruments 822S) and a CCIA-38ER CO₂ isotope analyser (Los Gatos Research, Mountain View, CA, USA), which measured [CO₂] in ppm and δ¹³C values at 60 Hz before passing through the subsampling pump. The subsampling flow rate was set at 1 l min⁻¹ by adjusting the pump speed and a throttle valve on the outflow of the isotope analyser, and was visually confirmed to be stable using a LCD on the 0–2 l flow meter. The CO₂ isotope analyser was periodically calibrated with a certified gas mixture of 2000 ppm CO₂, 20.85% O₂, balance N₂ (Linde AG, special gases) for which the δ¹³C (−36.133) and δ¹⁸O (−24.49) of CO₂ (both relative to PDB) were measured in quadruplicate at Lund University Department of Biology Stable Isotope Laboratory. The calibration gas was run at the start and end of each day to confirm performance, but small variations in δ¹³C values were not corrected for because the δ¹³C values of bird breath varied over two orders of magnitude from background. δ¹³C values did not require adjustment for CO₂ because the CCIA-38ER CO₂ isotope analyser has a linear response over a wide dynamic range (200–25,000 ppm CO₂).

For a subset of NaBi runs (7 runs for 2 birds), we subsampled an additional 0.2 l min⁻¹ of the chamber excurrent flow for measurement of O₂ consumption and CO₂ production during the 5 min of stable rest immediately preceding flight. The flow was dried with a small polycarbonate indicating Drierite column (30 g; W.A. Hammond, Drierite, Xenia, OH, USA) and then passed through CO₂ and O₂ analysers (Field Metabolic System, Sable Systems). The gas analysers were calibrated with the certified 2000 ppm CO₂ gas mixture. We calculated V̇_O2 and V̇_CO2 using eqns 10.6 and 10.7 in Lighton (2008), and respiratory exchange ratio (RER) by dividing V̇_CO2 by V̇_O2 to confirm that the birds were oxidizing fat during the resting phase before flight.

Metabolic rate in flight was calculated using methods described previously (Hambly and Voigt, 2011; Hambly et al., 2002; Troxell and Holderied, 2019; Voigt and Lewanzik, 2011). The δ¹³C value of excurrent CO₂ was first corrected for the background breath δ¹³C of each bird. APE was calculated according to Slater et al. (2001), and the values were ln transformed and plotted against time. Peak lnAPE was identified to calculate N_c (Eqn 1) and the slope from ordinary least squares (OLS) regression during the 5 min immediately before removing the bird from the respirometry chamber, before flight was used to estimate fractional isotopic turnover (k_c; min⁻¹). We multiplied k_c by N_c to calculate the rate of CO₂ production (mol min⁻¹) and then converted the result to V̇_CO2 in ml min⁻¹ using the ideal gas law (1000×22.4 l mol⁻¹). V̇_CO2 was also calculated from the mean [CO₂] of the excurrent air during the same 5 min pre-flight period multiplied by flow rate (2500 ml min⁻¹). We compared the respirometric and isotopic measurements to assess the quality of the individual experiment (isotope equilibration dynamics, estimation of pool size), and considered the respirometic measurement of V̇_CO2 to be more robust for estimating flight metabolic rate. lnAPE at the start of the flight was predicted by forward extrapolating the pre-flight linear regression to the start time of flight determined from video. Post-flight lnAPE was similarly estimated by back extrapolating an OLS regression of the data between 4 and 9 min post-return of the bird to the chamber to the stop time of flight from video. This was done because it took a few minutes for the respirometry chamber to re-equilibrate and there was evidence of non-linear breath ¹³C enrichment dynamics immediately after the flight, which has been reported elsewhere (Hambly et al., 2002; Hambly and Voigt, 2011). The k_c during flight was calculated by dividing the change in lnAPE from the start to the end of flight by the flight duration. V̇_CO2 in flight was calculated by multiplying the ratio of flight k_c to resting k_c by the V̇_CO2 measured by respirometry in the pre-flight resting phase. As pre-flight RER indicated that birds were post-absorptive and oxidizing fat (RER=0.69±0.03), we did not consider carbohydrates to be used in flight. Because the birds were migratory species in a migratory state, we assumed a fuel mixture of fat and protein (Guglielmo, 2010). Previous wind tunnel experiments on yellow-rumped warblers indicate that the contribution of lean mass catabolism to energy is greatest early in flight (Guglielmo et al., 2017; Dick and Guglielmo, 2019). Thus, we allowed for a 20% use of protein as fuel in flight, and used a conversion of 27.12 J ml⁻¹ CO₂ (0.8×27.7 J ml⁻¹ for fat plus 0.2×24.8 J ml⁻¹ for protein with uric acid as a waste; Frayn, 1983) followed by appropriate time conversion to calculate P_met in watts. Fasted hummingbirds have been shown to be able to use fat alone to fuel immediate flight (Welch and Suarez, 2007), and assuming 100% fat oxidation with a conversion of 27.7 J ml⁻¹ would have a minimal effect on our results. Non-migratory budgerigars (Melopsittacus undulatus) weighing 36 g had RERs averaging 0.79 during flights up to 4 min across a variety of speeds (fasting state was not indicated; Bundle et al., 2007). If we assumed an RER of 0.8 (33% carbohydrate, 67% fat) during NaBi flights with a conversion of 25.46 J ml⁻¹ CO₂, our calculated flight energy expenditure would be reduced by 6%.

