University of Groningen
Energy expenditure and wing beat frequency in relation to body mass in free flying
Barn Swallows (Hirundo rustica)
Schmidt-Wellenburg, Carola A.; Biebach, Herbert; Daan, Serge; Visser, G. Henk; Heldmaier,
G.
Published in:
Journal of comparative physiology b-Biochemical systemic and environmental physiology
DOI:
10.1007/s00360-006-0132-5
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Schmidt-Wellenburg, C. A., Biebach, H., Daan, S., Visser, G. H., & Heldmaier, G. (Ed.) (2007). Energy
expenditure and wing beat frequency in relation to body mass in free flying Barn Swallows (Hirundo
rustica). Journal of comparative physiology b-Biochemical systemic and environmental physiology, 177(3),
327-337. DOI: 10.1007/s00360-006-0132-5
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J Comp Physiol B (2007) 177:327–337
DOI 10.1007/s00360-006-0132-5
ORIGINAL PAPER
Energy expenditure and wing beat frequency in relation to body
mass in free flying Barn Swallows (Hirundo rustica)
Carola A. Schmidt-Wellenburg Æ Herbert Biebach Æ
Serge Daan Æ G. Henk Visser
Received: 28 August 2006 / Revised: 3 November 2006 / Published online: 14 December 2006
Springer-Verlag 2006
Abstract Many bird species steeply increase their
body mass prior to migration. These fuel stores are
necessary for long flights and to overcome ecological
barriers. The elevated body mass is generally thought
to cause higher flight costs. The relationship between
mass and costs has been investigated mostly by interspecific comparison and by aerodynamic modelling.
Here, we directly measured the energy expenditure of
Barn Swallows (Hirundo rustica) flying unrestrained
and repeatedly for several hours in a wind tunnel with
natural variations in body mass. Energy expenditure
during flight (ef, in W) was found to increase with body
mass (m, in g) following the equation ef = 0.38 · m0.58.
The scaling exponent (0.58) is smaller than assumed in
aerodynamic calculations and than observed in most
interspecific allometric comparisons. Wing beat frequency (WBF, in Hz) also scales with body mass
(WBF = 2.4 · m0.38), but at a smaller exponent. Hence
there is no linear relationship between ef and WBF. We
propose that spontaneous changes in body mass during
endurance flights are accompanied by physiological
Communicated by G. Heldmaier.
C. A. Schmidt-Wellenburg (&) H. Biebach
Department of Biological Rhythms and Behaviour,
Max Planck Institute for Ornithology,
Von-der-Tann-Str. 7, 82346 Andechs, Germany
e-mail: [email protected]
S. Daan G. H. Visser
Zoological Laboratory, University of Groningen,
P.O. Box 14, 9750 AA Haren, The Netherlands
G. H. Visser
Centre for Isotope Research, University of Groningen,
Nijenborgh 4, 9747 AG Groningen, The Netherlands
changes (such as enhanced oxygen and nutrient supply
of the muscles) that are not taken into consideration in
standard aerodynamic calculations, and also do not
appear in interspecific comparison.
Keywords Bird flight Energy expenditure Wing beat frequency Migration Body mass
List of
b
BMR
DLW
ef
efmax
symbols
wing span (m)
basal metabolic rate (W)
Doubly labelled water
energy expenditure during flight (W)
energy expenditure during flight (W) when er
assumed to be 0 W
efmin
energy expenditure during flight (W) when er
assumed to be ef
efS
energy expenditure during flight (W), er
estimated from interrupted flights
er
energy expenditure during non-flight (W)
Er
energy expenditure during rest (J)
m
body mass (g)
M
body mass (kg)
S
wing area (m2 )
V
flight speed (m s-1)
WBF wing beat frequency (Hz)
Introduction
Birds can accumulate internal energy stores to cover
periods of food shortage. While fat is the main substrate (Blem 1976, 1980), protein stores can also be
increased (Lindström et al. 2000). The optimal amount
of energy stored depends on the balance between
123
328
benefits and costs. Energy resources accumulated increase the probability of surviving during cold exposure or food shortage. This also holds for migratory
flights, when birds have to cross ecological barriers
such as the Mediterranean Sea or the Sahara Desert.
Energy stores also relieve them temporarily from the
need to forage such that they can allocate more time to
other activities. On the cost side, increased mass reduces manoeuvrability and take-off ability and increases predation risk (Lindström and Alerstam 1992;
Lind et al. 1999; Nudds and Bryant 2002). There is only
a small metabolic cost of maintenance of fat (SchmidtNielsen 1997), but carrying an increased mass during
flight in general may well raise the energetic costs of
locomotion in a significant way. Little direct information on these costs is available.
