Allometry of kinematics and energetics in carpenter bees (Xylocopa varipuncta) hovering in variable-density gases
1 Department of Biological Sciences, University of Nevada, Las Vegas, 4505
S. Maryland Parkway, Las Vegas, NV 89154-4004, USA
2 School of Life Sciences, Arizona State University, Tempe, AZ 85287-1501,
USA
3 Department of Integrative Biology, University of California, Berkeley, CA
94720-3140, USA
4 Smithsonian Tropical Research Institute, PO Box 2072, Balboa, Republic of
Panama
* Author for correspondence (e-mail: sroberts{at}ccmail.nevada.edu)
Accepted 28 December 2003
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Summary |
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Key words: aerodynamics, allometry, energetics, flight, reserve capacity, Xylocopa, bee
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Introduction |
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The use of tethering and attachment of weights potentially influence both
the behavioral motivation to fly and features of flight capacity
(Dudley and Chai, 1996;
Willmott and Ellington, 1997
;
Dudley, 2000
). For example,
weight addition may significantly alter the insect's center of gravity
(although cumulatively applied loading to dragonflies suggests no effect on
capacity; Marden, 1987
)
whereas tethering may artificially constrain body orientation to non-preferred
angles. Some of these issues can be circumvented by use of normoxic but
hypodense gas mixtures to elicit increases in lift and power. Orchid bees
(Eulaema sp. and Euglossa spp.) are capable of hovering in
normoxic heliox (density of 0.41 kg m3) and increase power
production by
45% relative to flight in normal air
(Dudley, 1995
). By contrast,
ruby-throated hummingbirds (Archilocus colubris; mass of 34 g)
hovering in normoxic helium/nitrogen mixtures exhibit aerodynamic failure at
densities intermediate to those of normodense air and heliox (0.500.79
kg m3, depending on lipid loading and molt condition; Chai
and Dudley, 1995
,
1996
,
1999
;
Chai et al., 1996
;
Chai, 1997
). In this group,
metabolic and aerodynamic power reserves relative to hovering in normal
conditions average 36% and 25%, respectively. Both orchid bees and
hummingbirds increase stroke amplitude in response to hypodense challenge,
although complementary changes in angle of attack and wing rotation speed at
the ends of half-strokes await testing via high-speed video analysis.
The general nature of modulatory responses to flight in hypodense air is not
clear, however, given that only two volant taxa have been studied to date.
Here, we examine the hovering flight of carpenter bees (Xylocopa
varipuncta) in variable-density but normoxic gas mixtures
(Dudley and Chai, 1996) to
assess aerodynamic and metabolic limits to flight performance. We chose
Xylocopa to assess maximal hovering performance because their basic
flight physiology is well understood
(Chappell, 1982
;
Nicolson and Louw, 1982
;
Heinrich and Buchmann, 1986
;
King et al., 1996
;
Gäde de and Auerswald,
1998
) and because these bees are more heavily wing loaded than
orchid bees (Nicolson and Louw,
1982
; Casey et al.,
1985
; Dudley,
1995
). Hovering capacity in hypodense air is inversely
proportional to wing loading (e.g. Chai et
al., 1996
), and Xylocopa is thus more likely than orchid
bees to fail at low gas densities that are experimentally feasible. Carpenter
bees also exhibit a wide range of body masses intraspecifically, which enables
allometric analysis of limits to flight performance without untoward
complications of phylogenetic variance. Also, changes in metabolism and
kinematics in low-density, high-thermal conductance gas mixtures should, in
Xylocopa, reflect aerodynamic responses as opposed to
thermoregulatory responses. The latter might be expected by species, such as
honeybees (Harrison et al., 1996; Roberts
and Harrison, 1999
) and various Centris spp
(Spangler and Buchmann, 1991
;
Roberts et al., 1998
), that
thermoregulate during hovering flight by varying kinematics and metabolic heat
production. However, because Xylocopa hovering flight metabolism is
independent of air temperature between 22°C and 38°C
(Chappell, 1982
;
Nicolson and Louw, 1982
),
increases in Xylocopa metabolism/kinematic performance in hypodense
gases should not be confounded by an aerodynamically mediated thermoregulatory
response as described above. Finally, oxygen diffusivity is inversely
proportional to gas density, and thus tracheal diffusion is substantially
enhanced in O2/N2/He mixtures. It is extremely unlikely
that O2 diffusion would limit kinematic and metabolic performance
during flight in hypodense gas mixtures
(Dudley and Chai, 1996
).