Not all NaBi experimental flights were successful, mainly because of the flight behaviour of the bird, difficulty capturing the bird, or issues with isotopic equilibration before or after the flight, and so we defined criteria to accept runs for further statistical analysis. NaBi runs were considered usable if they met the following criteria. (1) The injection had no or minimal leakage (<10 µl) and any leakage was recovered and quantified. In most cases, the subcutaneous injection was without leakage. (2) The pre-flight δ¹³C equilibration peak was smooth and unimodal, and occurred between about 5 and 10 min of injection. In some experiments, enrichment of the bicarbonate pool did not seem uniform, was very fast (1 min) or very slow possibly because of the influence of subcutaneous fat pads or variation in blood flow to the injection site. (3) The flight was continuous and lasted approximately 1–2 min. In many cases the bird would not fly at the speed required for long enough or would land repeatedly (this occurred especially at speeds <4 m s ⁻¹ and >11 m s⁻¹, i.e. outside their preferred flight speed range). In some trials, we returned the bird to the chamber for 10 min and attempted a second flight, and although data often looked reasonable we rejected these runs because of concerns that the assumption of single pool kinetics no longer holds after about 30 min post-injection in small animals (Hambly and Voigt, 2011; Hambly et al., 2002). (4) The bird was recaptured immediately at the end of the flight and did not fly out of the wind tunnel test section. Blackcaps were often difficult to capture cleanly and therefore a net was used. (5) The post-flight δ¹³C curve rose quickly with no obvious overshoot or re-enrichment of the bicarbonate pool. In many runs, the post-flight curve was very curvilinear and this was improved but not completely eliminated by flushing the chamber. (6) The back-extrapolation from the linear phase of the post-flight δ¹³C curve to the stop time of the flight was below the estimated lnAPE at the start of the flight. In some cases, there appeared to be re-enrichment of the bird during or after flight, possibly because of additional mixing of the dose. (7) The calculated V̇_CO2 from the isotopic data had to match the V̇_CO2 from the respirometry data within ±25%. About 75% of runs met this criterion, and we interpreted a poor match to indicate problems with the injection or isotopic equilibration.

The NaBi technique can be used to measure energy expenditure during very short flights immediately after a bird (or bat) is removed from a chamber where it has been resting for approximately 15–20 min. In a second set of experiments conducted after the blackcap study, we wanted to determine the quantitative accuracy of the NaBi method by cross-validating it against the QMR method that measures energy expenditure integrated over long, stable flights. Therefore, we flew birds repeatedly at a single comfortable speed and used both the NaBi and QMR methods to quantify energy expenditure.

