Navigation Between Stopovers by Greater White-Fronted Geese: Comparing Compass Mechanisms and Efficiency Benchmarks

Navigation Between Stopovers by Greater White-Fronted Geese: Comparing Compass Mechanisms and Efficiency Benchmarks | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Navigation Between Stopovers by Greater White-Fronted Geese: Comparing Compass Mechanisms and Efficiency Benchmarks Ali Moayedi, Jed Long, Andrea Kölzsch, Helmut Kruckenberg, Fernando Benitez-Paez, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8080422/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract Background Long-distance migration in many birds proceeds as a series of chained flight segments between stopovers, each undertaken under shifting winds, light conditions, and geomagnetic contexts. Yet, most analyses still model journeys as continuous paths across entire trips, applying global optima or fixed compass rules and overlooking leg-specific variations. This obscures how conditions at departure reshape headings and route geometry at the segment scale, where decisions are made. Methods We analysed 1524 flight segments (2014–2024) from 122 GPS-tagged greater white-fronted geese ( Anser albifrons ). For each segment, we simulated five biologically plausible compass mechanisms (geographic and geomagnetic loxodromes, magnetoclinic route, time-compensated sun compass, local wind-aligned route) and two efficiency benchmarks (great-circle route, global wind-optimal route). Simulations were initialised with the observed departure bearing, time-aligned to each track, and driven by data on hourly winds and spatiotemporally varying geomagnetic fields. Similarity between observed and simulated routes was quantified using median geodesic distance, dynamic time warping and directional consistency. We then modelled environmental correlates of closest matched routes and tested within-individual repeatability across journeys. Results Efficiency benchmarks showed seasonal structure. In autumn, segments most often matched the global wind-optimal path. In spring, segments more frequently matched the great-circle route. Across seasons, the geographic loxodrome was the most frequent compass match, with magnetoclinic routes commonly second. Geographic and geomagnetic loxodromes often alternated as winner and runner-up with small margins, which indicates structural redundancy. Local wind-aligned routes were least common overall but occurred more often in spring. Alignment patterns varied with tailwind support, departure light regime, short pauses en route and segment position (initial, mid-journey, terminal). No within-individual repeatability was detected for either efficiency class or compass assignment. Conclusions Our results support a multi-cue, context-sensitive navigation process with functional redundancy among compass options and seasonal differences in efficiency alignment. Decisions made at stopovers reshape subsequent legs, arguing for segment-focused modelling to understand how environmental conditions translate into realised routes. Avian migration compass orientation movement ecology navigation strategies route planning Anser albifrons Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Background Billions of birds migrate across continents each year, linking breeding and wintering grounds through journeys mostly punctuated by a series of stopovers [ 1 ]. These stopovers divide the overall trajectory into successive flight segments, each undertaken under a new combination of internal conditions such as fuel reserves and circadian timing, and external factors including wind patterns and light regime [ 2 , 3 ]. As these conditions shift between departures, the navigational choices guiding each segment can differ considerably. However, most studies continue to treat migration as a single continuous process from origin to destination, overlooking how variation among segments shapes the structure of migratory routes [ 3 , 4 ]. Theoretical approaches to avian navigation are often contrasted as globally optimised routes and locally guided compass mechanisms [ 5 , 6 ]. Efficiency benchmarks describe theoretical optima such as the great-circle path, which minimises distance, and a global wind-optimal path, which minimises wind-related energetic cost [ 7 , 8 ]. These benchmarks rely on non-local knowledge, including destination geometry or future winds. Compass mechanisms are biologically plausible decision rules based on local cues, including a geographic loxodrome [ 9 ], a geomagnetic loxodrome [ 10 ], magnetoclinic orientation [ 11 ], a time-compensated sun compass [ 12 ], and local wind-aligned headings [ 7 ]. However, the navigational strategies that dominate in practice remain unclear [ 13 ], likely varying with species and life stage and shifting with environmental conditions, while interpretations are further complicated by heterogeneity in study designs and analyses [ 14 , 15 ]. Migratory