Flight of Xylocopa in variable-density gases thus offers an excellent
opportunity to assess the allometry, kinematics and energetics of maximal
hovering flight performance.
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Materials and methods |
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Each bee was exposed, in random but non-repeating order, to six
variable-density gas mixtures ranging in density from 0.41 kg
m3 to 1.21 kg m3
(Table 1), the latter value
corresponding to normodense air. Canisters of pure O2,
N2 and He were used with calibrated flow rotameters to generate
experimental gas mixtures and subsequently to flush the flight chamber at a
rate of 60 l min1 (STP). This gas infusion yielded an
approximate mean flow velocity of 0.01 m s1 through the
chamber. Individual bees were flown within each gas mixture for 3 min. If bees
landed, they were immediately persuaded to fly or attempt flight by chasing
them with a small magnet on the bottom of the chamber that could be moved
using a magnetic wand moved around the external surface of the chamber floor.
Bees that landed on the sides of the chamber were immediately persuaded to fly
or attempt flight by tapping on the external surface of the chamber. The
kinematic analysis was limited to data from flight bouts within the last 2 min
of exposure to both normal air and the minimal gas density necessary for
hovering. Aerodynamic failure was defined as the inability of an individual to
ascend two or more body lengths from the chamber floor and then hover for at
least 2 s. Dynamic viscosities of gas mixtures were calculated using the
formulae of Reid et al.
(1987).
|
Wingbeat kinematic parameters were determined from frame-by-frame video
playbacks using a Panasonic AG1980 video player and NIH Image software and
included the stroke amplitude (), stroke plane angle (ß) relative to
the horizontal, and body angle (
) relative to the horizontal (definitions
follow Ellington, 1984c
).
Acoustic recordings of wingbeat frequency (f) were analyzed using
SoundEdit software for Macintosh (see
Roberts et al., 1998
). Within
each gas mixture, mean values of kinematic variables were determined from
three separate measurements. Each estimate of wingbeat frequency was
determined from a sequence containing 1020 clearly distinguishable,
uninterrupted wingbeats, for which the mean wingbeat frequency was determined
by dividing the number of wingbeats in the sequence by the sequence duration.
Only those sequences in which the insect exhibited controlled, unaccelerated
flight two or more body lengths (or at least 60 mm) above the floor and away
from the walls and ceiling of the flight chamber were used for analysis, so as
to minimize the possibility of underestimating power due to the boundary
effect when vortices become `trapped' between the flyer and nearby
surfaces (Raynor and Thomas,
1991
). Ascending, descending or maneuvering flight was
ignored.
Morphological parameters for use in aerodynamic calculations were
determined for each insect (Ellington,
1984b) and included body mass (Mb), relative
wing mass (Mw) for both wing pairs (expressed as a
fraction of body mass), wing length (R), total wing area (S;
the area of both wing pairs), body length, thoracic mass and thoracic muscle
mass. Thoracic muscle mass was determined indirectly by cutting the thorax
(shorn of legs) in half and removing trace non-muscular features such as fats
and components of the digestive tract. The two thoracic halves were weighed
and then soaked in 0.5 mol l1 NaOH for 24 h. The cuticular
residue was weighed after digestion of the muscle tissue. Relative thoracic
muscle mass (Mmuscle) was expressed as a fraction of total
body mass. Wing loading
(pw=Mbg/S, where
g is gravitational acceleration) and wing aspect ratio
(AR=4R2/S) were calculated for each bee.
Non-dimensional radii for moments of wing mass, virtual mass and wing area
were determined following standard methods (see
Ellington, 1984b
).
Lift and power requirements
Lift and power output during normal and maximal hovering flight were
calculated using the aforementioned kinematic and morphological data and the
aerodynamic model of Ellington
(1984a,b
,c
,d
,e
,f
).
