Birds use different compass mechanisms based on celestial (stars, sun, skylight polarization pattern) and geomagnetic cues for orientation. Yet, much remains to be understood how birds actually use these compass mechanisms on their long-distance migratory journeys. Here, we assess in more detail the consequences of using different sun and magnetic compass mechanisms for the resulting bird migration routes during both autumn and spring migration. First, we calculated predicted flight routes to determine which of the compasses mechanisms lead to realistic and feasible migration routes starting at different latitudes during autumn and spring migration. We then compared the adaptive values of the different compass mechanisms by calculating distance ratios in relation to the shortest possible trajectory for three populations of nocturnal passerine migrants: northern wheatear Oenanthe oenanthe, pied flycatcher Ficedula hypoleuca, and willow warbler Phylloscopus trochilus. Finally, we compared the predicted trajectories for different compass strategies with observed routes based on recent light-level geolocation tracking results for five individuals of northern wheatears migrating between Alaska and tropical Africa. We conclude that the feasibility of different compass routes varies greatly with latitude, migratory direction, migration season, and geographic location. Routes following a single compass course throughout the migratory journey are feasible for many bird populations, but the underlying compass mechanisms likely differ between populations. In many cases, however, the birds likely have to reorient once to a few times along the migration route and/or use map information to successfully reach their migratory destination. Keywords: Sun compass, Magnetic compass, Bird migration, Orientation Background polarization patterns) provide birds with directional in- It is well established that birds use a variety of orienta- formation relative to a true geographic reference (e.g., tion and navigation mechanisms to find their way during geographic North) [7–12]. Magnetic compass informa- migration. Young, inexperienced birds on their first mi- tion is based on the alignment of the Earth’s magnetic gration are generally assumed to use a genetically field, with magnetic North (or magnetic South) as refer- encoded program, providing them with information on ence [13, 14]. Because of irregularities and changing the direction and distance to migrate [1–3]. Navigational properties of the geomagnetic field, the magnetic poles map information collected during this first migration al- do not coincide with the geographic poles . This lows them then to navigate back to the known breeding may pose problems for migratory birds using celestial area and during future migrations, as has been shown by and magnetic compass cues interchangeably along their several displacement experiments [4–6]. Birds use a var- migratory journey, because they are exposed to a chan- iety of different compass mechanisms for orientation ging relationship between the two reference systems, i.e., during migration, based on celestial or geomagnetic changing magnetic declination, which is the difference cues. Celestial compass cues (stars, sun, skylight between magnetic and geographic North/South [16–19]. Birds have been shown to regularly calibrate the differ- ent compasses with each other [20–23], but there is an * Correspondence: Rachel.Muheim@biol.lu.se ongoing debate about which of the compass mechanisms Department of Biology, Lund University, Biology Building B, 223 62 Lund, Sweden acts as the primary reference, and how this compass Full list of author information is available at the end of the article © The Author(s). 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Muheim et al. Movement Ecology (2018) 6:8 Page 2 of 16 information is translated into the migration trajectories simple compass orientation which do not include that we observe in nature. pre-programmed directional changes requiring new One possibility to shed light on this question is to start directions at specific locations along the migra- compare predicted trajectories based on assumptions of tion route, as has been shown to occur in several bird constant orientation according to different compass populations (cf. [3, 33, 34]). Also, we do not include mechanisms with the observed geometry of bird migra- the possibility that birds may use map information to tion routes. A number of studies have predicted migra- navigate to their migratory destination, despite of tion trajectories of birds for different celestial and convincing evidence that migrants are able to com- geomagnetic compass mechanisms, usually by extrapo- pensate for displacements [4–6, 35–37], in some cases lating known directional choices of passerine bird popu- already during their first return migration during lations from orientation experiments or various tracking spring [6, 37]. methods, and comparing the output with the known tra- jectories or goal areas of the respective populations (e.g. Simulations of bird migration routes based on [18, 24–31]). Often, these studies did not find strong different sun compass mechanisms agreement with observed routes suggesting that the The first compass mechanism to be discovered and orientation task might be more complex than to simply explored in birds was the time-compensated sun com- follow a single compass course throughout the journey. pass [7, 35]. Birds can determine the compass direction In this contribution we approach this question more from the sun (or from sun-related cues like the skylight systematically and in more detail than has previously polarization pattern) by compensating, through their cir- been done to assess the consequences of using different cadian clock sense, for the sun’s apparent daily move- compass mechanisms for the resulting bird migration ment in azimuth. This compass mechanism seems to be routes for both autumn and spring migration. We fo- highly flexible, and differences in rates of sun azimuth cused primarily on migration routes of passerines and changes during different hours of the day and at used three main approaches: First, we calculated pre- different latitudes and seasons may be taken into dicted flight routes based on four types of sun compass account [10, 11, 38–41]. Birds may use such a and two types of magnetic compass mechanisms and time-compensated sun compass also for orientation at discuss the geometric characteristics of these routes the times of sunset (in the case of nocturnal mi- compared to great circle (orthodromes) and rhumbline grants) or sunrise (in the case of diurnal migrants) routes (loxodromes). We discuss the suitability of routes [12, 42] (see section on time-compensated sunset only from a geometric point of view, disregarding geo- compass below). Alternatively, birds could orient at a graphic or ecological factors along the routes. We then fixed angle relative to sunset or sunrise without time compared the adaptive values of the different compass compensation (menotaxis) ; see section on fixed mechanisms by calculating distance ratios in relation to (menotactic) sunset compass below). Day migrants the shortest possible trajectory (the orthodrome, along could theoretically take sun-compass readings once a the great circle) for three example populations of noc- day at noon or once an hour during the light hours turnal passerine migrants, namely northern wheatears of the day (see sections on time-compensated noon Oenanthe oenanthe migrating from Greenland to west- and time-compensated hourly sun compass below). ern Africa, and pied flycatchers Ficedula hypoleuca and In this series of analyses, we simulated flight routes for willow warblers Phylloscopus trochilus migrating from unspecified model migrant populations based on differ- northern Scandinavia to western and eastern Africa, re- ent sun compass courses. We calculated the routes in spectively. Finally, we made a critical comparison be- daily steps of 200 km, determining a new course for each tween predicted trajectories for five compass strategies step based on astronomical conditions at each daily de- for autumn and spring migration and the observed parture location/time, and assuming a constant geo- routes based on recent light-level geolocation tracking graphic course within a step. In the case of the results for five individuals of northern wheatears migrat- time-compensated hourly sun compass, which could be ing between Alaska and eastern Africa . These three used by diurnal migrants, a new direction was deter- lines of investigation allow us to draw novel