The energetic cost of variations in wing span and wing asymmetry in the zebra finch Taeniopygia guttata
1 Aberdeen Centre for Energy Regulation and Obesity, School of Biological
Sciences, University of Aberdeen, Aberdeen AB24 2TZ, Scotland, UK
2 The Waltham Centre for Pet Nutrition, Waltham-on-the-Wolds,
Leicestershire, LE14 4RT, England, UK
3 Aberdeen Centre for Energy Regulation and Obesity, Division of Energy
Balance and Obesity, Rowett Research Institute, Bucksburn, Aberdeen AB21 9BS,
Scotland, UK
* Author for correspondence (e-mail: c.hambly{at}rowett.ac.uk)
Accepted 10 August 2004
![]() |
Summary |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Key words: flight cost, wing asymmetry, labelled bicarbonate technique, zebra finch, Taeniopygia guttata, kinematics
![]() |
Introduction |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
It may be that traits used during courtship for sexual selection express
higher correlations with stress and therefore may be a reliable indicator of
individual `quality' (Moller and
Pomiankowski, 1993; Grammer et
al., 2003
). Female birds often choose mates with the biggest,
brightest and most symmetrical sexual ornaments. The handicap hypothesis
(Zahavi, 1975
) indicates that
males with such ornamentation are more preferable to the opposite sex because
the ornaments are costly to maintain, and by implication males that have
survived such costs must have good genes to pass on to their offspring. If
asymmetry causes an increased energy cost of flight or affects flight
performance, then according to the handicap theory, females might be expected
to select males that are the most asymmetrical, because these individuals
would have a larger handicap. However, Moller's developmental stability model
(Moller, 1992b
) suggests that
females should mate with more symmetrical males because symmetry is an
indication of the genomes ability to buffer against environmental and genetic
stresses.
It has been suggested that birds with bigger sexual ornaments must maintain
a high degree of symmetry to reduce the costs of having the ornament
(Evans et al., 1994). However,
in horned beetles Onthophagus taurus, larger sexually selected traits
are more asymmetrical (Hunt and Simmons,
1997
). Consequently, it is possible that some traits are more
important when choosing a mate than others, with size being selected over
symmetry because the size of the trait depends highly on stresses affecting
the individual (Hunt and Simmons,
1997
; Bjorksten,
2000
).
Wing feathers in birds show less extreme asymmetry than tail feathers, and
natural asymmetries in wing feathers are lower in birds that spend a higher
proportion of the day in flight (Balmford
et al., 1993). If asymmetry occurs in the primary flight feathers,
the consequences include a reduction in flight performance. Additionally there
may also be raised energetic costs. If flight behaviour is affected there may
be a change in flight parameters such as speed or wing beat frequency. If
there is a cost for having asymmetrical wings, it may therefore be energetic,
behavioural, or a direct impact on the fitness of the individual via
mate choice.
The fitness and behavioural consequences of being asymmetrical are well
documented. For example, zebra finches Taeniopygia guttata made
asymmetrical by adding different coloured leg bands had significantly fewer
offspring than symmetrically banded males
(Swaddle, 1996). Birds can
therefore suffer from a reduced reproductive success as a result of asymmetry
(Forkman and Corr, 1996
;
Moller, 1992b
). Behavioural
consequences include increased predation due to a decreased flight performance
(Moller, 1996
;
Moller and Nielsen, 1997
;
Swaddle, 1997
), or increased
mortality such as in laying hens Gallus gallus domesticus, where
larger asymmetrical birds tend to be cannibals while smaller asymmetrical
birds are cannibalised (Yngvesson and
Keeling, 2001
). Little is known about the energetic consequences.
The energetic consequences of a reduction in wingspan, however, can be
predicted using aerodynamic theory (e.g.
Pennycuick, 1989
;
Pennycuick et al., 1996
;
Rayner, 1999
). Pennycuick
(1989
;
Pennycuick et al., 1996
)
developed a simple computer program that allows predictions to be made of
mechanical flight costs in individuals of known mass and wingspan. The program
predicts that reducing wingspan by 5% in a 20 g bird will increase the
mechanical flight cost by around 7.3%. This program, however, assumes that the
reduction in wingspan is symmetrical, affecting both wings by the same degree,
and cannot make any predictions about the energetic effects of asymmetry. The
energetic cost of wing asymmetry therefore needs to be determined
empirically.
