Characterisation and identification of the navigational processes in homing pigeons

With the help of miniaturized GPS recorders I recorded 167 tracks of 48 individual pigeons during their flight from 6 different sites around Frankfurt. The experiments consisted of two main series of repeated releases from two sites 30 km north and south from the pigeons' home loft. From the site in the south the pigeons homed 12 times and from the site in the north 16 times. After the final release from these sites, the pigeons were released at 60 km distance from home. These additional sites were selected so that the pigeons would presumably fly over the previous release site with which they were highly familiar. After conclusion of the main series two additional releases were performed, one within the magnetic anomaly of the Vogelsberg and one in a magnetically quiet region. To make these releases comparable, both release sites were selected so that the distance from the home loft was 40 km. All data obtained during these experiments were subjected to a threefold analysis, mostly based on methods that I had developed by myself or adapted for this specific study. In the first step, data were analyzed traditionally, evaluating variables similar to those that can be found in current literature. I therefore calculated values that correspond to those obtained by visual observation, like virtual vanishing bearings and intervals after one minute and after 2.5 km. Additionally I calculated the efficiency of the flights and efficiencies for specific portions of each flight, to derive variables that describe the behavior after vanishing. In the second step, which served also as a preparation for the mathematical analysis, the flight of the pigeons was separated into distinctive phases of the flight by the so-called points of decision. The flight of the pigeon can usually be separated into an initial phase of flying about, a departure and/or final homing phase. In more complex cases, however, several points of decision and a multitude of intermediary phases can be defined. Yet, the initial phase, the departure phase and the final homing phase can be defined for all tracks and therefore have been selected as appropriate candidates for a thorough analysis. In the last step I employed the so-called method of time lag embedding to reconstruct the underlying navigational process of the pigeons' homing flight. This method is based on the principles of chaos theory and is regularly employed for the analysis of dynamic systems. Its application allows the reconstruction of the underlying processes from experimentally recorded data without any a priori knowledge of the underlying system itself. For these reconstructed systems I calculated characteristic properties which are unique for each system. These are the so-called correlation dimension, describing the complexity of the system, and the so-called largest Lyapunov exponent, describing its predictability. Based on the knowledge gathered from these reconstructions, I used a variation of the previous methods to identify navigational phases, by calculating the correlation dimension as a sliding mean over the complete track. From these data I then derived further characteristics of the underlying process, such as its precision and differences in complexity depending on the pigeon's current position. ...Mit Hilfe von miniaturisierten GPS-Rekordern habe ich 167 Flugwege von 48 Tauben bei ihren Flügen von 6 verschiedenen Auflassorten aufgezeichnet. Die Experimente bestanden dabei aus zwei Hauptserien, während derer die Tauben wiederholt von Orten in 30 km Entfernung vom Heimatschlag aufgelassen wurden. Insgesamt flogen die Tauben dabei 12 mal von einem Auflassort im Süden und 16 mal von einem Auflassort im Norden. Nach der letzten Auflassung vom jeweiligen Ort wurden die Tauben zusätzlich in 60 km Entfernung vom Heimatschlag aufgelassen. Diese zusätzlichen Auflassorte wurden dabei so gewählt, dass die Tauben aller Wahrscheinlichkeit nach über den vorherigen Auflassort, mit dem sie ja nun vertraut waren, flliegen würden. Nach Beendigung dieser beiden Hauptserien wurden noch zwei zusätzliche Versuche, einmal innerhalb der magnetischen Anomalie des Vogelsbergs und einmal in einer magnetisch normalen Region durchgeführt. Um sicherzustellen, dass auch diese Auflassungen vergleichbar sind, wurden die Auflassorte so gewählt, dass in beiden Fällen die Distanz zum Schlag ungefähr 40 km betrug. Alle so gewonnen Daten wurden im Folgenden einer dreischichtigen Analyse unterzogen. Die angewendeten Methoden sind dabei fast ausschliesslich von mir selbst entwickelt oder von mir speziell für diese Studie adaptiert worden. Im ersten Schritt wurden die Daten entsprechend der in der aktuellen Literatur verwendeten Methoden, sozusagen "auf traditionelle Weise", analysiert. Dabei wurden Werte ermittelt, die denen entsprechen die bei Beobachtung mit dem Fernglas gemacht werden, wie virtuelle Verschwinderichtungen nach einer Minute und in 2.5 km Entfernung vom Auflassort, sowie Verschwindezeiten in 2.5 km Entfernung vom Auflassort. Zusätzlich wurden Effizienzen für die einzelnen Flüge und einzelne Flugabschnitte bestimmt, um das Verhalten über das bei traditionellen Experimenten unzugängliche Verhalten nach dem Verschwinden zu erhalten. Im zweiten Schritt, der auch als eine Art Vorbereitung für den letzten Analyseschritt diente, wurden die Flugwege der Tauben durch Bestimmung sogenannter Entscheidungspunkte ("Points of Decision"), nach objektiven Kriterien, in charakteristische Phasen des Fluges aufgeteilt. Der Flug einer Taube lässt sich dabei üblicherweise in eine Anfangsphase ("Initial Phase"), während der die Vögel scheinbar ungezielt in der Nähe des Auflassortes umherfliegen, und eine Abflug ("Departure Phase") und/oder eine Heimkehrphase ("Final Homing Phase") aufteilen. In komplizierteren Fällen lassen sich jedoch auch mehrere "Zwischenphasen" definieren. Die Anfangsphase, die Abflugphase und die finale Heimkehrphase lassen sich jedoch für alle Flüge definieren und sind somit ideale Kandidaten für eine genauere Untersuchung. Im letzen Schritt wurden dann, basierend auf der Methode des sogenannten "Time Lag Embedding", die einzelnen Phasen des Fluges dazu verwendet, um den der Navigation zugrundeliegenden Prozess zu rekonstruieren. Die verwendete Methode basiert dabei auf den Prinzipien der Chaos-Theorie und wird oft dazu eingesetzt, dynamische Systeme zu charakterisieren. Sie erlaubt es, die zugrundeliegenden Prozesse eines Systems aus experimentellen Daten zu rekonstruieren, ohne dass genaueres Wissen über das Zusammenspiel der involvierten Faktoren vorhanden sein muss. Für den so rekonstruierten Prozess habe ich dann für das System charakteristische Eigenschaften bestimmt. Diese Eigenschaften beschreiben zum einem die Komplexität des Systems, die sogenannte "Korrealtions Dimension" und zum anderen die Vorhersagbarkeit des Systems, der sogenannte "größte Lyapunov Exponent". Basierend auf den so gewonnenen Erkenntnissen über die Eigenschaften des Systems, habe ich dann eine Variation der vorangehenden Methode entwickelt, um navigatorische Phasen im Flug der Tauben zu identifizieren. Hierzu wurde die Korrelations Dimension als gleitendes Mittel über den gesamten Flugweg der Taube berechnet. Aus diesen zusätzlichen Ergebnissen habe ich dann weitere Eigenschaften des Systems, wie die Genauigkeit der Kursbestimmung und die räumliche Abhängigkeit der Komplexität des Systems, abgeleitet. ..