The five yellow-rumped warblers selected for flight experiments were kept in individual cages (W×D×H: 70×50×60 cm) for ease of food removal and capture. Birds were fasted with access to water for 2 h before each experimental flight. From 3 to 15 April (15 flight attempts) and 20 to 29 June (6 flight attempts) each bird was flown repeatedly (3–5 times with minimum 2 day breaks) for up to 181 min at 8 m s⁻¹, 15°C and 70% relative humidity (9 g H₂O m⁻³). Immediately before and after each flight, birds were weighed (0.001 g) and fat and lean mass were measured by QMR (Guglielmo et al., 2011). Flights ≥53 min were used for energetics. Flight energy expenditure was calculated from the loss of fat and lean mass (fat 39.6 kJ g⁻¹, wet lean 5.3 kJ g⁻¹; Gerson and Guglielmo, 2011). Energy expenditure was also measured by the NaBi method in each of the 5 warblers either after (April) or before (June) the QMR flights. We used the same equipment and methods (subcutaneous injection, 54–121 s flight duration, video recording) as used for the blackcap experiments, except that we did not measure RER in any of the pre-flight periods. Each bird was fasted with access to water for 2 h and then weighed and injected subcutaneously anterior to the thigh with 100 µl of 0.29 g ml⁻¹ NaH₂¹³CO₃ in sterile saline (same solution as used with blackcaps). Each bird was measured 5–7 times at 8 m s⁻¹, 15°C and 70% relative humidity, and calculations of P_met were made using the same methods and assumptions regarding fuel use as for blackcaps (see above). We also used the same criteria for selecting runs for statistical analysis (see ‘Criteria for successful flight experiments using NaBi’, above).

We defined a right-handed coordinate system with the x-axis aligned with the freestream direction, the y-axis in the spanwise direction, and the z-axis in the vertical upwards direction. For the flow measurements, we used a tomographic PIV setup, with four high-speed cameras (LaVision Imager pro HS 4 mol l⁻¹, 2016×2016 pixels) aiming obliquely from above and behind at a transverse (y, z plane) light sheet (LDY304PIV laser, Litron Lasers Ltd, Rugby, UK) situated in the wake of the birds. The light sheet was approximately 5 mm thick. We used di-ethyl-hexyl-sebacate particles, 1 µm diameter, as tracer particles to visualize the flow. Images of the laser-lighted particles were captured at a frame rate f_L of 640 Hz for an imaged area of approximately 33×24 cm (width×height). We calibrated the cameras using the LaVision calibration plate (type 22) and performed the PIV analysis using Davis 8.3.1 (LaVision Gmbh, Göttingen, Germany).

As a first step in the PIV analysis, we performed image preprocessing (subtract sliding minimum 3 pixels, Gaussian 3×3 smoothing, sharpening and multiplication with a factor 10). Thereafter, we used the FastMart reconstruction routine to generate a 3D particle space (38×2493×1791 voxels), which was followed by a direct volumetric correlation with decreasing box size [64³ with 50% overlap with 4³ binning (8 pixel search length), followed by 48³ with 50% overlap with 2³ binning (4 pixel search length), followed by 32³ boxes with 50% overlap (2 pixel search length), and finally 24³ boxes with 50% overlap (1 pixel search length) three times]. Between each round of correlations we used a 2× remove (threshold 2) and replace (threshold 3) outlier detection (5×5×5 voxels) to remove erroneous vectors, followed by a 3× smoothing (3×3×3 voxels). We post-processed the resulting vector fields using a 2× remove (threshold 2) and replace (threshold 3) outlier detection (7×7×7 voxels) to remove erroneous vectors, filling empty spaces by interpolation and finally smoothing vectors (1× with a 3×3×3 box Gaussian filter). The resulting vector field (3×208×149 vectors) had a resolution of ∼6.3 vectors cm⁻¹ in each dimension. We used the second plane in the x-dimension for all further analyses (i.e. force and power calculations).