In this study we aimed to investigate whether there are energetic and/or behavioural costs associated with artificially increasing wing asymmetry in zebra finches, and if energetic costs correspond with the predictions from aerodynamic theory based on span change alone. Natural asymmetries in wild animals do not lend themselves to testing ideas about energy costs of asymmetry, because natural asymmetries may involve other conflicting factors such as parasitism that may incidentally affect energy expenditure. Artificially manipulating asymmetry in healthy captive birds controls for the effects of natural stresses that cause asymmetry. We therefore examined the energetic cost of flight before and after a series of manipulations to the wing area and span, in addition to examining the time-averaged wing kinematics to evaluate any related change in behaviour.
![]() |
Materials and methods |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
![]() | (1) |
![]() | (2) |
Wing manipulations
The energy cost of flight was measured in 17 zebra finches. Bird mass
(±0.01 g) was recorded prior to each flight and wing areas and spans
were measured prior to and after manipulation, both by photography and drawing
around the outstretched wings on graph paper. The wings were carefully
stretched out to the same degree in all birds to maintain a comparable
estimate of area across individuals. From the wing tracings, the squares were
counted to measure the combined area of the two wings and body, excluding the
head and tail. In addition, the birds were photographed using a Leitz Reprovit
camera (GMBH Wetzler, Germany) based around a Leica M3 camera system. The wing
outlines from the photographs (excluding the head and tail) were traced onto
acetate and transferred onto a PC using PC Image for Windows, which was used
to calculate the area after calibration using known areas. The area
calculations were averaged for each bird. For the flight study the birds were
placed in the same cylindrical Plexiglas® chamber as was used in the
calibration. Dried air was pumped through the chamber at the same rate as used
during the calibrations (485 ml min1). Unlabelled breath
samples were taken every minute for 4 min prior to injection to obtain a basal
enrichment level for 13C. A weighed volume of 0.2 ml of the same
0.29 mol l1 NaH13CO3 solution as used
in the calibration was then administered via an intraperitoneal
injection. The bird was returned to the chamber and breath samples were
collected 1014 min after injection. At 15 min after injection the bird
was released from the chamber and encouraged to fly between two perches, 20 m
apart, for a timed period of approximately 2 min. The bird was then rapidly
re-caught and placed back in the chamber where further breath samples were
collected for the following 8 min. Flights were simultaneously filmed using a
Hi-8 video camera (Sony CCD-V800E) to measure the total time in flight to the
nearest second and mean flight speed. In addition a Kodak EM high-speed video
camera was used to film each flight at a frequency of 500 frames
s1. This recorded 19 s of footage for each flight. The video
footage was used to examine mean wing beat frequency (Fb),
wing amplitude and up- and downstroke duration during each flight. Three
repeated flights were completed for each individual on separate days.
After completion of the initial flights, three different wing manipulations occurred. The birds were given a minimum of 4 days to adjust to the manipulation and were then involved in further flight measurements. The first two manipulations produced an artificial wing asymmetry as well as changes in wingspan and area. First, approximately 0.5 cm was trimmed off each primary feather of the right wing in ten individuals. Then a further 0.5 cm was trimmed from six of these birds, making the total feather loss up to 1.0 cm of the primary feathers of the right wing. The final manipulation controlled for the effects caused by changes in wingspan and area while still maintaining wing symmetry. To achieve this reduction approximately 0.25 cm was trimmed off the primary feathers of both wings in seven different individuals. Birds were photographed and traced again following manipulation, and the flight procedure and filming was repeated three further times on each bird. High-speed video footage was examined to calculate wing kinematics by slowing the 19 s of footage recorded to individual frames. The exact time for each wing beat or up- and downstroke duration could be calculated to the nearest 0.002 s. This was repeated for at least 20 beats throughout the film duration for Fb and at least three measurements for up- and downstroke duration for birds flying both towards and away from the camera. Wing amplitude was measured by freezing the frame at the top of the wing beat and tracing the wing angle on acetate. The point at the tip of the beak was also marked. The film was then forwarded to the point when the wing was at the bottom of the wing beat and the acetate was placed over the bird with the beak in the same location and the wing retraced. The angle between the up- and downstroke was calculated. Flight speed was measured by slowing the normal high-8 video down to individual frames, and accurately measuring the time taken to fly between the perches located 20 m apart. A minimum of ten flights between perches were timed and these were spread over the whole 2 min flight interval consisting of flights both towards and away from the camera.
