Fig. 1

Simulated migration routes based on different sun compass mechanisms. a Time-compensated sunset compass orientation (green), b fixed (menotactic) sunset compass orientation (blue), and c time-compensated noon (pink) and d hourly sun compass orientation (yellow). The routes were calculated in daily steps of 200 km, with a new course for each step based on astronomical conditions at each daily departure location/time and assuming a constant geographic course within a step. In the case of the time-compensated hourly sun compass, a new direction was determined once an hour between 08:00 and 17:00, with steps of 20 km per hour. Autumn migration routes were simulated with 1 Sept as initial departure date and with initial departure directions of 90°, 135°, 180°, 225° and 270° from departure locations at latitudes 70°N, 50°N and 30°N. Spring migration were simulated with 1 April as departure date and with initial departure directions of 300°, 330°, 360°, 30° and 60° from departure locations at latitudes 30°S, Equator (0°) and 30°N. Dotted sections of sunset routes indicate situations where the sun did not set once the birds reached higher latitudes, thus where the lowest sun elevation was taken as reference instead. Great circle routes (dark grey dashed) are given for comparison to indicate the shortest routes. Since sun compass routes are independent of longitude, we show no maps here. The routes are plotted in a Mercator projection in which constant geographic courses (rhumblines or geographic loxodromes) are indicated as straight lines. See text for more details on simulations