The PIV measurements are associated with errors resulting in variation in the estimated flow. In order to determine the effect of this error on our power estimate, we performed an error propagation analysis (Johansson et al., 2018a,b). We determined the root mean square (RMS) of the velocity components (RMSu, RMSv, RMSw) using DaVis 8.3 by sampling sequences of free-stream flow. As the RMS values for each velocity component (u, v, w) did not vary substantially between flight speeds, we used an average for each of the components. The error propagation to our wake energy estimates was determined using a Monte Carlo simulation in Matlab (Johansson et al., 2018a,b). We did not implement the Helmholtz–Hedge decomposition, but only used the full span wake (see above), as the extension of the vector field to the full wind tunnel size takes a very long time to run. For each of our analysed velocity vectors we simulated a random error, in each dimension, using normal distributions of the errors with standard deviations set to the RMS of the different components (using the Matlab function normrnd) and added this error to the original vectors. For each sequence we simulated the errors 10,000 times. In each of the 10,000 simulations we also varied the free-stream velocity (U_∞), by adding an error (based on RMSu in the same way as for the velocity vectors) to the measured free-stream velocity. For each of the wakes with simulated errors, we then determined the energy in the wake using Eqn 2.

Based on the distribution of the simulated results, we estimated the median and the first and third quartiles. We present two measures of the error: the deviation of the median (Med) from the original estimate based on our actual measurements (E₀) divided by E₀, which indicates the relative effect of errors in the velocity vectors on the estimated energy. We also calculated the variation in the estimate around the median [(Q1−Med)/Med; (Q3−Med)/Med; where Q1 is the first quartile and Q3 is the third quartile], which indicates the precision of the measurement as a result of errors in the vectors.

In total, 17 measurements with QMR analysis (flight durations from 53 to 181 min; Table 1) and 15 usable measurements using the NaBi method (from 31 attempts; Table 1) were made to estimate metabolic power in 5 yellow-rumped warblers flying at an air speed of 8 m s⁻¹. Average estimated P_met was 1.5±0.4 and 1.7±0.6 W, using the NaBi method and QMR, respectively. There was no significant interaction between method and body mass and the term was therefore dropped from the model. There was a significant difference between the two methods (linear mixed model: F_1,26.1=5.96, P=0.022) (Fig. 2A), and a significant positive relationship between mass and P_met (linear mixed model; F_1,23.9=8.68, P=0.007) (Fig. 2B).

We conducted a total of 49 flights using the NaBi method to estimate P_met, distributed between 4 individual blackcaps. Based on pre-determined criteria for successful runs (see Materials and Methods, ‘Criteria for successful flight experiments using NaBi’), a total of 17 measurements were retained for further analyses (Table 2). For these birds, resting V̇_CO2 calculated from respirometry and NaBi were strongly correlated (Fig. 3), even over a small range of metabolic rates (F_1,15=50.73, P<0.001, r²=0.77). The highest value for weight-corrected power was considered an outlier (Grubb’s test: G=2.67, U=0.53, P=0.019) and was therefore excluded from further analysis. The corresponding value for measured P_met was therefore also excluded from further analysis. Metabolic power across all air speeds varied between 0.8 and 2.6 W, and weight-specific power varied between 4.7 and 14.7 W N⁻¹. Estimated average power across all birds was highest at the lowest speed, 4 m s⁻¹, and then decreased at 6 and 8 m s⁻¹, to increase again at 10 and 11 m s⁻¹ (Fig. 4A). Estimated average weight-specific power followed the same pattern, but different from estimates of power, the minimum weight-specific power was reached at 10 m s⁻¹ (Fig. 4B). When fitting a generic aerodynamic flight power model (P=k₁+k₂/U_∞+k₃) against power and weight-specific power, a U-shaped function was discerned (Fig. 4), but the coefficients were not significant (power: k₁: P=0.40, k₂: P=0.13, k₃: P=0.67; weight-specific power: k₁: P=0.66, k₂: P=0.15, k₃: P=0.5).

