Circulatory variables and the flight performance of birds
School of Biological Sciences, University of Wales Bangor, Bangor, Gwynedd LL57 2UW, UK
e-mail: c.bishop{at}bangor.ac.uk
Accepted 8 March 2005
Summary
When considering the `burst' flight performance of birds, such as during take-off, one of the most important structural variables is the ratio of the mass of the flight muscle myofibrils with respect to body mass. However, when considering `prolonged' flight performance the variable of interest should be the body mass ratio of the mass of the flight muscle myofibrils that can be perfused sustainably with metabolites via the blood supply. The latter variable should be related to blood flow (ml min-1), which in turn has been shown to be a function of heart muscle mass, the value of which is more easily obtainable for different species than that for the mass of perfused muscle.
The limited empirical evidence available suggests that for birds and mammals the rate of maximum oxygen consumption scales with heart mass (Mh) as Mh0.88 and that for birds Mh scales with body mass (Mb) as Mb0.92, leading to the conclusion that the rate of maximum oxygen consumption in birds scales with an exponent of around Mb0.82. A similar exponent would be expected for the rate of maximum oxygen consumption with respect to the flight muscle mass of birds. This suggests that the sustainable power output from the flight muscles may ultimately be limiting the flight performance of very large flying animals, but as a result of circulatory constraints rather than biomechanical considerations of the flight muscles per se.
Under the particular circumstances of sustainable flight performance, calculations of rates of metabolic energy consumed by the flight muscles can be compared directly with the estimates of biomechanical power output required, as calculated using various aerodynamic models. The difference between these calculated values for rates of energy input and output from the muscles is equivalent to the `apparent' mechanochemical conversion efficiency. The results of one such analysis, of the maximum sustainable flight performance of migratory birds, leads to the conclusion that the efficiency of the flight muscles appears to scale as Mb0.14. However, much of this apparent scaling may be an artefact of the application and assumptions of the models. The resolution of this issue is only likely to come from studying bird species at either extreme of the size range.
Key words: aerobic flight, muscle efficiency, scaling, heart mass, avian energetics
Introduction
Aerodynamic considerations of bird flight suggest that, for geometrically
similar animals, the biomechanical power required to fly at the minimum power
speed (Pmin) is relatively greater for large species than
for smaller species, as the biomechanical power required should scale with
respect to body mass (Mb) as approximately
Mb1.17
(Pennycuick, 1975;
Rayner, 1979a
). When
converting the aerodynamic model predictions for biomechanical power output
(Pmech) in watts (W) into estimates for the rate of
metabolic energy input (Pmet) required to support it
(often taken for convenience as equivalent to the rate of oxygen consumed in
ml min-1), Pennycuick
(1975
) assumes that the
mechanochemical conversion efficiency of the flight muscles
(Efm) is independent of body mass and recommends the use
of a constant value of around 0.23. If Efm is a constant
and the `central' cardiovascular adaptations closely reflect the `peripheral'
aerobic adaptations of the flight muscles, as predicted by the hypothesis of
symmorphosis (Weibel et al.,
1991
), it would be expected that the cardiovascular systems of
large birds that are capable of `prolonged' flight should be adapted to meet
the relatively high power required. However, it is clear that the relative
rate of blood flow available to the flight muscles of large birds is actually
reduced compared to small birds, due to the steady decline in maximal heart
rate with increasing body mass (Bishop and
Butler, 1995
; Bishop,
1997
), as in mammals (Weibel
et al., 1991
).
The finding that the maximum heart rate of mammals is primarily an
allometric function of body size, regardless of morphological adaptations to
sedentary vs athletic locomotor performance such as relative heart
mass (Weibel et al., 1991), is
nicely supported by work on dogs
(Stray-Gundersen et al., 1986
)
and pigs (Hammond et al.,
1992
). In both these studies, the pericardial membrane that
surrounds the heart was surgically removed and the maximum cardiac output and
the rate of maximum oxygen consumption were substantially increased, but
maximum heart rate was unaffected. Perhaps surprisingly, in addition to an
allometric decline in heart rate measured during the flight of birds, there is
also a tendency for the heart mass ratio to decline with increasing body mass
(Lasiewski and Calder, 1971
;
Bishop and Butler, 1995
;
Bishop, 1997
). Indeed, Bishop
(1997
) calculated that the
maximum rate of oxygen consumption
O2max, in ml
min-1) of extant species of birds generally scales as approximately
Mb0.82±0.08 (body mass exponent ±
standard error), although the intrinsic cardiovascular capacity for the
O2max of birds
and mammals appears to scale as
Mb0.88±0.02
(Bishop, 1999
). As suggested by
Pennycuick (1989
) the
exponents for the scaling of basal metabolic rate and maximal metabolic rate
appear to be selected for independently in endotherms, with the consequence
that the potential for aerobic scope should be greater in both larger birds
and mammals (Koteja, 1987
;
Bishop, 1999
;
Ellerby et al., 2003
).
The minimum rate of oxygen consumption
(O2min,, in ml
min-1) measured from birds during flights in wind tunnels scales as
approximately Mb0.77
(Butler, 1991
;
Bishop et al., 2002
), which is
consistent with the calculated scaling factor of
Mb0.756 for the non-wind tunnel flights of
birds (Masman and Klaasen, 1987). Part of the discrepancy between the scaling
exponents for Pmet and Pmech could be
accounted for by the fact that the aspect ratios of the wings of extant
species of birds tend to increase with increasing body mass
(Pennycuick, 1982
). In
addition, smaller species may be flying faster during the non-wind tunnel
flights than their minimum power speeds, as it has been suggested that smaller
species have a very much greater excess capacity for aerobic flight
(Pennycuick, 1996
). However,
the aerodynamic predictions of minimum power speeds are highly dependent on
the values used for body drag coefficients (CD,par) and it
is not clear what values for drag should be used in these models
(Pennycuick et al., 1996
;
Hedenström and Liechti,
2001
). Assuming that both the aerodynamic models and the
physiological models and measurements outlined above are broadly correct would
lead to the view that the Efm resulting from the
conversion of Pmet into Pmech may
scale positively with increasing body mass (Rayner,
1988
,
1990
;
Bishop and Butler, 1995
;
Kvist et al., 2001
). It has
also been suggested that Efm may change positively with
respect to flight speed (Rayner,
1999
; Ward et al.,
2001
).
As the aerodynamic lifting line model of Pennycuick
(1975,1989
)
in particular has frequently been applied to behavioural, ecological and
evolutionary studies (e.g. Hedenström
and Alerstam, 1992
; Pennycuick
et al., 1994
; Gudmundsson et
al., 1995
), it is necessary to be confident that the estimates for
Pmech and the value of Efm and, thus,
the subsequent calculation of Pmet required to fly at a
particular speed, are realistic. This is particularly relevant with regard to
issues such as aerobic scope, the optimisation of bird flight behaviour, the
maximum mass-specific power output and
O2max of avian
muscle and the upper limit to the size of flying animals. Ward et al.
(2004
) have demonstrated how
sensitive estimates for Pmet are to changes in
Efm when based on calculations of
Pmech, as the latter is such a small part of the overall
energy budget.
Bishop (1997) showed that it
is possible to provide reasonable predictions for the
O2max of birds
during flight by assuming that avian cardiac muscle has a similar
physiological and biomechanical performance to that of terrestrial mammals.
Thus it is now possible, theoretically, to derive and compare two independent
estimates for the rate of energy utilisation of birds during maximum
sustainable flight activity, and to look at the implications of using the
default values for these models for predicting the maximum flight performance
of birds and the scaling of Efm.
