Fig. 2. Orientation of monarch butterflies exposed to different celestial cues. Each dot at the circle periphery (A,D,E,H) indicates the mean orientation of one butterfly flight. The arrows indicate group mean vectors. The broken circles indicate the radius of the mean vector required for significance at the P<0.05 and P<0.01 levels according to the Rayleigh test (Batschelet, 1981). B,C and F,G show the virtual flight paths flown by individual butterflies assuming a constant flight speed. They start in the center of the diagram and travel towards the periphery. Distances have been normalized. (A,B) With a 120° view of the clear blue sky including the sun, monarchs orient in their south–southwesterly migratory direction. (C,D) Under simulated overcast with only the geomagnetic field available, but no sun or polarized light cues, the butterflies were randomly oriented. (E–G) A 44° visual field of clear blue sky in the zenith but no direct view of the sun also led to random orientation (E) both for monarchs tested in the morning (grey dots, tracks in F) and in the afternoon (open dots, tracks in G). Since a few flights are bimodal and only the prominent peak of each bimodal distribution is indicated on the circular diagrams, a few points in the circular diagrams do not seem to coincide with the corresponding tracks. (H) The monarchs also did not show any preference to line up with the axis of skylight polarization in the zenith (indicated by four parallel lines).