conclusions mined once an hour (every 25 km) between 08:00 and about constraints in the feasibility of different compass 16:00. For simplicity, we assumed that the birds travelled mechanisms for long-distance migration depending on each day, without making any stopovers along the jour- latitude and season, about the costs in terms of extra ney. Thus, travel as well as migration speed were travel distance for different compass mechanisms, and 200 km/d for the simulations, which is not unreasonable about the likelihood for constant compass orientation for long-distance migrants (see supplementary review on an intercontinental and global scale. We would table in ). We acknowledge, however, that daily like to stress that we only consider routes based on travel speed can have a substantial influence on the Muheim et al. Movement Ecology (2018) 6:8 Page 3 of 16 resulting trajectories, as exemplified in Additional file 1: by adopting the orientation angle in relation to the ob- Figure S1. Autumn migration routes were simulated served sunset azimuth according to the time-compensated with 1 Sept as initial departure date, and spring migra- sunset compass at their initial departure site. Hence, tion routes with 1 April as departure date. These dates orientation at the next flight step will change because of were chosen for generic model populations with no the combined effects of the change in sunset azimuth at specific species in mind. Since the timing of the mi- the new site compared to the initial site and the change in gration season affects sun compass routes, popula- the bird’s orientation in relation to the sun position be- tions migrating earlier or later in the season will cause of the time difference from the initial departure site. therefore migrate along slightly different routes (for Equivalent results would have been obtained under the al- example see Additional file 2:FigureS2).Autumn ternative assumption that the birds established orientation routes were simulated with initial departure directions at the new site at a fixed time according to the daily clock of 90°, 135°, 180°, 225°, and 270°, from departure lo- in phase with local time at the initial site, applying the cations at latitudes 70°N, 50°N and 30°N. Spring mi- orientation angle at this time in relation to the observed gration routes were simulated with initial departure sun azimuth at the new site. Hence, the course for the directions of 300°, 330°, 360°, 30°, and 60°, from next flight step would change because of the change in departure locations at latitudes 30°S, Equator (0°) and sun azimuth at the bird’s fixed departure time. It should 30°N. Unlike routes based on magnetic compass be noted that it is not necessary to assume that the birds courses which are dependent on geographic latitude maintain their daily clock in phase with local time at the and longitude (see below), sun compass routes are only initial departure site throughout the migration, i.e., never dependent on latitude, but not longitude. The simula- resetting their daily clock during migration. The import- tions were carried out in MATLAB R2008a-R2016b ant condition is that the birds do not reset their circadian (The MathWorks Inc., Natick, MA, USA). Sun posi- clock to local time between successive flight steps. They tions were calculated using the Matlab script sun_posi- may adjust their daily clock and sun compass mechan- tionR.m by Vincent Roy based on the solar position ism to new local time and solar conditions at a few algorithm by . stopover sites along the migration route and still con- tinue along the same curved route, if they depart Time-compensated sunset compass from a reset stopover site on the same true course as Assumptions they had when arriving at this site (see below). Birds are assumed to use their time-compensated sun compass to establish their orientation around sunset Results: Characteristics of routes [12, 42, 46]. We focus on sunset here, since a large Autumn routes are closely similar to great circle routes proportion of passerines migrate at night and are be- (Fig. 1a), hence the time-compensated sunset compass lieved to establish their departure direction around furnishes the birds with the means of great circle orien- sunset [12, 22, 43, 47]. For diurnal migrants, a tation. Agreement with great circle routes is large at time-compensated sunrise compass would work high latitudes until equatorial latitudes are reached, equally well. This compass will allow migrants to where the agreement with great circle routes deterio- compensate for the change in sun azimuth during the rates, but total routes from higher to lower latitudes are hours before and after sunset according to the local still distance saving to a high degree. Spring migration conditions at the departure site. The rate of change routes starting at lower latitudes with an east component of sun azimuth at sunset depends on latitude, as ex- show a good agreement with great circle routes, while plained by Alerstam and Pettersson . When the routes starting with a west component show significant birds establish their orientation at a new site without deviations from the shortest route. Spring routes starting having reset their inherent circadian clock to local at lower latitudes on either side of (or at) the equator time at the new site (still having their daily clock in will be very sensitive to small differences in departure phase with the time at their initial or former depart- courses due to small differences in sunset directions over ure site), their new course will differ from the courses latitude and time in the tropics (see Additional file 3: during preceding flight steps. The result will be that Figure S3 for illustration). the birds follow curved routes as they migrate across Orientation with a time-compensated sunset compass longitudes. These routes are similar to great circle is for obvious reasons problematic under polar condi- routes at high latitudes, but only if the birds use this tions when the sun never sets below the horizon (dotted compass at sunset (or sunrise), and not at other times lines in Fig. 1a). A possible solution could be for the of the day (see below and ). birds to use the lowest sun elevation instead of a true Routes were simulated by assuming that the birds sunset. However, the lowest sun elevation is much more determine the departure direction at the time of sunset difficult to identify than sunset, so this might pose Muheim et al. Movement Ecology (2018) 6:8 Page 4 of 16 ab c d 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 substantial problems. Additional problems arise when since the majority of passerines migrates at night. As in birds cross polar regions with a time-compensated sun- the case of the time-compensated sunset compass, this set compass. The rapid changes in absolute directions compass mechanism will be difficult to use during polar that birds experience when flying across polar longitudes summers. Under polar summer conditions, we used the may result in sigmoid deflections of the routes near the lowest sun elevation as reference instead, as we did in North Pole (see Additional file 4: Figure S4A for illustra- the case of the time-compensated sunset compass. tion). Further problems with time-compensated sunset compass orientation are discussed in the last section. Results: Characteristics of routes The routes resulting from fixed sunset compass orienta- Fixed (menotactic) sunset compass tion are in general closer to rhumbline than great circle Assumptions routes (Fig. 1b). In the Northern Hemisphere the routes Birds following fixed (menotactic) sunset compass routes show a course change to the left (anticlockwise) in au- are assumed to orient at a fixed angle in relation to the tumn (migration away from the pole) and to the right local sunset azimuth throughout the migratory journey (clockwise) in spring (migration towards the pole). This [43, 47, 49, 50]. Hence, the flight course will change ac- holds also for movements from northerly latitudes con- cording to the change in sunset azimuth along the bird’s tinuing into the Southern Hemisphere, and for spring migration route at the seasonal time of the bird’spas- movements departing from the Southern Hemisphere sage. Also here, we focus on sunset, rather than sunrise, towards northerly breeding latitudes. This means that Muheim et al. Movement Ecology (2018) 6:8 Page 5 of 16 birds migrating along the NE/SW axis will fly along the time-compensated noon sun compass will break down courses that are shifting in a distance-saving way, at equatorial latitudes where the sun culmination occurs