Data analysis
Values are means ± standard error (S.E.M.) unless
otherwise stated. Repeated one-way analysis of variance (ANOVA), multiple
linear regression and paired t-tests were applied to our data using
Minitab 11 software.
![]() |
Results |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Flight costs
Flight energy costs were calculated using the protocol described by Hambly
et al. (2002). In brief, each
flight was not continuous as the birds rested intermittently on perches at
either end of the flight corridor. The time resting on the perches was
calculated from the high-8 video footage, and the flight was assumed to have
occurred continuously in the middle of the flight period, preceded and
succeeded by rest time of equal duration. As with a previous study on zebra
finches (Hambly et al., 2002
)
the relationship between the time since injection and the log-converted
isotope enrichment was linear prior to the flight
(Fig. 1). After flight the
enrichment rose to a peak on average 4 min after the end of flight, and then
declined. A second-order polynomial best fitted this pattern of elimination,
in all cases. The resulting best-fit regression equations for the enrichment
decline with time were extrapolated to the adjusted time when the flight began
and ended, accounting for the time spent on the perches. This generated two
estimated enrichments, the gradient between them being the isotope elimination
rate during the flight (kc). This kc
was interpolated onto the calibration equations (Equations
1 and
2) to predict the oxygen
consumption and carbon dioxide production during flight, which was converted
to energy expenditure in W using the measured respiratory quotient (RQ;
Hambly et al., 2004
).
|
Flight cost in the pre-manipulated individuals averaged 1.90±0.1 W. There was a significant difference in the mean flight costs measured in different individuals (one-way ANOVA; F16,47=4.1, P<0.001). Some individuals flew with a consistently higher flight cost than others. A multiple-linear regression model was used to examine the morphological and behavioural parameters that were related to flight cost (in the pre-manipulated birds). These parameters included mean flight speed, wing beat frequency, wing area and span, body mass, amplitude, up- and downstroke duration and wing loading. The only parameters that had a significant influence on flight cost were body mass (regression; F1,47=5.5, P=0.02), mean wing amplitude (regression; F1,43=6.4, P=0.02) and wing span (regression; F1,47=4.7, P=0.04) (Fig. 2).
|
The differences between the flight energy costs (W) of the pre and post-manipulated birds were calculated (Table 1 and Fig. 3). After trimming approximately 0.5 cm of the right wing, all but one bird maintained normal flight between the perches. One individual (Pink 141) had difficulty maintaining flight and the flight cost after manipulation was 3x that from before manipulation. This bird was removed from the study. Excluding this individual, the mean difference in flight cost when 0.5 cm was trimmed from the right wing was slightly increased from the pre-manipulated flight cost (0.04±0.1 W). This difference was not significant (paired t-test; T=0.3, P=0.8). After removing a further 0.5 cm from six of these birds there was an increase in flight cost, with a difference from the pre-manipulated birds of 0.12±0.2 W, which was also not significantly different to the pre-manipulated cost (paired t-test; T=0.6, P=0.6). The birds used in the third `control' manipulation, where 0.25 cm was trimmed from the primary feathers of both wings, had a significant increase in flight cost compared to the pre-manipulated birds (paired t-test; T=3.8, P=0.01) with a mean difference of 0.45±0.2 W (Fig. 3).
|
|
The relationships between flight cost and wingspan and body mass in the pre-manipulated birds were significant, with flight cost decreasing with a larger body mass and increasing with a larger wingspan (Fig. 2). These results, however, were not consistent with our findings when wingspan was experimentally manipulated. Body mass remained the same in the experimentally manipulated birds (paired t-test; P>0.05), while wingspan was reduced and the resulting flight cost increased, which is opposite to the predictions of the multiple linear regression model. Flight cost differences with changes in wingspan within individuals due to our manipulations were, therefore, inconsistent with the natural differences observed between individuals.
