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Additional file 2: of Feasibility of sun and magnetic compass mechanisms in avian long-distance migration

Figure S2. Effect of time of season on flight trajectories of migrants following time-compensated sunset and fixed (menotactic) sunset compass routes. Autumn migration routes were simulated with 1 Aug (blue), 1 Sept (green), and 1 Oct (red) as initial departure dates and with initial departure directions of 90°, 135°, 180°, 225° and 270° from departure locations at latitudes 70°N. Spring migration were simulated with 1 March (blue), 1 April (green), and 1 May (red) as departure dates and with initial departure directions of 300°, 330°, 360°, 30° and 60° from departure locations at latitudes 30°S. All 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. Dotted sections of routes indicate situations where the sun did not set anymore 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. The routes are presented in Mercator projection. (PDF 357 kb

Additional file 5: of Feasibility of sun and magnetic compass mechanisms in avian long-distance migration

Figure S5. Visualisation of the magnetoclinic compass. Magnetoclinic orientation refers to the case where migratory birds fly at a constant “apparent angle of inclination” (γ′ in blue). The apparent angle of inclination is the inclination of the geomagnetic field projected on a plane orthogonal to the bird’s heading or body axis. As inclination changes with latitude, a migrant must change its course in order to keep γ′ constant. In horizontal flight the apparent angle of inclination is a function of the geomagnetic inclination (γ in red) and the bird’s flight course (α in green), according to the relationship tan(γ′) = tan(γ)/ sin(α). The illustration shows the headings of a bird flying along a fixed γ’ in areas with different angles of inclination γ1 (left graph) and γ2 (right graph). The bird maintains a fixed γ′ by adjusting its heading from more westerly directions α1 to more southerly directions α2 with decreasing geomagnetic inclination from γ1 (left graph) and γ2 (right graph). Magnetoclinic orientation will be affected if birds do not fly horizontally and also by wind conditions depending on whether the birds perceive the apparent inclination magnetostatically in relation to their body axis or by a magnetic induction process in relation to their trajectory through the magnetic field, as evaluated by Alerstam (1987: J Exp Biol. 1987;130:63–86). These effects are not included in the simplified geometric explanation in the figure here. (PDF 173 kb

Additional file 1: of Feasibility of sun and magnetic compass mechanisms in avian long-distance migration

Figure S1. Effect of daily travel distance on flight trajectories of migrants following time-compensated sunset and fixed (menotactic) sunset compass routes. The routes were calculated in daily steps of 100 km (blue), 200 km (green), and 300 km (red) 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. 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. 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. Dotted sections of routes indicate situations where the sun did not set anymore 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. The routes are presented in Mercator projection. (PDF 371 kb

Additional file 8: of Feasibility of sun and magnetic compass mechanisms in avian long-distance migration

Figure S8. (A) Magnetoclinic compass routes of a northern wheatear (B070) departing from 66°N at different longitudes (155° E, 160° E, 175° W, 160° W, 155° W; black triangles) in westerly directions (270° relative to magnetic North). Because of the different angles of magnetic inclination at the different starting locations (γ = 79.1°, 76.9°, 75.5°, 75.2°, 76.2° from easterly to westerly sites), the bird starts with different apparent angles of inclination (γ′ = γ). Depending on the distribution of magnetic inclination, the birds are either led immediately southwards (solid lines, where γ′ > γ) or along the magnetic inclination isoclines (dashed lines, where γ > γ′). (B) Magnetoclinic compass routes of the same bird starting from its initial departure location with different γ′. It is possible for the bird to reach its destination (black dot at 13°N, 37°E) by using a magnetoclinic compass and without resetting the compass along the journey, but the path is highly sensitive to minute changes of the apparent angle of inclination (sensitivity < 2 × 10− 8 deg.), making this strategy highly unlikely. The maps are in Mercator projection. (PDF 388 kb

Additional file 3: of Feasibility of sun and magnetic compass mechanisms in avian long-distance migration

Figure S3. Time-compensated sunset compass routes during spring migration with initial departure directions of 354°, 356°, 358°, 0°, 2°, 4° and 6°. Spring routes starting at lower latitudes on either side of (or at) the equator are very sensitive to small differences in departure courses due to small differences in sunset directions over latitude and time in the tropics. Great circle routes (dark grey dashed) are given for comparison to indicate the shortest routes. The routes are presented in Mercator projection. (PDF 120 kb