whereas movements along the NW/SE axis will be in a close to the zenith and where noon azimuth changes from distance-wasting way (see also below). However, the re- southerly to northerly directions (or vice versa) with small verse pattern applies for autumn and spring migration in changes in latitude/seasonal time. By way of example, ser- the Southern Hemisphere where routes along the NW/ ious complications occur for spring migration routes start- SE axis are closer to great circle routes (Southern Hemi- ing near the equator close to spring equinox, when the sphere seasons; not shown). Thus, the seasonal favour- sun over the course of about 15 min changes from an ability of fixed sunset compass routes for migratory easterly position during the morning to a westerly position birds breeding in the Southern Hemisphere is the re- in the afternoon (see Additional file 4: Figure S4B for illus- verse of that for migratory birds breeding in the North- tration). This means that this compass will not be useful ern Hemisphere. Birds reaching higher latitudes during for migration in the latitude range between the Tropics of spring migration relatively late in the season also face Cancer and Capricorn, neither in autumn nor in spring. the problem that they will encounter midnight sun, thus where they have to resort to alternative means of identi- Time-compensated hourly sun compass fying “sunset”, e.g., by using the lowest sun elevation Assumptions instead. Diurnal migrants may also use a time-compensated hourly sun compass, which differs from the former com- Time-compensated noon sun compass passes in the assumption that orientation is not estab- Assumptions lished only once each day (at noon), but at hourly Diurnal migrants could in theory use a time-compensated intervals from 08:00 to 16:00 each day, with a 25 km ad- sun compass to establish their orientation around noon, a vancement between hours. The birds are then assumed case that may not be very likely in passerine migrants, but to change their orientation in relation to the observed that may be relevant for raptors that use thermal soaring sun azimuths at these hourly intervals according to the flight. Such a time-compensated noon sun compass would time-compensated sun compass at their initial departure allow the birds to compensate for the change in sun azi- site. It has been demonstrated that the sun compass muth during the hours before and after noon according to mechanism among homing pigeons is flexible and takes the local conditions at the departure site. Routes were into account differential changes of sun azimuth during simulated assuming that the birds establish orientation at different hours of the day [11, 38, 51], making this as- solar noon by changing their orientation angle in relation sumption about hourly orientation intervals not to the observed sun azimuth according to the unreasonable. time-compensated sun compass at the birds’ initial depart- ure site. The principles are thus the same as for orienta- Results: Characteristics of routes tion with a time-compensated sunset compass, but routes Time-compensated hourly sun compass routes are simi- will be quite different because of the difference in the ap- lar to those based on a noon sun compass, except for parent angular movement of the sun around noon com- the occurrence of a distinct daily curvature of tracks pared to at sunset/sunrise (see ). Angular rates of (Fig. 1d). The course changes anticlockwise during the change in sun azimuth are maximal at noon with large dif- daily migration period when the birds proceed south- ferences between latitudes, and azimuth changes are most wards in autumn. This daily effect becomes gradually accentuated at lower latitudes . more pronounced as the birds reach successively lower latitudes. During spring, the daily course shifts are in the Results: Characteristics of routes clockwise direction, increasing with increasingly north- Routes curve in a distance-saving way at intermediate and erly latitudes. The daily course changes become much higher latitudes in both autumn and spring, like the routes exaggerated for migrants that have departed from equa- resulting from the time-compensated sunset compass (see torial latitudes, applying the time-compensated sun above) (Fig. 1c). However, the routes associated with the compass for these latitudes to the solar conditions at the time-compensated noon sun compass are close to great higher latitudes. Hence, as for the noon sun compass, circle routes only at the highest latitudes, while they curve the hourly sun compass is useful only for migration at more strongly than great circle routes at moderately high intermediate and higher latitudes in autumn as well as and intermediate latitudes, thus being clearly longer than spring. It is interesting to note that regular course routes based on the time-compensated sunset compass. changes during the daily migration period (anticlockwise This difference is due to the differential rates of for movements away from the pole and clockwise for change of sun azimuth at noon versus sunset/sunrise as movement towards the pole in the northern Hemi- explained by Alerstam and Pettersson . Furthermore, sphere, and vice versa in the Southern Hemisphere) are Muheim et al. Movement Ecology (2018) 6:8 Page 6 of 16 diagnostic for routes determined by this type of compass magnetic compass mechanism based on the apparent mechanism (may be revealed by analyses of angle of magnetic inclination, which is the projected high-resolution daily tracking data). angle of the inclination of the Earth’s magnetic field on a plane perpendicular to the movement direction of the Conclusions about feasibility of sun compass routes bird (see Additional file 5: Figure S5 for an illustration We conclude and confirm that the time-compensated and  for details on how to calculate the apparent sunset compass, when used without correcting for the angle of inclination). These magnetoclinic compass shift in local time as the bird moves along its migra- routes will change with changing inclination angles of tory path, provides birds with a means of following the magnetic field along a birds’ migratory route and will distance-saving routes with shifting courses that are lead the birds on shifting magnetoclinic compass courses similar to great circle routes . Such a compass in agreement with several cases of observed routes and strategy will work well during autumn migration and experimental courses [30, 31, 55]. However, the hypoth- also during spring migration at mid- or high latitudes esis of magnetoclinic compass orientation has failed to (> 30°N). However, we also demonstrate that using gain any support from studies of magnetoreception this compass strategy for northward spring migration mechanisms , nor from analyses of migration routes out of the tropics has critical limitations, i.e., sensitiv- in the Arctic  or at a magnetic anomaly . ity to small differences in departure courses, often For the simulations of magnetic compass routes, we leading to distance-wasting routes (see Additional file 3: used the same initial departure directions (relative to Figure S3). We therefore conclude that it is probably im- geographic North) and a migration speed of 200 km/d practical for the birds to use the time-compensated sunset as for the sun compass routes. Since magnetic field pa- compass when departing from the tropics on spring mi- rameters are sensitive to both date and location, we set gration. Only at higher latitudes will it be useful for them initial departure dates to 1 Sept 2010 for autumn and 1 to adopt this compass mechanism during spring migration April 2011 for spring migration, and calculated two and follow close to great circle routes from there onwards versions of magnetic compass routes, one centered on to their final breeding destinations at high latitudes. the Palaearctic-African and the other on the The feasibility of fixed (menotactic) sunset compass Nearctic-Neotropic migration system. Magnetic field pa- orientation depends on the migratory axis. During both rameters were calculated with the Matlab script magdf.m spring and autumn migration, routes along the NE/SW by Maurice A. Tivey at Woods Hole Oceanographic axis in the northern Hemisphere and along the NW/SE Institution, USA, with the International Geomagnetic axis in the Southern hemisphere are shifting in a Reference Field (IGRF) model 2010 . The apparent distance-saving way. The use of time-compensated sun angles of inclination used for the magnetoclinic compass compass orientation based on the sun azimuth at noon routes were calculated based on the angle