The energetic costs of transport have been approached both theoretically, from aerodynamic theory,
and empirically, from interspecific allometry. Aerodynamic predictions are rather equivocal. The basic
assumptions (Norberg 1996; Rayner 1990) lead to a
prediction of scaling of the energetic costs during flight
with a mass exponent of 7/6 (=1.17). If morphometric
data are taken into account the exponents derived
from modelling of mechanical power increase to 1.59
(Rayner 1990). In Pennycuick’s model ‘‘flight’’ (Version 1.10) an exponent of 1 is used. Allometric studies
based on direct measurements of energy expenditure in
different species also yield a wide range of exponents:
from 0.74 (Butler and Bishop 2000) to 1.36 (Rayner
1990). These interspecific equations compare birds
with different morphology. Some studies take morphology into account by including parameters such as
wing length, wing area and aspect ratio in the models
fitted. In such studies the mass exponents tend to be
larger (0.87–1.93; Rayner 1990) than when only body
mass is included. Even these calculations are not satisfactory for considerations at the intraspecific or
individual level. In the intraspecific comparison there is
little variation in morphology such as wing shape, but
individual physiology may well change with spontaneous changes in mass, for instance on an annual basis. In
the Red Knot (Calidris canutus) during the migration
seasons major changes were reported for pectoral
muscle mass, size of the stomach and intestines, and fat
stores probably all having an impact on the basal
metabolic rate (Piersma et al. 1996; Biebach and
Bauchinger 2003). In the interspecific comparison, both
physiology and morphology represent adaptive states
coevolved with body mass. Hence inter- and intraspecific scaling may yield different dependencies of
energy turnover on body mass.
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J Comp Physiol B (2007) 177:327–337
Two empirical studies have addressed the effect of
body mass on energy expenditure during sustained
flights at the intraspecific level. These were done on
Red Knots, with body mass ranging from 100 to 190 g
(Kvist et al. 2001) and Rose Coloured Starlings (Sturnus roseus, 56–87 g; Engel et al. 2006). Both studies
observed lower additional costs at a higher body mass
than predicted by aerodynamic theory (exponent 1.2–
1.6) or interspecific allometry (exponent 0.7–1.4). Energy expenditure during flight scaled with body mass to
the power of 0.35 (Kvist et al. 2001) or 0.55 (Engel
et al. 2006).
It would be of interest to know how this intraspecific
scaling exponent itself varies with the size of the species. The interspecific allometric scaling exponent for
mass-specific metabolic rates is negative. Thus, such
rates tend to be higher in smaller species, and lower in
larger birds. It is possible that the cost of transport of
extra energy stores varies in an adaptive manner between birds of different size. It is therefore of interest
to further explore intraspecific relations between body
mass and flight costs. We measured the energetic costs
of changes in body mass in a smaller sized species, the
Barn Swallow. The spontaneous accumulation of energy stores during the migratory period resulted in
changes of body mass of up to 35% in these swallows.
Individual birds were repeatedly flown in the wind
tunnel at different body mass exploiting these natural
variations, and their cost of flight was measured with
the doubly labelled water (DLW) method.
Materials and methods
Birds
We used the Barn Swallow, a long distance migrant, as a
model species. Nine birds were taken from nests at
about day 7 of age and hand raised. The chicks were fed
a diet of heart, curd, crickets, and bee larvae, supplemented with vitamins and minerals. We raised the birds
in a large aviary so that they could practise flight
immediately after fledging. During the experiment, the
birds were kept in an aviary (l · w · h ca.
2 m · 5 m · 2 m), sufficiently spacious to allow flight.
They received standard food ad libitum (insects, heart,
curd, rusk, and egg, supplemented with minerals and
vitamins) and had free access to fresh water. Day length
followed the course of the swallows’ natural year. From
the autumn equinox onwards, day length was set to LD
12.8:11.2 h. This reflects the light conditions (12.8 h
from dawn civil twilight till dusk civil twilight) of a
J Comp Physiol B (2007) 177:327–337
southward migration towards the equatorial region. We
used Osram Biolux fluorescent lights simulating the
spectral composition of natural sunlight.
Body mass varied naturally due to premigratory
hypertrophy, followed by gradual weight loss. No
artificial mass was added, and the birds were not food
restricted to manipulate weight. Intraindividual variations (maximum–minimum) in body mass ranged from
2 to 36% of the minimum body mass, similar to
observations in the field (Pilastro and Magnani 1997;
Rubolini et al. 2002). In the middle of the experimental
phase, wing length was measured with a ruler to the
nearest 0.5 mm (mean wing length was 11.9 cm, SD
between individuals 0.3 cm).
Wind tunnel and flight speed
The experiments were performed in the wind tunnel of
the Max Planck Institute for Ornithology in Seewiesen,
Germany (Fig. 1), situated at 688 m above sea level
(see Engel 2006). The technical specification of the
closed-circuit tunnel is nearly identical with the one in
Lund, Sweden (Pennycuick et al. 1997). The flight
section is 2 m long with an octogonal cross section of
1.2 m high and 1.2 m wide. It consists of transparent
acrylic plates and glass to allow observation of the
birds during flight. The air speed distribution is
homogeneous over the entire flight section (in crosssection as well as longitudinally) and turbulence in the
flight section is negligible (0.04% at 10 m s–1; Engel
2005). Downstream from the flight section there is a
gap of 0.5 m giving access from outside. The birds
329
enter the tunnel through it, after which it is closed with
netting. The wind tunnel is secured with mist nets upstream of the flight section and 2.3 m downstream of
the gap.