navigation occurs within a dynamic environment where the cues that guide orientation fluctuate in their availability and reliability [ 16 , 17 ]. The visibility of celestial references depends on the light regime and cloud cover [ 2 ], the magnetic compass itself is light-dependent [ 18 ], and winds continually restructure the energetic cost and stability of candidate routes [ 7 ]. Geomagnetic conditions also fluctuate, and during periods of strong solar activity measured by the planetary Kp index [ 19 ], disturbances in Earth’s magnetic field can disrupt orientation [ 20 ]. These fluctuations mean that the relative advantage of alternative strategies is not constant across a migration Stopovers provide crucial opportunities to refuel, rest, and recalibrate compass systems, preparing birds for the next flight segment [ 21 , 22 ]. At departure, migrants adjust when they leave and which headings they take to balance fuel state and time constraints with prevailing winds and weather [ 23 , 24 ]. Individuals with low fuel reserves are less likely to depart and are more likely to leave under tailwinds, whereas time-limited migrants may depart despite sub-optimal winds or adopt drift-aligned headings to maintain progress [ 7 , 24 ]. In greater white-fronted geese ( Anser albifrons ), longer spring stopovers and shorter autumn flights further illustrate how seasonal context modifies route choice [ 21 ]. Each flight segment is influenced by its unique ecological and physiological context. Therefore, if migration is treated as one continuous path, we overlook the important decisions made at intermediate stopovers regarding each segment. Research on avian migration advances along three complementary paths. Laboratory experiments isolate orientation under controlled conditions, establishing core sensory capacities, including a stellar and a magnetic compass [ 25 , 26 ]. Field experiments test responses in situ through displacement releases and cue manipulations under natural skies [ 27 , 28 ]. These approaches establish what cues birds can use, but they do not explain how such mechanisms generate sustained routes across dynamic, large-scale environments [ 29 , 30 ]. Route simulations of migratory navigation test whether theoretically specified navigation rules reproduce the large-scale movements observed in tracking data [ 10 , 31 ]. However, the realism of these models depends on behaviourally grounded design and dynamic environmental representation [ 10 , 32 ], which remain limited in most existing studies. Many studies initialise routes from idealised or population-average headings rather than from the empirically observed departure directions of tracked birds, reducing correspondence with individual behaviour [ 10 , 33 ]. Environmental drivers such as wind and geomagnetic fields are often treated as static or averaged conditions, overlooking their strong spatiotemporal variability [ 34 , 35 ]. Moreover, most models represent migration as a single, uninterrupted path, neglecting the adjustments that occur at intermediate stopovers [ 31 , 36 ]. Addressing these limitations requires modelling migration as a sequence of empirically grounded flight segments that capture the environmental variability and behavioural context birds experience between stopovers. This study evaluates which routing strategies align most closely with observed GPS tracks of greater white-fronted geese, focusing on flight segments between stopovers. We consider five biologically plausible compass mechanisms: geographic loxodrome, geomagnetic loxodrome, magnetoclinic, time-compensated sun compass, and local wind-aligned headings, alongside two efficiency benchmarks: the great-circle path and a global wind-optimal path. For each segment, simulations are initialised with the empirically observed departure bearing, aligned in time to the corresponding track, and driven by hourly winds and spatiotemporally varying geomagnetic fields. We analyse compass mechanisms and efficiency benchmarks separately, because the former relies on locally available cues during flight whereas the latter assume non-local knowledge of destination geometry or future winds. We then identify the closest matching compass mechanism for each observed leg, evaluate proximity to the two benchmarks, examine how these proximities vary with season and with environmental context, and test whether the resulting patterns recur within individuals across migrations. Methods GPS Tracking Data and Preprocessing We analysed high-resolution GPS tracking data from 122 adult greater white-fronted geese, collected between 2014 and 2024 across five coordinated studies (see Data Availability). Birds were captured either on the breeding grounds at Kolguyev Island, Russia, or at wintering sites in the Netherlands and Germany [ 21 , 37 ]. Each was equipped with a 35 g GPS/GPRS neckband transmitter (madebytheo) programmed to record timestamped coordinates at intervals