Wing kinematics
Wing beat frequency (Fb) ranged between 19.6 and 28.7
beats s1 and increased with the loss of wing area from each
manipulation. The increase in mean Fb when 0.5 cm was
trimmed from one wing, compared to pre-manipulated values, was 1.1±0.6
beats s1. This increase was not significant (paired
t-test; T=1.8, P=0.1). There was a larger increase
(2.6±0.6 beats s1) when 1.0 cm was removed from one
wing, which was significantly different from the Fb of the
same individuals prior to wing trimming (paired t-test;
T=4.0, P=0.01). When 0.25 cm was trimmed from both wings the
average difference in Fb from the pre-manipulated value
was also significantly higher, by 1.87±0.5 beats s1
(paired t-test; T=4.0, P=0.007)
(Fig. 4).
|
Wing amplitude in the pre-manipulated birds averaged 121.4±1.34°. When the right wing was trimmed to produce an asymmetry the mean wing amplitude of the right wing did not differ from the same individuals prior to manipulation (P>0.05) but the left wing increased in amplitude, with the change becoming larger and significant the greater the extent of asymmetry (paired t-test; 0.5 cm trimmed, T=2.07, P=0.07; 1.0 cm trimmed, T=3.3, P=0.002). However, when the wings were altered by removing 0.25 cm off both wings but maintaining symmetry, neither the left nor right wing amplitude changed from the pre-manipulated value (paired t-test; left wing, T=0.29, P=0.78; right wing, T=0.69, P=0.52; Fig. 5)
|
In addition to the adaptations in wing amplitude and wing beat frequency there were changes in both up- and downstroke duration. The left wing up- and downstroke durations did not significantly differ from pre-manipulated values (P>0.05), but the right wing up- and downstroke durations significantly decreased (0.5 cm removed, paired t-test; upstroke T=3.32, P=0.01, downstroke T=3.56, P=0.008; 1.0 cm removed, paired t-test; upstroke T=4.31 P=0.008, downstroke T=6.17, P=0.002; Fig. 6). When the wings were trimmed on both sides wing stroke duration achieved a significant increase on both the left (paired t-test; T=2.80, P=0.031) and the right upstroke (paired t-test; T=4.07, P=0.007; Fig. 6).
|
Flight speed ranged between 4.7 and 7.6 m s1. The increase in flight speed from the speed recorded in the pre-manipulated individuals was 0.2±0.2 m s1 higher when 0.5 cm was trimmed (paired t-test; T=1.3, P=0.2) and 0.5±0.3 m s1 higher when 1.0 cm was trimmed (paired t-test; T=2.2, P=0.1), neither of which were significantly higher than pre-manipulation values (Fig. 7). When both wings were trimmed to be symmetrical there was a significant decrease in flight speed of 0.6±0.2 m s1, compared to the pre-manipulated individuals (paired t-test; T=3.3, P=0.02).
|
In summary, when birds were manipulated to become asymmetric by trimming the primary feathers on one wing, there was no significant increase in flight cost. The birds responded to the change in wing area by maintaining flight speed. They also increased the left wing amplitude and decreased the right up- and downstroke durations to counteract the changes in wing shape, which meant that they had an increase in wing beat frequency. In contrast, when the wing area was reduced by 3.2% while maintaining symmetry, the birds had a significantly elevated flight cost combined with a slower flight speed. In this case wing amplitude did not change and wing upstroke slightly decreased causing an increased wing beat frequency.
Aerodynamic models
Two aerodynamic models were used to predict the effect that the change in
wingspan would have on flight cost; the Pennycuick
(1989) model, which is a
simplistic model using wing span, area and body mass to predict flight costs,
and the Rayner (1999
) model,
which uses other kinematic parameters of speed, wing beat frequency,
amplitude, up/down stroke ratio and estimates for stroke plane angle relative
to the horizon and the body, which were assumptions taken from Tobalske et al.
(1999
) for the appropriate
average speed. These models predict mechanical power, which has to be
converted to metabolic power using the measured efficiency. The efficiency was
measured by dividing the measured flight cost in pre-manipulated birds by the
mechanical flight cost prediction from the model. The efficiency for the
pre-manipulated birds using the Pennycuick model was 13.01% while the Rayner
model predicted an efficiency of 13.17%. These values were used to convert
predicted mechanical power from the models to estimate total power for the
future manipulations. The models did not predict a significant change in
flight cost using the individual bird data, for any of the manipulations
(P>0.05) with similar differences in flight costs compared to the
pre-manipulated values.