of inclination or at hourly intervals during the day has significant limi- of the Earth’s magnetic field at the initial departure loca- tations. Orientation with a time-compensated noon or tion and the departure direction relative to magnetic hourly sun compass is therefore not feasible at all at North , and kept constant for the remainder of the lower latitudes on either side of the equator, neither dur- route. When a bird reached a location where the angle ing autumn nor spring migration. of inclination was larger than the apparent angle of in- clination, we assumed that it would follow the inclin- Simulations of bird migration routes based on ation isoclines by flying due magnetic east or west, as different magnetic compass mechanisms suggested by Kiepenheuer . When the bird again Birds can sense the Earth’s magnetic field and use the in- reached a new location with an inclination angle smaller formation for orientation [13, 14, 52, 53]. The avian than the apparent angle of inclination, it continued magnetic compass is sensitive to the axial alignment, but along the magnetoclinic compass route. Since we as- not the polarity, of the magnetic field lines, thus birds sumed that the birds read their compass only once a determine the direction towards the magnetic equator day, every 200 km, and not constantly, as assumed by or the closest magnetic pole using the inclination of the Kiepenheuer , no resetting of the compass was ne- magnetic field lines . They use the sign of the angle cessary in our simulations for the birds to get back to of inclination, i.e., whether the inclination is positive or areas with inclination angles smaller than the apparent negative, and not the exact angle of inclination, to distin- angle of inclination. guish equatorwards from polewards [14, 52, 54]. An al- ternative approach for birds to use magnetic field Fixed (menotactic) magnetic compass information for compass orientation is to fly along mag- Assumptions netoclinic compass routes . In a pioneering and Migratory birds using a magnetic compass for orienta- highly stimulating study, Kiepenheuer  suggested a tion follow a constant magnetic compass course which Muheim et al. Movement Ecology (2018) 6:8 Page 7 of 16 will lead them along trajectories with a changing geo- Hemisphere during autumn migration follow great graphic course. The discrepancy between constant mag- circle routes more closely than spring routes starting netic and constant geographic compass courses occurs in the southern hemisphere. The reverse is true for because the poles of the Earth’s magnetic field do not birds migrating within the Nearctic-Neotropic migra- coincide with the geographic poles, and the horizontal tion system. Here, spring routes along fixed magnetic polarity of the magnetic field varies over space and time, compass courses are generally closer to great circle which results in a changing relationship between the routes than autumn routes, specifically if the birds geographic and magnetic reference systems [15, 57]. depart from wintering areas in South America. Trajectories following fixed magnetic compass routes It has to be emphasized that trajectories based on (magnetic loxodromes) will therefore vary with magnetic fixed magnetic compass courses depend on the prop- declination, i.e., the difference between the magnetic and erties of the Earth’s magnetic field at the departure geographic direction at a specific location and time, and location and along the migratory routes, thus they will depend strongly on the geographic region a bird is can vary considerably between sites and over time, es- crossing [18, 26]. pecially close to the magnetic poles where differences in magnetic declination can be large between nearby Results: Characteristics of routes locations [18, 26, 58]. In general, fixed magnetic compass routes within the Palaearctic-African migration system run closer to Magnetoclinic compass great circle routes than the routes within the Assumptions Nearctic-Neotropic migration system (Fig. 2a). Within Birds are assumed to follow the fixed apparent angle of the Palaearctic-African migration system, fixed mag- inclination determined at the initial departure location, netic compass routes starting in the Northern as long as the inclination angle of the Earth’s magnetic ab Fig. 2 Simulated migration routes based on different magnetic compass mechanisms. a Fixed (menotactic) magnetic compass (red) and b magnetoclinic compass orientation (orange). The routes are calculated in daily steps of 200 km, determining a new course for each step based on geomagnetic conditions at each daily departure location and assuming a constant geographic course within a step. Autumn migration routes were simulated with 1 Sept 2010 as initial departure date, spring migration routes with 1 April 2011 as departure date. For each compass mechanism, routes were centred on the Palaearctic-African (left panels) and Nearctic-Neotropic (right panels) migration systems, respectively. Dotted sections of magnetoclinic compass routes indicate situations where the angle of inclination of the Earth’s magnetic field was larger than the apparent angle of inclination, thus where a magnetoclinic compass could not be used, and the birds instead were assumed to orient a fixed magnetic compass instead. Great circle routes (dark grey dashed) are given for comparison to indicate the shortest routes. All maps are in Mercator projection. See Fig. 1 and text for more details Muheim et al. Movement Ecology (2018) 6:8 Page 8 of 16 field remains smaller than the apparent angle of inclin- unpredictable and susceptible to variations of the ation . Birds following such a magnetoclinic compass magnetic field than fixed magnetic compass routes. It route will change direction when the inclination angle cannot be excluded, however, that magnetoclinic and magnetic declination change along the route . routes might be feasible in the case of specific bird Magnetoclinic compass routes therefore depend on the populations. initial departure settings (magnetic inclination at depart- ure location and initial departure direction relative to Comparison of simulated routes for three magnetic North), as well as the properties of the Earth’s populations of passerine migrants magnetic field (magnetic inclination and declination) In this second series of analyses, we compared autumn along the route. One common feature for all magnetocli- and spring compass routes for three examples of noctur- nic compass routes is that they cross the magnetic equa- nal long-distance migrants, northern wheatears, migrat- tor (where magnetic inclination is 0°) orienting due ing from Greenland to western Africa, and pied north or south relative to magnetic North. An important flycatchers and willow warblers migrating from northern restriction for the use of a magnetoclinic compass is that Scandinavia to western and eastern Africa, respectively. it cannot be used when the absolute value of the angle We calculated autumn and spring migration routes of inclination at a location along the route becomes lar- based on different compass mechanisms between speci- ger than the fixed apparent angle of inclination . In fied departure and destination locations. As in the previ- such situations, we assumed that the birds would follow ous sections, we calculated the routes in daily steps of the inclination isoclines by flying due magnetic east or 200 km, determining a new course for each step based west, as suggested by Kiepenheuer . on astronomical and geomagnetic conditions at each daily departure location/time, and assuming a constant Results: Characteristics of routes geographic course within a step. We intentionally chose Magnetoclinic compass routes during autumn follow the initial departure directions so that the birds success- great circle routes more closely within the fully reached their destination. In the case of the north- Nearctic-Neotropic migration system compared to the ern wheatears migrating across the North Atlantic, Palaearctic-African migration system (Fig. 2b). However, stopovers are of course not possible over the open these differences are rather small and depend highly on ocean, but for simplicity and to be able to compare the location within the migration system. During spring mi- different routes between populations, we assumed the gration, the majority of magnetoclinic compass routes in same rules for all of them. Autumn migration routes both migration systems vary considerably in not very were simulated with 1 August 2010 and spring migration favourable ways. The outcome of the routes during with 1 April 2011 as