of 1–30 minutes (median: 5 minutes). The dataset spans both migration seasons and a broad flyway corridor, capturing variation in compass orientation across space, time, and diel phases in a species that migrates day and night [ 21 ]. To maintain positional accuracy, we retained only GPS fixes with low horizontal error (≤ 30 m) and sufficient satellite connections (≥ 4). Outliers were removed when they fell outside the expected spatial bounds (40–85° N, 0–120° E), exhibited unrealistic speeds (> 45 m s⁻¹), or formed systematic trajectory anomalies. Finally, to avoid within-flock duplication, we ensured that only one bird per flock was included in the analyses. Stopover Detection and Flight-Segment Delineation We identified stopovers as periods of limited movement, defined by explicit spatial and temporal constraints while allowing for small within-period excursions [ 38 ]. We first scanned for sequences of temporally contiguous fixes that exceeded a duration threshold. For each candidate period, we fitted a minimum enclosing disk to 95% of locations nearest to the median centre and retained the period as a stopover if the resulting cluster remained within 30 km for at least 48 hours, consistent with established criteria for migratory geese [ 21 , 37 ]. This approach mirrors density-based residence region methods, which reduce spatial noise by excluding peripheral fixes before boundary estimation [ 39 ]. Flight segments were defined as uninterrupted movements between consecutive stopovers, from the first post-departure fix to the last pre-arrival fix. We retained only segments within the migration windows (1 March–31 May for spring; 15 August–15 November for autumn; Kölzsch et al., 2019) and excluded segments with data gaps > 2 h. To distinguish migratory transit from localised repositioning, we required a net displacement ≥ 150 km [ 40 ], on the premise that shorter movements may reflect stopover switching due to predation, habitat loss, or competition [ 3 ]. To standardise temporal resolution and mitigate the influence of irregular sampling intervals, all retained flight segments were resampled at hourly intervals via linear interpolation. Simulation framework We simulated seven alternative routes for each observed flight segment: five compass-based strategies—geographic loxodrome (GL), geomagnetic loxodrome (ML), magnetoclinic (MC), time-compensated sun compass (SC), and local wind-aligned route (LW)—and two efficiency benchmarks: the wind-optimal route (WO) and the great-circle route (GC). All simulations began at the same departure point and time as the corresponding empirical segment, ensuring alignment in origin, timing, and duration under the experienced environmental conditions. For compass-based strategies, initial bearings were set to the observed departure direction, calculated as the mean heading over the first 100 km from the stopover centre. We advanced the simulation using the observed displacement magnitudes from the track, while directions were given by the navigational rule under test. Details of each simulated strategy are listed in Additional file 1: Table S1 . Geographic Loxodrome Route The geographic loxodrome (GL), or rhumb-line route, models orientation along a constant azimuth relative to geographic (true) north (Fig. 1 ). This approach reflects navigation based on celestial rotation cues, such as star trails or the solar arc, which provide a fixed reference to Earth’s rotational axis and have been proposed as biologically plausible in migratory birds [ 8 ]. Under this strategy, the initial bearing is maintained unchanged relative to true north, and positions are projected along the resulting rhumb‐line path. Geomagnetic Loxodrome Route The geomagnetic loxodrome route (ML) assumes a constant bearing relative to magnetic north, consistent with experimental evidence for a magnetic compass in birds [ 10 , 41 ] (see Fig. 1 ). This strategy was simulated by preserving the initial magnetic azimuth and converting it dynamically to geographic headings at each step using local geomagnetic declination, producing a magnetic rhumb-line path. Declination values were interpolated in time and space from precomputed hourly rasters (10 × 10 km) generated from satellite geomagnetic data using the MagGeo tool [ 42 ], capturing both secular variation and transient disturbances that static and gridded world geomagnetic models fail to capture [ 32 ]. Geomagnetic storm exposure was then defined for each flight segment using the maximum planetary Kp index during its duration, with Kp > 5 marking disturbed conditions [ 19 ]. Magnetoclinic Route The magnetoclinic route (MC) assumes birds maintain a constant apparent inclination (often termed the apparent dip) during flight (Fig. 2 ). The apparent inclination is defined as the angle between the movement vector and the local geomagnetic field [ 11 ]. We set this constant at departure based on the initial heading and local field