A total of 11 reliable PIV measurements were obtained for air speeds of 6 and 8 m s⁻¹ (5 and 6, respectively). No PIV measurements for lower and higher speeds fulfilled our criteria of weight support while staying within the measurement area. The average measured P_mech was 0.4±0.1 and 0.3±0.1 W, for 6 and 8 m s⁻¹, respectively (Fig. 4A). Lift-corrected P_mech for the same speeds was 1.6±0.3 and 1.3±0.5 W N⁻¹, respectively (Fig. 4B). The deviation of the median errors (MedE−E₀/E₀) in the PIV measurements was on average 3.9% for the data and the precision (Q1−MedE/MedE and Q3−MedE/MedE) varied between −0.7% and 1.7%.

As the results of the comparison between the NaBi and QMR revealed a ∼12% difference in P_met using the NaBi method compared with QMR, we present the calculated efficiencies as an interval, with the upper limit representing direct NaBi measurements and the lower limit with a 12% correction of P_met. For the two speeds, 6 and 8 m s⁻¹, where both P_met and P_mech were measured for blackcaps, the average whole-animal energy conversion efficiency was 19–22(±8)% (variation presented as the propagated error of P_met and P_mech) and 19–21(±11)%, respectively. For weight/lift-corrected values, the average whole-animal energy conversion efficiency was 14–16(±6)% and 15–16(±8)% for 6 and 8 m s⁻¹, respectively.

Our estimate of whole-animal energy conversion efficiency is based on measured P_met and P_mech. When considering non-weight/lift-corrected quantities, efficiency ranged between 19% and 22%, and for lift/weight-corrected quantities, efficiencies were 14–16% for the two speeds taken together. Our results are within or close to the range of measured partial efficiency of laughing gull (Larus atricilla), 19–28% (Tucker, 1972), American fish crow (Corvus ossifragus), 20–29% (Bernstein et al., 1973), and budgerigar (Melospittacus undulatus), 18–29% (Tucker, 1972).

Both our estimated P_met values for yellow-rumped warbler, using NaBi (1.5±0.4 W) and QMR (1.7±0.6 W), although significantly different from each other, were similar to those from previous studies of the species (Dick and Guglielmo, 2019; Guglielmo et al., 2017; Ma et al., 2018; Yap et al., 2018) (Table 3). Guglielmo et al. (2017) estimated average P_met to be 1.6 W, while Yap et al. (2018) estimated average P_met for three experimental groups (before treatment in all groups) to range between 1.9 and 2.0 W. In another study, Ma et al. (2018) estimated average P_met to be 1.6 W. In a fourth study, Dick and Guglielmo (2019) estimated average P_met in three experimental groups, fed with different diets with respect to fatty acids, to range between 1.5 and 1.7 W, with no statistical difference between these groups. Similar to this study, the yellow-rumped warblers were flown at 8 m s⁻¹ and the measurements were made using QMR, and the same wind tunnel was used in all studies (including ours) (Dick and Guglielmo, 2019; Guglielmo et al., 2017; Ma et al., 2018; Yap et al., 2018). Despite the difference in measured P_met between the two methods, the NaBi method roughly differed in estimated P_met by only 12% compared with QMR, which we consider acceptable to consider the NaBi method useful for measuring flight cost in birds.

Our estimates of P_met for the blackcap (1.5±0.4 W at 8 m s⁻¹) are smaller than the allometric equations for flight metabolic rate, 2.8 and 2.5 W (using a body mass of 19 g), by Butler and Woakes (1985) and Rayner (1990), respectively. However, for yellow-rumped warblers, our estimate (1.5±0.4 W at 8 m s⁻¹) corresponds well with Rayner's (1990) equation of 1.5 W (using a body mass of 13 g), but not for the equation by Butler and Woakes (1985), which predicts 2.1 W. This suggests that estimates of flight power obtained by allometric equations should be treated with caution.