initial departure date, respectively. spring is also highly sensitive to small differences in the The following five compass routes were calculated initial departure directions, and thereby the apparent between the specified breeding and wintering loca- angle of inclination (see Additional file 6: Figure S6 for tions: (1) time-compensated sunset compass route illustration), requiring a highly sensitive compass. In (see assumptions and characteristics above); (2) fixed many cases, the birds reached areas with angles of mag- (menotactic) sunset compass route (see assumptions netic inclination larger than the apparent angle of inclin- and characteristics above); (3) fixed (menotactic) mag- ation (dotted lines in Fig. 2b), forcing them to follow netic compass route (see assumptions and characteris- magnetic inclination isoclines during parts or the entire tics above); (4) magnetoclinic compass route (see migration. assumptions and characteristics above); (5) rhumbline (loxodrome) route, which birds may follow if they use Conclusions about feasibility of magnetic compass routes astar compass sensu  (no time compensation), a We conclude that fixed magnetic compass routes are gen- time-compensated sunrise/sun/sunset compass where erally more feasible than magnetoclinic compass routes. the birds reset their circadian clock in phase with the Fixed magnetic compass routes run closer to great circle new local conditions at each step of orientation, or a routes, and are thereby more distance saving, within the magnetic compass regularly calibrated by averaging Palaearctic-African than within the Nearctic-Neotropic polarized skylight information at sunrise and sunset, migration system. As the use of fixed magnetic compass as proposed by [19, 22, 23, 59]. We used the exact routes depends on the local magnetic declination along great circle route (orthodrome), i.e., the shortest route the migration route, it varies over both space and time, between two locations on Earth, as reference of com- thus the trajectories differ between geographic areas. parison for the other routes. Since we compared noc- The trajectories of the magnetoclinic compass turnal passerine migrants which usually depart at or routes depend on both the inclination and declination shortly after sunset (cf. [60, 61]), we did not consider of the Earth’s magnetic field, which makes them more sun compass mechanisms based on sun observations Muheim et al. Movement Ecology (2018) 6:8 Page 9 of 16 at noon or during the day (time-compensated noon fixed sunset compass routes, on the other hand, are only and time-compensated hourly sun compass). within 1% of unity in the case of the pied flycatcher (case with NE/SW migratory axis). For systems with a NW/SE Results: Characteristics of routes migration axis, like the northern wheatear and willow The migratory axes of the three populations in Fig. 3 are warbler, trajectories based on fixed sunset orientation all rather close to N/S, making the differences in dis- may incur up to 9% extra distance, both in autumn and tance between the rhumbline and great circle routes in spring (Fig. 3; Table 1). Such levels of extra costs may small (≤1%; Table 1). Several of the compass mecha- be important, thus there may be significant selection nisms provide efficient trajectories with distance ratios against the use of the time-compensated sunset compass exceeding unity with only a minor amount (≤1%). This during spring migration as well as against the use of a holds true for all time-compensated sunset compass fixed sunset compass in both seasons for populations routes, with the exception of willow warblers which fly with a NW/SE axis. an extra distance of around 6% compared to the great For the case of fixed magnetic compass routes, the circle route during spring migration. Distance ratios of routes of the three populations all fall within a Fig. 3 Simulated autumn and spring migration routes of three populations of songbirds. Migration routes for populations of northern wheatears migrating from Greenland to their wintering areas in western Africa, and pied flycatchers and willow warblers, migrating from northern Scandinavia to their wintering areas in western and eastern Africa, respectively. Autumn migration routes were simulated with 1 Aug 2010 as initial departure date, spring migration routes with 1 April 2011 as departure date. Illustrated are the rhumbline routes (black), time-compensated sunset compass routes (green), fixed (menotactic) sunset compass routes (blue), fixed (menotactic) magnetic compass routes (red), and magnetoclinic compass routes (orange). The exact great circle routes (dark grey dashed) are shown for comparison. Initial departure locations are indicated as black triangles and destinations as black dots. All maps are in Mercator projection. See Table 1 for details Muheim et al. Movement Ecology (2018) 6:8 Page 10 of 16 Table 1 Distance ratios in relation to the shortest great circle distance for simulated trajectories based on different compass mechanisms in three examples of songbird migration systems (shown in Fig. 3) Breeding Wintering Distance Autumn + Spring Autumn Spring location location of great Rhumbline Fixed Magnetoclinic Time-comp. Fixed Time-comp. Fixed circle route (menotactic) compass sunset (menotactic) sunset (menotactic) route magnetic route compass sunset compass sunset (km) compass route route compass route compass route route Northern 70° N, 54° W 15° N, 15° W 6672 1.01 1.00 1.01 1.00 1.09 1.01 1.07 wheatear Willow 68° N, 20° E 10° S, 30° E 8710 1.00 1.00 1.00 1.00 1.04 1.06 1.04 warbler Pied 68° N, 20° E 10° N, 10° W 6814 1.01 1.00 1.02 1.00 1.00 1.00 1.01 flycatcher The rhumbline route, the route associated with a fixed (menotactic) magnetic compass course and the magnetoclinic compass route do not differ between seasons, thus the distance ratios are given only once. For the other two compass mechanisms (time-compensated and fixed (menotactic) sunset compass) trajectories differ between autumn and spring seasons with different distance ratios as given in the table. Distance ratios (always > 1) are rounded to two decimals, meaning that ratios between 1.000 and 1.0049 are given as 1.00 geographic zone where the trajectories curve in a courses differ much more, making it more likely to find distance-saving way in relation to the rhumbline (a zone biological significant differences between the courses extending from Greenland and across Europe; see ). and the route selected by the birds. Magnetoclinic compass routes for northern wheatears and willow warblers lie within < 1% distance of the great Possible compass mechanisms used by northern circle route, while pied flycatchers take an about 2% lon- wheatears breeding in Alaska ger route. Since the efficiencies of these routes highly In this third series of analyses, we investigate which depend on the global pattern of magnetic declination compass routes most closely match the actual routes and inclination, they do not apply everywhere. In other taken by northern wheatears migrating between the zones, e.g., in North America, routes along magnetic breeding sites in Alaska and wintering sites in eastern loxodromes and magnetoclinic routes will curve in an Africa during autumn and spring. We compare the five unfavourable way, leading to extra distances (see Fig. 2 compass strategies described in the previous sections above). This means that the use of fixed magnetic com- with the actual routes of five individual birds estimated pass and magnetoclinic compass orientation may be se- from light-level geolocation information . For the lected against in some zones, but selectively promoted route simulations, we used the individual birds’ actual in other zones [18, 62]. departure and arrival locations and departure and arrival dates from the breeding and wintering sites, respectively. Conclusions about feasibility of different compass routes For each individual, we calculated the daily migration Overall, all compass mechanisms examined in the three flights by dividing departure and arrival dates by the selected examples in Fig. 3 successfully led the birds number of days the bird spent on migration (see  for from the breeding to the non-breeding areas, and back details). As in the earlier described simulations, we de- again, without the need for a resetting of the compass termined a new course for each step based on astronom- settings or change to alternative compass mechanisms. ical and/or geomagnetic conditions at each daily Thus, we would like to stress that all compass mecha- departure location/date, and assumed a constant geo- nisms are feasible for