Mean lift coefficients (CL) were calculated according to
Ellington (1984f
) such that
vertical force production averaged over the wingbeat period equaled body
weight. Mechanical power requirements were estimated by evaluating individual
components of profile (Ppro) and induced
(Pind) power requirements. Taxa with asynchronous flight
muscle, such as bees, are likely to store kinetic energy elastically during
the deceleration phase of the wing stroke, so that inertial power requirements
are probably negligible (see Ellington,
1984f
; Dickinson and Lighton,
1995
). Therefore, total power output (Pmech)
for a flight sequence was calculated for the cases of perfect elastic storage
of wing inertial energy and corresponds to the aerodynamic power requirements
alone (=Ppro+Pind; see
Ellington, 1984f
). Recent
studies (Dickinson et al.,
1999
; Sane and Dickinson,
2001
; Usherwood and Ellington,
2002
) have experimentally measured unsteady drag coefficients
(CD) and demonstrate unequivocally that flow separation
and leading edge vortices yield much higher drag than previously realized.
Usherwood and Ellington (2002
)
studied continuously revolving bumblebee wing planforms at Reynolds numbers
similar to those of hovering Xylocopa and showed that Reynolds number
and aspect ratio, together with wing shape, yield small effects on drag
relative to changes in the angle of attack. We did not use high-speed
photography in the present study and thus were unable to measure angle of
attack or its variation with air density (although this is probably a major
factor during hovering in hypodense gas). Mean CLs for
Xylocopa were 1.41.7. For bumblebee wing planforms, this range
of CLs corresponds to the beginning of the plateau for the
lift:drag polar, at which point the CD is
1. Sane and
Dickinson (2001
) demonstrate
that the stroke pattern of model Drosophila wings that optimizes lift
(where mean CL=1.9) generates a mean
CD of 2.7. The Reynolds numbers are much higher in
Xylocopa, so lift:drag ratios would in principle be higher in these
large insects. Furthermore, angle of attack almost certainly changes as air
density is reduced, rendering direct comparisons of calculations with a
constant CD difficult to interpret. Despite these
uncertainties, we have calculated power assuming CDs of 1
and 3 instead of (7/Re)0.5, where Re is the mean
Reynolds number of the wing chord (see
Ellington, 1984f
).
Metabolic power input (Pinput; W kg1)
during hovering was estimated from measurements of rates of carbon dioxide
production, which were determined using flow-through respirometry. Metabolic
rates were analyzed only for periods identified on the videotape as being
periods of active hovering. The gas excurrent from the flight chamber was
subsampled and directed to a Licor 6252 carbon dioxide analyzer (Licor,
Lincoln, NE, USA) calibrated with a known span gas and CO2-free
air. The output of the carbon dioxide analyzer was digitized and monitored
online using a Sable Systems (Henderson, NV, USA) data acquisition system.
Metabolic power input was calculated assuming metabolism of simple
carbohydrates and a respiratory quotient of one (21.4 J ml1
CO2; Gäde de and
Auerswald, 1998). Reserve capacities for kinematic parameters,
mechanical power input and metabolic power output were calculated as the ratio
of the difference between maximal and normodense values to the normodense
value and were expressed as percentages. Values of muscle efficiency were
calculated as the ratio of mechanical power output to metabolic power input
and were also expressed as percentages.
Thoracic temperatures
We measured thoracic temperatures of all bees within 10 s of exposure to
the final gas mixture used in each trial. The lid of the flight chamber was
removed, the bee was gently restrained, and a microprobe thermocouple
(diameter 0.33 mm; time constant 0.025 s) connected to a Physitemp BAT-12
thermometer (Clifton, NJ, USA) was inserted dorsally into the thorax.