and updated headings hourly to preserve it as conditions changed, using the simulation framework described by Åkesson & Bianco [ 10 , 36 ]. Magnetic inputs (declination, inclination) were spatiotemporally interpolated from the same precomputed hourly rasters (10 × 10 km) generated from satellite geomagnetic data via the MagGeo tool [ 42 ]. Time-Compensated Sun Compass Route The time-compensated sun compass (SC) enables birds to navigate by referencing the sun’s azimuth against an internal circadian clock [ 43 ]. In the clock-synchronous mode, the internal clock is reset to local solar time, producing a constant compass bearing and a geographic loxodrome [ 10 , 34 ]. In the departure-time‐locked mode, the clock remains fixed at its calibration phase, causing a progressive mismatch between local time and internal time as the bird moves across longitudes [ 44 ] (Fig. 3 ). This mismatch progressively distorts the perceived solar azimuth, producing systematic curvature in the route, often approximating a great-circle path at mid and high latitudes [ 9 , 44 ]. Seasonal changes in solar declination also shift the azimuth of reference events (e.g., sunrise, sunset), requiring explicit correction [ 12 , 33 ]. In our simulations, each flight segment was assigned a calibration sun based on departure light conditions—sunrise for daytime departures, sunset for night, or solar midnight/noon in polar-light regimes. Headings were then updated hourly from the initial direction according to: Here, θ s (φ,λ) is the azimuth of the chosen solar event at position (φ,λ), and ω ref is the solar angular velocity at departure [ 44 ]. The solar-geometry correction accounts for seasonal/latitudinal changes in the calibration sun’s azimuth between the current and departure positions, while the clock-drift correction represents the accumulated shift in perceived solar position due to longitudinal displacement, scaled by Earth’s 15 ∘ h − 1 rotation. Local Wind-aligned Route The local wind-aligned route (LW) models a navigation strategy in which birds continually adjust their heading to maximise instantaneous tailwind support by aligning with the prevailing wind direction (Fig. 4 ). Unlike global wind‐optimal paths, which minimise energy or time costs across the entire flight segment [ 7 ], this approach is a greedy, locally optimal heuristic, consistent with observations that birds select favourable winds at departure [ 2 ], and adjust headings to exploit them during flight [ 45 , 46 ]. In the simulation, hourly headings were set to the wind direction at the simulated position and time, obtained from the ERA5 reanalysis (100 m above ground level) at hourly resolution [ 47 ]. Global Wind-Optimal Route The global wind-optimal route (WO) is the first efficiency benchmark, modelling the path that minimises total travel time (as a proxy for energy cost) between origin and destination by exploiting the spatial and temporal structure of winds (Fig. 4 ). Based on control theory and optimal path planning [ 7 ], it represents a theoretical upper bound on time savings achievable through perfect wind use. Studies indicate that such flow-aware movement is mathematically tractable and consistent with detours that enhance migratory efficiency [ 5 , 48 ]. Graph-based algorithms such as Dijkstra, A*, and isochrone routing can approximate these paths efficiently; however, their reliance on static or simplified wind fields limits performance under dynamic conditions [ 49 ]. In contrast, dynamic programming is widely used in aviation and maritime navigation to solve minimum-time routing under spatiotemporally varying fields, reliably producing globally optimal solutions [ 50 ]. Following established approaches in aviation and maritime optimisation [ 50 , 51 ], we implemented a dynamic programming framework to compute wind-optimal trajectories between each segment’s observed departure and arrival points (Additional file 1: Fig. S1 ). The search space was represented as a time‐expanded graph constrained to a fixed‐width corridor centred on the great‐circle bearing but allowing lateral detours up to half the great‐circle distance. The corridor was discretised into hourly time slices, with candidate positions (nodes) spaced at 10 km intervals perpendicular to the main axis. For each potential transition between nodes, travel time was calculated as the great‐circle distance divided by wind‐adjusted ground speed, estimated by adding a constant airspeed of 15 m s⁻¹ [ 52 ] to the wind support component, projected onto the transition bearing. To capture within‐step variability in wind, vectors were evaluated at the spatiotemporal midpoint of each transition, improving ground‐speed estimates under dynamic conditions [ 53 ]. The dynamic programming algorithm then evaluated all feasible transitions in a forward pass and reconstructed the minimum‐time route through backtracking. Great-Circle Route The great-circle (GC) route, or