Thus far, there are few studies where P_met has been estimated during flight in passerines within the mass range of about 10–30 g. However, our estimates for both yellow-rumped warbler and blackcap accord well with those available. For example, estimated P_met for thrush nightingale (Luscinia luscinia, 26 g) flying at 10 m s⁻¹ was 1.9 W (Klaassen et al., 2000) and for estimates of two species of freely flying Hirundinidae ranged between 1.1 and 1.8 W (Westerterp and Bryant, 1984) (Table 3). Our average estimates are lower than those found in 30–40 g budgerigars by Tucker (1972) (∼4.2 W at ∼8 m s⁻¹) and Bundle et al. (2007) (6.7 W at 8 m s⁻¹; calculated from presented data on V̇_O2 and RER using the oxyjoule equivalent; Lighton, 2008), and in ∼35 g Swainson's thrushes (Catharus ustulatus, 3.9 W at 10 m s⁻¹) by Gerson and Guglielmo (2011) and Groom et al. (2019) (Table 3). This is expected because of the higher masses of these birds. Comparison of weight-specific values of P_met (see Table 3) yields a slightly different picture with more interspecific variation. However, mass-specific comparisons across taxa should be interpreted with caution as the relationship between mass and energy expenditure is not linear, and normalization for allometric effects is not taken into account (Lighton, 2008). Overall, our findings further support that the NaBi technique under controlled experiments yields reasonable estimates of P_met during flight.

We did not find a statistically significant U-shaped relationship between P_met or weight-specific P_met and air speed for blackcaps, but there was a pattern of a decrease from lower to intermediate speeds, and an increase from intermediate to the highest measured speed. There are several analytical and methodological reasons why no statistically significant U-shaped curve was found in this study, despite the pattern. First, the sample size was low for each speed, there was considerable variation and not all individuals were represented at each speed. Second, we were unable to obtain estimates at the higher end of possible speeds, which has turned out to be a general difficulty in wind tunnel studies (Engel et al., 2010; Johansson et al., 2018a). Thus, the measurements in this study do not refute the existence of a U-shaped relationship between air speed and P_met in blackcaps (cf. Engel et al., 2010), and future studies involving larger sample size and wider speed range are merited.

Variation in estimated P_met could be due either to errors in the measurements or to individual variation, which may have arisen for two main reasons. First, the mass among the experimental blackcaps varied between 17 and 22 g, which could influence individual flight kinematics and aerodynamic properties. In general, heavier birds have higher P_met requirement compared with lighter birds (Fig. 2B; Klein Heerenbrink et al., 2015; Pennycuick, 2008), but this should be controlled for by calculating lift- or weight-specific power (i.e. dividing power by body weight). However, we still found considerable variation (Fig. 4). It is possible that other unknown factors unrelated to mass, or the interaction between mass and morphology, may have an effect on P_met. Such factors may include body frontal area, stroke plane and/or body angle compared with the horizontal (e.g. Johansson et al., 2018a), or variation in individual flight behaviour. However, we are currently lacking detailed data on these factors, which should be a scope for further investigation. Second, different individuals may behave differently under experimental conditions (e.g. during handling) as a result of stress levels and individual idiosyncrasies, such as different levels of exploratory behaviour (i.e. bold or shy), both of which may co-vary with metabolic rate (Careau et al., 2015). For example, individual variation in stress response, measured by corticosterone production, has been shown in house sparrow (Passer domesticus) during banding (Lendvai et al., 2015), and individual stress response, as measured by elevated metabolic rate, has been correlated with level of exploratory behaviour in great tits (Parus major) (Carere and Van Oers, 2004). Thus, if particular individuals are more prone to stress, this may bias estimated individual metabolic rate during flight in a wind tunnel. Disentangling variation due to measurement errors and those due to propagated individual variation can only be done with more samples and repeated measurement, something admittedly lacking in the current study, and should encourage future experiments.