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Results |
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Kinematics and flight performance
The minimal gas density necessary for hovering (MGD) was
0.771±0.187 kg m3 (mean ±
S.D., N=31), was positively correlated with
body mass (model II regression,
MGD=0.001+0.928Mb,
r29=0.80, P<0.001) but was negatively
correlated with relative thoracic muscle mass
(Fig. 2). The four bees with
the highest relative thoracic muscle mass were able to fly in pure heliox
(density 0.41 kg m3). For these bees, we assumed that the
kinematic and energetic parameters of these individuals during hovering in
heliox represented maximal performance. Wingbeat frequency during maximal
hovering was 125.0±4.0 Hz (N=28) and was significantly greater
(paired t-test, P=0.0013) than that in normodense hovering
(122.0±4.8 Hz, N=29). Wingbeat frequency increased
significantly with body mass in normodense hovering but was mass independent
in maximal flight (Fig. 3).
Stroke amplitude during maximal hovering was 137.9±2.4°
(N=30) and was significantly greater (paired t-test,
P<0.0001) than in normodense hovering (117.8±7.1°;
N=31). Stroke amplitude increased significantly with body mass in
normodense hovering but was mass independent during maximal hovering flight
(Fig. 4). Reserve capacities
for wingbeat frequency and stroke amplitude significantly decreased with
increasing body mass, although reserve capacity in stroke amplitude exceeded
that of wingbeat frequency across all body masses
(Fig. 5).
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Stroke plane angle during normodense hovering averaged 6.6±1.9° (mean ± S.D., N=31) and was significantly greater (paired t-test, P<0.0001) than that in maximal hovering (1.8±2.1°, N=30). Stroke plane angle decreased significantly with body mass in normodense hovering but was mass independent in maximal flight (Fig. 6). Body angle during maximal hovering flight was 49.2±4.2° (N=30) and was significantly greater (paired t-test, P<0.0001) than that in normodense flight (41.8±5.6°, N=31). Body angle was independent of body mass during both normodense (model II regression, r29=0.31, P=0.08) and maximal hovering flight (model II regression, r28=0.13, P=0.43). The angle of the stroke plane relative to the body increased slightly but significantly from 48.3±4.5° during normodense hovering to 50.9±4.6° during maximal hovering (paired t-test, P<0.0001).
|
Mechanical power production
Body mass-specific power output during maximal hovering flight
(Pbody,max) was 92.1±9.9 W kg1
and 221.3±31.9 W kg1 (mean ±
S.D., N=28), assuming CDs
of 1 and 3, respectively. For both CD values,
Pbody,max was significantly greater (paired
t-test, P<0.003) than body mass-specific power output
during normal hovering flight (Pbody,norm;
CD=1, 85.0±11.2 W kg1;
CD=3, 208.9±33.4 W kg1;
N=29). Log Pbody,max was independent of log
Mb for both CD values, while log
Pbody,norm increased significantly with log
Mb assuming CD=1 but was independent
of log Mb assuming CD=3
(Fig. 7). Muscle mass-specific
power output during maximal hovering flight (Pmuscle,max)
was 280.2±68.0 W kg1 and 677.6±183.4 W
kg1 (N=28), assuming CDs of 1
and 3, respectively. For both CD values,
Pmuscle,max was significantly greater (paired
t-test, P<0.002) than during normodense hovering
(Pmuscle,norm; CD=1, 261.2±68.6
W kg1; CD=3, 640.7±175.0 W
kg1; N=29). Log Pmuscle,max
significantly increased with log Mb for both
CD values, while log Pmuscle,norm
significantly increased with log Mb for
CD=1 but was independent of log Mb for
CD=3 (Fig.
8). Reserve capacity for Pmuscle significantly
decreased with Mb for CD=1 but was
independent of Mb for CD=3
(Fig. 9). The mean
CL during maximal hovering was 1.67±0.24
(N=28) and was significantly greater (paired t-test,
P<0.0001) than in normodense hovering (1.45±0.19;
N=29). In both cases, mean CLs were independent
of Mb (Fig.
10).
