S31.2: Maximum hovering performance of hummingbirds:
Capacities, constraints, and trade-offs
Peng Chai
Department of Zoology, University of Texas at Austin, Austin, Texas
78712-1064, USA, fax 512 471 9651, e-mail pengchai@utxvms.cc.utexas.edu
Chai, P. 1999. Maximum
hovering performance of hummingbirds: Capacities, constraints, and trade-offs. In: Adams,
N.J. & Slotow, R.H. (eds) Proc. 22 Int. Ornithol. Congr., Durban:
1810-1822. Johannesburg: BirdLife South Africa.
Aerodynamic and energetic
concerns of flight strongly mold the body design of flying animals. However, avian fliers
also face other survival challenges, such as courtship, migration, and plumage renewal.
Morpho-physiological trade-offs to these activities can compromise their flight
performance in the face of ecological demands such as competition and predator avoidance.
Intraspecific differences of Ruby-throated Hummingbirds in maximum hovering performance
and associated capacities in kinematics, aerodynamics, muscle mechanics, and metabolism
were investigated. Hummingbirds were tested with the strenuous activity of hovering in
low-density gas mixtures - a lift assay for the capacity to generate vertical force. Adult
males having shorter wings were less capable of generating lift force while hovering in
hypodense air, despite displaying muscle mechanical and metabolic capacities equivalent to
those of females. Body mass is the primary constraint on maximum hovering performance, and
heavier birds showed aerodynamic failure at higher air densities. Muscle mechanical power
output was constrained by wing kinematics because wingbeat frequency operated only within
a narrow range, and wingstroke amplitude at maximum hovering reached its limit of near 180o,
regardless of birds' mass and air density. Moulting birds with reduced wing area suffered
from weight loss and reduction in hovering capacity and muscle power, reflecting
transiently high cost of moults. Under multiple functional constraints, the study
hummingbirds demonstrated versatile reserve capacities in their hovering performance.
However, morpho-physiological adaptations to multiple survival requirements could reduce
the biomechanical margin of safety during hovering and potentially impose fitness costs.
INTRODUCTION
Locomotor specialisations of an animal
essentially determine its ecological and physiological characters. Hummingbirds are the
only avian taxon capable of prolonged hovering and function as effective nectarivores and
pollinators. Hovering flight is frequently viewed as a measure of extreme locomotor
performance with very high demand of rates of lift and mechanical/metabolic power
production. Hummingbirds operate close to the lower limit of body mass in vertebrate
homeotherms, while during hovering, they exhibit mass-specific metabolic rate close to the
upper limit (Suarez 1992; Chai & Dudley, 1995). They thus serve as ideal models for
testing hypotheses concerning performance capacities, constraints, and trade-offs.
It has been suggested that the structure and
function of these animals are tightly integrated to maximise flight performance but with
less reserve capacity (Diamond 1990; Hochachka 1994; Suarez et al. 1997). Under
limiting resources, excess capacity inflicts extra costs. Natural selection should favor
reduced reserve when the survival cost of such excess relative to its benefit is high
(Diamond & Hammond 1992). Thus, there should exist strong selection against excess
capacity in this energetic-costly functional system. Here, reserve capacity is defined as
excess hovering performance relative to that exhibits at normal hovering, and indeed power
requirements in vertical ascent or load carrying can exceed values that characterise
hovering.
Reserve hovering capacity may also represent
safety margin and provide excess power to aid hummingbirds in predator avoidance,
interference competition, carrying load, and overcoming pathological situations. However,
diverse adaptive challenges such as escape flight, courtship, migration, and plumage
renewal faced by individual hummingbirds and morpho-physiological specialisations
associated with such activities can compromise flight machinery and impose limits as well
as trade-offs to aerodynamic and energetic performance. For example, flight is
energetically expensive, and fliers need to carry fuel (e.g. fat) loads to ensure energy
security. Yet such increased loads can be deleterious to flight performance and will also
increase the energetic costs of flight (Ellington 1984a; Rayner 1990; Hedenström
1992; Norberg 1995). Furthermore, small endothermic fliers such as hummingbirds run the
risk of energy deficits, but must be light to maintain agility in the face of
mass-dependent predation risks (Gosler et al. 1995; Kullberg et al. 1996).