orthodrome, represents the shortest geodesic path between two points on a sphere (Fig. 1 ). Unlike compass-based strategies that maintain a fixed bearing, it requires continual adjustment of heading to follow the minimal-distance arc [ 8 , 9 ]. As it defines the lower bound on distance, the great-circle route is widely used as an efficiency benchmark in avian navigation [ 12 , 34 ]. Route Summary Measures For each flight segment, we calculated key descriptive statistics summarising its geometry, timing, and environmental context. These measures provided the quantitative basis for later comparisons with simulated routes and for assessing seasonal differences in segment properties. Segment duration was defined as the elapsed time between the first post-departure and last pre-arrival fix. Cumulative travel distance was calculated as the sum of successive step lengths. To measure path directness, we calculated the straightness index as the ratio of the great-circle distance to the cumulative distance. Each flight segment was also annotated with the maximum planetary Kp index recorded during its duration, to quantify exposure to geomagnetic disturbances. In addition, we measured solar altitude at departure and classified departures as nocturnal when the sun was more than 6° below the horizon, a threshold corresponding to civil twilight and widely used in avian movement studies. Route Similarity Measures A rigorous, quantitative comparison between simulated and empirical flight paths is essential for assessing the plausibility of candidate navigation mechanisms in migrating birds [ 31 , 32 ]. Traditional approaches based solely on endpoint proximity or qualitative visual agreement [ 36 , 54 , 55 ] cannot determine whether two routes share fine-scale spatiotemporal structure or consistent directional tendencies along their entire course [ 56 , 57 ]. Trajectory-similarity analysis, using distance-based measures such as Dynamic Time Warping (DTW), Fréchet distance, or the Longest Common Subsequence (LCSS), provides a formal means of detecting such correspondences [ 56 , 58 ], with metrics falling broadly into three complementary classes: spatial similarity, spatio-temporal similarity, and directional similarity. To represent each of these dimensions, we applied three corresponding metrics to every flight segment. Spatial similarity was quantified as the median point-wise geodesic distance (MGD) between temporally matched fixes [ 59 ]. Spatio-temporal alignment was quantified using Dynamic Time Warping (DTW) on fix coordinate sequences, accommodating differences in pacing, sampling rate, or stop duration [ 60 ]. Directional consistency (DIR), a key aspect of navigational behaviour, was measured as the cosine similarity between successive heading vectors derived from consecutive fix positions [ 61 ]. For definitions and expected ranges, see Additional file 1: Table S2. Statistical Analyses Route-similarity scores quantify correspondence between simulated strategies and observed segments, yet they leave open the relationships among strategies, the conditions under which certain patterns emerge, and the extent to which individuals behave consistently across migrations. We therefore applied statistical analyses to reveal the environmental structure and behavioural consistency underlying these similarities, moving beyond spatial correspondence toward ecological interpretation. Each flight segment was assigned to its closest-matching simulated route using the three trajectory-similarity metrics described above. We then computed pairwise Pearson correlations between segment-level similarity scores to quantify structural overlap among compass-based strategies. For each segment, we also identified the most frequent runner-up strategy and calculated the mean margin in similarity score between the winner and this competitor, providing a measure of decision margin. We fitted a generalised linear model to assess environmental and temporal correlates of which efficiency benchmark was closest. The dependent variable was a binary indicator of whether the closest matching efficiency benchmark to an observed flight segment was the wind-optimal route (coded 1) or the great-circle route (coded 0). The independent variables we considered were: season (spring; autumn), mean tailwind support (m s⁻¹), mean crosswind (m s⁻¹), geomagnetic-storm exposure during the segment (storm: Kp ≥ 5; no storm: Kp < 5), light regime at departure (day; night), great-circle distance (km), segment duration (h), segment type (origin–stopover; stopover–stopover; stopover–destination), presence of a short pause (yes; no), and durations of the preceding and following stopovers (h). Model selection was performed via stepwise comparison of additive models using the Akaike Information Criterion (AIC). Collinearity among predictors was assessed, but no variables required removal (all variance inflation factors < 3). Model adequacy was assessed