One of the benefits with the NaBi method (compared with, for example, DLW or mass loss) is that measurements of P_met can be achieved from short flight durations and at flight speeds that cannot be sustained for long periods. One potential concern with short flights is the level of anaerobic metabolism and/or utilization of different energy substrates compared with longer flights (Rothe et al., 1987). However, pre-flight fasting can precondition birds to oxidize fat and birds in a migratory state are primed to oxidize fat at very high rates (Jenni-Eiermann and Jenni, 2012). This is attributed to the uniform fast oxidative fibres of their flight muscles, and high activity of fatty acid transporters and oxidative enzymes (Guglielmo, 2010). We detected no evidence for carbohydrate oxidation during the pre-flight resting phase in our birds (hence the average RER was 0.69; see Materials and Methods), even though they were in an excited state after capture and handling, and there was no indication that birds were fatigued or unable to fly after the short NaBi or long QMR flight tests. Thus, we have no evidence that anaerobic metabolism may impose a bias in our study. Interestingly, measurements obtained of P_met using the NaBi technique (i.e. ∼2 min flights) were lower (∼12%) than those made using QMR (i.e. >50 min flights), and thus did not overestimate flight cost, as one might expect for short flights where birds may not be sufficiently relaxed. Even though the estimated flight costs by NaBi and QMR differed statistically, the fact that they were within ∼12% despite a nearly 70-fold difference in flight duration, and were similarly sensitive to the effect of body mass, was reassuring. These findings suggest that the NaBi technique reflects speed-specific energy expenditure that would be measured in longer flights if the birds were capable of sustaining them. If the birds had used up to 33% carbohydrate during NaBi flights, our calculated energy expenditure would be reduced by 6% (i.e. from 1.5 to 1.4 W in blackcaps flying at their minimum flight cost and from 1.5 to 1.4 W in yellow-rumped warblers), but calculated efficiency would change insignificantly (e.g. from 21% to 22% in blackcaps based on measured values).

A large proportion (65%) of the measurements of blackcaps were removed from further analysis based on pre-decided criteria (see Materials and Methods, ‘Criteria for successful flight experiments using NaBi’). Our success improved considerably with experience and 55% of flights were successful with yellow-rumped warblers. Despite the obvious benefits of using the NaBi method, such as the possibility for un-instrumented, short flights, there are some difficulties relating to the methodology and experimental protocol that have to be considered. Here, we would like to highlight some important points that are associated with potential pitfalls of which the list of criteria describing successful or unsuccessful runs is based on. First, the isotope injection should be administrated properly and without leakage. Small leakage immediately at injection is tolerable because the NaBi method does not technically require the pool size to be known, only that there is a precise and accurate measurement of k_c simultaneous with measurement of CO₂ by respirometry during the pre-flight resting period. Large or continued leakage may alter the enrichment dynamics in such a way that the resting elimination rate (i.e. the pre- and post-flight curves) becomes unpredictable and ultimately leads to errors in the estimation of elimination rate during flight, which is used to estimate P_met (Hambly and Voigt, 2011; von Busse et al., 2013). All previous studies used intraperitoneal injections, which may reduce the likelihood of leaks. However, for small birds we found that subcutaneous injection above the thigh was easier, well tolerated, eliminated any risk of injury to organs or air sacs, and resulted in the same isotopic equilibration kinetics as reported in other studies (Hambly et al., 2002, 2004). Second, the experimental birds need to be properly habituated to handling and flight tests as well as be quiet in the respirometer chamber prior to and after flight. Third, the time between the respirometer chamber and flight in the wind tunnel should be kept to a minimum, as prolonged periods will lead to uncertainty about the ¹³C enrichment at the start and after the end of flight, and most likely result in an underestimation of P_met. By placing the isotope analyser right next to the wind tunnel, we were able to reduce this time to <15 s. This point also relates to the capture of birds from the wind tunnel after the desired flight time. Manipulating the wind tunnel lighting, wind speed or access to avoid chasing or escape is crucial. Finally, the decay of ¹³C enrichment in the pre-flight phase was very smooth and consistent, and usually agreed closely with the results of respirometry for energy expenditure. The post-flight phase was most problematic and many runs were excluded because of apparent re-enrichment during or after the flight or other poorly understood irregularities in isotope dynamics. Flushing the chamber of ¹³C-enriched CO₂ while the bird was flying seemed to help but did not fully eliminate the problem. In the final yellow-rumped warbler flights, we arranged a system of 3-way stopcocks to divert the incurrent flow and subsampling by the isotope analyser to and from a small mask (Mitchell et al., 2015) so that we could measure the breath ¹³C enrichment immediately at the end of the flight. This showed a similar relative depletion of ¹³C that arose after the bird was placed into the respirometry chamber. So, the linear back extrapolation appears to be a good solution, supported by the agreement of the NaBi and QMR measurements.