Hummingbird wing morphology also reflects an aerodynamic trade-off because the two extreme
forms of flight along the airspeed spectrum (hovering and fast forward flight) differ
substantially in their mechanical power requirements. During hovering, flapping wings
maximise vertical forces (lift) by moving air downwards for weight support. Longer wings
can enhance lift production, whereas weight loss and concomitantly lower wing loading
(body weight relative to wing area) can reduce the cost of lift generation. During fast
forward flight, horizontal force (thrust) is increased to offset increased drag forces
primarily over the body and secondarily over the wings. A streamlined body, shorter wings,
and a higher wing loading should decrease frictional resistance and thereby promote faster
flight (Pennycuick 1975; Rayner 1988; Norberg 1990).
In the present study, intraspecific
differences of Ruby-throated Hummingbirds in hovering capacity were compared to
investigate how different functional levels including wing morphology, wingbeat
kinematics, flight muscle contractile mechanics, and whole-body metabolism integrate
during maximum hovering performance. Maximum biomechanical and energetic capacities of
hummingbirds with shorter wings (adult males), with increased body weight, and with loss
of wing area (during moult) are systematically compared with aerodynamic predictions.
Birds with reduced wing length and area or with increased body weight are predicted to
exhibit inferior hovering capacity.
Hummingbirds were tested with the strenuous
activity of hovering in low-density gas mixtures - a lift assay for the capacity to
generate vertical force. We have non-invasively induced maximum hovering performance in
individual Ruby-throated Hummingbirds Archilochus colubris L. using normoxic but
hypodense mixtures of air and heliox (21% O2 and 79% He). Oxygen availability
is not limiting in such studies, but the density of heliox is only one-third that of
normal air (Chai & Dudley 1995; Dudley & Chai, 1996). Hovering in low-density air
is analogous to increasing treadmill speeds for runners in that hummingbirds must increase
their mechanical power output to generate lift force sufficient to stay airborne. Limits
to the locomotor capacity of hovering hummingbirds are unequivocally indicated by
aerodynamic failure at low air densities (Chai & Dudley, 1995).
During maximum hovering, reserve capacities
of multiple functional systems of kinematics, mechanics, and metabolism reflect the
overall design of the flight machinery of hummingbirds as shaped by both physical laws and
natural selection (see Arnold 1983; Bennett 1991; Diamond & Hammond 1992; Wainwright
1994). How much reserve capacity is built into each functional level, and what are the
invariant vs. malleable elements of flight design in hummingbirds? Thus, the goal of this
study is to explore the links between aerodynamic and energetics of hummingbird flight on
the one hand, and on the other hand evaluate potential behavioural and ecological
influences on hovering performance.
METHODS
Experimental procedures for manipulating air
densities have been described previously (Dudley 1995; Chai & Dudley 1995). Flight
experiments were implemented within an airtight plexiglas cube (90 x 90 x 90 cm). The bird
was trained to hover-feed approximately every 20 min through a mask which allowed for
collection of respiratory gases using an open-flow feeder-mask respirometry system (Chai
& Dudley 1995). Oxygen consumption rates during hovering were obtained from the
expired respiratory gases. At the same time, wingbeat kinematics were video-recorded (Sony
CCD-TR600 at 60 fields s-1 with a high-speed shutter of 1/4000 s). Data were
collected initially from birds hover-feeding in unmanipulated sea-level air (density 1.20
kg m-3). Air within the cube was then gradually replaced by filling with
normoxic heliox (21% O2 and 79% He, density 0.40 kg m-3). As the air
became thinner and hovering flight became more strenuous, the bird gradually reduced its
hover-feeding duration (Chai & Dudley 1995). Heliox filling was terminated after the
bird showed aerodynamic failure while hover-feeding in hypodense air. The bird drastically
descended to the chamber floor and momentarily lost the ability to fly. Maximum transient
hovering performance was taken as the short hover-feeding sequence (2 - 4 s) recorded
immediately prior to aerodynamic failure. Wingbeat kinematics (i.e. wingbeat frequency n
and stroke amplitude
F ) and
morphological parameters of individual birds then were used to estimate the mechanical
power requirements at maximum hovering performance (see Ellington 1984a).