True air speed (and hence flight speed) was set at
10.3 m s–1 (SD over all 21 flights 0.04 m s–1). We chose
this speed on the basis of observations of the birds’
flight performance. In a pilot study, we recorded the
wing beat frequencies (WBF) of one bird flying over a
range of air speeds of 8.4–10.9 m s–1. WBF followed a
U-shaped curve, from which—analogously to the
‘maximum range speed’ of the power curve (see Pennycuick et al. 1996; Bruderer et al. 2001)—we calculated 10.4 m s–1 as the speed where number of wing
beats per distance covered is minimized. According to
‘minimum power speed’, the speed with least wing
beats per time was calculated as 9.6 m s–1 (Fig. 2).
During the experiments, mean air pressure was
932.9 mbar (SD 9.2 mbar), and relative humidity
65.7% (SD 11.5%), and air temperature was held
constant at 16.4C (SD over 21 all flights was 0.8C).
Experimental protocol
Prior to the experimental flights, the birds were trained
to fly in the wind tunnel for prolonged periods of time
(2–6 h). All birds flew during one autumn migration
period (end of September until end of November).
Some birds flew first with low and later with high body
mass, others vice versa.
The birds flew in pairs for 3.6–6.4 h (mean 5.4 h, SD
between 21 flights 1.0 h), covering on average 200 km.
Fig. 1 Wind tunnel.
Schematic drawing of the
technical devices. The air
circulates anti-clockwise in
the closed system as indicated
by the arrows. Before it
reaches the flight section,
turbulences are broken down
in the settling chamber.
Netting up- and down-stream
of the flight section is
indicated by dashed lines
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J Comp Physiol B (2007) 177:327–337
7.6
wing beat frequency [Hz]
7.4
7.2
7.0
6.8
6.6
6.4
2
1
6.2
8.0
8.5
9.0
9.5
10.0
flight speed [m
10.5
11.0
11.5
s-1]
Fig. 2 Wing beat frequencies (WBF, in Hz) of one Barn Swallow
flying over a range of speeds (average ± SE). From the fitted
curve (WBF = 0.4 · V2 – 7.6 · V + 43.0; with V as flight speed
in m s–1) we calculated ‘minimum WBF speed’ as 9.6 m s–1 (1)
and ‘minimum WBF per distance’ speed as 10.4 m s–1 (2)
When birds tried to land, we chased them by waving
our hand at them. However, if birds interrupted the
flight by landing or tried to land repeatedly, they were
allowed to rest for at least 1 h before continuing the
flight. Such flights are referred to as ‘‘interrupted’’,
whereas continuous flights are referred to as ‘‘nonstop’’. During resting periods of interrupted flights
birds were put in a box (ca. 0.2 m · 0.2 m · 0.2 m) to
avoid high locomotory activity. During the flights, the
observer was with the birds all the time, standing next
to the wind tunnel. Body mass was taken immediately
before and after the flight to the nearest 0.01 g. In the
analysis of energy expenditure and wing beat frequency, we used the calculated average body mass (m)
during the experimental flight.
Energy expenditure during flight (ef)
Energy expenditure was measured with the DLW
method. The evening before the experiment, food was
removed from the aviaries to enhance the accuracy of
the DLW measurement. The next morning the birds
were injected intraperitoneally with about 0.11 g of a
DLW mixture (enriched in 18O by 59.9 atom percent,
and in 2H by 36.7 atom percent). The injected dose was
weighed on an analytical balance (Sartorius BP 1215)
to the nearest 0.1 mg. After the injection, the bird was
placed in a dark box without access to water and food
to let the DLW mixture equilibrate with the bird’s
water pool. One hour later, the bird was weighed and
the ‘‘initial blood sample’’ of about 60 ll was taken
from the jugular vein. The jugular vein was chosen to
123
avoid any impairment of flight performance as might
arise by any accidental haemorrhage at the brachial
vein. After the flight, usually 6.6 h after the initial
blood sample, the bird was weighed again, and another
blood sample was taken as described before: the ‘‘final
sample’’. To calculate total body water at the end of a
flight and thus increase the accuracy of the DLW
method, some birds were reinjected with DLW afterwards, followed by another blood sample after one
hour of equilibration in a dark box. All blood samples
were divided over four capillaries, sealed immediately,
and stored at 5C for isotope analysis (see below).
From five birds blood samples were taken prior to the
injection of isotopes to determine the average background levels for 2H and 18O during our study, which
were about 0.0145% for 2H and 0.200% for 18O. In
view of the high difference between natural background levels and injected dose, we refrained from
taking more background measurements (Nagy 1980).
The isotope analyses were performed in triplicate or
quadruplicate at the Centre for Isotope Research
according to the method described by Visser et al.
(2000). Briefly, for each sample 2H/1H and 18O/16O
isotope ratios were determined with the CO2 equilibration method and the uranium reduction methods,
respectively (Speakman 1997). The coefficients of
variation for 18O and 2H enrichments relative to the
background levels were 0.97 and 0.76%, respectively.
