Harmonic oscillatory orientation relative to the wind in nocturnal roosting flights of the swift Apus apus
Department of Animal Ecology, Ecology Building, Lund University, S-22362 Lund, Sweden
* e-mail: Johan.Backman{at}zooekol.lu.se
Accepted 11 December 2001
![]() |
Summary |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Key words: common swift, Apus apus, flight, Fourier transform, harmonic oscillation, orientation, roosting, wind, tracking radar, autocorrelation
![]() |
Introduction |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Here, we have chosen a selection of trackings of considerably longer duration, lasting up to 1 h, to analyse in detail the flight behaviour of individual roosting swifts. If we assume that the swifts try to remain as stationary as possible relative to the ground, there will be three different situations with respect to the wind: (i) the wind speed is higher than the flight (air) speed of the swift, (ii) the wind speed is approximately equal to the air speed of the swift and (iii) the wind speed is lower than the air speed of the swift. We predict that, in situations i and ii, the swifts should orient consistently into the wind direction, as we observed previously from the short-duration trackings. The variation in flight direction relative to the wind should be small, and flight paths relative to the air should be straight. In case i, we would expect the swifts to drift `backwards'. In case ii, in contrast, we would expect the drift to be small and in a random direction. An especially interesting situation emerges in case iii, when the wind speed is considerably lower than the flight speed of the swift. In this case, there is a potential risk that the swifts will overshoot their desired stationary position relative to the ground.
When swifts maintain their mean flight direction into the wind in a weak
wind, as demonstrated in our previous study
(Bäckman and Alerstam,
2001), the risk of displacement could be dealt with in a number of
ways. (i) `Don't care' maintain the headwind direction without
variation. The swift will overshoot maximally by air speed x time (for
negligible wind speed) and potentially face a return flight in the morning of
the same distance. Usually, there is some wind, and the displacement distance
will then be shorter and the return flight will also take place with a
favourable tail wind. (ii) Circle in the absence of wind, this will be
the optimal solution. In light winds, the phase of headwind flying should, on
average, be longer than the tailwind phase, with the proportion of time spent
flying into opposing winds increasing with increasing wind speed. (iii) Keep
the average flight direction into the wind and let the instantaneous flight
direction fluctuate around the mean direction, alternately to the left and
right of the headwind course in a more-or-less cyclic way.
In this study, we investigate long nocturnal flights of swifts, as recorded by tracking radar, to determine the patterns of flight paths and orientation behaviour at different wind speeds. At high wind speeds, we expect straight flights relative to the air, with the swifts consistently oriented into the wind, thus minimising displacement during the night. In contrast, at wind speeds below the swifts' air speed, we expect more sophisticated strategies of circling, or oscillating and meandering orientation, effectively neutralising any long-term resulting movement over the ground.
![]() |
Materials and methods |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
For a sample of targets considered to be swifts (N=21), we
recorded and analysed the wingbeat frequency. The wingbeat frequency was
7.0-8.3Hz (mean 7.6Hz), which is in good agreement with earlier recordings for
roosting swifts (Bruderer and Weitnauer,
1972). We tracked only single birds, and our intention was to
track each individual for as long as possible. The radar recorded azimuth,
elevation and range every 2s. The accuracy of radar measurements was limited
to 0.06° in angle (azimuth, elevation) and 10m in range. Wind data were
collected every second hour by releasing and tracking helium balloons.
Azimuth, elevation and range were transferred from the radar to a computer
every 2s by automated data-logging software. Horizontal and vertical positions
were calculated. The position data were averaged from five successive
readings, and the resulting 10s intervals were used to calculate the speed and
track direction (the ground speed vector) of the target. Air speed and heading
direction (the air speed vector) were calculated for each 10s interval by
vector subtraction of the wind velocity at the altitude at which the bird was
flying from its ground speed vector. We used the heading, which is the
directional part of the air speed vector, for further analyses of the swifts'
orientation.
Calculations of mean directions, mean vector lengths (r) and
circular statistics were performed according to Batschelet
(1981). The heading in relation
to the wind (H-W) corresponds to the angular difference between
heading (H) and wind (W) direction; H-W=0° thus
means that the swift is flying straight into the headwind,
H-W=90° that it is heading perpendicular to the wind and
H-W=180° that it is flying in the direction of the tailwind. An
index of straightness (IS) was calculated by dividing the length of
the resulting flight vector by the cumulative sum of the subvectors of each
10s interval. IS is a measure of the straightness of the flight path
and ranges from 0 for a flight with the same start and end positions to 1 for
a perfectly linear flight path. We calculated the index of straightness for
the flight path both relative to the ground (ISg) and
relative to the surrounding air (ISa).