Only a limited number of studies have made use of PIV to directly estimate mechanical power output in vertebrates (Håkansson et al., 2017; Johansson et al., 2018a,b; von Busse et al., 2014) and only one of them has been concerned with a bird species (Johansson et al., 2018a), the pied flycatcher (Ficedula hypoleuca). Our estimates of P_mech were higher than those of the flycatchers, which at 7 m s⁻¹ was estimated to be 0.16 W (Table 3). This most likely reflects the higher body mass in blackcaps (21 versus 16 g average mass). However, mass-specific power was still higher in blackcaps at around 7 m s⁻¹, indicating that other factors, such as morphology and flight behaviour, may determine P_mech.

We only obtained estimates of P_mech for two air speeds, 6 and 8 m s⁻¹, and our results are consequently not sufficient to evaluate how P_mech varies over a wider speed range. Estimated P_mech values for 6 and 8 m s⁻¹ were above the predicted values from a flapping flight model (Fig. 4) (Klein Heerenbrink et al., 2015). This difference has a number of possible explanations, including methodological procedures. However, considering that measurement errors have a small effect on the power estimate (∼3.9%), and that the size of the flow field expansion using Helmholtz–Hodge decomposition has a relatively small effect beyond 0.5 m² cross-section for this size of bird (Johansson et al., 2018a), the discrepancy between predicted and the estimated P_mech could be due to incorrect model assumptions. One model parameter that can still be regarded as uncertain is the body drag coefficient, but also the estimated body frontal area can be problematic (Rayner, 1979). Both these parameters are influenced by the body angle compared with the horizontal, which varies across flight speed and is usually not included in the model (but see Johansson et al., 2018a). Another source of error could be horizontal or vertical acceleration of the bird within the chosen sequences of PIV measurements, which would result in overestimated P_mech. A possible remedy would be to use kinematics to compensate for any change in position. However, we admittedly were not able to attain sufficient usable measurements for this purpose. Regardless, the measurements and model are still similar enough to conclude that we are within a reasonable range of P_mech. However, we note that if the true value for P_mech is closer to the model predictions for the two speeds, our calculated efficiencies would be smaller.

In this study, we used state of the art techniques to estimate P_met and P_mech in flying blackcaps as well as the resulting energy conversion efficiency at two air speeds. Both P_met and P_mech are crucial to obtain reliable power curve estimates, with undisturbed flow (i.e. resulting in natural drag and lift generation) and measurements at challenging flight speeds. Given the similarity of estimates of P_met and P_mech to previous studies of similarly sized birds and other methods (here using QMR), we conclude that the current approach (NaBi combined with PIV) is an operational protocol for further investigation of flight energetics in birds over a wider range of speeds. Even though the methods can sometimes be challenging, we consider our approach highly promising for studies of flight energetics over a wider range of speeds, allowing us to answer some of the outstanding questions regarding bird flight energetics.

We thank Susanne Åkesson (Lund University) and Long Point Bird Observatory for helping capture blackcaps and yellow-rumped warblers used in the study. We thank Alexander Macmillan for his assistance flying warblers.