Rates of CO2 production were calculated as described
by Engel et al. (2006). As a last step, these values were
converted to energy expenditure using a conversion
factor of 27.8 kJ l–1 (Gessaman and Nagy 1988). On
average the turnover rate of 18O was 2.96 (SD 0.277)
times higher than that for 2H. As a consequence, the
DLW method as employed in this study appeared to be
rather insensitive to analytical errors. For example, if
we changed one of the measured isotope values by 1%,
the calculated level of energy expenditure changed by
3.5% on average.
The DLW method integrates the energy expenditure over the whole measurement period between the
‘‘initial’’ and the ‘‘final’’ samples. This includes both
the energy expenditure during flight (ef) and the energy
metabolised during times in which the birds did not fly
(er). In the birds with interrupted flights the interruptions considerably affected the mean energy metabolism measured. As a sensitivity analysis, we calculated
the range of ef estimates using two assumptions of
energy expenditure during non-flight periods: (1)
Neglecting the energy expenditure during the resting
time. These calculations are indicated as efmax [W]; (2)
Assuming the same energy levels during flight and nonflight. Calculated flight costs are referred to as efmin
J Comp Physiol B (2007) 177:327–337
[W]. efmax and efmin are the most extreme estimates of
the actual flight costs, with efmax providing the upper
and efmin the lower boundary. As true flight costs lie
between these boundaries, we estimated er using the
DLW sessions with longer non-flight periods. The
estimated flight costs are indicated as efS (in W).
Wing beat frequency (WBF)
Wing beat frequency [WBF (Hz)] was visually evaluated from digital video records (Canon XL 1) of the
experimental flights: we counted the wing beats from
the video tape every half hour for about 10 min (with a
resolution 25 pictures s–1). We selected sequences of at
least 15 wing beats of the birds staying stationary, and
evaluated 20 such sequences during each interval. The
Barn Swallows rarely flew with regular wing flapping.
Mostly they showed bounding flight with short ‘‘upstroke pauses’’ (Liechti and Bruderer 2002; Bruderer
et al. 2001; Pennycuick et al. 2000). These pauses were
too brief to quantify their duration. Therefore, WBF
refers to the ‘‘effective wing frequency’’, including sequences of bounding flight. As WBF did not change
during the flights, mean WBF per flight was used for
further analysis.
Statistical analysis
The statistical analysis was performed in SPSS 13.0.
Energy expenditure during flight (ef) and wing beat
frequency (WBF) were analysed in separate models
with the emphasis on unravelling patterns related to
body mass. As the calculations of ef in interrupted
flights were very sensitive to the assumption on
metabolism during times the birds did not fly, we restricted the analysis of ef to non-stop flights. We used
mixed models with Restricted Maximum Likelihood
for both parameters. Parameters that did not significantly contribute to the explained variance were excluded from the models in stepwise fashion. During the
elimination procedure, the AIC value was used as a
criterion for the improvement of the model. For the
analysis of the effects on log10(ef) we initially included
individual as random and log10(m), log10(WBF),
log10(WBF)*log(m), and wing length as fixed factors.
The final model for log10(ef) in non-stop flights is based
on individual and log10(m). For log10(WBF), we first
included individual as random and log10(m), flight
performance (interrupted or non-stop), flight performance*log10(m), and wing length as fixed factors. The
final model for log10(WBF) is based on individual and
log10(m).
331
Results
Energy expenditure during flight (ef)
We measured energy expenditure in 21 flights. Thirteen sessions (in 6 individuals) had non-stop flights
lasting on average 92% of the session, i.e. of the total
time between initial and final blood sample. There
were eight sessions (in seven individuals), where flights
were interrupted. These flights lasted on average for
66% and at most for 77% of the experimental time. We
do not yet understand why flights became interrupted.
Two birds flew exclusively non-stop (two and three
flights), three individuals performed interrupted flights
only (four flights). In four birds, which flew both nonstop and interrupted, the interrupted flight was always
at the lightest body mass measured (eight non-stop and
four interrupted flights).
As non-flight time in the interrupted flights was on
average 34% and assumptions on metabolism during
non-flight strongly affect the calculated ef, we do not
think that these data allow us to carefully measure the
cost of flight in these flights. Hence we restrict the
analysis of flight cost to the 13 non-stop flights. Even in
these sessions, we need to allow for a different metabolic rate during the non-flying time than during flight.
This metabolic rate during rest, indicated as er [W], is
unknown, but it must be somewhere between two extreme boundaries: a minimum of 0 and a maximum
equal to the metabolic rate during flight [ef (W)]. We
first derive flight costs from the non-stop flights for
these two extreme assumptions, and then we use the
interrupted flights to obtain a more realistic estimate in
between these boundaries. Body mass in non-stop
flights ranged from 14.5 to 22.2 g, with an average of
18.5 g (SD 2.3 g). Birds flew on average for 6.0 h (SD
0.5 h).
Upper and lower boundaries to flight costs
Neglecting the resting time, i.e. setting the metabolism
er during non-flight at 0 W, leads to an average efmax of
2.28 W (range 2.06–2.79 W, SD 0.23 W). efmax [W] increased with body mass m [g] following the equation
(Table 1)
log10 (efmax ) = 0.292 + 0.511 log10 (m).
ð1Þ
Minimal flight costs can be computed under the
assumption that resting is equally costly as flight.