the populations in Fig. 3, and that graphic course within a step. For simplicity, we esti- the costs for using one rather than the other mechanism mated the distance of the actual migration route of the are rather small. This illustrates that for many migratory northern wheatears as the cumulative distance following routes all or several compass mechanisms would suc- fixed sunset compass routes between the migratory cessfully guide birds to their migratory destination. Still, starting point, every stopover and the migratory destin- it is important to note that such evaluations of migration ation (“actual migration route” hereafter). Since the ac- routes highly depend on the geographic location, migra- curacy and precision of the location estimates obtained tory season, and migratory axis (NE/SW or NW/SE), from the geolocators are not exact, it should be kept in thus the findings cannot be generalized beyond these ex- mind that the distances for these actual migration routes amples. In the next section, we therefore modelled com- are rough approximations. Also, since the location esti- pass routes for a population of extreme long-distance mates from the light-level geolocators are missing at migrants, northern wheatears breeding in Alaska and high latitudes in spring because of the dependency of migrating to eastern Africa, where the different compass the tracking method on sunrise and sunset times, Muheim et al. Movement Ecology (2018) 6:8 Page 11 of 16 migration distance was calculated from the actually journey (see Additional file 7: Figure S7 for illustration). tracked route plus the distance of the birds’ last location However, as mentioned earlier, the birds can circum- estimate to the breeding area in Alaska (Table 2). Devia- vent this problem by resetting their inner clock to tions from this simplified course are not incorporated local time and use the local sun ephemeris as refer- here, so that the actual migration routes are somewhat ence for the sun compass at a few selected stopover shorter than the “true” migration distances capturing the sites along the migration route . When departing birds’ migratory movement in more detail (cf. ). from one of these sites on the same compass course as arriving to that site, the birds will continue along Results: Characteristics of routes the same curved route as before the stopover, with a The fixed (menotactic) sunset compass routes provide minor effect associated with the lack of course change the best fit to the actually flown routes by the individual at this site. In our simulations we therefore intro- wheatears as estimated from light-level geolocation in- duced such a resetting of the inner clock and com- formation during both autumn and spring migration, pass setting whenever the difference between sunset (Fig. 4). These routes also most closely match the dis- at the initial departure location and the current loca- tances flown by the birds, with average distance ratios tion exceeded 45°. During autumn and spring migra- closest to the distance of the actual routes (Table 2). tion, birds flying along time-compensated sunset The trajectories of the time-compensated sunset compass routes also encounter the midnight sun at compass routes run close to the great circle across high latitudes (in autumn at latitudes > 80° and there- the Arctic Ocean past the North Pole during autumn, fore not visible in Fig. 4;dottedlines in spring.For thus much farther north than the actual migration routes. these and other reasons (barrier crossing over long It was not possible to simulate time-compensated sunset distances of the Arctic Ocean), time-compensated compass routes during spring migration without resetting sunset compass routes are therefore not very feasible, the compass at least once, since the movement of the even though they would guide the birds along the equatorial sun near spring equinox used as reference led shortest routes between the breeding and wintering to sudden, large shifts in direction towards the end of the sites. Table 2 Distance ratios in relation to the distance of the actual migration route, as calculated in this study, for simulated trajectories based on different compass mechanisms in five individuals of northern wheatear migrating between Alaska and Eastern Africa, as revealed by light-level geolocation (cf. ); see Fig. 4) Autumn Departure Arrival Distance of Great Rhumbline Time-comp. Fixed (menotactic) Fixed (menotactic) Magnetoclinic migration location location actual route (km) circle route sunset compass sunset compass magnetic compass compass route route route route route B070 66°N, 145° 13°N, 12840 0.88 1.17 0.88 1.01 1.15 – E 37°E E552 65.5° 7°N, 30° 14440 0.83 1.08 0.83 0.96 1.11 – N,145.4°E E E553 68.6°N, 3°N, 30° 13970 0.87 1.14 0.88 0.99 1.13 – 149.5°E E B801 65°N, 145° 8°N, 34° 13950 0.85 1.13 0.85 0.99 1.12 – E E B823 65°N, 146° 12°N, 14160 0.81 1.08 0.81 0.94 1.09 – E 31°E Spring Departure Arrival Distance of Great Rhumbline Time-comp. Fixed (menotactic) Fixed (menotactic) Magnetoclinic migration location location actual route (km) circle route sunset compass sunset compass magnetic compass compass route route route route route B070 12°N, 40°E 65.5° 13310 0.86 1.13 0.92 0.98 1.11 0.99 N,145.4° E552 5°N, 30°E 66°N, 14270 0.85 1.10 0.94 0.97 1.14 1.01 145°E E553 3°N, 30°E 68.6°N, 13450 0.90 1.19 0.98 0.98 1.19 1.04 149.5°E B801 9°N, 36°E 65°N, 13370 0.88 1.18 0.95 1.00 1.15 1.03 145°E B823 6°N, 31°E 65°N, 13620 0.89 1.17 0.96 1.03 1.19 1.04 146°E Muheim et al. Movement Ecology (2018) 6:8 Page 12 of 16 Fig. 4 Simulated autumn and spring migration routes of northern wheatears migrating breeding in Alaska. Migration routes are shown between the breeding sites in Alaska and the wintering areas in eastern Africa in comparison to the actual routes taken by the individual birds as estimated from geolocator information [see 32 for details on tracks]. Illustrated are the rhumbline routes (black), time-compensated sunset compass routes (green), fixed (menotactic) sunset compass routes (blue), fixed (menotactic) magnetic compass routes (red), and magnetoclinic compass routes (orange). The exactgreat circle routes (dark grey dashed) are shown for comparison. Initial departure locations are indicated as black triangles and destinations as black dots. Green dots indicate locations where the compass courses were reset. Dotted sections of time-compensated sunset compass routes indicate locations where the sun did not set below the horizon, thus where the birds had to use the lowest sun elevation as sunset. Dotted sections of magnetoclinic compass routes indicate locations where the angle of inclination of the Earth’s magnetic field was larger than the apparent angle of inclination. Estimates of locations, incl. 95% credible intervals are given in yellow to green shades (see  for details). All maps are in Mercator projection. For further information see Table 2 and main text Both the rhumbline and fixed magnetic compass the final section of their journey along the inclination routes run along far more southerly courses than esti- isocline. mated by the light-level geolocation data. Following along rhumbline routes would involve the crossing of the Bering Sea, the Sea of Okhotsk, and the Arabian Conclusions about feasibility of possible compass routes Sea, while fixed magnetic compass routes results in used by northern wheatears breeding in Alaska the crossing of the Sea of Okhotsk and the Arabian Clearly, in the case of the northern wheatears breeding Sea. While such sea crossings per se are not expected in Alaska, fixed (menotactic) sunset compass routes to pose any major problems for migrants like north- most closely agree with the actual routes flown by the ern wheatears, the estimated tracks do not indicate individual birds as estimated from light-level geolocation that the northern wheatears flew along any of these information. During both autumn and spring migration, trajectories. birds orienting at a fixed angle relative to local sunset, Autumn trajectories of the magnetoclinic compass determined at the departure location, will successfully routes consistently led the birds in all five examples im- reach their migratory destination without the need to re- mediately southwards (Fig. 4). This phenomenon is set the compass at any time during the journey. They caused by the distribution of the magnetic inclination will follow trajectories that are very close to the actually isoclines and magnetic declination in this area, mak- flown routes in location and distance (Fig. 4; Table 2). ing the use of magnetoclinic routes from these loca- Still, as