In the following analysis I have applied my approach
(Bishop, 1997) to a study of
the maximum sustainable climbing flight of 15 species of birds migrating over
southern Sweden (Hedenström and
Alerstam, 1992
). These authors used the default values from the
model of Pennycuick (1975
) to
estimate the maximum aerobic biomechanical power output continuously available
(Pac) from the flight muscles of birds (see
Pennycuick, 1972
). I have used
their data but have recalculated the estimates for Pac
using the default values of Pennycuick's computer program 1A
(Pennycuick, 1989
, version
1.1) as this is easy to use, has the same range of values for the body drag
coefficient (CD,par from 0.25 to 0.4) and the results can
then be applied with consistency to large numbers of additional species. The
two data sets are listed in Appendix
A for comparison. On average, the new calculations only lead to a
reduction of Pac by 3.4% (range -14.7% to +7.1%) so
overall conclusions are not seriously affected. By comparing the estimated
values of Pac with those for Pmet,
using calculations of
O2max available
based on heart mass (Bishop,
1997
) and converted to watts, it is possible to estimate the
`apparent' scaling of the Efm. Subsequently, I apply these
results to the data collected for 228 species of birds by Magnan
(1922
), and look at the
predictions for the aerobic flight performance of different taxa. I will also
discuss the implications for the scaling of power output in birds with respect
to the myofibrillar content of the flight muscles.
|
Modelling the maximal aerobic flight performance of birds
It is usual, when considering the amount of aerobic metabolic energy
(Pmet in W or
O2 in ml
min-1) that would actually be continuously available to supply the
flight muscles (Pmet,fm), to take account of the
additional costs of maintaining some kind of basal metabolic rate along with
the necessary circulatory and respiratory costs
(Pennycuick, 1989
). Thus, it
is assumed that a proportion of the total
O2 equal to
basal metabolic rate (BMR) must be spent on general maintenance of tissue
function during flight, while an additional 10% of the remaining
O2 is subtracted
to cover the respiratory and circulatory costs
(Tucker, 1973
; Pennycuick,
1975
,
1989
). Pennycuick
(1975
,
1989
) uses the two basal
metabolic rate equations of Lasiewski and Dawson
(1967
), which give a lower
basal metabolic rate for species of non-passerine than species of passerine
birds. However, I prefer to take values for BMR from the literature where
possible (e.g. Bennett and Harvey,
1987
). In addition, where a suitable measure of BMR is not
available, I used the more recent work of Prinzinger and Hanssler
(1980
), which suggests that,
in general, passerines and non-passerines of a similar body mass have the same
basal metabolic rate, and this is also supported by Reynolds and Lee
(1996
):
![]() | (1) |
In order to estimate values for the
O2max available
for birds for comparison with the data of Hedenström and Alerstam
(1992
), I have essentially
used my model II approach (Bishop,
1997
), which assumes that birds have a similar cardiovascular
performance to that of mammals, and is based on the Fick equation:
![]() | (2) |
where is maximum cardiac output
(ml min-1) and is found to scale as
= 213Mh0.88
± 0.04 (where Mh is in g);
CaO2 is the oxygen content of the arterial
blood (ml O2 100 ml-1 blood) and is calculated as
haemoglobin concentration (in g) per 100 ml blood x1.36 (to calculate
saturated oxygen carrying capacity) and then by 0.94 (assuming 94% saturation
during maximal activity); and
C
O2 is the
oxygen content of the mixed venous blood returning to the heart and is taken
to be 0.038 (ml O2 100 ml-1 blood) under conditions of
O2max (for
details, see Bishop, 1997
).
However, to simplify the calculations and the need to estimate haemoglobin
concentrations for many different species, particularly when applying the
results to the data set of Magnan
(1922), I have used the
simplified general equation for
O2max, which
assumes an average value for haemoglobin concentration based on 15 g
ml-1 blood, where the general equation for mammals was:
![]() | (3) |
Using Eq. 3 and the above assumptions, I have estimated the
O2max available
to the flight muscles and hence Pmet,fm for various bird
species, using relative Mh data from Magnan
(1922
) and Hartman
(1961
), available for each
individual species in the study of Hedenström and Alerstam
(1992
), except for a couple of
cases where I used a value for the same genus or family.
The energetics of forward flapping flight during maximum sustained climbs
Fig. 1 shows the calculated
maximum aerobic Pmet,fm available based on heart mass and
two estimates for maximum Pac (i) based on the data of
Hedenström and Alerstam
(1992) and the default values
of Pennycuick's computer program 1A
(Pennycuick, 1989
, version
1.1) with CD,par ranging from 0.25 to 0.4, and (ii) based
on the same approach but using a constant and low CD,par
of 0.1 for all species (see Pennycuick et
al., 1996
). Data are plotted against body mass for the 15 species
of birds during maximum `sustained' climbing flight
(Hedenström and Alerstam,
1992
).
|
Maximum aerobic Pmet,fm scales as:
![]() | (4) |
and maximum Pac scales as:
![]() | (5) |
or
![]() | (6) |
These estimates for Pmet,fm and Pac clearly have significantly different Mb exponents (F2,39=16.58, P<0.0001). In addition, both the Mb exponents and the coefficients are affected by the changes in default CD,par between the two estimates for Pac, although only the coefficients are significantly different (F1,27=19.68, P<0.0001).
Bishop (1997) showed that
the estimates for total
O2max, based on
measurements of Mh, are reasonably accurate compared to
currently available empirical values from wind tunnel studies, with typical
errors ranging up to a maximum of 17%. Recently, Ward et al.
(2004
) have shown that
measurement of Pmet for starlings Sturnus
vulgaris flying in a wind tunnel were similar when using three different
techniques (doubly-labelled water, mask respirometry and heat transfer
modelling) and that they were also similar to measurements made on free-living
starlings (Westerterp and Drent,
1985
) and those predicted from the cardiac model of Bishop
(1997
). The slightly more
derived estimates for Pmet,fm depend on the validity of
the assumptions for taking into account the costs for maintaining BMR, and
covering the circulatory and respiratory functions. However, these assumptions
should only introduce a minimal amount of additional error as they represent a
relatively small amount of the total energetic costs of flight.
There is currently no similar basis on which to test the aerodynamic
predictions for Pac. Eq. 5 and 6 represent two different
extreme predictions and vary simply due to alterations in the default values
for CD,par. The different values are the result of
differing assumptions with regard to the scaling effect on body drag of
changes in Reynold's number as body mass increases. Eq. 5 is based on
Pennycuick (1975,
1989
, version 1.1) and uses a
default value for CD,par for small birds of 0.4, which is
then reduced in magnitude for larger birds down to 0.25. More recent work
(Pennycuick et al., 1996
)
suggested that CD,par could be as low as 0.05-0.1 for even
relatively small species of birds (based on wing beat frequency and estimates
of minimum power speeds), and so Eq. 6 is based on an extreme hypothesis of
CD,par as 0.1 for all species. However, it should be noted
that Hedenström and Liechti
(2001
) investigated the
maximum diving velocities of a range of small passerines and concluded that
the original default value of 0.4 for CD,par for this
group was probably appropriate. They also found evidence to support the idea
that CD,par should be reduced as Reynold's number
increases.
The `apparent' scaling of flight muscle efficiency during flapping flight
The difference between the calculation for the Pmet,fm
available and the two estimates for the Pac required can
be used to calculate values for the `apparent' scaling of
Efm (Fig.
2). The results indicate that the Efm of birds
performing maximum climbing flights appears to scale positively with respect
to body mass as:
![]() | (7) |
|
or
![]() | (8) |
The value for the wigeon Anas penelope was not included in the
analysis as the calculated efficiency (0.49) was very much higher than any
other species, despite the wigeon being only 0.7 kg in mass. A relative heart
mass value of 0.93% was taken from Magnan
(1922) for the wigeon and it
seems likely that this may be an underestimate. Two other species of the genus
Anas had figures of 1.15% and 1.23%, as reported in Hartman
(1961
), and a relative
Mh of 1.2% would have brought the estimate for efficiency
down to 0.4, which is similar to those calculated for the other species of
migratory wildfowl.