![]() |
Discussion |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Thomas (1993) stated that
there are two possibilities that birds could use to overcome the impacts of
asymmetry. The first is to pull the longer wing in to equal the length of the
shorter one, which will be costly unless the bird flies above normal cruising
flight speeds. As the cost did not increase dramatically with increasing
asymmetry and the birds did not significantly increase their flight speed in
this study, they were unlikely to be using this method to compensate. In
addition, when both wings were trimmed, reducing the span in the same way as
pulling in one wing, there was a significant increase in flight cost. An
alternative hypothesis (Thomas,
1993
) was that the birds might counteract the spanwise
distribution of lift across the wings, by altering either the camber or the
angle of attack independently in each of the wings. Our kinematic data
indicated that the birds did alter the amplitude of the longer wing while
reducing the stroke duration of the shorter wing, supporting this latter
hypothesis.
In the control group, where the span and area were reduced without changing
the symmetry, flight cost did increase. If Thomas'
(1993) second hypothesis is
correct, then when wing area was reduced while maintaining symmetry, the
spanwise distribution of lift across the wings would be symmetrical and
therefore, beating both wings independently could not compensate for the
change in area.
Pennycuick's aerodynamic model
(Pennycuick, 1989) predicted
that using the mean wingspan, area and body mass in the pre-manipulated birds
there would be an increase in flight cost of 7.3% with a reduction in wingspan
of 5%. This does not account for asymmetrical changes in wingspan or
adaptations to behaviour, which reduced the affect for the birds in this
study. When flight costs are examined over a range of speeds, the resulting
relationship tends to conform to either a U-shaped
(Pennycuick et al., 1996
) or
J-shaped (Rayner, 1999
) curve.
These models predict that at low or high flight speeds the energetic cost
would increase, with an optimum `minimum power' speed
(Vmp) where the bird flies at the lowest power
requirement. Using the mean body mass and wingspan for the birds in the
present study and keeping all other factors constant, the minimum power speed
was predicted to be 5.7 m s1 using the Pennycuick model and
4.3 m s1 using the Rayner model. The pre-manipulated birds
were initially flying, on average, above the minimum power speed at 6.3 m
s1, which may be attributed to the short distance that they
were flying over and the range of behaviours that are involved in repeated
take-off and landings. When the primary feathers were asymmetrically trimmed,
flight speed did not change and there was therefore no associated increase in
flight cost. However, when the wings were trimmed symmetrically, the speed was
reduced to be closer to Vmp and therefore flight cost
should also have decreased. Instead, contradictory to the models, flight cost
increased by 24.7%. Tobalske et al.
(1999
) examined the effect
that changes in speed had on flight kinematics of zebra finches. A reduction
in speed was associated with a reduction in wing beat frequency while
increasing the wing amplitude. When symmetry was maintained while reducing
wing span, speed reduced, but the expected associations were not present. Wing
amplitude did not alter while wing beat frequency increased. This may explain
why flight cost in these individuals did not follow the patterns predicted by
the aerodynamic models and care must be taken when using models for birds that
are in moult or have undergone stresses, which have a different wing shape
from the norm.
In conclusion the birds observed in this study were able to modify their
behaviour to respond to the imposed asymmetrical morphological changes
minimising the impact on flight energetics. Consequently any costs of
asymmetry are likely to be manifested primarily as behavioural effects, which
may affect the risk of predation (Moller,
1996; Moller and Nielsen,
1997
; Swaddle,
1997
).
![]() |
Acknowledgments |
---|
![]() |
References |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Balmford, A., Jones, I. L. and Thomas, A. L. R. (1993). On avian asymmetry: evidence of natural selection for asymmetrical tails and wings in birds. Proc. R. Soc. Lond. B 252,245 -251.
Bjorksten, T. A. (2000). Fluctuating asymmetry of sexual and non-sexual traits in stalk-eyed flies: a poor indicator of developmental stress and genetic quality. J. Evol. Biol. 13,89 -97.[CrossRef]
Bjorksten, T. A., Fowler, K. and Pomiankowski, A. (2000). What does sexual trail FA tell us about stress? Trends Ecol. Evol. 15,163 -166.[CrossRef][Medline]
Evans, M. R., Martins, T. L. F. and Haley, M. (1994). The asymmetrical cost of tail elongation in red billed streamertails. Proc. R. Soc. Lond. B 256,97 -103.