outlined earlier, the feasibility of fixed sunset tions highly unlikely. However, departure from more compass orientation depends on the migratory axis. In westerly locations leads the birds along the magnetic the northern Hemisphere, birds like the northern wheat- inclination isoclines (see Additional file 8: Figure S8 ears from Alaska migrating along the NE/SW axis will for illustration), bringing them westwards, as sug- fly along courses that are shifting in a distance-saving gested by earlier studies [29, 31, 55]. During spring way. This is not the case for birds migrating along a migration, the trajectories along the magnetoclinic NW/SE axis, which should be kept in mind when mak- compass route successfully led all birds to their des- ing general conclusions about the use of compass tination. In all cases, however, the local inclination mechanisms. angle exceeded the apparent angle of inclination when Previous studies modelling constant compass courses the birds reached eastern Russia, forcing them to fly for the migration routes of northern wheatears breeding Muheim et al. Movement Ecology (2018) 6:8 Page 13 of 16 in Alaska did not include fixed sunset compass routes course, following fixed sunset compass orientation, in their models, and both found that the magnetocli- which fits well with the realized migration tracks of nic compass routes spatially coincided best with the free-flying birds. All other compass routes involve actual routes of the birds [29, 31]. Both studies, how- substantial detours and lead the birds along trajector- ever, used different departure locations and dates than ies far from the known tracks. This suggests that the we used in the current study, and the simulations by birds might indeed follow fixed sunset compass orien- Åkesson and Bianco  included a resetting of the tation, and recalibrate their other compass cues rela- apparent angle of inclination along the autumn migra- tive to this information. tion route, which explains some of the discrepancies It is reasonable to assume that different bird popu- between the different studies. Irrespective of these dif- lations use the compass mechanism that brings them ferences, there is currently no experimental evidence to their destination with as few changes as possible in that birds are able to sense the apparent angle of in- the compass settings. Also, it is probably less likely to clination, thus this model still lacks an empirical assume that a bird migrating along one of the com- background [29, 55, 58]. Together with the problem pass courses will switch to an entirely different mech- of using a magnetoclinic compass in areas with local anism in the middle of the migration, but rather reset angles of magnetic inclination exceeding the apparent the current course to a new start direction. As men- angle of inclination, it is therefore less likely that the tioned above, this does not mean that the birds do northern wheatear breeding in Alaska use a magneto- not use different compass cues to determine their de- clinic compass for orientation, but that these popula- parture direction, thus that they still recalibrate the tions use a fixed sunset compass courses instead. different compass cue with each other to be able to switch between them, if necessary, for example when Conclusions weather conditions change. The feasibility of different compass mechanisms varies Taken together, routes following a single compass greatly with latitude, migratory direction, and migration course throughout the migratory journey might not be season. In the case of the magnetic compass mecha- very common, thus birds of many populations likely nisms, the magnetic field properties at different geo- have to reorient once to a few times along the graphic location are the main factors that determine the migration route to successfully reach their destination. course of the routes. Our simulations in the first section Such pre-programmed directional changes at specific show that there is little support for the use of a locations along the migration route have been experi- time-compensated noon or hourly sun compass by diur- mentally demonstrated in several bird populations (cf. nal migrants, especially not at lower latitudes and for [3, 33, 34]). In addition, there is growing evidence longer journeys. Time-compensated and fixed sunset that birds use map information to navigate to their compass routes on the other hand may be feasible, but migratory destination already during their first return primarily at higher latitudes (time-compensated sunset migration during spring [6, 37]. It should also be kept compass) or along the NE/SW axis (fixed sunset com- in mind that several factors besides compass mecha- pass in Northern Hemisphere). The feasibility of the two nisms may affect migratory routes at both proximate magnetic compasses depends on geographic location, and ultimate levels. Distributions of resources and with the magnetoclinic compass further being restricted habitats, along with topographical features and wind to areas with lower angles of inclination. conditions, will determine which routes are optimal. Nevertheless, as shown in Fig. 3, there are areas on In addition, navigation capability and responses to Earth where all compass mechanisms may be used by wind drift are also important determinants of migra- different populations of migrants without inflicting too tion routes (e.g. [30, 62, 64–66]). Thismeansthatthe large deviations from the optimal routes. This, however, course control of migratory birds may be so complex does not mean that they should randomly switch from and variable (violating the assumption of constant one compass course to another depending on the avail- orientation according to a single compass mechan- ability of orientation cues, as this might lead to substan- ism) that it will be difficult to identify probable tial detours (see supplement in ). Instead, the birds compass mechanisms from the geometry of the ob- should follow one compass course and regularly cali- served routes. On the other hand, the possibilities brate different compass cues (solar, stellar, magnetic) for critical comparisons between predicted theoretical with each other in order to be able to use both magnetic trajectories and observed routes have improved with and celestial compass information during the actual the recent and ongoing tracking revolution in the animal flight [19, 22, 63]. migration field, where novel techniques provide much In the case of the northern wheatears from Alaska new and precise information about travel routes of indi- our simulations show that there is only one compass vidual animals (e.g. [32, 67–73]). Muheim et al. Movement Ecology (2018) 6:8 Page 14 of 16 Additional files (right graph). Magnetoclinic orientation will be affected if birds do not fly horizontally and also by wind conditions depending on Additional file 1: Figure S1. Effect of daily travel distance on flight whether the birds perceive the apparent inclination magnetostatically in relation to their body axis or by a magnetic induction process in trajectories of migrants following time-compensated sunset and fixed (menotactic) sunset compass routes. The routes were calculated in relation to their trajectory through the magnetic field, as evaluated daily steps of 100 km (blue), 200 km (green), and 300 km (red) with by Alerstam (1987: J Exp Biol. 1987;130:63–86). These effects are not a new course for each step based on astronomical conditions at each included in the simplified geometric explanation in the figure here. (PDF 173 kb) daily departure location/time and assuming a constant geographic course within a step. Autumn migration routes were simulated with 1 Sept as initial Additional file 6: Figure S6. Two examples of magnetoclinic compass departure date and with initial departure directions of 90°, 135°, 180°, 225° routes during spring migration starting from the equator (0° latitude; left and 270° from departure locations at latitudes 70°N. Spring migration were graph) or 20°S (right graph) with initial departure directions of 354°, 356°, simulated with 1 April as departure date and with initial departure directions 358°, 0°, 2°, 4° and 6°. Great circle routes (dark grey dashed) are given for of 300°, 330°, 360°, 30° and 60° from departure locations at latitudes 30°S. comparison to indicate the shortest routes. The routes are presented in Dotted sections of routes indicate situations where the sun did not Mercator projection. (PDF 171 kb) set anymore once the birds reached higher latitudes, thus where the Additional file 7: Figure S7. Explanation for why birds