Mathematical analysis of the homing flights of pigeons based on GPS tracks.

To analyse the effect of magnetic and olfactory deprivation on the homing flight of pigeons, we released birds from a familiar site with either their upper beak or their nostrils anaesthetized. The tracks were analysed by time lag embedding to calculate the short-term correlation dimension, a variable that reflects the degrees of freedom and thus the number of factors involved in a system. We found that higher natural fluctuations in the earth's magnetic field characterized by A P-indices of 8 and above caused a reduction of the correlation dimension of the control birds. We thus separated the data into two groups according to whether they were recorded on magnetically quiet days or on days with higher magnetic fluctuations. Anaesthetizing the upper beak had no significant effect. Making pigeons anosmic reduced the correlation dimension on magnetically quiet days, but did not cause any reduction on days with higher fluctuations. Altogether, our data suggest an involvement of magnetic cues and olfactory factors during the homing flight and point to a robust, multi-factorial map.