Morphological parameters used in aerodynamic
calculations included body mass m, wing length R, total wing area S
(the area of both wings), aspect ratio AR (=4R2/S), and
wing loading pw (= mg/S, where g is
gravitational acceleration). Aerodynamic calculations assumed simple harmonic motion and
horizontal stroke plane of the wings, and the mean lift coefficient 
(derived by assuming that vertical
force production averaged over the wingbeat period equal the bird's body weight; see
Ellington 1984a) is presented. Mechanical power requirements were estimated by
evaluating individual components of body mass-specific profile (P*pro)
and induced (P*ind) power requirements. P*pro
represents energetic expenditure to overcome frictional drag forces on the flapping wings,
and P*ind is the power needed to generate downward momentum to the
surrounding air so as to offset the body weight (for Ruby-throated Hummingbirds, P*ind
is 3 - 4 times greater than P*pro; Chai et al. 1997). Total power
expenditure (P*per) was calculated assuming perfect elastic storage of
wing inertial energy, representing minimum estimates of required mechanical power. Thus, P*per
= P*pro + P*ind, and P*per is equal
to the aerodynamic power requirement (i.e. power required to move the air). Hummingbirds
can probably store kinetic energy elastically during the deceleration phase of the
wingstroke, so that inertial power requirements are probably negligible (see Greenewalt
1975; Ellington, 1984a; Wells 1993).
Metabolic cost during hovering was derived
from rates of oxygen consumption (
). As hovering became
more strenuous due to air density reduction, birds gradually reduced their feeding
duration. Oxygen consumption rates at aerodynamic failure could not be reliably obtained
given the short duration of hover-feeding. Instead, measurements were taken from
hover-feeding bouts greater than 5 s in duration but at densities similar to the value at
which birds failed aerodynamically. Flight efficiency was then taken as the ratio of
mechanical power output to metabolic power input for the same hover-feeding sequence.
Furthermore, reserve capacities of wingbeat frequency, stroke amplitude, lift capacity of
the wings, mechanical power output, and rates of oxygen consumption were expressed as the
% increase relative to values obtained when hovering in unmanipulated sea-level air prior
to replacement with heliox.
Analysis of covariance (ANCOVA) was conducted
on kinematic, aerodynamic, mechanical, and metabolic variables relating to maximum
hovering performance in hypodense gas mixtures. ANCOVA was used to assess effects of body
mass and bird group. Four bird groups were identified given different sex and plumage
conditions: moulting birds, non-moult females, juvenile males, and adult males.
Least-squares means adjusted for the covariate effect of body mass as well as for
unbalanced sample sizes were calculated to indicate the expected mean and estimated
standard error for each bird group (SAS PROC GLM, SAS Institute 1989). Least-squares means
(i.e. population marginal means) are the expected value of bird group means in a balanced
design involving bird groups with the body mass covariate set at its mean value (Milliken
& Johnson 1992).
RESULTS
We conducted a total of 34 density reduction
experiments on 18 individual hummingbirds with varying body mass and wing condition. Each
individual bird received 1 - 3 density reduction trials either with unimpaired wings or
during the annual moult (measured during peak moult of flight feathers in the spring).
Dissimilar plumage during moult justifies treating performance capacity measured from each
density reduction trial as an independent observation (i.e. n = 34). Adult males
had the shortest and smallest wings; wing loading was correspondingly higher than those of
juvenile males and females (Table 1 and Fig. 1).
Juvenile males had wing lengths between those of females and adult males (wing morphology
of juvenile and adult females is indistinguishable). Non-moulting birds were thus divided
into three groups (Table 1). Moulting birds still possessed 2 - 3
outer primaries (and thus exhibited constant wing length), but on average retained only
78± 8% (mean ± 1 s.d.) of non-moult wing area, yielding high aspect ratio (Fig. 1 and Chai 1997).