Obviously, the above calculations only represent the apparent
Efm calculated when specifically applying these particular
models for estimating Pmet,fm and Pac
to the climbing flight data of Hedenström and Alerstam
(1992). The general
applicability of this result to bird flight studies will depend on the
validity of a number of potential assumptions, and errors in either model will
lead to errors in the calculations of Efm. The most
striking observation, however, is that the data underlying Eq. 7 exhibit a
2.5-fold range in calculated Efm that scales positively
with respect to body mass, with an exponent of 0.14±0.03. In addition,
despite the overall simplicity of the approach, the average calculated
Efm for the 14 species was 0.27, which is close to the
commonly used value of 0.23 recommended by Pennycuick
(1989
). The average calculated
Efm using a fixed CD,par of 0.1 was
0.2.
Ward et al. (2001)
presented data on the possible Efm of starlings
Sturnus vulgaris flying in a wind tunnel and give a detailed
discussion on previous values calculated for the Efm of
various species of birds. In general, Efm varies from 0.19
to 0.28 for the budgerigar Melopsittacus undulatus
(Tucker, 1968
) up to 0.32-0.4
for the white-necked raven Corvus cryptoleucos
(Hudson and Bernstein, 1983
).
Calculated Efm for the starlings appeared to vary with
flight speed, with a range 0.15-0.23 and an average of 0.18, using the lifting
line model of Pennycuick
(1975
). Mean efficiency was
found to be similar for the starlings when the vortex ring aerodynamic model
of Rayner (1979b
) was used to
estimate biomechanical power, although apparent Efm
appears to increase more steeply with changes in flight speed
(Ward et al., 2001
). The
overall picture from these experimental data sets is that
Efm appears to show a tendency to increase with increasing
body mass and/or decreasing wing-beat frequency, which is consistent with the
modelling approach presented in this review. Clearly, if it really is true
that Efm is a constant value of around 0.23 (e.g.
Pennycuick, 1989
) and does not
scale with body mass or wing-beat frequency, then we require an explanation
that takes into account the systematic change in `apparent'
Efm shown in Fig.
2.
Theoretically, the maximum efficiency of the contractile machinery alone
should not exceed 0.39 (Pennycuick,
1992). As this does not take into account the efficiency of
oxidising fuel substrates to produce ATP, it should not be possible for muscle
fibres to operate with an overall efficiency greater than around 0.28
(Rall, 1985
). Thus, in most
cases muscle fibres are usually assumed to operate with maximal efficiencies
of around 0.2-0.25 (Taylor,
1994
). Logically, even if Efm did initially
scale with body mass, there should come a point for relatively large species
of birds where the Efm must reach a plateau (theoretically
at around 0.28), so that very large birds have greatly reduced sustained
flight performance as a result (Bishop and
Butler, 1995
). It has been suggested that bird
Efm would be expected to scale independently with respect
to body mass (Taylor, 1994
),
as bird wings have to work against their environment. Thus, the flight muscles
should be selected to operate with maximal efficiency and power production
(Rome, 1994
), rather than for
economic force production as appears to be the case in mammals
(Taylor, 1994
). This would
tend to suggest that we should be cautious about the possibility of a 2.5-fold
variation of efficiency in birds. There would appear to be a number of
possible errors in the above analysis of maximum aerobic flight
performance.
The most obvious issue is that the estimated values for
O2max are
inappropriate. I have already argued above that the limited data available on
the circulatory performance of birds during sustainable flight performance are
reasonably consistent with those from mammals during maximal activity
(Bishop, 1997
) and that the
errors involved may only account for around ±20%. Obtaining values of
O2max from birds
during flight is extremely difficult and there is very little data. It is
possible that, as birds tend to maintain slightly higher body temperatures
than mammals, the relationship between
O2max and heart
mass would be slightly greater for birds. Currently, there is insufficient
data on
O2max
and heart mass to show such a difference. However, if this turns out to be the
case, the potential error in the calculation of Efm is
likely to be small, but would reduce it downwards. Of course, errors may also
be introduced due to miscalculations of bird morphologies such as relative
heart mass, haemoglobin concentration, total body mass and relative fat
loading etc. The data for the wigeon suggest that the value for relative
Mh used was probably an underestimate. Likewise, the value
of 1.06% for the relative Mh of the song thrush Turdus
philomelos may also be slightly low, as the values of
Mh for three other species of Turdus taken from
Hartman (1961
) are 1.04%,
1.22% and 1.31%, and this could account for the rather high value of
Efm calculated for this species.
Perhaps the other obvious factor is whether these birds were really
performing at a similar level of `effort' and relatively close to their
maximal aerobic abilities. If not, then this could account for much of the
apparent systematic change in Efm with body mass for the
smaller species. The larger species tended to gain altitude at slower rates
and did not maintain their climbing flights for as long as the smaller
species. As the minimum time recorded for the climbs was 4 min it seems
reasonable to assume that the larger species were probably performing
aerobically and close to their sustainable limits
(Hedenström and Alerstam,
1992). One flock of eider ducks was recorded maintaining near
maximal climbing rates for 25 min. Intermediate sized birds, down to the mass
of the dunlin, tended to show high climb rates well in excess of 4 min, and
data from Piersma et al.
(1990
) indicated that the
dunlin are probably showing climb rates that are proportional to their
relative fuel loads. The very smallest species, the chaffinch, siskin and
swift, exhibited relatively poor maximal climb rates, which were somewhat at
odds with the other species, so it is more difficult to conclude that they are
likely to be near their maximal aerobic capabilities, although they were
flying quite fast horizontally
(Hedenström and Alerstam,
1992
). If these last three species were not as close to their
maximum sustainable climb rates relative to the other species then the
predictions for their rate of
O2 would have
been overestimates and this would have underestimated their flight muscle
efficiencies.
Calculations of Pac are dependent on accurate
measurements of drag coefficients, which are difficult to make
(Pennycuick, 1989;
Spedding, 1994
;
Hedenström and Liechti,
2001
), and there is much uncertainty about the relevant values to
incorporate into aerodynamic models of bird flight. The downwards modification
of the body drag coefficient along the lines suggested by Pennycuick et al.
(1996
) clearly has a
significant influence on the estimation of Pac and,
therefore, the apparent Efm of the flight muscles. The use
of a constant and very low value of 0.1 for CD,par would
reduce all the species estimates of Efm (mean value of
0.2) but it would also increase the scaling exponent from
Mb0.14 to
Mb0.18. The lowering of
CD,par for very small species of birds has not been
justified on aerodynamic grounds
(Hedenström and Liechti,
2001
) and the assumption used by Pennycuick et al.
(1996
) that the minimum
wing-beat frequency can be used to determine the minimum power speed, may not
be valid for all species (Tobalske et al.,
2003
). However, if only the relatively large species of birds,
operating at higher Reynold's numbers, actually have
CD,par around 0.1 or less then this would account for much
of the increase in `apparent' Efm for the larger species.
For example, to bring the Efm estimate for the mute swan
down to around 0.28 would require a Pac value of around
180 W and a CD,par of approximately 0.05, but it would
increase the estimate of the minimum power speed. It is also possible that
some other constant or variable should be adjusted in the model, perhaps
concerning the profile power component
(Rayner, 1999
).
Pennycuick's model approach (Pennycuick,
1975,
1989
) ignores the inertial
costs of accelerating and decelerating the wing. Pennycuick argues that the
wing inertia can be used to do useful aerodynamic work during the deceleration
phase and so it should not be added to the overall costs. This would appear to
be justified, at least for moderate-to-large species of birds, based on the
results of Hedrick et al.