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Metabolic power requirements and body temperatures
Metabolic rate increased 1.5-fold with decreasing air density
(Fig. 11). Body mass-specific
metabolic rate during maximal hovering in hypodense gases averaged
519±187 W kg1 (mean ±
S.D., N=24) and was significantly greater
(paired t-test, P=0.0005) than during normodense hovering
(393±112 W kg1, N=24;
Fig. 12). Log
Mb-specific metabolic rates significantly decreased with
log Mb during both normal and maximal hovering flight
(Fig. 12). Reserve capacity in
Mb-specific metabolic power averaged 33.6±26.5%
(N=24) and was independent of Mb (model II
regression, r22=0.37, P=0.13). Muscle
mass-specific metabolic rate during maximal hovering averaged 1491±416
W kg1 (mean ± S.E.,
N=24) and was significantly greater (paired t-test,
P=0.0003) than in normodense hovering (1141±243 W
kg1; N=24). Neither normodense nor maximal muscle
mass-specific metabolic rates varied significantly with body mass (model II
regression; normodense: r22=0.24, P=0.27; max:
r22=0.14, P=0.27). Muscle efficiencies
during both normodense and maximal hovering significantly increased with
Mb for CD=1 but were independent of
Mb for CD=3
(Fig. 13). Muscle efficiencies
were slightly, but significantly, higher during normodense hovering than
during maximal hovering (paired t-test, P=0.0012) for both
CD values.
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Thoracic temperatures immediately following flight trials averaged 40.8±1.7°C (mean ± S.D., N=29) and were independent of both Mb (model II regression, r27=0.35, P=0.06) and final gas density (model II regression, r27=0.17, P=0.37).
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Discussion |
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Body mass varied nearly threefold among the X. varipuncta females
used in this study, and the bees were not isometric across this range. Abdomen
mass scaled to body mass with a coefficient of 1.69, meaning that the largest
bees possessed abdomens that composed nearly 50% of total body mass and were
nearly five times heavier than the abdomens of the smallest bees, which
represented only 25% of their total body mass. Because the bees were caught in
the field, variation in abdominal mass could be partly due to varying nectar
loads or reproductive condition, with larger females carrying greater masses
of reproductive tissues and eggs. However, nectar loading and reproductive
condition could not have been the sole determinants of body mass variation
because wing area and thorax mass (parameters that should be unaffected by
nectar loading or reproductive status) were 25% and 65%, respectively, higher
in the heaviest bees than in the lightest bees. Thorax mass scaled to body
mass with a coefficient of 0.63 and, as a consequence, flight muscle composed
nearly 50% of the total mass of the smallest bees yet only 25% of the total
mass of the largest bees (Fig.
1). Wing loading scaled with body mass with a surprisingly high
coefficient of 0.79, compared with a coefficient of 0.33 predicted by isometry
and a coefficient of 0.29 based on an empirical multi-species analysis of
insects (Dudley, 2000).
Morphological variation had pronounced effects on several performance
parameters of hovering flight in X. varipuncta. The positive
relationship between wingbeat frequency and body mass is unusual given that
larger wings have greater inertia and empirical studies of wingbeat frequency
almost always show a negative relationship between frequency and body mass
(see Dudley, 2000). However,
our finding is not unprecedented in that Wekesa et al.
(1998
) showed that wingbeat
frequency is positively correlated with wing length in two species of
Anopheles mosquitoes. The largest X. varipuncta, which had
relatively the smallest wings and flight muscles, operated at greater wingbeat
frequencies (Fig. 3) and stroke
amplitudes (Fig. 4) and lower
stroke plane angles (Fig. 6) in
normodense hovering than did smaller bees. However, these parameters were
independent of body mass during hovering flight at MGD. Therefore,
the kinematic performance of large bees in normodense hovering approached
their limits, whereas smaller bees possessed greater reserve capacities
(Fig. 5). Due to their small
kinematic reserve capacities, the larger bees experienced aerodynamic failure
at higher absolute air densities, with some individuals having MGDs
only 14% lower than in normal air. Because the major factor driving the
decrease in reserve capacity in larger bees was mass allocation to the
abdomen, it is possible that X. varipuncta suffer a decrease in
flight capacity as a cost of increased reproductive ability, as has been shown
for dragonflies (Marden,
1989
). Such tradeoffs may generally limit the ovarian size of bees
and other insects of a given thorax size.
Carpenter bees respond to hypodense aerodynamic challenge by increasing
stroke amplitude, as do euglossine bees
(Dudley, 1995) and
hummingbirds (Chai and Dudley,
1995
,
1996
). Hovering flight in
hypodense gas also elicits small, but significant, increases in wingbeat
frequency in carpenter bees and hummingbirds (Chai and Dudley,
1995
,
1996
) but not in euglossines.