The capacity to hover in hypodense air
inversely varied with body mass, with heavier birds displaying aerodynamic failure at
higher air densities (Table 1 and Fig. 1).
Weight effect was confounded with effects due to differences in wing morphology. For
non-moult birds, adult males were least capable of hovering, whereas females were most
capable. Moulting birds with reduced wing area also lost weight, yielding values of wing
loading similar to that of non-moult birds (Table 1 and Fig. 1). Despite such presumably adaptive weight loss, moulting birds
still failed at higher air densities relative to non-moult birds (Table
1 and Fig. 1).
Hovering birds met the challenge of
low-density air by modulating wingbeat kinematics. However, wingbeat frequency varied by
only 4 - 6%, and modulation of wingstroke amplitude was a more important means of
generating mechanical power. Maximum power was attained at a stroke amplitude near 180o
(Table 1 and Fig. 2). Wing length and
wingbeat frequency were negatively correlated. Males showed inferior lift performance of
the wings (lower >) and failed at higher air
densities. Moulting birds showed the least capacity for lift generation (Table 1 and Fig. 2).
Despite variable hovering capacity in
hypodense gas mixtures among bird groups (Fig. 1), maximum
mass-specific mechanical power outputs (P*per) of non-moult bird groups
were actually similar (Table 1). No statistical differences in
power output were found among non-moult bird groups, and the moulting bird group was again
the least capable of producing useful mechanical power (Table 1
and Fig. 3). Relative to hovering in normal air, heavier birds at
maximum performance exhibited proportionally less power reserve (Table
1 and Fig. 3). Male birds also suffered from a reduced power
reserve, while females showed the highest margin for excess power. Moulting birds during
hovering also showed the least amount of power reserve (Table 1
and Fig. 3).
Maximum rates of oxygen consumption indicated
a significantly positive weight effect. No statistical differences existed among non-moult
bird groups in metabolic expenditure, whereas moulting birds showed a significant increase
in metabolism (
; Table 1 and Fig. 3). Reserve capacity in mechanical power output (P*per
reserve) varied significantly among bird groups, yet metabolic reserve capacities (reserve) were similar (Table 1 and Fig. 3). Increased mechanical power requirements due to weight gain
were accompanied by an increased rate of oxygen consumption, but this increase was not
commensurate with the rise in mechanical power. Overall flight efficiency (ratio of
mechanical power output to metabolic power input) was also improved with weight gain (Table 1 and Fig. 3). During strenuous hovering
performance, moulting birds were least capable of generating useful mechanical power and
also experienced the highest metabolic cost, thereby displaying the lowest flight
efficiency. Flight efficiency did not significantly vary among non-moult birds.
DISCUSSION
Air densities at aerodynamic failure were
significantly different among the four bird groups. Of the non-moult bird groups, females
with the longest wings and lowest wing loading were the most capable of hovering, whereas
adult males with the shortest wings and highest wing loading were the least (Table 1). Weight gain is associated with reduced hovering
performance, and heavier birds failed at higher air densities. Moulting birds renewing
their primary flight feathers reduced both wing area and body mass. Despite wing loading
similar to that of non-moult birds, moulting birds exhibited the lowest capacity to hover.
Thus, congruent with the aerodynamic predictions, hummingbirds with shorter wings (adult
males), with increased body weight, and with loss of wing area (during moult) exhibited
inferior hovering capacity (Table 1 and Fig. 1).
However, aerodynamic predictions are based on energetic costs of flight and could be
unsatisfactory because reserve capacities of energy supply are largely unknown. For
example, our empirical measurements showed that moulting inflicted high energetic costs
during hovering (Fig. 3). Such birds possess suboptimal wing
shapes, which may interfere with neuromuscular co-ordination (Ellington 1984b,
Swaddle et al. 1996; Chai 1997). Furthermore, moulting can exert multiple energetic
costs, including loss of plumage insulation and an increase of basal metabolism (Walsberg
1983; Lindström et al. 1993; Jenni & Winkler 1994; Murphy 1996).