(er = ef). This yields for the non-stop flights an average
efmin of 2.09 W (range 1.68–2.46 W, SD 0.20 W). The
123
332
J Comp Physiol B (2007) 177:327–337
Table 1 Effects of log10(m) on log10(ef) (N = 13 in six individuals, flight time >80%)
log10(efmax)
Intercept
log10(m)
log10(efmin)
Intercept
log10(m)
log10(efS)
Intercept
log10(m)
Estimated effect
SE
df
t
F
95% CI
P
–0.292
0.511
0.20
0.16
10.68
10.06
–1.47
3.28
2.16
10.73
–0.73–0.17
0.17–0.86
<0.05
–0.440
0.594
0.22
0.17
8.94
8.81
–1.99
3.43
3.96
111.77
–0.94–0.06
0.20–0.99
<0.05
–0.416
0.580
0.22
0.17
8.61
8.48
–1.91
3.40
3.64
11.53
–0.91–0.08
0.19–0.97
<0.01
log10(WBF) did not significantly affect log10(ef) and was excluded from the models
relationship between efmin [W] and body mass m [g] is
described as (Table 1)
log10 ðefmin ) = 0.440 + 0.594 log10 (m).
ð2Þ
The upper and lower boundaries are plotted on
double logarithmic scale as a function of body mass in
Fig. 3.
These extreme assumptions provide us with a welldefined range in which the true flight costs must lie.
That this range is narrow is simply due to the fact that
the analysis is restricted to those sessions where there
was little rest, so that assumptions concerning er have
not too much impact. Yet in view of the unrealistic
nature of these extreme assumptions, it is desirable to
have a more realistic estimate.
energy expenditure during flight [W ]
3.2
3
2.8
2.6
2.4
2.2
2
1.8
Estimate of flight costs
We can not apply Basal Metabolic Rates such as provided by Gavrilov (1.41 kJd–1 g–1) and Kespaik
(1.51 kJd–1 g–1, both cited in Gavrilov and Dolnik
1985) to estimate er, as these are standardly derived
during night. A better estimate of er in the experimental situation can actually be derived from the eight
sessions with interrupted flights. We have used the
DLW measurements in these sessions as follows. We
first assumed that flight costs in these sessions followed
Eq. 2, i.e. at the minimum boundary. Subtracting the
energy thus calculated for flight from the total energy
turnover in each session yielded a figure Er (Joule) for
the energy spent during rest time (seconds), which
could be translated into Watt. We then used the
average mass-specific er (in W g–1) of these interrupted
flights to estimate Er in the 13 non-stop flights again
and obtain a new ef value. As before, we analysed the
relation of ef and body mass for the non-stop flights in a
mixed model. With the new relation of ef and body
mass, we again estimated ef and consequently er in
interrupted flights. We continued the iterative procedure until the approximation was stable. This results in
an average efS of 2.13 W in the non-stop flights (range
1.74–2.55 W, SD 0.21 W). efS [W] correlates with body
mass m [g] as
1.6
log10 (efS ) = 0.416 + 0.580 log10 (m).
ð3Þ
1.4
14
16
18
20
22
24
body mass [g]
Fig. 3 Upper and lower boundary estimates of energy expenditure during flight (ef in W) in relation to body mass (in g), plotted
on a double-logarithmic scale (N = 13 flights in 6 individuals).
The maximum and minimum estimates for ef are indicated by
black symbols and a solid line (efmax) and grey symbols and a
dashed line (efmin), respectively. Different estimates for single
flights are connected by lines. The grey shaded area between the
two regressions indicates the range of the most extreme
predictions of ef
123
For statistical details see Table 1. The scaling of the
estimate of efS with body mass is displayed in Fig. 4.
Irrespective of the different assumptions on er, the
slope of the relation ef and m is very robust and in all
cases relatively low (between 0.51 and 0.59).
Wing beat frequency (WBF)
Mean wing beat frequency of all 21 flights was 7.00 Hz
(range 5.67–8.18 Hz, SD 0.62 Hz among n = 21 flights
J Comp Physiol B (2007) 177:327–337
333
WBF did not explain ef and was not correlated with
either of the estimates of ef (Spearman’s rho with
efmax = 0.082, P > 0.05, and with efmin = 0.253,
P > 0.05, N = 13).
energy expenditure during flight [W ]
3.2
3
2.8
2.6
2.4
2.2
Discussion
2
1.8
Energy expenditure (ef)
1.6
Five previous measurements of energy expenditure
during flight in Barn Swallows in the field have been
published. All five were taken during the breeding
season and calculated flight costs via time-budgets or
mass-loss: according to Hails’ (1979) calculations, a
barn swallow of 18.5 g would fly at 1.27 W, Lyuleeva’s
(1970) measurements would result in 1.39 W, and
Turner’s would range from 1.57 (Turner 1982a, b) to
1.90 W (1983). Based on Westerterp and Bryant’s
measurements (1984) we would expect flight costs of
1.51 W in a bird of 18.5 g. The average efS of 2.13 W
observed in our study thus is about 10–70% higher
than the flight costs of Barn Swallows estimated in the
field. Even our lowest estimates of flight costs (efmin,
2.09 W) are 11–66% higher. Generally, wind tunnel
measurements seem to yield higher ef than measurements during free flight in the field (Masman and
Klaassen 1987; Rayner 1994).