(2004
) and their analysis of
accelerometer measurements of 87 g cockatiels. It is not known, however, if
this result can be applied to very small species of birds, such as
hummingbirds, operating at very high wing-beat frequencies where the inertial
costs may be relatively large (Van den
Berg and Rayner, 1995
). The argument used for hummingbirds is
usually based on the idea that they may have sufficient elastic storage
capabilities that they can store the inertial costs during wing deceleration
and use the energy to reaccelerate the wing on the next beat
(Wells, 1993
;
Chai and Dudley, 1995
). Any
increment of the inertial costs in accelerating the wings of very small
species of birds that must be powered by the flight muscles will increase the
estimate of the `apparent' Efm.
Aerobic flight performance of birds based on heart mass
Despite the uncertainties that underlie some of the assumptions involved in
calculating flight muscle efficiency, it should still be possible to use Eq. 7
to specifically relate these two models for the maximum aerobic
Pmet,fm available
(Bishop, 1997) and the
biomechanical power required (Pennycuick,
1989
, version 1.1) for flight, and to draw some broad conclusions
regarding the aerobic flight performance of particular species of birds. The
first step is to calculate the
O2max for
various species of birds based on measurements of heart mass and convert this
to an estimate for the maximum Pmet,fm available, and then
convert this to an estimate of maximum Pac using Eq. 7. I
shall then compare these values for maximum Pac to those
for the Pmin required to fly from the model of Pennycuick
(1989
, version 1.1). The
predictions for
O2max based on
33Mh0.88 and the predictions for
Pmin based on the aerodynamic model are linked by body
mass, regardless of whether the change is seen between species or within
species. Thus, whenever body mass changes in the calculation a new figure for
Efm must be calculated from Eq. 7.
I shall first apply the above models to the excellent data collected by
Magnan (1922) on the
morphometrics of 228 species of mostly European birds. I shall also consider
the importance of some selected measurements of relative heart masses of birds
reported by Hartman (1961
) and
Crile and Quiring (1940
). All
calculations assume an altitude at sea level (unless otherwise stated). Magnan
(1922
) collected all the
necessary data required to calculate reasonable estimates for the
Pmin required to fly, and to compare them to the potential
maximum Pac of each species, except that his measurements
for wing area did not include the body area between the wings
(Pennycuick, 1989
).
Fortunately, Hartman (1961
)
measured the glide, tail and wing area of 340 species of birds. By subtracting
the wing and tail areas from the glide area for each species we can estimate
the value for body area, which gives a value for the scaling of body area with
respect to body mass as:
![]() | (9) |
Using Eq. 9 I have arrived at a slightly modified value for the wing areas
for Magnan (1922).
Fig. 3 shows the ratio of
the calculated maximum Pac available divided by the
estimated Pmin required plotted against
Mb (numbered species are listed in
Appendix B).
Fig. 4 uses the same data to
plot the mean family ratio of the Pac available /
Pmin required. It is clear from Figs
3 and
4 that the majority of birds,
particularly those less than 0.1 kg in mass, appear to have more than enough
power available to `sustain' at least Pmin (i.e. a
Pac/Pmin ratio >1) and some of the
smaller species appear to be able to sustain up to 3 times the
Pmin required. If we assume that the intra-species scaling
of the power required to fly scales at around
Mb1.59
(Rayner, 1990), then a species
with a ratio of Pac/Pmin >3 should
be able to sustain Pmin (in level flight at sea level)
when carrying approximately an additional 100% of body mass. Of course, the
predicted minimum flight speed will also increase and the bird will probably
not be able to take off or land, so this prediction is likely to be a bit
optimistic in reality. Errors in the data set will also make individual
assessments even more imprecise along with the difficult of motivating a bird
to give it a try in the first place! Interestingly, Dial and Biewener
(1993
) reported on some
load-carrying flights for two captive pigeons Columba livia trained
to fly for 20 m to a perch in an enclosed hall. These two birds could carry
and take off from the ground with a weighted backpack representing an
additional 50% of body mass and could even manage level flapping flight with
100% additional mass if assisted into the air. Although C. livia was
not included in the data of Magnan
(1922
), there is data for
C. palumbus, C. oenas and Turtur turtur. All three species
are morphologically similar, with average relative Mh of
1.32%, flight muscle masses of 27.3% and a calculated aerobic
Pac/Pmin ratio of 2.05 (1.8, 2.7 and
1.65, respectively). The Pac/Pmin
ratio of
2 certainly appears broadly consistent with the data of Dial and
Biewener (1993
) for C.
livia.
|
|
|
Species with ratios >3 have relatively large Mh and,
usually, large wing areas and/or high aspect ratio wings, and include some
examples of finches, swifts, swallows and martins, common tern, hobby, knot,
red kite among others. In general, the reverse is true for those species that
fall below the line for a ratio of 1, and these include species such as
grouse, pheasants, partridge, an eagle owl and the red-winged tinamou. Also of
interest are those relatively large species of birds (>2 kg), which have a
ratio between 1 and 3, and these include species such as the common cormorant,
gannet, eagles, vultures, storks, geese, whooper swan, wandering albatross and
the European great bustard. These latter species are tending to show
morphological adaptations either to reduce the costs of flight or to supply
increased metabolic input to the muscles. Clearly, despite the uncertainties,
some species of birds have a significant amount of extra aerobic capacity
above the minimum requirement. Presumably, these abilities have evolved to
provide added load lifting and/or enhanced climbing performance as well as the
ability to fly much faster than the minimum or even maximum range speed if
necessary. However, the results of Ward et al.
(2001) appear to indicate that
estimates of Efm increase with flight speed, at least for
the starling, so that birds flying close to their minimum power speeds may
operate with a lower Efm than when near their maximum
aerobic speeds. Maximum reported Efm for the two starlings
was 0.2 and 0.3, which is similar to that of 0.21 calculated from Eq. 7 for a
species of similar body mass. This supports the general approach in estimating
maximum Pac using Eq. 7, but also suggests that the excess
metabolic capacity above that required to support Pmin
would not be as great as the biomechanical capacity, which is plotted in Figs
3 and
4.
The relative heart mass of the bustard family (Otidae) appears to be
unusually large compared to other birds of their mass
(Bishop, 1997). The estimated
Pac for a 9 kg European great bustard Otis tarda
is 242 W based on a value for Mh of 1.4%
(Magnan, 1922
), which is 20%
greater than the estimated Pmin (208 W). The
Pac for a large male Kori bustard Ardeotis kori
studied by Pennycuick (1969
),
and using a value of 1.0% for Mh
(Crile and Quiring, 1940
), is
246 W, which is just below Pmin at both 1500 m (300 W)
where the bird was studied, and for sea level (278 W).
The large aerobic capability of some species relative to others requires
considerable differences in the biochemistry of their flight muscles
(Pennycuick and Rezende, 1984;
Rosser and George, 1986
). In
particular, the relatively aerobic nature of the flight muscles of some
relatively large species of birds, such as the bustards and swans, has
important implications for the interpretation of the size limitations to the
flight performance of birds. The flight muscles of medium to large species of
birds are of a mixed composition, with some fast glycolytic (FG) fibres
specialised primarily for anaerobic metabolism and some fast oxidative
glycolytic (FOG) fibres specialised primarily for aerobic metabolism
(Rosser and George, 1986
).
Thus, it is necessary to distinguish between `burst' flight performance, and
`prolonged' or aerobic flight performance
(Marden, 1994
), and to compare
flight muscles that are adapted for similar types of flight. The data of
Marden (1987
) and Pennycuick
et al. (1989
) on the maximum
load lifting ability of flying animals refer only to `burst' flight
performance, and bird species that have predominantly FG flight muscle fibres
will be at an advantage compared to species with predominantly FOG fibres.