The present study identified constraints
relating to wingbeat kinematics, and muscle mechanical and metabolic capacities. Hovering
in variable-density gas mixtures requires modification of wingbeat kinematics to attain
the requisite aerodynamic force balance and associated mechanical power output.
Constraints on the rate of muscle contraction are implicated by the limited range of
values for wingbeat frequency, with the frequency reserve averaging only 5%. A strong
negative correlation also existed between wing length and wingbeat frequency (Table 1). Such patterns of relatively fixed wingbeat frequency and
but an inverse relationship between this parameter with wing length are typical of all
flying birds (Pennycuick 1996). This result suggests that the flight muscles of
hummingbirds are probably adapted to work at a particular resonant frequency to optimise
mechanical power output of the oscillatory rhythm (Greenewalt 1975). The existence of such
a resonant system should be strongly favored because the mechanical power requirement with
perfect elastic energy storage (i.e. P*
per)
is less than half of that with no such storage (Wells 1993; Chai & Dudley 1995).
Modulation of wingstroke amplitude is the
primary means of varying mechanical power during hovering, with maximum power output
attained near a geometrical constraint of 180o (see also Chai & Dudley
1995). However, the duration of maximum hovering performance was brief. A negative
relationship existed between magnitude and duration of mechanical power production,
indicating limits to the aerobic capacity for sustainable performance (Josephson 1993;
Chai & Dudley 1995).
Our data were derived from captive
hummingbirds with food provided ad libitum during captivity. Indeed, body masses of
the study birds were higher than those of wild Ruby-throated Hummingbirds (e.g.
wild-caught males: 3.3± 0.2 g; wild-caught females: 3.5± 0.4 g in September; Robinson et
al. 1996). Weight gain is highly detrimental to hovering because whole-bird power
requirements increase with the 1.5 power of body mass given a fixed wing length (Weis-Fogh
1977). If our birds had not substantially gained weight in captivity, their hovering
capacity would likely have been higher.
Among non-moult bird groups, females having
the longest wings were most efficient in generating lift force in low density gas mixtures
(highest and reserve) and displayed the highest reserve capacity, but incurred
metabolic costs similar to other bird groups (, Table 1 and Fig. 3). In spite of dissimilar
hovering capacities, maximum values of mechanical power output (P*per) among non-moult bird groups were surprisingly
similar. The major component of P*per is P*ind, which
varies in approximate proportion to the square root of wing disk loading (= mg/(FR2), see Ellington 1984a). Energetic costs of hovering thus vary inversely
with wing length and are highest in adult males with the shortest wings, and this group
displayed the lowest mechanical power reserve (P*per reserve) among non-moult birds. In contrast to variable mechanical power
reserves, the reserve capacity of the metabolic machinery ( reserve) was invariant among bird groups, implying a similar
underlying constraint in metabolic flux capacity. Given equivalent muscle mechanical and
metabolic potential, reduced hovering performance in males probably reflects a trade-off
in wing morphology for increased speed and agility.
Maximum mass-specific mechanical power output
(P*per) remained similar
among non-moult bird groups, whole-bird power output was thus mass-dependent and increased
linearly with body mass. Muscle power output is generally proportional to the product of
contraction frequency (i.e. wingbeat frequency), muscle strain (proportional to stroke
amplitude), and myofibrillar stress (Pennycuick & Rezende 1984). Because wingbeat
kinematics (wingbeat frequency and stroke amplitude) were mass-independent at the point of
maximal hovering (Table 1), difference in force production (muscle
stress) may have been primarily responsible for difference in whole-bird power output
between heavy and light birds. Mass-dependent whole-bird power output could also be due to
a proportional increase in flight muscle mass with body weight gain, and a morphological
study investigating the link between flight muscle mass and weight gain is badly needed
(see Carpenter et al. 1991).