True flight costs in the interrupted flights are difficult to assess, as they are sensitive to assumptions on
energy expenditure during non-flight er. Estimates of
efmax yielded higher flight costs in interrupted than in
non-stop flights, especially at a lower body mass. Flight
costs might well have been higher in these flights: We
chased the birds that landed repeatedly. This may have
increased their energy expenditure since it is known
that take-off flights as well as the starting phase of a
flight are more expensive than steady state flights
(Nudds and Bryant 2000). Calculating ef assuming the
same energetic costs during flight and rest resulted in
slightly lower efmin in the interrupted than in non-stop
flights. We cannot distinguish whether in interrupted
flights (a) flight costs were higher than in non-stop
flights, (b) energetic costs during non-flight were higher
than the often assumed resting metabolism during
daytime of 1.25· Basal Metabolic Rate, or (c) whether
a combination of both effects occurred.
Assuming the same flight costs for interrupted and
non-stop flights, we obtained an improved estimate for
er. Mass-specific er in these sessions was on average
0.09 W g–1. That is 320% more than the 0.02 W g–1
calculated from Gavrilov’s and Kespaik’s measurements (Gavrilov and Dolnik 1985) as 1.25· Basal
1.4
14
16
18
20
22
24
body mass [g]
Fig. 4 Energy expenditure during flight, ef in W, plotted in
relation to body mass (in g) on a double logarithmic scale. The
regression (solid black line) refers to efS (dots). The grey shaded
area is the area between the upper and lower boundary (grey
solid and dashed lines, respectively), taken from Fig. 3
in 9 individuals). Average body mass was 17.8 g (range
14.5–22.2 g, SD 2.25 g). WBF did not change during
flight (i.e., we found no differences between the
beginning of the flight, after 30 min, after 150 min, and
as an average over the whole flight time). WBF was
positively correlated with body mass (linear mixed
model for log10(WBF) in 21 flights (9 individuals), with
individual as random and log10(m) as fixed factor;
F17.0 = 9.3, t = 3.05, P < 0.01 for log10(m), 95% CI of
the slope was 0.12–0.64). This relationship can be described as (Fig. 5)
log10 (WBF) = 0.381 + 0.376 log10 (m).
ð4Þ
wing beat frequency [Hz]
8
7.5
7
6.5
6
5.5
14
16
18
20
22
24
body mass [g]
Fig. 5 WBF in relation to body mass on a double logarithmic
scale (N = 21 flight in 9 individuals). Filled circles refer to nonstop and open squares to interrupted flights, the common
regression (Eq. 4) is indicated with a solid line
123
334
Metabolic Rate (the factor translating BMR into the
active phase of the day, Aschoff and Pohl 1970). This
difference may appear to be high, but our birds were
neither kept in the dark nor at thermoneutrality during
non-flight. Average flight costs (efS) measured in this
study equal 6.8· estimated BMR or 1.3· estimated er.
The sensitivity analysis showed, that estimates of ef
in non-stop flights were very robust with regard to
different assumptions on er due to the fact that the
birds flew during nearly all of the DLW session. On
average, the estimates for the upper and lower
boundary differed by only 0.19 W, i.e. efmax was on
average 9% higher than efmin. The following discussion
on the effects of changes in body mass on ef is based on
our best estimate of ef.
Aerodynamic theories
Theoretical aerodynamic literature (Table 2a) reports
mass exponents for the energy expenditure of avian
flight which range from 1.16 to 1.59 (Pennycuick 1975,
1978; Rayner 1990; Norberg 1996). We found an
exponent of 0.58 (95% CI 0.19–0.97). This was significantly lower than the lowest theoretical value. The
applicability of aerodynamic theories is difficult. They
are based on fixed wing theory and better applicable to
airplanes than to birds (Videler 2005). Flight costs
predicted from theory are often lower than directly
measured. That is not only a problem of assumptions
on conversion efficiency, which are necessary to
translate (predicted) mechanical power into chemical
power, ef. Also other assumptions in the theory may
not have robust foundations: In a study by Pennycuick
et al. (2000) on a Barn Swallow flying in a wind tunnel,
predicted flight costs were 50% lower than the costs
calculated from flight behaviour. The authors fitted the
prediction by empirically changing the assumptions for
body drag and profile power ratio, but without aerodynamic explanation.
J Comp Physiol B (2007) 177:327–337
Barn Swallows, and therefore it overlaps with some of
the interspecifically observed scaling exponents.
In migratory flights, the question of costs for transporting fuel cannot be answered by interspecific allometric comparison. These regressions are based on
diverse species, with not only differences in size, but
also in morphology, ecology and evolutionary background. In addition, an increase in body mass within
individuals is qualitatively distinct from differences in
body mass between species. Within individuals, mainly
fat is deposited, which is metabolically rather inert and
does not increase maintenance costs and basal metabolic rate as other tissues would. Among species, larger
birds are not necessarily fatter than smaller ones. Instead they carry larger quantities for instance of muscle
tissue, which is metabolically more active than fat.