starting from lowest sun elevation was taken as reference instead. Great circle equatorial latitudes during spring migration may not reach their routes (dark grey dashed) are given for comparison to indicate the shortest destinations if following a time-compensated sunset compass. Example routes. The routes are presented in Mercator projection. (PDF 371 kb) of a bird departing on spring migration in eastern Africa (12°N, 20°E; blue Additional file 2: Figure S2. Effect of time of season on flight triangle) on 14 April 2014 towards its destination in Alaska (black dot), trajectories of migrants following time-compensated sunset and advancing 295 km/d. Graphs on the right show the sun ephemeris curves, i.e. fixed (menotactic) sunset compass routes. Autumn migration routes the azimuth of the sun relative to Universal time, for three consecutive days were simulatedwith1 Aug(blue), 1Sept(green), and1Oct(red) illustrated in red, green and turquoise, incl. local sunset (dots in respective as initial departure dates and with initial departure directions of colours). The blue ephemeris curves give the azimuth of the sun at 90°, 135°, 180°, 225° and 270° from departure locations at latitudes the departure location and departure date, which the bird uses as 70°N. Spring migration were simulated with 1 March (blue), 1 April reference. The blue triangles show the sun azimuth at the departure (green), and 1 May (red) as departure dates and with initial departure location at the time of local sunset for each of the three days. The directions of 300°, 330°, 360°, 30° and 60° from departure locations at bird determines its departure direction at local sunset, but uses the sun latitudes 30°S. All routes were calculated in daily steps of 200 km ephemeris from the departure location and departure date as reference. with a new course for each step based on astronomical conditions at Thus, it changes its daily departure direction by the difference between the each daily departure location/time and assuming a constant geographic local sunset azimuth and the azimuth of the sun at that specific time at the course within a step. Dotted sections of routes indicate situations where the departure location and date. The sudden shift in compass direction is the sun did not set anymore once the birds reached higher latitudes, thus result of the sun changing its position relatively quickly from west to south where the lowest sun elevation was taken as reference instead. Great circle to east at noon at the departure location. These shifts are most dramatic at routes (dark grey dashed) are given for comparison to indicate the shortest the geographic equator, thus affects birds departing from areas close to the routes. The routes are presented in Mercator projection. (PDF 357 kb) equator, and migrate enough days for the local sunset time to coincide with the time of noon at the departure location. Birds can avoid this by updating Additional file 3: Figure S3. Time-compensated sunset compass routes their inner clock at least once along their journey at higher latitudes and during spring migration with initial departure directions of 354°, 356°, then continue using the sun ephemeris of the reset location as reference 358°, 0°, 2°, 4° and 6°. Spring routes starting at lower latitudes on either for the remaining journey. The map is in Mercator projection. (PDF 236 kb) side of (or at) the equator are very sensitive to small differences in departure courses due to small differences in sunset directions over Additional file 8: Figure S8. (A) Magnetoclinic compass routes of a latitude and time in the tropics. Great circle routes (dark grey dashed) are northern wheatear (B070) departing from 66°N at different longitudes given for comparison to indicate the shortest routes. The routes are (155° E, 160° E, 175° W, 160° W, 155° W; black triangles) in westerly presented in Mercator projection. (PDF 120 kb) directions (270° relative to magnetic North). Because of the different angles of magnetic inclination at the different starting locations (γ =79.1°, Additional file 4: Figure S4. (A) The time-compensated sunset compass 76.9°, 75.5°, 75.2°, 76.2° from easterly to westerly sites), the bird starts with route is deflected near the geographic North Pole because of the rapid different apparent angles of inclination (γ = γ). Depending on the distribution changes in absolute directions that the bird is experiencing when flying of magnetic inclination, the birds are either led immediately southwards across longitudes near the poles. Red crosses give the positions of a putative (solid lines, where γ > γ) or along the magnetic inclination isoclines (dashed bird departing from Alaska along a time-compensated sunset compass route lines, where γ > γ). (B) Magnetoclinic compass routes of the same bird towards the North Pole, reorienting every 200 km. Gnomonic map projection. starting from its initial departure location with different γ . It is possible (B) Sun position (azimuth) at the equator (0° latitude, 0° longitude) over a 24-h for the bird to reach its destination (black dot at 13°N, 37°E) by using a period on spring equinox (21 March). Birds starting near the equator close to magnetoclinic compass and without resetting the compass along the spring equinox on a time-compensated sunset compass route will run into journey, but the path is highly sensitive to minute changes of the problems because of the sudden shift of the sun from the east to − 8 apparent angle of inclination (sensitivity < 2 × 10 deg.), making this the west over the course of about 15 min. See also Additional file 6: strategy highly unlikely. The maps are in Mercator projection. (PDF 388 kb) Figure S6. (PDF 141 kb) Additional file 5: Figure S5. Visualisation of the magnetoclinic compass. Magnetoclinic orientation refers to the case where migratory Acknowledgements birds fly at a constant “apparent angle of inclination” (γ in blue). The We thank Franz Bairlein, Anna Gagliardo and three anonymous reviewers for apparent angle of inclination is the inclination of the geomagnetic field valuable comments on the manuscript. 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 Funding inclination is a function of the geomagnetic inclination (γ in red) and the This work was financially supported by grants from the Swedish Research bird’s flight course (α in green), according to the relationship tan(γ)= Council (2007–5700, 2011–4765 and 2015–04869 to R.M.) and from the tan(γ)/ sin(α). The illustration shows the headings of a bird flying along a German Research Foundation (SCHM 2647/1–2 to H.S.). fixed γ’ in areas with different angles of inclination γ (left graph) and γ 1 2 (right graph). The bird maintains a fixed γ by adjusting its heading Availability of data and materials from more westerly directions α to more southerly directions α 1 2 The datasets used and/or analysed during the current study are available with decreasing geomagnetic inclination from γ (left graph) and γ 1 2 from the corresponding author on reasonable request. Muheim et al. Movement Ecology (2018) 6:8 Page 15 of 16 Authors’ contributions 19. Muheim R, Moore FR, Phillips JB. Calibration of magnetic and celestial RM and TA designed the study; RM carried out simulations; HS provided compass cues in migratory birds - a review of cue-conflict experiments. data; RM and TA wrote the manuscript with important input from HS; all J Exp Biol. 2006;209:2–17. authors approved the final version. 20. Able KP, Able MA. Calibration of the magnetic compass of a migratory bird by celestial rotation. Nature. 1990;347:378–80. Ethics approval and consent to participate 21. Wiltschko W, Wiltschko R. Magnetic orientation and celestial cues in Not applicable. migratory orientation. Experientia. 1990;46:342–52. 22. Muheim R, Phillips JB, Åkesson S. Polarized light cues underlie compass Competing interests calibration in migratory songbirds. Science. 2006;313:837–9. The authors declare that they have no competing interests. 23. Muheim R, Phillips JB, Deutschlander ME. White-throated sparrows calibrate their magnetic compass by polarized light cues during both autumn and spring migration. J Exp Biol. 2009;212:3466–72. https://doi.org/10.1242/jeb.032771. Publisher’sNote 24. Gudmundsson GA. Spring migration of the knot, Calidris c. canutus, over Springer Nature remains neutral with regard to jurisdictional claims in southern Scandinavia, as recorded by radar. J Avian Biol. 1994;25:15–26. published maps and institutional affiliations. https://doi.org/10.2307/3677290. 25. Sandberg R, Holmquist B. 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Published: Jun 6, 2018