Such knowledge of possible variation in
flight muscle mass will serve to distinguish whether mass-dependent whole-bird power
output derives from the presence of more muscle or from improved mechanical efficiency
associated with weight gain. More importantly, maximum P*per in the present study were derived from hovering flight through manipulation of
air density, and P*per only
represents the minimum mechanical power necessary to hover and to overcome two aerodynamic
forces: induced drag and profile drag. Mass-invariant maximum P*per derives from mass invariance in P*ind, a parameter that is proportional to the mean downwards velocity
of air associated with weight support (see Ellington, 1984a). Heavier birds failed
at higher air densities but imparted similar downwards velocities to this denser air, thus
expending greater induced and thus total power. Failure at different air densities
reflects constraints imposed by wingbeat kinematics which then set upper limits to P*per (Table 1 and Fig. 3). Thus, mass-invariant P*per at maximum performance in low-density flight media reflects complex interactions
among kinematic constraints, available mechanical power, and aerodynamic force production
(Ellington 1991). Furthermore, the brief duration of maximum P*per , as compared to relatively long periods of
hovering in normodense air at reduced P*per, reflects interactions between anaerobic metabolic pathway for burst power and
aerobic pathway for endurance. Hummingbirds are capable of anaerobic hovering (Chai &
Dudley 1996). In load-lifting study, hummingbirds carrying maximum loads reached similar
kinematic constraints as birds hovering in hypodense gas mixtures, but generated 50% more
maximum muscle power (Chai et al. 1997). However, the duration was very brief, of
the order of 1 s. This again demonstrated an inverse relationship between the magnitude
and duration of maximum power output.
Moulting birds generated less mechanical
power at higher metabolic cost, in comparison to non-moult hummingbirds among which muscle
mechanical and metabolic capacities were equivalent. Moulting birds thus displayed the
lowest flight efficiency among the four bird groups (Table 1 and Fig. 3). Moult involves complex morpho-physiological changes, and high
metabolic costs of hovering for moulting birds may be attributed to multiple causes.
Moulting and associated reduction in flight performance is however transient. Since this
study examined birds at their peak moult when wing area is at its minimum, the measured
parameter values relating to hovering likely reflect the worst possible performance in
this species.
Through intraspecific comparisons on
hummingbirds with shorter wings (adult males), with increased body weight, and with wing
area reduction (during moult), the present study demonstrated performance trade-offs that
presumably reflect diverse flight challenges due to sexual dimorphism, migration, and
plumage renewal. The integrated responses of multiple functional systems such as
morphology, kinematics, muscle mechanics, and whole-bird metabolism define the range of
flight activities that a hummingbird enjoys. The present study delineated reserve
capacities of such systems at maximum hovering, reflecting functional design and safety
margins shaped by both physical laws and natural selection. Future studies should explore
if such varying hovering capacities are associated with behavioural and ecological
compensation, particular in the context of foraging and resource utilisation as well as
distribution and overall fitness of individuals.
ACKNOWLEDGMENTS
I thank R. Dudley for reviewing the manuscript. This work was supported
by NSF grant IBN-9601089.
REFERENCES
Arnold, S.J. 1983. Morphology, performance and fitness. American
Zoologist 23: 347-361.
Bennett, A.F. 1991. The evolution of activity capacity. Journal
of Experimental Biology 160: 1-23.
Carpenter, F.L., Hixon, M.A., Beuchat, C.A., Russell, R.W. &
Paton, D.C. 1993. Biphasic mass gain in migrant hummingbirds: body composition
changes, torpor, and ecological significance. Ecology 74: 1173-1182.
Chai, P. 1997. Hummingbird hovering energetics during moult of
primary flight feathers. Journal of Experimental Biology 200: 1527-1536.
Chai, P. & Dudley, R. 1995. Limits to vertebrate locomotor
energetics suggested by hummingbirds hovering in heliox. Nature (London) 377: 722-725.
Chai, P. & Dudley, R. 1996. Limits to flight energetics of
hummingbirds hovering in hypodense and hypoxic gas mixtures. Journal of Experimental
Biology 199: 2285-2295.
Chai, P., Chen, J.S.C. & Dudley, R. 1997. Transient hovering
performance of hummingbirds under conditions of maximal loading. Journal of Experimental
Biology 200: 921-929.
Diamond, J.M. 1990. How to fuel a hummingbird. Nature (London)
348: 392.
Diamond, J.M. & Hammond, K.A. 1992. The matches, achieved by
natural selection, between biological capacities and their natural loads. Experientia 48:
551-557.