Videler (2005) showed that the dimensionless cost of
transport (amount of work per unit weight and distance
covered) is not independent of body mass, but decreases with size. He concluded that small and large
birds are not scale models of each other.
Interspecific comparisons of ef are commonly based
on different methods of measurement. In wind tunnel
studies, ef has often been measured by mask respirometry, which adds additional mass and changes
aerodynamics. Calculating energy consumption via
mass loss is prone to error when ambient temperature is
not defined. Many studies are necessarily restricted to
short flights, which have to be seen in a different ecological and physiological context. Energy expenditure
at the beginning of a flight, and thus during short flights,
is higher than in a later phase (Nudds and Bryant 2000).
Furthermore, birds may well adjust physiological traits
to time. Flight costs during summer can therefore be
different from flight costs during long distance migration. Carrying food during short foraging flights is a
different task than flying for hundreds of kilometres
without rest and refuelling. These situations may well
be associated with different physiological adaptations.
Intraspecific scaling
Interspecific comparisons
In interspecific allometries mass exponents range from
0.67 (Videler 2005) to 1.93 (Rayner 1990). Wind tunnel
studies in general appear to yield small exponents,
around 0.7–0.9, whereas allometric comparisons that
include other studies yield exponents of 0.8–1.4 (Table 2b). The exponent of 0.58 measured in this study
lies below this range, but is not significantly different
from Videler’s value (0.67). The scaling exponent
measured in our study has a wide confidence interval
due to the unavoidably small range of body mass in
123
All three intraspecific studies on the effect of body mass
on ef used DLW to measure energy expenditure. The
fraction of time in flight was similar in both cases to our
study (96% in Red Knots, Kvist et al. 2001; 94% in Rose
Coloured Starlings, Engel et al. 2006). er was corrected
by 1.5· Basal Metabolic Rate in Red Knots, and 1.25·
Basal Metabolic Rate in Rose Coloured Starlings.
Both studies found mass exponents (Red Knot 0.35;
Rose coloured starling 0.55) that were similar or
slightly smaller than those observed in the Barn
Swallow (0.58). We may thus safely conclude that the
J Comp Physiol B (2007) 177:327–337
335
Table 2 Regressions for energy expenditure during flight (ef, in W) in relation to body mass
Exponent Equation
Comment
Species
Reference
(a) Aerodynamic measurements and predictions
At minimum power speed
1.05
Pout = 12.9M1.05
At maximum range speed
1.16
Pout = 15.0M1.16
At maximum range speed
1.16
Pout = 14.95M1.16
Theoretical prediction
7/6
Pout ~ M7/6
Isometric wing morphology
1.5
Pout ~ M1.5
At minimum power speed
1.19
Pout = 10.9M1.19
At minimum power speed
1.56
Pout = 24.0M1.56b–1.79S0.31
At maximum range speed
1.59
Pout = 27.21M1.59b–1.82S0.275
At maximum range speed; for individuals
1.59
Pout = 27.21M1.59
Norberg 1990
Norberg 1996
Rayner 1990
Rayner 1990, Norberg 1996
Pennycuick 1975, 1978
Norberg 1996
Norberg 1996
Rayner 1990
Rayner 1990
Direct measurements
(b) Interspecific
0.67
ef ~ 60M0.67
0.68
ef = 44.54M0.682
0.74
ef = 60.5M0.735
0.76
ef = 0.305m0.756
0.76
ef = 58.8M0.76
0.79
ef = 0.471m0.786
0.79
ef = 66.97M0.79
0.81
ef = 57.3M0.813
0.81
ef = 66.17M0.814
0.83
ef = 1875.76M0.834b–1.690S1.732
0.85
ef = 49.4M0.851
0.87
ef = 75.87M0.866b–0.175S0.279
0.87
ef = 69.5M0.87
1.01
ef = 17.36M1.013b–4.236S1.926
1.36
ef = 542.73M1.355
1.37
ef = 51.5M1.37b–1.60
1.51
ef = 98.39M1.505b–2.539S0.236
1.93
ef = 39.84M1.93b–1.690S–0.553
Videler 2005
Rayner 1990
Norberg 1996
Masman and Klaassen 1987
Butler and Bishop 2000
Masman and Klaassen 1987
Rayner 1990
Norberg 1996
Rayner 1990
Rayner 1990
Norberg 1996
Rayner 1990a
Butler and Bishop 2000a
Masman and Klaassen 1987
Rayner 1990
Norberg 1996
Rayner 1990
Rayner 1990
(c) Intraspecific
0.35
ef = cm0.35
cmin = 2.24
cmax = 2.57
0.55
ef = 0.74m0.55
0.58
ef = 0.38m0.58
Maximum flight costs
Non-passerines
Wind tunnel
Non-wind tunnel
Wind tunnel
Wind tunnel
All studies
Wind tunnel
Non-passerines
DLW; time-energy budget
Wind tunnel
Wind tunnel
All studies
Passerines
All studies
Passerine
Non-passerine
Calidris canutus Kvist et al. 2001
Passerine
Passerine
Sturnus roseus
Hirundo rustica
Engel et al. 2006
this study
The first column gives the exponent of the correlation of ef and body mass. In the second column the different equations are listed. Pout
mechanical output, ef to total power consumed during flight, M (m) is body mass in kg (g), b wing span in m, and S wing area in m2.