Limitations to muscle mass-specific power output
A number of studies contain observations about the limits to bird flight performance that include implicit assumptions concerning the flight muscles, but which do not take explicit account of possible differences in the `physiological' or functional characteristics of those flight muscles. Two examples are discussed below, during which I shall assume that all the flight muscle myofibrils are recruited during burst flight activity, while only those fibres that reside in the highly oxygenated regions of the flight muscles are recruited during aerobically `prolonged' activity.
Example 1
Ellington (1991) concludes
that perhaps the available Pmech may not be limiting burst
flight performance in large birds, as the analysis of Marden
(1987
,
1990
) suggests that the 12 kg
Kori bustard should just be capable of a standing take-off, although this is
apparently not the case (Pennycuick,
1969
). In contrast, Marden
(1994
) observed that the 10 kg
North American wild turkey Meleagris gallopavo was capable of a
near-vertical take-off from a standing start. Like other Galliformes, the
turkey probably has a relatively small Mh and the flight
muscles are relatively large and predominately made up of FG fibres
(Rosser and George, 1986
).
This contrasts with the Kori bustard, which has a relatively large
Mh of 1% (Crile and
Quiring, 1940
) but moderately sized pectoralis musculature of
around 16.4% (Pennycuick,
1969
). Therefore, the average body mass-specific mass of myosin
and actin myofibrils in the Kori bustard is probably considerably lower than
those of large Galliformes such as the wild turkey. If we assume that the FOG
fibres of large birds can only deliver 2/3 of the Pmech of
FG fibres and that the Kori bustard's flight muscles are composed of 50% FOG
and 50% FG, then the Pmech would be 5/6 of the predicted
value if the muscles were made up of 100% FG, i.e. equivalent to a flight
muscle ratio of only 13.7%. In addition, some account must be taken of the
altitude at which the Kori bustard was studied. Therefore, in the case of the
Kori bustard at 1500 m, it may still be that the available
Pmech was limiting take-off performance. The lowland
living European great bustard has both a relatively larger
Mh of 1.4% and relatively larger flight muscles of 22.5%
(Magnan, 1922
) and appears to
be capable of local migratory flights. I would predict that this species
should be more capable during take-off than that of the Kori bustard. This
argument would also apply to birds such as swans, which have a relatively
large Mh (around 1.1%). Thus, when considering `burst'
flight performance such as required for take-off, the important variable is
not the flight muscle mass ratio but the myofibrillar protein mass ratio.
Example 2
Gudmundsson et al. (1995)
studied the migration of brent geese Branta bernicla from Iceland to
Greenland, and tracked them by satellite as they flew up to and across the
Greenland ice-cap. These authors concluded that the failure of brent geese
(fitted with 57 g satellite transmitters) to fly continuously over the
Greenland ice-cap supports the predictions of Pennycuick
(1969
,
1989
), that the myofibrillar
mass-specific Pmech available from the flight muscles
per se scales directly in proportion to wing beat frequency, so that
large birds should show a severely restricted capacity to fly with heavy fuel
burdens during climbing flight. Gudmundsson et al.
(1995
) contrast this
prediction with the conclusions of Marden
(1987
) and Ellington
(1991
) that the size-dependent
Pmech constraints may not be so acute. However, the
results of Marden's studies are only relevant to the first few seconds of
flight and so large species of birds would not be capable of sustaining these
power outputs. As we have seen, this is primarily due to the negative scaling
of the mass-specific oxygen supply to the muscles, due to the reduction in the
maximum heart beat frequency with increasing body mass and the failure of
relative Mh to scale positively in order to compensate for
this shortfall. Thus, while anaerobic flight performance may be almost
independent of body mass, the aerobic flight performance of relatively large
birds such as geese must decline. Marden's results should, therefore, be fully
compatible with the study by Gudmundsson et al.
(1995
) and explain why these
geese would have been able to perform the presumably short anaerobic flights
required for them to travel over the Greenland ice-cap.
The biomechanical Pac calculated for the brent geese
(estimated Mb of 1.364 kg) tracked climbing at 0.53 m
s-1 over southern Sweden, at a horizontal speed of 16.4 m
s-1, was 32 W, of which 7.1 W was required for the climb
(Hedenström and Alerstam,
1992). The first 21 km of the Greenland ice-cap would have
required brent geese to climb at a rate of around 0.7 m s-1, using
an additional 2.3 W, or 7% extra Pmech. Thus, it would
appear that the birds migrating across Sweden with a relatively low fat
loading (estimated ratio of 1.1 with a lean mass of 1.24 kg) and at low
altitude would not have been capable of flying aerobically up the first face
of the Greenland ice-cap, but it would have been a close call. The next 95 km
required a climb rate of only 0.21 m s-1 and the Swedish brent
geese should have been able to cope with the second part of the climb. Indeed,
one flock of 26 Swedish greylag geese Anser anser (estimated
Mb of 3.58 kg) achieved an overall climb rate of 0.32 m
s-1 for 20 min (Hedenström
and Alerstam, 1992
).
Post-moult adult barnacle geese Branta leucopsis with a body mass
of 1.8 kg have a relative heart ventricular mass of 0.86%, while pre-migratory
barnacle geese with a body mass of 2.372 kg have a relative ventricular mass
of 0.83% (Bishop et al., 1998).
Thus, it seems reasonable to assume that the pre-migratory brent geese
preparing to head towards Greenland might have showed a similar heart
hypertrophy and could retain a relative heart mass of around 1.07% of body
mass (Magnan, 1922
) during the
migration. Gudmundsson et al.
(1995
) calculated a
provisional estimate of 1.8 kg for the body mass of the brent geese as they
arrived at Greenland, which would require a Pmin of 37 W.
A relative Mh of 1.07% would yield an estimated
Pac of 44.6 W (at an apparent efficiency of 34%), giving a
climb power of only 7.6 W, instead of the 12.4 W required for the first phase
of the climb. The second phase of the climb would have required only 3.7 W of
climbing power and, therefore, it should have been possible to maintain
flight. These calculations suggest, at the very least, that even a shallow
climb could bring these migratory geese close to the threshold of their
aerobic abilities. Any further burden, such as that caused by carrying a 57 g
satellite transmitter, may have forced them to utilise supplementary anaerobic
metabolism. This could have forced them to take much longer over the traverse
of Greenland, as lactate takes much longer to remove from the tissues than to
produce it.
In conclusion, I suggest that the empirical data of Gudmundsson et al.
(1995) are compatible with the
predictions of Marden (1987
,
1990
) and Bishop
(1997
) and show that it is not
the Pmech available from the flight muscle myofibrils
per se that is primarily limiting the performance of larger migratory
birds. When considering aerobic flight performance, the important variable is
the body mass ratio of the mass of myofibrils that can be continuously
supported by the surrounding tissue.
Myofibrillar mass-specific power output
Data from Marden (1987,
1990
) showed that flight
muscle mass-specific lifting force during take-off appeared to scale almost
directly with body mass, and was not closely correlated with wing beat
frequency (assuming no additional inertial energy is required). Ellington
(1991
) also interpreted these
data to indicate that muscle mass-specific `burst' Pmech
might even scale with a very slightly positive exponent with respect to body
mass. Pennycuick (1969
,
1989
) predicted that
regardless of the muscle type, the mass-specific Pmech
should scale directly with wing beat frequency, i.e. negatively relative to
increasing body mass, as work per unit myofibrillar mass should be a constant.
The data of Marden (1987
,
1990
) appear to contradict
these predictions. Detailed work on the take-off performance of different
species of Phasianidae have also shown that myofibrillar power output appears
to show very little scaling with body mass
(Askew et al., 2001
).
Little is known, however, about prolonged or aerobic flight performance.