Interestingly, carpenter bees and some smaller euglossines (Euglossa
spp.) decrease stroke plane angle while hovering in hypodense gas, while
stroke plane angle is independent of gas density in hummingbirds
(Chai and Dudley, 1996
) and a
larger euglossine, Eulaema meriana
(Dudley, 1995
).
Xylocopa, like many insect species
(Ellington, 1984c
;
Ennos, 1989
;
Dudley, 1995
) hovers in
normodense air at a slightly inclined stroke plane angle. During flight in
hypodense gas, the additional `weight' of the abdomen causes a negative
rotation in pitch and perhaps a slight bending at the petiole such that the
stroke plane angle approaches true horizontal and the body angle becomes
larger. We suspect that similar, although much more subtle, effects occur as a
result of proportionately heavier abdomens in larger individuals. Although
increasing stroke amplitude was the primary means by which X.
varipuncta generated additional power during hovering in hypodense gas,
smaller bees were also aided by the modest increase in wingbeat frequency
because the profile component of power output increases with the cube of
wingbeat frequency. Given the significant increase in mean lift coefficient
during hypodense hovering (Fig.
10), it is also highly probable that carpenter bees are employing
other lift-generating mechanisms during hypodense hovering such as changing
the angle of attack or rotational timing at the transition to each subsequent
half-stroke. Further analysis of the kinematic mechanisms used by carpenter
bees to generate high lift requires greater temporal resolution of wing
motions than that used here.
Limits to hovering flight performance in carpenter bees are indicated by a
maximum stroke amplitude of 140° at the point of hypodense failure
(Fig. 4). This value is
remarkably constant in spite of the considerable size-mediated variation seen
in stroke amplitude during hovering under normodense conditions (see
Fig. 4). Maximum stroke
amplitudes are similar for euglossines
(Dudley, 1995
) yet are much
higher (
180°) in hummingbirds
(Chai and Dudley, 1995
),
although dramatically different phylogenetic associations preclude direct
comparison of wingbeat kinematics between these taxa. Nonetheless, the
size-independent constancy of limits to wing motions in carpenter bees is
strongly suggestive of an anatomical constraint to angular wing displacements
that is much lower than that observed in hummingbirds.
The apparent constraint on wingbeat kinematics, and thus on aerodynamic
force production, may also be congruent with limits to power availability, at
least for larger bees. Assumed values of CD had
significant effects on calculated power, with higher power estimates when
CD=3. However, this CD value reduced
the likelihood of significant allometries for power, reserve capacity and
muscle efficiency, despite significant allometries for kinematic variables and
their reserve capacities (Figs
7,
8,
9). For this reason, and the
fact that muscle efficiencies were unrealistically high (5060%) when
CD=3 (Fig.
13), we believe that the assumption of CD=1 is
more valid for hovering Xylocopa. Under this more reasonable
CD value, maximum muscle mass-specific power output
increases substantially with increased body size
(Fig. 8), reaching 400 W
kg1 flight muscle in the largest individuals. However, the
larger bees, with their relatively smaller flight muscle mass, fail in
hovering at similar stroke amplitudes (Fig.
4) and body mass-specific power outputs
(Fig. 7) reached by smaller
bees. Excess capacity in mechanical power output is relatively smaller in
larger bees and appears to approach a limit near the upper end of the body
size range (Fig. 9). This
finding is suggestive of limits on power production in larger bees that may
also coincide with constraints on wing motions. Smaller bees, by contrast,
have more capacity to increase stroke amplitude
(Fig. 5) and, to a lesser
degree, power production (Fig.
9) but nonetheless fail at limiting values of the former quantity.
In general, excess lift and power capacity under hypodense but normobaric
conditions is probably associated with the requirement in normodense air for
supplemental power in vertical ascent, climbing flight or for translational
accelerations and fast forward flight. The present data nonetheless
demonstrate, over a threefold intraspecific range of body masses, a pronounced
size dependence of maximum flight performance that is mediated primarily by
the relative amount of flight muscle.