Dudley, R. 1995. Extraordinary flight performance of orchid bees
Apidae: Euglossini hovering in heliox 80 % He/20 % O
2. Journal of Experimental Biology 198: 1065-1070.
Dudley, R. & Chai, P. 1996. Animal flight mechanics in
physically variable gas mixtures. Journal of Experimental Biology 199: 1881-1885.
Ellington, C.P. 1984a. The aerodynamics of hovering
insect flight. VI. Lift and power requirements. Philosophical Transactions of the Royal
Society of London B, Biological Sciences 305: 145-181.
Ellington, C.P. 1984b. The aerodynamics of hovering
insect flight. II. Morphological parameters. Philosophical Transactions of the Royal
Society of London B, Biological Sciences 305: 17-40.
Ellington, C.P. 1991. Limitations on animal flight performance.
Journal of Experimental Biology 160: 71-91.
Gosler, A.G., Greenwood, J.J.D. & Perrins, C. 1995.
Predation risk and the cost of being fat. Nature (London): 377: 621-623.
Greenewalt, C.H. 1975. The flight of birds. Transactions of the
American Philosophical Society 65: 1-67.
Hedenström, A. 1992. Flight performance in relation to fuel
load in birds. Journal of Theoretical Biology 158: 535-537.
Hochachka, P.W. 1994. Muscles as Molecular and Metabolic
Machines. Boca Raton, Florida; CRC Press: 158pp.
Jenni, L. & Winkler, R. 1994. Moult and aging of European
passerines. London; Academic Press: 224pp.
Josephson, R.K. 1993. Contraction dynamics and power output of
skeletal muscle. Annual Review of Physiology 55: 527-546.
Kullberg, C., Fransson, T. & Jakobsson, S. 1996. Impaired
predator evasion in fat blackcaps (Sylvia atricapilla). Proceedings of the Royal
Society of London B, Biological Sciences 263: 1671-1675.
Lindström, Å , Visser, G.H. & Daan, S. 1993. The energetic
cost of feather synthesis is proportional to basal metabolic rate. Physiological Zoology
66: 490-510.
Milliken, G.A. & Johnson, D.E. 1992. Analysis of messy data.
New York; Von Nostrand Reinhold: 473pp.
Murphy, M.E. 1996. Energetics and nutrition of molt. In: Carey,
C. (ed.) Avian energetics and nutritional ecology. New York; Plenum Press: 158-198.
Norberg, U.M. 1990. Vertebrate flight: mechanics, physiology,
morphology, ecology and evolution. Berlin; Springer-Verlag: 291pp.
Norberg, U.M. 1995. How a long tail and changes in mass and wing
shape affect the cost of flight in animals. Functional Ecology 9: 48-54.
Pennycuick, C.J. 1975. Mechanics of flight. In: Farner, D.S.
& King, J.R. (eds) Avian biology. Vol. 5; New York; Academic Press: 1-75.
Pennycuick, C.J. 1996. Wingbeat frequency of birds in steady
cruising flight: new data and improved predictions. Journal of Experimental Biology 199:
1613-1618.
Pennycuick, C.J. & Rezende, M.A. 1984. The specific power
output of aerobic flight muscle, related to the power density of mitochondria. Journal of
Experimental Biology 108: 377-392.
Pennycuick, C.J., Fuller, M.R., Oar, J.J. & Kirkpatrick, S.J.
1996. Wingbeat frequency and the body drag anomaly: wind tunnel observations on a thrush
nightingale (Luscinia luscinia) and a teal (Anas crecca). Journal of
Experimental Biology 199: 2757-2765.
Rayner, J.M.V. 1988. Form and function in avian flight. In:
Johnston, R.F. (ed.) Current ornithology. Vol. 5; New York; Plenum Press: 1-66.
Rayner, J.M.V. 1990. The mechanics of flight and bird migration
performance. In: Gwinner, E. (ed.) Bird migration: physiology and ecophysiology. Berlin;
Springer-Verlag: 283-299.
Robinson, T.R., Sargent, R.R. & Sargent, M.B. 1996.