To investigate the flight behaviour in relation to the wind, we focused on
the variations in H-W during a single flight of a swift. To detect
any periodicity in the heading fluctuations relative to the wind direction,
individual H-W data were analysed (i) by autocorrelation for periods
up to n/2, where n is the total number of 10s intervals for
the complete track of an individual swift, and (ii) by frequency analysis,
using the discrete Fourier transform (DFT)
(Chatfield, 1996;
Priestley, 1981
). In the DFT
analysis, the H-W data were first `normalised' (residual values from
a linear regression were used) and windowed with the Hanning function. We then
applied a discrete Fourier transform to the data. The resulting power spectrum
was tested for significant (P<0.05) frequency components
(
2-test of sample spectrum estimator for white noise)
(Jenkins and Watts, 1968
). If
there was more than one significant frequency component, we selected the
strongest. We used MATLAB v5.2 (The MathWorks Inc., MA, USA) for all
calculations, and the built-in FFT function for the DFT analysis. As a
control, we applied DFT analysis to 12 long trackings of climbing helium
balloons, using the same criteria as for the analysis of bird trackings, and
found no significant frequency components.
![]() |
Results |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
|
Fig. 1 illustrates three sample tracks. Tracks A and B are from swifts flying in moderate winds (7-8 m s-1), and track C is from a swift flying in weak winds. In moderate winds, the swifts often move rather slowly over the ground. The swift in track A has a net movement towards the wind direction because the air speed of the swift (9.9 m s-1) is higher than the wind speed (6.9 m s-1). The resulting ground speed is much lower (3.9 m s-1). The heading direction of the swift in track A fluctuates around the headwind direction and causes an undulating movement sideways but, on average, the difference between the heading and wind direction (H-W) is only 0.6° and ISa=0.97. The swift in track B also flies with a mean heading direction almost straight towards the wind (H-W is on average 9°). In track B, the air speed of the swift (8.9 m s-1) and the average wind speed (8.1 m s-1) are very similar. Early in the observed track, the swift shows the same behaviour as in track A, with H-W fluctuating around zero, but after approximately 500s the heading direction is on average slightly to the right of the wind direction; H-W>0. This causes a resulting slow movement relative to the ground, perpendicularly and to the right of the wind direction (track B). The ISa is 0.98, revealing a very consistent orientation into the wind.
|
In track C, the wind speed is only 2.9 m s-1, which is far below the air speed of the swift (10.2 m s-1). Ground speed is on average 9.6 m s-1. The swift changes its heading continuously and apparently without consideration of the wind direction. There are several circling flights, and the ISa is only 0.31. The slightly higher air speed of this swift may be associated with the fact that it is descending gently (vertical speed -0.4 m s-1) in contrast to cases A and B where the swifts fly at almost constant altitude (vertical speeds +0.15 m s-1 and -0.1 m s-1 respectively).
The index of straightness relative to the ground ISg does not vary significantly with wind speed (Fig. 2A). However, we observed only a small number of swifts flying at wind speeds lower than 5 m s-1. For the index of straightness relative to the air, ISa (Fig. 2B), the result is slightly clearer. For wind speeds over 8 m s-1, the flight paths in relation to the surrounding air are very straight, but there are a few cases with low ISa values at lower wind speeds.
|
We were particularly interested in analysing the flight behaviour of the swifts in relation to the wind direction. In Fig. 3, we illustrate the time series (10 s intervals) of H-W over the entire tracking for the same three trackings as in Fig. 1. In tracks A and B, the deviations in flight direction from the wind direction are rather small (within ±50°). In contrast, H-W in track C fluctuates widely. The largest amplitudes are actually an artefact, since we are displaying data with a circular distribution on a linear scale (H-W=+180° is the same as H-W=-180°). In the case of tracks A and B, this does not matter because the deviations from H-W=0° are small (H-W is far less than ±180°, see below), but in case C, where the bird sometimes flies in circles, this way of analysing course fluctuations becomes inappropriate. Rapid shifts from H-W=+180° to H-W=-180° should be interpreted as circling flights.
|
In the second column in Fig. 3, we have analysed the autocorrelation of the H-W values shown in the first column for tracks A and B. There is an indication of a cyclic component in the undulating flight path of track A with a period of approximately 160 s. The corresponding DFT analysis also shows that the dominant and only statistically significant frequency component is approximately 7 mHz (seven cycles in 1000 s). In track B, there are no such clear-cut oscillations of the flight path in the autocorrelation analysis. The DFT power spectrum shows a number of components, the strongest, but not significant, component being approximately 2.5 mHz. It is not appropriate to analyse track C with this method since this swift was flying in circles.