The original calculations of Hedenström and Alerstam
(1992) also appeared to
contradict the predictions for muscle mass-specific power output of Pennycuick
(1969
,
1989
) and, similar to that of
take-off power, the maximal Pac appears to scale almost
directly with respect to body mass and flight muscle mass
(Mfm) as Pac =
128Mfm0.978. These authors assumed that flight
muscle mass was around 20% of lean body mass. I have recalculated their data
using flight muscle masses from the literature, as flight muscle mass can be
more accurately estimated from Magnan
(1922
) and Hartman
(1961
) for all 15 species
(except for the eider duck, for which I used data from
Parker and Holm, 1990
), and
these values can vary greatly from that of 20% (data in
Appendix A). In addition, I
have used actual body mass as the reference (rather than lean body mass),
because it is clear from numerous studies that flight muscles are dynamic
structures that usually undergo hypertrophy in association with total body
mass changes (Fry and Ferguson-Lees,
1972
; Marsh, 1984
;
Driedzic et al., 1993
;
Bishop et al., 1996
;
Lindström et al., 2000
;
Swaddle and Biewener, 2000
).
Unfortunately, even this is a simplification as small species may tend to
exhibit a relatively smaller hypertrophy than larger species (cf.
Driedzic et al., 1993
).
Nevertheless, the results again support the apparent scaling of
Pac almost independently of body mass and flight muscle
mass (Pac = 109Mfm1.01). If
we plot estimated
O2max against
body mass we find that it scales as
O2max =
274Mb0.807, which is not quite directly
proportional to that for wing-beat frequency, where fH =
5.33Mb-0.139.
If we plot
O2max against
flight muscle mass we find that it scales as
O2max =
880Mfm0.837, which demonstrates that the
relative volume of blood being delivered to the flight muscles declines as
bird species scale up in mass. This explains why larger species of birds must
develop flight muscles with mixed fibre type compositions. We might
hypothesise that blood flow to the muscles should be in proportion to their
aerobic or FOG fibre content, with the consequence that the effective
proportion of flight muscle actually being recruited during maximum
sustainable climbing flights would decline as the bird species increased in
mass. If the
O2max estimates
based on Mh from Bishop
(1997
) are reasonable and
Efm were really a constant then we would predict that
Pac per unit FOG muscle mass, or perhaps more accurately
per FOG myofibrillar protein mass, would be a constant
(M1.0) as appears to be the case for `burst' power output
(Marden, 1987
;
Ellington, 1991
;
Askew et al., 2001
). If the
scaling of Pac follows the predictions calculated from
Pennycuick's model (Pennycuick,
1989
, version 1.1) and the volume of FOG fibres in the flight
muscles is proportional to the estimated
O2max based on
Bishop (1997
), then it would be
predicted that Pac should scale with respect to FOG
myofibrillar protein mass with an exponent of around M1.17
or more, which might seem unlikely.
Discussion
In conclusion, there would appear to be insufficient data to completely
differentiate between the hypotheses that the `true' Efm
is either a constant, or that it scales with a positive exponent with respect
to body mass for smaller species followed by a plateau for the larger species.
However, given the extremely simple models used in the current analysis and
the uncertainties regarding the maximal climbing rates of the smaller species
studied by Hedenström and Alerstam
(1992), there is a close
agreement between the expected Efm of around 0.2-0.25 and
the overall average calculated value of 0.2-0.27. The Efm
values for the larger species are unacceptably high but it could be argued
that it is these very species that are most likely to be flying close to their
maximal capabilities. Either the heart mass approach underestimates maximal
O2max for these
species, or the aerodynamic model is overestimating the
Pac, or both. It is possible that the values used for
Mh are too low or that there is an additional influence of
an increase in haemoglobin
(Landys-Ciannelli et al.,
2002
), which would lead to an underestimate of
O2max. If avian
cardiac hypertrophy has the potential to be very rapid, as in the Burmese
python Python molurus (Andersen et
al., 2005
), then it may be necessary to sample birds actually
migrating in order to accurately assess their relative heart size. It is
tempting to assume that the smaller species of passerines were not flying near
their maximum capabilities but Hedenström and Alerstam
(1992
) point out that both the
chaffinch and the siskin were flying forward at quite a fast speed for their
body mass. The swift would appear to be the weakest performer overall. While
it would seem to be impossible that the larger species could really have such
high Efm, it remains possible that the smaller species
that are operating with relatively high wing-beat frequencies are suffering a
real reduction in Efm, as appears to be the case for
hummingbirds (assuming perfect elastic storage of inertial energy). The
resolution of these issues is only likely to come from studying species at
either extreme of the size range.
Current aerodynamic theories suggest that for birds of similar proportions
the cost of flight should scale as Mb1.17, and
this exponent will be slightly reduced due to the tendency for larger birds to
have higher aspect ratio wings (Pennycuick,
1989,
1996
). During primarily
anaerobic `burst' activity this scaling exponent for the power required could
be partially compensated for by having a larger mass of total myofibrils per
unit Mb. This might be done by increasing the proportion
of anaerobic fibre types within the flight muscle without increasing the
relative Mfm per unit Mb.
Alternatively, a similar result could be achieved by increasing the total
relative Mfm. However, as we have seen
Mfm generally scales independently of
Mb so it would appear that the latter strategy is not
adopted by larger species of flying animals. Why not?
Ultimately, sustained flight performance is constrained by the performance
of the respiratory and cardiovascular system. For birds specialising in
prolonged flight it would be wasteful to have an ability to take-off with a
body mass that greatly exceeded it's ability to sustain that mass during
forward flight (although it might improve take-off speed and, therefore,
predator avoidance). The empirical evidence is that
O2max scales
approximately with Mh0.88±0.02, and that
Mh scales approximately as
Mb0.91±0.01, with the result that
O2max scales
with respect to both Mb and Mfm with
an exponent of approximately Mb0.82±0.08
(Bishop, 1997
). Why not
increase relative Mh? If the analysis of Bishop
(1997
) is broadly accurate,
then for a large bird to maintain a similar body mass-specific
O2max as that of
a smaller bird, Mh must increase with respect to around
Mb1.13. Eventually, whatever the exact nature
of the limiting factors, the upward divergence from direct proportionality
might prove to be too costly.
It is interesting that one of the most extreme examples from the
Mh data sets of Magnan
(1922) and Hartman
(1961
) is that of the Otidae.
If these medium-to-large, savannah-living birds, had flight muscles consisting
completely of anaerobic FG fibres (perhaps similar to the Phasianidae), rather
than a mosaic of FG and FOG fibres, then they might be capable of a standing
take-off but at the cost of only being able to fly for an extremely limited
distance and becoming highly vulnerable to cursorial predation. As they are
not forest dwelling species like the Phasianidae, the bustard's best strategy
is a compromise in which it is able to sustain flight for long enough to cover
a sufficient distance as to exceed the give-up time of any potential
predators. The only alternative strategy would be to give up flight altogether
and to become a fast runner like the ostrich Struthio camelus.
Studies of exercising mammals and migratory species of birds have indicated
that both the pectoralis and cardiac musculature are dynamic structures that
can vary in mass seasonally and in direct response to changing circumstances
(Marsh, 1984;
Bishop et al., 1996
;
Lindström et al., 2000
;
Swaddle and Biewener, 2000
).
This raises the interesting question as to whether the appropriate response in
any given situation, or for a particular species, should be primarily
anaerobic or aerobic. Maximal animal flight performance reflects a continuum
between species specialised for burst activity, through to species adapted
primarily for prolonged activity. Wing morphology can modify, to a certain
extent, the power required for flight, but the power available is provided by
the wing and cardiac muscles. If a species is adapted for prolonged flight
activity then there may be a cost to carrying large amounts of anaerobic
muscle fibres, or even excess aerobic fibres that cannot be adequately
perfused by the blood supply. Thus, even large species of birds, such as
swans, which undertake long distance aerobic flights, appear to have fairly
average sized flight muscle masses of between 18-22%
(Magnan, 1922
;
Hartman, 1961
). However, even
these species have anaerobic FG fibres, which are presumably important in
providing extra power during take-off and brief manoeuvres. It would be
expected that birds undergoing premigratory fattening before long distance
flights should require an hypertrophy of both FG and FOG fibres. It would seem
to be logical that these species only acquired sufficient FG fibres to enable
them to take-off with a load that is not much greater than that which can then
be supported aerobically by the FOG fibres, during subsequent prolonged
flights.