Forkman, B. and Corr, S. (1996). Influence of size and asymmetry of sexual characteristics in the rooster and hen on the number of eggs laid. Appl. Anim. Behav. Sci. 49,285 -291.[CrossRef]
Grammer, K., Fink, B., Moller, A. P. and Thronhill, R. (2003). Darwinian aesthetics: sexual selection and the biology of beauty. Biol. Rev. 78,385 -407.[CrossRef][Medline]
Hambly, C., Harper, E. J. and Speakman, J. R. (2002). Cost of flight in the zebra finch (Taenopygia guttata): a novel approach based on elimination of 13C labelled bicarbonate. J. Comp. Physiol. 172,529 -539.[CrossRef]
Hambly, C., Pinshow, B., Wiersma, P., Verhulst, S., Piertney, S.
B., Harper, E. J. and Speakman, J. R. (2004). Comparison of
the cost of short flights in a nectarivorous and a non-nectarivorous bird.
J. Exp. Biol. 207,3959
-3968.
Hunt, J. and Simmons, L. W. (1997). Patterns of fluctuating asymmetry in beetle horns: and experimental examination of the honest signalling hypothesis. Behav. Ecol. Sociol. 41,109 -114.[CrossRef]
Kellner, J. R. and Alford, R. A. (2003). The ontogeny of fluctuating asymmetry. Amer. Nat. 161,931 -947.[CrossRef][Medline]
Moller, A. P. (1992a). Patterns of fluctuating asymmetry in weapons: evidence for reliable signalling of quality in beetle horns and bird spurs. Proc. R. Soc. Lond. B 248,199 -206.
Moller, A. P. (1992b). Female swallows preference for symmetrical male sexual ornaments. Nature 357,238 -240.[CrossRef][Medline]
Moller, A. P. (1996). Sexual selection, viability selection and developmental stability in the domestic fly Musca domestica. Evolution 50,746 -752.
Moller, A. P. and Nielsen, J. T. (1997). Differential predation costs of a secondary sexual character: sparrow hawk predation on barn swallows. Anim. Behav. 54,1545 -1551.[CrossRef][Medline]
Moller, A. P. and Pomiankowski, A. (1993). Fluctuating asymmetry and sexual selection. Genetica 89,267 -279.
Pennycuick, C. J. (1989). Bird Flight Performance: A Practical Calculation Manual. Oxford: Oxford University Press.
Pennycuick, C. J., Klaassen, 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.
Putman, R. J. and Sullivan, M. S. (2000). Fluctuating asymmetry in the antlers of fallow deer (Dama dama): the relative roles of environmental stress and sexual selection. Biol. J. Linn. Soc. 70,27 -36.[CrossRef]
Rayner, J. M. V. (1999). Estimating power
curves for flying vertebrates. J. Exp. Biol.
202,3449
-3461.
Ruben, G. I. (1992). Plasticity of development in natural and experimental populations of Siberian sturgeon Acipenser baeri Brandt. Acta. Zool. Fenn. 191, 43-46.
Swaddle, J. P. (1996). Reproductive success and symmetry in zebra finches. Anim. Behav. 51,203 -210.[CrossRef]
Swaddle, J. P. (1997). Developmental stability and predation success in an insect predator-prey system. Behav. Ecol. 8,433 -436.[Abstract]
Swaddle, J. P. and Witter, M. S. (1994). Food feathers and fluctuating asymmetry. Proc. R. Soc. Lond. B 255,147 -152.
Thomas, A. L. R. (1993). The aerodynamic cost of asymmetry in wings and tails of birds: asymmetric birds can't fly round tight corners. Proc. R. Soc. Lond. B 254,181 -189.
Tobalske, B. W., Peacock, W. L. and Dial, K. P.
(1999). Kinematics of flap-bounding flight in the zebra finch
over a wide range of speeds. J. Exp. Biol.
202,1725
-1739.
Yngvesson, J. and Keeling, L. J. (2001). Body size and fluctuating asymmetry in relation to cannibalistic behaviour in laying hens. Anim. Behav. 61,609 -615.[CrossRef]
Zahavi, A. (1975). Mate selection a selection for a handicap. J. Theor. Biol. 53,205 -214.[Medline]