We performed these analyses on all swift tracks where there were no circling flight paths. The results of the DFT and autocorrelation analyses are presented in Fig. 4, where we have divided the values into discrete categories. We found significant frequency components in 36 trackings and distinct autocorrelation periods in 31 cases, out of 49 trackings. There was no correlation between the wind speed and the observed distinct autocorrelation periods or between wind speed and significant frequency components (Fig. 5A,B).
|
|
![]() |
Discussion |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Because of the time resolution of 10s for the time series, we cannot detect frequencies higher than 50 mHz, corresponding to a period of 20s. In our set of data, the shortest period was 40s and the highest frequency was 20 mHz, which are well within our resolution. Furthermore, it is not possible to detect frequencies lower than two periods during a flight path. Since the average tracking duration is 1366s (Table 1), there are few opportunities of finding periods longer than 683s (approximately 11 min), corresponding to a frequency of approximately 1.5 mHz. Still, some very low significant frequencies and long periods emerged from the analyses of the longest radar trackings in our data set, with the lowest frequency at 0.3 mHz and the longest period at 25 min. Thus, it is possible that there exist even slower cyclic patterns than we have described here.
There seemed to be no consistent relationship between cycle
period/frequency of orientation changes and wind speed
(Fig. 5). This provides no
support for our expectation that swifts might show a regular variation of
their orientation primarily to remain stationary relative to the gound when
flying in rather slow winds. Thus, the possible function of the cyclic
orientation changes during the swifts' flights is unclear. However, we found
that the swifts' flights were sometimes less straight, and occasional circling
occurred, at low wind speeds (Fig.
2), which will contribute to reducing the displacement with
respect to the ground during the night. The cyclic variation in the swifts'
orientation may reflect a behaviour in which the birds do not adjust their
orientation continuously, but rather correct or over-correct it at regular
intervals. However, we found no evidence for any well-defined characteristic
frequency/period for these course corrections. Such behaviour might be
associated with a reduced level of alertness if the swifts are, in some sense,
`sleeping' during their nocturnal flights
(Lack, 1956), or it may be a
phenomenon associated with bird orientation in general.
This is, to our knowledge, the first study in which the existence of harmonic oscillations in birds' orientation has been investigated and demonstrated. We have shown that Fourier and autocorrelation analyses provide useful tools for such investigations of orientation time series. The finding that swifts flying at night orient into the wind and weave slowly from side to side by varying their heading into the wind direction with a cycle period of 1-16 min is intriguing. Perhaps this remarkable behaviour is associated with the swifts' special ability to orient into the wind during the night and at high altitudes. What is the sensory basis for such behaviour? Is such a behaviour also involved in the orientation of other birds, for example on their migratory flights? Unfortunately, these questions cannot be answered from our existing data, and we have to limit ourselves to proving that oscillatory orientation occurs in the roosting flights of swifts.
This finding may be of potential importance for understanding the process of bird orientation. Further analyses of the pattern of variation in orientation of free-flying birds and of birds in orientation cages are needed to determine whether such cyclic heading changes should be regarded as a normal feature of bird orientation or whether they are confined to the special case of nocturnal roosting flights of swifts orienting into a headwind.
![]() |
Acknowledgments |
---|
![]() |
References |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Bäckman, J. and Alerstam, T. (2001). Confronting the winds: orientation and flight behaviour of roosting swifts, Apus apus. Proc. R. Soc. Lond. B 268,1081 -1087.[Medline]
Batschelet, E. (1981). Circular Statistics in Biology. London: Academic Press.
Bruderer, B. and Weitnauer, E. (1972). Radarbeobachtungen über Zug und Nachtflüge des Mauerseglers (Apus apus). Rev. Suisse Zool. 79,1190 -1200.[Medline]
Chatfield, C. (1996). The Analysis of Time Series. London: Chapman & Hall.
Jenkins, G. M. and Watts, D. G. (1968). Spectral Analysis and its Applications. San Fransisco: Holden-Day.
Lack, D. (1956). Swifts in a Tower. London: Methuen.
Priestley, M. B. (1981). Spectral Analysis and Time Series, Vols 1 and 2. London: Academic Press.
Weitnauer, E. (1952). Übernachtet der Mauersegler, Apus apus, in der Luft? Orn. Beobachter 51,37 -44.
Weitnauer, E. (1954). Weiterer Beitrag zur Frage des Nächtigens beim mauersegler, Apus apus. Orn. Beobachter 51,66 -71.
Weitnauer, E. (1960). Über die Nachtflüge des Mauerseglers, Apus apus. Orn. Beobachter 57,133 -141.