One way of reducing the requirement to have large amounts of excess FG
fibres is to gain speed by running before taking off, and a number of species
of birds that are capable of prolonged types of flapping flight run across the
surface of the ground (or water) before becoming airborne. Thus, the flight
muscles of most extant species of birds that are capable of prolonged flight
are likely to reflect the compromise between the `burst' power required for
take-off and the aerobic power required to sustain flight. The `running
take-off' of some large bird species, such as swans, could be viewed as a
behavioural adaptation to minimise the mass of the additional FG fibres
required for take-off, thus optimising the requirement for
O2 and the
number of FOG fibres in order to prolong flight activity and/or improve
aerobic load-lifting capacity. Likewise, the relatively small flight muscle
mass of diving species, such as the red-throated diver Gavia
stellata, could be viewed as being the result of selection for enhanced
underwater swimming performance. Running during take-off for this species
could then be viewed as a behavioural adaptation for improved diving
efficiency.
Acknowledgments
I would like to thank the two anonymous referees for their helpful comments.
References
Andersen, J. B., Rourke, B. C., Caiozzo, V. J., Bennett, A. F. and Hicks, J. W. (2005). Postprandial cardiac hypertrophy in pythons. Nature 434,37 -38.[CrossRef][Medline]
Askew, G. N., Marsh, R. L. and Ellington, C. P.
(2001). The mechanical power output of the flight muscles of
blue-breasted quail (Coturnix chinensis) during take-off.
J. Exp. Biol. 204,3601
-3619.
Bennett, P. M. and Harvey, P. H. (1987). Active and resting metabolism in birds: allometry, phylogeny and ecology. J. Zool. Lond. 213,327 -363.
Bishop, C. M. (1997). Heart mass and the maximum cardiac output of birds and mammals: Implications for estimating the maximum aerobic power input of flying animals. Phil. Trans. R. Soc. Lond. B 352,447 -456.[CrossRef]
Bishop, C. M. (1999). The maximum oxygen consumption and aerobic scope of birds and mammals: getting to the heart of the matter. Proc. R. Soc. Lond. B 266,2275 -2281.[CrossRef][Medline]
Bishop, C. M. and Butler, P. J. (1995). Physiological modelling of oxygen consumption in birds during flight. J. Exp. Biol. 198,2153 -2163.[Medline]
Bishop, C. M., Butler, P. J., El Haj, A. J., Egginton, S. and Loonen, M. J. J. E. (1996). The morphological development of the locomotor and cardiac muscles of the migratory barnacle goose (Branta leucopsis). J. Zool. 239, 1-15.
Bishop, C. M. Butler, P. J., El Haj, A. J. and Egginton, S. (1998). Comparative development of captive and migratory populations of the barnacle goose. Physiol. Zool. 71,198 -207.[Medline]
Bishop, C. M., Ward, S., Woakes, A. J. and Butler, P. J. (2002). The energetics of barnacle geese (Branta leucopsis) flying in captive and wild conditions. Comp. Biochem. Physiol. 133,225 -237.
Butler, P. J. (1991). Exercise in birds. J. Exp. Biol. 160,233 -262.
Chai, P. and Dudley, R. (1995). Limits to vertebrate locomotor energetics suggested by hummingbirds hovering in heliox. Nature 377,722 -725.[CrossRef]
Crile, G. and Quiring, D. P. (1940). A record of the body weight and certain organ and gland-weights of 3690 animals. Ohio J. Sci. XL,219 -259.
Dial, K. P. and Biewener, A. A. (1993).
Pectoralis-muscle force and power output during different modes of flight in
pigeons (Columba livia). J. Exp. Biol.
176, 31-54.
Driedzic, W. R., Crowe, H. L., Hicklin, P. W. and Sephton, D. H. (1993). Adaptations in pectoralis muscle, heart mass, and energy metabolism during premigratory fattening in semipalmated sandpipers (Calidris pusilla). Can. J. Zool. 71,1602 -1608.
Ellerby, D. J., Cleary, M., Marsh, R. L. and Buchanan, C. I. (2003). Measurement of maximum oxygen consumption in guinea fowl Numida meleagris indicates that birds and mammals display a similar diversity of aerobic scopes during running. Physiol. Biochem. Zool. 76,695 -703.[CrossRef][Medline]
Ellington, C. P. (1991). Limitations on animal flight performance. J. Exp. Biol. 160, 71-91.
Fry, C. H. and Ferguson-Lees, I. F. (1972). Flight muscle hypertrophy and ecophysiological variation of yellow wagtail (Motacilla flava) races at Lake Chad. J. Zool. Lond. 167,293 -306.
Gudmundsson, G. A., Benvenuti, S., Alerstam, T., Papi, F., Lilliendahl, K. and Åkesson, S. (1995). Examining the limits of flight and orientation performance: satellite tracking of brent geese migrating across the Greenland ice-cap. Proc. R. Soc. Lond. B 261,73 -79.
Hammond, H. K., White, F. C., Bhargava, V. and Shabetai, R. (1992). Heart size and maximal cardiac output are limited by the pericardium. Am. J. Physiol. 263,H1675 -H1681.[Medline]
Hartman, F. A. (1961). Locomotor mechanisms of birds. Smithson. Misc. Collns 143, 1-91.
Hedenström, A. and Alerstam, T. (1992). Climbing performance of migrating birds as a basis for estimating limits for fuel-carrying capacity and muscle work. J. Exp. Biol. 164, 19-38.
Hedenström, A. and Liechti, L. (2001).
Field estimates of body drag coefficient on the basis of dives in passerine
birds. J. Exp. Biol.
204,1167
-1175.
Hedrick, T. L., Usherwood, J. R. and Biewener, A. A.
(2004). Wing inertia and whole-body acceleration: an analysis of
instantaneous aerodynamic force production in cockatiels (Nymphicus
hollandicus) flying across a range of speeds. J. Exp.
Biol. 207,1689
-1720.
Hickson, R. C., Galassi, T. M. and Dougherty, K. A.
(1983). Repeated development and regression of exercise-induced
cardiac hypertrophy in rats. J. Appl. Physiol.
54,794
-797.
Hudson, D. M. and Bernstein, M. H. (1983). Gas exchange and energy cost of flight in the white-necked raven, Corvus crytoleucus. J. Exp. Biol. 103,121 -130.[Abstract]
Koteja, P. (1987). On the relation between basal and maximum metabolic rate in mammals. Comp. Biochem. Physiol. 87,205 -208.[CrossRef]
Kvist, A., Lindström, Å., Green, M., Piersma, T. and Visser, G. H. (2001). Carrying large fuel loads during sustained bird flight is cheaper than expected. Nature 413,730 -732.[CrossRef][Medline]
Landys-Ciannelli, M. M., Jukema, J. and Piersma, T. (2002). Blood parameter changes during stopover in a long-distance migratory shorebird, the bar-tailed godwit Limosa lapponica taymyrensis. J. Avian Biol. 33,451 -455.[CrossRef]
Lasiewski, R. C. and Calder, W. A. (1971). A preliminary allometric analysis of respiratory variables in resting birds. Respir. Physiol. 11,152 -166.[CrossRef][Medline]
Lasiewski, R. C. and Dawson, W. R. (1967). A re-examination of the relation between standard metabolic rate and body weight in birds. Condor 69,13 -23.