Maximum power output observed in carpenter bees lies close to mean values
of power output (based on unsteady values of CD
see Introduction) estimated for ruby-throated hummingbirds (Chai and Dudley,
1995,
1996
) that failed to sustain
hovering in similar hypodense conditions and also lies within the range for
three species of euglossine bees flying in heliox
(Dudley, 1995
). One of these
euglossine species was comparable in body mass to the carpenter bees studied
here (E. meriana; 820 mg) and exhibited the highest value of the
three species for mechanical power output. Maximal flight performance, even in
hovering flight, may also be strongly context dependent. For example,
ruby-throated hummingbirds engaged in vertical load-lifting exhibit
short-duration but high-intensity power outputs that exceed by 50% the maxima
found in density-reduction trials (Chai et al., 1997). Similar experiments
with carpenter bees that demonstrated stroke amplitudes or mechanical power
outputs exceeding those in hypodense air would clearly necessitate
re-evaluation of proposed anatomical constraints on flight performance.
Hypodense but hyperoxic gas mixtures might also elicit hovering capacities
supplemental to those exhibited here (e.g.
Harrison and Lighton,
1998
).
As with stroke amplitude and mechanical power output, metabolic rates of
hovering carpenter bees substantially increased under hypodense challenge
(Figs 11,
12). Maximal mass-specific
power output increased by an average of 10% and metabolic rate by 33% compared
with during normal hovering. These increases in power output relative to
normal hovering are somewhat less than the 45% estimated for euglossine bees
(Dudley, 1995). The relatively
low power and metabolic scope of carpenter bees, particularly larger
individuals, may occur because the higher wing loading of these reproductive
females requires them to utilize rates of power production close to their
maximal capacities just to hover. Indeed, the smallest bees in the present
study, with wing loading values more similar to those of the euglossines, had
power scopes approaching 20%.
Flight muscle efficiencies of individual bees, by contrast, were only
slightly different between normo- and hypodense conditions
(Fig. 13), indicating that
increases in mechanical power output are matched by comparable increases in
metabolic power input. Again, efficiencies averaged 5060% when
CD was assumed to be 3, indicating that this assumed value
is probably less realistic than a value of 1, which yielded efficiencies
averaging 2025%. Muscle efficiencies thus tend to increase
systematically with increased body size (assuming CD=1),
approximately doubling across the size range of bees in this study. This trend
was also noticed by Casey et al.
(1985) in an interspecific
comparison of euglossine bees in normodense hovering and has been described
for volant taxa in general (Ellington,
1991
; Harrison and Roberts,
2000
). The increase in efficiency with size has most commonly been
attributed to lower cycle frequencies, with consequent savings in muscle
efficiencies. However, this cannot explain the size effects on efficiency
during maximal power production in this study as bees of different sizes had
similar wingbeat frequencies (Fig.
3). During maximal hovering, none of the kinematic variables
varied with mass (Figs 3,
4,
6) and neither did body
mass-specific power output differ with size
(Fig. 7). Flight muscle
mass-specific power output significantly increased with size as the larger
bees required more power from their relatively small flight muscles to keep
them aloft. Efficiency increased because this greater muscle mass-specific
power output occurred at similar muscle-specific metabolic rates, with greater
power requirements in larger bees perhaps due to higher
CDs in these individuals.
The mechanisms responsible for the positive correlation between size and
efficiency are unclear. There could be differences in the efficiency of
conversion of muscular power to wing mechanical power; for example, elastic
energy storage within the thorax may increase with size in this species.
Finally, there could be size-related differences in the use of lift-generation
mechanisms such as leading edge vortices, wake capture and clap-and-fling (see
Dudley, 2000;
Birch and Dickinson, 2001
;
Sane and Dickinson, 2001
).
Despite the higher muscle efficiencies of larger carpenter bees, reserve capacity for hovering flight declines at larger body sizes. This effect derives from the disproportionate increase in thoracic muscle mass at smaller body sizes. In summary, larger carpenter bees exhibit absolutely greater maximal muscle mass-specific power outputs than smaller bees but are less capable of flying in hypodense air because of the negative intraspecific allometry of flight muscle mass.
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