Strategies for pre-emptive mid-air collision avoidance in Budgerigars

We have investigated how birds avoid mid-air collisions during head-on encounters. Trajectories of birds flying towards each other in a tunnel were recorded using high speed video cameras. Analysis and modelling of the data suggest two simple strategies for collision avoidance: (a) each bird veers to its right and (b) each bird changes its altitude relative to the other bird according to a preset preference. Both strategies suggest simple rules by which collisions can be avoided in head-on encounters by two agents, be they animals or machines. The findings are potentially applicable to the design of guidance algorithms for automated collision avoidance on aircraft

Repeated training of homing pigeons reveals age dependent idiosyncrasy and visual landmark use.

Recent research into the navigational strategies of homing pigeons (Columba livia) inthe familiar area has highlighted the phenomenon of route fidelity – birds formingidiosyncratic flight paths to which they are loyal over multiple releases from the samesite, and even returning to this path when released from a near-by unfamiliar location.Such results highlight the potential importance of visual landmark cues in the homingprocess. However, not all birds have been shown to produce idiosyncratic routes orshow this route-joining behaviour. Here we use birds with and without flight experienceto study the formation of idiosyncratic routes when released repeatedly from a singlelocation, followed by two off-route releases with differing topography to see how flightexperience and local landmark features can influence navigational strategy in thefamiliar area. We found that, over the course of 20 sequential releases, birds withgreater flight experience tended to form idiosyncratic routes whereas less experiencedbirds did not show this tendency. When released from near-by sites (from which thebirds had not previously been released), a range of navigational strategies were seen,including flying parallel to the learned route (suggestive of a learned compassdirection), a direct flight path towards home (again indicative of compass use), re-joining the learned route, and following the coastline. These latter strategies aresuggestive of landmark usage. Analysis using time lag embedding was also used toassess the off-route releases, and the short-term correlation dimension valuesproduced (ranging from 1.5-2.5) were also indicative of strategies using one or twofactors (landmarks, compass, or a combination of these two). Individual birds oftenshowed different strategies at different sites, suggesting that the use of differentnavigational cues is highly flexible and situationally dependent

Pigeon navigation: Different routes lead to Frankfurt

Background: Tracks of pigeons homing to the Frankfurt loft revealed an odd phenomenon: whereas birds returning from the North approach their loft more or less directly in a broad front, pigeons returning from the South choose, from 25 km from home onward, either of two corridors, a direct one and one with a considerable detour to the West. This implies differences in the navigational process