Additional file 6: of Feasibility of sun and magnetic compass mechanisms in avian long-distance migration

Figure S6. Two examples of magnetoclinic compass routes during spring migration starting from the equator (0° latitude; left graph) or 20°S (right graph) with initial departure directions of 354°, 356°, 358°, 0°, 2°, 4° and 6°. Great circle routes (dark grey dashed) are given for comparison to indicate the shortest routes. The routes are presented in Mercator projection. (PDF 171 kb

data nocturnal departure time and sun elevation

There are ten columns: 1. “dep.min.sunset”: This variable details the individual nocturnal departure timing in minutes after sunset. 2. “sunele.dep.2”: This variable details the sun’s elevation at the moment of the nocturnal departure in degrees below the horizon. 3. “Sex”: "Sex": This is a factor with two levels. "1" says that the bird was a male and "2" that it was a female. 4. "Age.ad": This is a factor with two levels, i.e., "young" and "old". In autumn, "young" means 1st calendar year bird and "old" means that the individual was older than "young". In spring, "young" means 2nd calendar year bird and "old" means that the individual was older than "young". 5. "subsp": This is a factor with two levels. "leu" says that the bird belonged to the leucorhoa subspecies of the northern wheatear and "oen" says that the bird belonged to the oenanthe subspecies of the northern wheatear. 6. “season”: This variable indicates whether the bird was caught in spring or autumn. 7. “energystores_release”: This is a numeric variable and it provides the individual energy stores at release, estimated as detailed in eqn. 2 of the paper. 8. “year”: This variable indicates the year in which the bird was caught. 9. “jd_arr”: This is the day of year of capture with 1 Jan is 1. 10. “rho.act.dep”: We converted departure direction (circular variable) into a measure of deviance between observed (radio-tracked) departure direction and seasonally appropriate migration direction which enabled the inclusion of directional information in subsequent multivariate analyses, cf. Müller et al. (2018, Journal of Animal Ecology, https://doi.org/10.1111/1365-2656.12821 ). This measure of deviance, the resultant vector length ρ (rho; rho of departure direction), was calculated using the “circ.summary” function of the R package “circular”, for details see corresponding paper. It ranges from 1 (no deviance between observed departure direction and seasonally appropriate migration direction) to 0 (deviance of 180°)

data rates of energy accumulation

There are seven columns: 1. “subsp”: This is a factor with two levels. "leu" says that the bird belonged to the leucorhoa subspecies of the northern wheatear and "oen" says that the bird belonged to the oenanthe subspecies of the northern wheatear. 2. "Age.ad": This is a factor with two levels, i.e., "young" and "old". In autumn, "young" means 1st calendar year bird and "old" means that the individual was older than "young". In spring, "young" means 2nd calendar year bird and "old" means that the individual was older than "young". 3. “season”: This variable indicates whether the bird was caught in spring or autumn. 4. “change.energystores_average”: This numeric variable details the change in the energy stores as an average value over the bird’s duration of stay in a cage. This value was calculated, as detailed in eqn. 3 of the paper. In the paper, this variable is called “rate of energy accumulation”. 5. “nights_in_cage”: This variable states how many nights a bird was in a cage. 6. “year”: This variable indicates the year in which the bird was caught. 7. “Sex”: This is a factor with two levels. "1" says that the bird was a male and "2" that it was a female

data departure direction

There are six columns: 1. “year”: This variable indicates the year in which the bird was caught. 2. “season”: This variable indicates whether the bird was caught in spring or autumn. 3. "subsp": This is a factor with two levels. "leu" says that the bird belonged to the leucorhoa subspecies of the northern wheatear and "oen" says that the bird belonged to the oenanthe subspecies of the northern wheatear. 4. "Age.ad": This is a factor with two levels, i.e., "young" and "old". In autumn, "young" means 1st calendar year bird and "old" means that the individual was older than "young". In spring, "young" means 2nd calendar year bird and "old" means that the individual was older than "young". 5. "Sex": This is a factor with two levels. "1" says that the bird was a male and "2" that it was a female. 6. “direction”: This is the departure direction in degree