Ruby-throated Hummingbird (Archilochus colubris). In: Poole, A. & Gill, F.
(eds) The birds of North America, No. 204. Washington, D. C.; The Academy of Natural
Sciences, Philadelphia, and the American Ornithologists' Union: 1-16.
SAS. 1989. SAS/STAT User's Guide, Version 6, 4th ed., Vol. 2;
Cary, NC; SAS Institute Inc: 846pp.
Slagsvold, T. & Dale, S. 1996. Disappearance of female pied
flycatchers in relation to breeding stage and experimentally induced molt. Ecology: 77:
461-471.
Suarez, R.K. 1992. Hummingbird flight: sustaining the highest
mass-specific metabolic rates among vertebrates. Experientia 48: 565-570.
Suarez, R.K., Staples, J.F., Lighton, J.R.B. & West, T.G.
1997. Relationships between enzymatic flux capacities and metabolic flux rates:
nonequilibrium reactions in muscle glycolysis. Proceedings of the National Academy of
Sciences (USA) 94: 7065-7069.
Swaddle, J.P., Witter, M.S., Cuthill, I.C., Budden, A. &
McCowen, P. 1996. Plumage condition affects flight performance in Common Starlings:
implications for developmental homeostasis, abrasion and moult. Journal of Avian Biology
27: 103-111.
Wainwright, P.C. 1994. Functional morphology as a tool in
ecological research. In: Wainwright, P.C. & Reilly, S.M. (eds) Ecological morphology,
integrative organismal biology. Chicago; University of Chicago Press: 42-59.
Walsberg, G.E. 1983. Avian ecological energetics. In: Farner,
D.S., King, J.R. & Parkes, K.C. (eds) Avian biology. Vol. 7; New York; Academic Press:
161-220.
Weis-Fogh, T. 1977. Dimensional analysis of hovering flight. In:
Pedley, T.J. (ed.) Scale effects in animal locomotion. London; Academic Press: 405-420.
Wells, D.J. 1993. Muscle performance in hovering hummingbirds.
Journal of Experimental Biology 178: 39-57.
Table 1.
Statistical results assessing effects of body mass and bird group on morphological,
kinematic, aerodynamic, and mechanical parameters relating to maximum hovering performance
in hypodense air (see text for explanation of parameters). For morphological variables,
ANOVA was used (body mass was not included as a covariate); for kinematic, aerodynamic,
and mechanical variables, ANCONA was used. Least-squares means adjusted for the covariate
effect of body mass as well as unbalanced sample size are used to show the mean and
estimated standard error at maximum performance for each bird group. Moulting birds
include 5 females, 3 juv. males, and 1 male.
Fig. 1. Air density at
maximum hovering performance prior to aerodynamic failure (A) of Ruby-throated
Hummingbirds and their morphological indicators (B, body mass; C, wing length; D, wing
area; E, aspect ratio; and F, wing loading) by bird groups. Values are means± 1 S.D. Four
major bird groups with dissimilar wing morphology are identified: females, adult males,
juvenile males (n = 5 birds), and molting birds. To demonstrate body mass effect, heavy
females (> 4 g, n = 6) are separated from light ones (n = 5), and heavy males (> 3.5
g, n = 5) from light ones (n = 4). Molting birds are separated by sex: 5 females and 4
males (including 3 juvenile males). Moulting females on average possessed 77± 10% of
non-moult wing area; moulting males 79± 5%. Their wing length did not change because 2 -
3 old, outer primaries still remained.
Fig. 2. Wingbeat frequency
(A), stroke amplitude (B), and mean lift coefficient (C) by bird groups. Values are
means± 1 S.D. Two values are presented for each bird group: left value comes from
hovering in sea-level, unmanipulated air; right one at maximum hovering performance.
Reserve capacity as % increase at maximum performance relative to normal hovering is
indicated on the top.
Fig. 3. Body
mass-specific power output assuming perfect elastic energy storage (A), rate of oxygen
consumption (B), and flight efficiency as ratio of
mechanical power output to metabolic power input (C). Values are means± 1 S.D.