Comments and study species are followed by the sources quoted in the last column.
a
After Masman and Klaassen (1987)
dependence of flight costs on spontaneous changes in
body mass is much less steep than in the comparison
between species. This also holds for a small species like
the Barn Swallow. Kvist et al. (2001) proposed a
change in flight muscle efficiency in heavier birds
allowing them to fly at lower costs than expected when
fuelling up for migration. A similar mechanism may be
applicable to Barn Swallows. However, it is not a priori
clear why flight muscle efficiency should not be maximized by birds with a lower mass.
Wing beat frequency
The average wing beat frequency of 7.0 Hz observed
lies well within the range of observations on Barn
Swallows flying in wind tunnels or in the field. In a
wind tunnel study, Pennycuick et al. (2000) observed
6.8 and 6.9 Hz in birds flying at 10 and 11 m s–1. Nudds
et al. (2004) reported 7.0 Hz in a 19 g bird. Bruderer
et al. (2001) measured frequencies of 2.5–8.5 Hz
(average 6.9 Hz) in birds flying over a range of speeds
in a wind tunnel. WBF during level flight was 7.2 Hz in
the wind tunnel, compared to 5.4 Hz during migration
in the field (Liechti and Bruderer 2002). Another field
study recorded 8.2 Hz during coursing (Warrick 1998).
The observed WBF is 20–30% lower than aerodynamic predictions for birds of that size, which range
from 8.4 Hz (Pennycuick 1990), and 9.1 (Pennycuick
1996) to 9.8 Hz (Pennycuick 2001) or even 12.9 Hz
(Norberg 1990). This discrepancy may be attributed to
123
336
the fact that Barn Swallows are aerial feeders with a
special wing shape and aspect ratio, which differ in
flight performance from other species. The observed
exponent of the allometric relationship between WBF
and body mass was 0.36 (95% CI 0.12–0.64). This range
includes the value of 0.5 suggested by Pennycuick
(1996) for the intraindividual scaling exponent. At the
individual level, morphological parameters like wingspan and wing area are constant, and they are similarly
scaled within a species. We therefore suggest that
Pennycuick’s proposition for the scaling of WBF with
body mass holds both at the individual and at the
intraspecific level.
Implications
We showed that ef of Barn Swallows flying for long
periods of time increases less with body mass than
aerodynamic calculations and interspecific comparisons suggest. Benefits of a shallow increase of flight
costs are obvious. During migration, birds can reach
farther regions and they are less dependent on stopover sites (Weber et al. 1994). Heavy birds could reach
their destination faster as they might increase their
flight speed as predicted from aerodynamic theory. The
consequences of the intraindividual scaling become
conspicuous, when we calculate the flight costs of a
Barn Swallow of 18.5 g that increases its mass by 1 g:
according to our measurements, energy consumption is
3.2% higher in the heavier bird, whereas the general
aerodynamic prediction (with an exponent of 7/6, see
Rayner 1990) predicts an increase of 6.6%. With the
passerine exponent (1.355; Rayner 1990), the increase
would be 7.7%, twice the increase observed. Predictions for migratory strategies or flight range have thus
to be applied carefully.
Why flight costs increase less with body mass than
expected from aerodynamic theory and from interspecific comparisons is not fully understood. Fat load in
migrants may cause only a small increase in energy
consumption during flight, as these species deposit
more fuel in the hind part of the body which then is
compensated for by lift power of the body and tail
(Dolnik 1995). It is possible that migratory birds undergo a training effect accompanied by physiological
changes, resulting in different muscle fibre composition
or an improved supply with oxygen and nutrients. Also
maintenance costs and basal metabolic rate are lowered during migration, as most organs are reduced in
size (Piersma et al. 1996; Biebach and Bauchinger
2003). This may reduce flight costs at least during long
migratory flights. Not only physiological parameters
but also flight behaviour can be flexible: stroke
123
J Comp Physiol B (2007) 177:327–337
amplitude, the extent to which the wings are stretched
and flexed, duration of upstroke pauses or wing beat
frequency are adaptable and are probably adjusted to
different requirements. That becomes obvious in the
fact that ef cannot be predicted from WBF. WBF scales
with body mass with a lower exponent than does ef,
indicating higher energy expenditure per wing beat at
an increased body mass. But as mentioned above, other
parameters of flight behaviour, which have not been
measured, are flexible as well. Mechanisms of these
changes in flight behaviour and physiology are not yet
understood and require further investigation.
Acknowledgements We remember with gratitude the late Prof.
Dr. E. Gwinner, whose inspiration and support let to this project.
We thank Ulf Bauchinger, Brigitte Biebach, Sophia Engel, and
Andrea Wittenzellner for their support especially of a temporarily one-handed student. Berthe Verstappen determined the
isotope enrichments at the Centre for Isotope Research. David
Rummel from the Institute of Statistics of the Ludwig-Maximilians-University Munich provided helpful feedback on statistics.
The experiment was conducted in accordance with the German
legislation on the protection of animals. We thank two anonymous reviewers for comments on the manuscript.
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