Lindström, Å., Kvist, A., Piersma, T., Dekinga, A.
and Dietz, M. W. (2000). Avian pectoral muscle size rapidly
tracks body mass changes during flight, fasting and fuelling. J.
Exp. Biol. 203,913
-919.
Magnan, A. (1922). Les caracteristiques des oiseaux suivant le mode de vol. Ann. Sci. Nat., ser. 10, 5,125 -334.
Marden, J. H. (1987). Maximum lift production during takeoff in flying animals. J. Exp. Biol. 130,235 -258.
Marden, J. H. (1990). Maximum load-lifting and induced power output of Harris' hawks are general functions of flight muscle mass. J. Exp. Biol. 149,511 -514.
Marden, J. H. (1994). From damselflies to pterosaurs: how burst and sustainable flight performance scale with size. Am. J. Physiol. 266,R1077 -R1084.[Medline]
Marsh, R. L. (1984). Adaptations of the gray catbird Dumatella carolinensis to long-distance migration: flight muscle hypertrophy associated with elevated body mass. Physiol. Zool. 57,105 -117.
Masman, D. and Klaassen, M. (1987). Energy-expenditure during free flight in trained and free-living Eurasian kestrels (Falco tinnunculus). Auk 104,603 -616.
Parker, H. and Holm, H. (1990). Patterns of nutrient and energy expenditure in female common eiders nesting in the high arctic. Auk 107,660 -668.
Pennycuick, C. J. (1969). The mechanics of bird migration. Ibis 111,525 -556.
Pennycuick, C. J. (1972). Animal flight. The Institute of Biology's Studies in Biology no. 33. London: Edward Arnold (Publishers) Limited.
Pennycuick, C. J. (1975). Mechanics of flight. In Avian Biology, vol. 5 (ed. D. S. Farner and J. R. King), pp. 1-75. New York: Academic Press.
Pennycuick, C. J. (1982). The flight of petrels and albatrosses (Procellariiformes), observed in South Georgia and its vicinity. Phil. Trans. R. Soc. B 300,75 -106.
Pennycuick, C. J. (1989). Bird Flight Performance. Oxford: Oxford University Press.
Pennycuick, C. J. (1992). Newton Rules Biology: A Physical Approach to Biological Problems. Oxford: Oxford University Press.
Pennycuick, C. J. (1996). Stress and strain in the flight muscles as constraints on the evolution of flying animals. J. Biomech. 29,577 -581.[CrossRef][Medline]
Pennycuick, C. J., Fuller, M. R. and McAllister, L. (1989). Climbing performance of Harris' hawks (Parabuteo unicinctus) with added load: implications for muscle mechanics and for radiotracking. J. Exp. Biol. 142, 17-29.
Pennycuick, C. J., Fuller, M. R., Oar, J. J. and Kirkpatrick, S. J. (1994). Falcon versus grouse-flight adaptations of a predator and its prey. J. Avian. Biol. 25, 39-49.
Pennycuick, C. J., Klaasen, M., Kvist, A. and Lindström,
Å. (1996). Wingbeat frequency and the body drag
anomaly: wind-tunnel observations on a thrush nightingale (Luscinia
luscinia) and a teal (Anas crecca). J. Exp.
Biol. 199,2757
-2765.
Pennycuick, C. J. and Rezende, M. A. (1984). The specific power output of aerobic muscle, related to the power density of mitochondria. J. Exp. Biol. 108,377 -392.
Piersma, T., Zwarts, L. and Bruggemann, J. H. (1990). Behavioural aspects of the departure of waders before long-distance flights: flocking, vocalizations, flight paths and diurnal timing. Ardea 78,157 -184.
Prinzinger, R. and Hanssler, I. (1980). Metabolism-weight relationship in some small non-passerine birds. Experientia 37,1299 -1300.
Rall, J. A. (1985). Energetic aspects of skeletal muscle contraction: Implications of fiber types. Exer. Sport Sci. Rev. 13,33 -74.[Medline]
Rayner, J. M. V. (1979a). A new approach to animal flight mechanics. J. Exp. Biol. 80, 17-54.
Rayner, J. M. V. (1979b). A vortex theory of animal flight. Part 2. The forward flight of birds. J. Fluid Mech. 91,731 -763.
Rayner, J. M. V. (1988). Form and function in avian flight. Curr. Orn. 5, 1-77.
Rayner, J. M. V. (1990). The mechanics of flight and bird migration performance. In Bird Migration: Physiology and Ecophysiology (ed. E. Gwinner), pp.283 -299. Berlin: Springer-Verlag.
Rayner, J. M. V. (1999). Estimating power
curves of flying vertebrates. J. Exp. Biol.
202,3449
-3461.
Reynolds, P. S. and Lee, R. M. (1996). Phylogenetic analysis of avian energetics: Passerines and nonpasserines do not differ. Am. Nat. 147,735 -759.[CrossRef]
Rome, L. C. (1994). The mechanical design of the muscular system. Adv. Vet. Sci. Comp. Med. 38A,125 -179.[Medline]
Rosser, B. W. C. and George, J. C. (1986). The avian pectoralis: histochemical characterization and distribution of muscle fiber types. Can. J. Zool. 64,1174 -1185.
Spedding, G. R. (1994). On the significance of unsteady effects in the aerodynamic performance of flying animals. Cont. Math. 141,401 -419.
Stray-Gundersen, J., Musch, T. I., Haidet, G. C., Swain, D. P., Ordway, G. A. and Mitchell, J. H. (1986). The effect of pericardiectomy on maximal oxygen consumption and maximal cardiac output in untrained dogs. Circ. Res. 58,523 -530.[Abstract]
Swaddle, J. P. and Biewener, A. A. (2000). Exercise and reduced muscle mass in starlings. Nature406 , 585-586.[CrossRef][Medline]
Taylor, C. R. (1994). Relating mechanics and energetics during exercise. Adv. Vet. Sci. Comp. Med. 38A,181 -215.[Medline]
Tobalske, B. W., Hedrick, D. L., Dial, K. P. and Biewener, A. A. (2003). Comparative power curves in bird flight. Nature 421,363 -366.[CrossRef][Medline]
Tucker, V. A. (1968). Respiratory exchange and evaporative water loss in the flying budgerigar. J. Exp. Biol. 48,67 -87.
Tucker, V. A. (1973). Bird metabolism during flight: evaluation of a theory. J. Exp. Biol. 58,689 -709.
Van den Berg, C. and Rayner, J. M. V. (1995). The moment of inertia of bird wings and the inertial power requirement for flapping flight. J. Exp. Biol. 198,1655 -1664.[Medline]
Ward, S., Moller, U., Rayner, J. M. V., Jackson, D. M., Bilo,
D., Nachtigall, W. and Speakman, J. R. (2001). Metabolic
power, mechanical power and efficiency during wind tunnel flight by the
European starling Sturnus vulgaris. J. Exp.
Biol. 204,3311
-3322.
Ward, S., Moller, U., Rayner, J. M. V., Jackson, D. M.,
Nachtigall, W. and Speakman, J. R. (2004). Metabolic power of
European starlings Sturnus vulgaris during flight in a wind tunnel,
estimated from heat transfer modelling, doubly labelled water and mask
respirometry. J. Exp. Biol.
207,4291
-4298.
Weibel, E. R., Taylor, C. and Hoppeler, H.
(1991). The concept of symmorphosis: A testable hypothesis of
structure-function relationship. Proc. Natl. Acad. Sci.
USA 88,10357
-10361.
Wells, D. J. (1993). Muscle performance in
hovering hummingbirds. J. Exp. Biol.
178, 39-57.
Westerterp, K. and Drent, R. (1985). Energetic costs and energy-saving mechanisms in parental care of free-living passerine birds as determined by the D2O method. Acta XVIII int. Ornithol. Congr. 1,392 -398.
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