Direct evidence for vision-based control of flight speed in budgerigars

We have investigated whether, and, if so, how birds use vision to regulate the speed of their flight. Budgerigars, Melopsittacus undulatus, were filmed in 3-D using high-speed video cameras as they flew along a 25 m tunnel in which stationary or moving vertically oriented black and white stripes were projected on the side walls. We found that the birds increased their flight speed when the stripes were moved in the birds’ flight direction, but decreased it only marginally when the stripes were moved in the opposite direction. The results provide the first direct evidence that Budgerigars use cues based on optic flow, to regulate their flight speed. However, unlike the situation in flying insects, it appears that the control of flight speed in Budgerigars is direction-specific. It does not rely solely on cues derived from optic flow, but may also be determined by energy constraints

Budgerigar flight in a varying environment: flight at distinct speeds?

How do flying birds respond to changing environments? The behaviour of budgerigars, Melopsittacus undulatus, was filmed as they flew through a tapered tunnel. Unlike flying insects - which vary their speed progressively and continuously by holding constant the optic flow induced by the walls - the birds showed a tendency to fly at only two distinct, fixed speeds. They switched between a high speed in the wider section of the tunnel, and a low speed in the narrower section. The transition between the two speeds was abrupt, and anticipatory. The high speed was close to the energy-efficient, outdoor cruising speed for these birds, while the low speed was approximately half this value. This is the first observation of the existence of two distinct, preferred flight speeds in birds. A dual-speed flight strategy may be beneficial for birds that fly in varying environments, with the high speed set at an energy-efficient value for flight through open spaces, and the low speed suited to safe manoeuvring in a cluttered environment. The constancy of flight speed within each regime enables the distances of obstacles and landmarks to be directly calibrated in terms of optic flow, thus facilitating simple and efficient guidance of flight through changing environments

Mathematical analysis of the navigational process in homing pigeons

In a novel approach based on the principles of dynamic systems theory, we analyzed the tracks of pigeons recorded with the help of miniaturized GPS recorders. Using the method of time lag embedding, we calculated the largest Lyapunov exponent to determine the system’s predictability and the correlation dimension to estimate the number of factors involved. A low Lyapunov exponent around 0.02, which proved to be rather constant over all calculations, indicates that the navigational process is almost deterministic. In the distribution of the correlation dimension estimates we found three distinctive peaks, at 3.3, 3.7 and 4.2, indicating that avian navigation is a complex multi-dimensional process, involving at least four or five independent factors. Additional factors, as indicated by an increase in the correlation dimension, seem to be included as the pigeons approach their home loft. This increase in correlation dimension and its fractal nature suggest that the various navigational factors can be included as required and weighted independently. Neither the correlation dimension nor the Lyapunov exponent is affected by increasing familiarity of the pigeons with the terrain. This suggests that the navigational strategy is stable with the same process controlling the flight across familiar as well as unfamiliar terrain

Homing flights of pigeons in the Frankfurt region: the effect of distance and local experience

In a meta-analysis, we analysed GPS-recorded tracks of homing pigeons, focusing on how initial behaviour and track structure change with increasing distance from the loft and on the effect of local experience. 'Points of Decision' divide the tracks into several phases, with the first marking the end of the initial phase, when the pigeon begins to leave the release site. With increasing distance, the number of Points of Decision increases significantly, whether pigeons are unfamiliar or familiar with the release site. In unfamiliar birds, the duration of the initial phase increases with increasing distance from the home loft, while agreement among birds decreases. These correlations with distance, not found in familiar birds, appear to reflect the necessity to interpret the still unfamiliar combination of 'map' factors. Pigeons starting a second time from a site take more time to leave and initially fly over a larger area, which we interpret as a procedure to integrate the respective site into their 'map'. When pigeons are released repeatedly from the same sites, the behaviour at the beginning of the flight does not change consistently, but there are fewer decision points and overall efficiency increases. The flight routes chosen by individuals continue to differ; route stereotypies, as described in the Oxford region, are not observed. This suggests loft-specific difference in the weighting and rating of navigational factors, probably caused by the availability and suitability of these factors in the respective regions. Our findings warn against simply transferring findings from one loft to another

Release sites and number of tracks.

<p>‘Tracks’ indicates the number of evaluable tracks; in parentheses: number of complete tracks, if different.</p><p>Release sites and number of tracks.</p

Virtual bearings, efficiencies and short-term correlation dimensions for the additional sites.

<p>Number of complete tracks is given in parentheses, if different; ‘Vector’ indicates the vector based on the virtual vanishing bearings at 2.5 km from the release point, Δ home, mean deviation from the home direction, with asterisks indicating a significant deviation (p<0.05) (release site bias) as indicated by the confidence interval [54]. The median of the correlation dimension, the quartiles qu1, qu3, and its range are given for all tracks, the respective efficiency data for all complete tracks.</p><p>Virtual bearings, efficiencies and short-term correlation dimensions for the additional sites.</p