Following the sun: a mathematical analysis of the tracks of clock-shifted homing pigeons.

We analysed the tracks of clock-shifted pigeons from six releases to determine how they cope with the conflict between their sun compass and other navigational cues. Time-lag embedding was used to calculate the short-term correlation dimension, a parameter that reflects the complexity of the navigational system, and with it, the number of factors involved. Initially, while pigeons were still at the release site, the short-term correlation dimension was low; it increased as the birds left the site, indicating that the birds were now actively navigating. Clock-shifted pigeons showed more scatter than the control birds, and their short-term correlation dimension became significantly smaller than that of the controls, remaining lower until the experimental birds reached their loft. This difference was small, but consistent, and suggests a different rating and ranking of the navigational cues. Clock-shifted pigeons do not seem to simply ignore the information from their manipulated sun compass altogether, but appear to merely downgrade it in favour of other cues, like their magnetic compass. This is supported by the observation that the final part of the tracks still showed a small deviation in the expected direction, indicating an effect of clock-shifting until the end of the homing flight.