using residual deviance, AIC, pseudo-R² (McFadden’s, Tjur’s), and standard diagnostic checks (residuals, discrimination, calibration, influence). We also fitted a multinomial generalised linear model to examine factors associated with compass-based route choice, distinguishing among five navigation types: geographic (reference), geomagnetic, magnetoclinic, sun, and local wind-aligned. The same set of candidate predictors used in the efficiency model was included, and the final additive structure was selected through stepwise comparison using the AIC. Collinearity checks confirmed that all adjusted variance inflation factors were below 3, and overall model adequacy was evaluated using standard measures of explanatory strength and predictive performance. Finally, we assessed within-individual repeatability for the efficiency benchmark (wind-optimal vs great-circle) and for the compass choices (GL, ML, MC, SC, LW; one-vs-rest). Analyses were restricted to individuals with at least two flight segments. For each binary outcome, we fitted a generalised linear mixed model with individual ID included as a random intercept, and computed repeatability (intra-class correlation, ICC) on the latent (logit) scale. Uncertainty was quantified using parametric bootstrap confidence intervals (B = 1000) and permutation-based p-values (P = 1000). Results We identified 1524 migratory flight segments from 122 individuals, consisting of 1137 spring and 387 autumn flight segments. Spring and autumn migration routes broadly overlapped along the Baltic–Barents–Kara corridor, though notable differences in spatial extent and path geometry were observed. Autumn flights tended to follow narrower, straighter routes, while spring routes showed more variable orientations and detours over eastern Europe (Fig. 5 ). These patterns are reflected in summary statistics of flight segment properties, such as straightness, duration, and directional spread (Additional file 1: Table S3). To illustrate the diversity of observed navigation behaviours before formal classification, we first present examples of real flight segments that are closely aligned with the navigation mechanisms previously identified. One autumn flight segment (Fig. 6 a) closely follows the geographic loxodrome, maintaining a stable heading over a 1057 km flight and deviating from the shortest path by only 37 km. Another flight segment (Fig. 6 b) shows a wind-aligned orientation response, curving northeast shortly after departure and tracking local wind structure rather than a fixed heading. The resulting 1626 km route was nearly 300 km longer than the shortest available path, highlighting an adaptive, wind-responsive course. Additional examples for the remaining compass strategies are provided in Additional file 1: Figs. S2–S4. The next autumn flight segment (Fig. 6 c) traced a broad arc that closely followed the global wind-optimal route, reflecting an adaptive response to large-scale wind patterns and a strategy that traded additional distance for improved ground speed and energetic efficiency. In contrast, another autumn flight segment (Fig. 6 d) exemplifies a close match to the great-circle route, diverging from both wind-optimal and compass-based strategies. A brief pause early in the flight likely marked a key decision point, after which the bird committed to a spatially direct course. Despite sustained headwinds averaging − 4.48 m s⁻¹, it maintained a prolonged, uninterrupted flight of 952 km, indicating a strong preference for spatial efficiency over wind support. We found evidence of structured and seasonally divergent patterns at both the efficiency and compass levels (Fig. 7 ). When routes were compared to the two efficiency benchmarks, results showed a clear seasonal shift: in autumn, a majority of flight segments aligned best with the global wind-optimal (WO) model (54.5–55.3% across DTW and MGD), whereas in spring more flight segments aligned with the great-circle (GC) route (56.1–59.6% across all three metrics). The geographic loxodrome (GL) was the compass strategy identified as the closest match with the largest share of flight segments in both autumn (42.1–52.7%) and in spring (30.0–40.5%). GL’s dominance is stronger under directional similarity, by roughly ten percentage points. Magnetoclinic (MC) routes were consistently the second most frequent mechanism identified as the closest match in both seasons (19.1–21.4% in autumn; 21.9–25.3% in spring). Assignments to the remaining compass strategies were less frequent. Geomagnetic loxodromes (ML) and sun compass (SC) models were each associated with roughly 10–16% of flight segments across seasons. Local wind-aligned (LW) strategies, while the least common in autumn (5.7–7.8%), were more common as the closest match in spring (12.7–18.0%). We next compared best-fitting strategies with their most frequent runner-up to evaluate how closely strategies overlap and compete for classification (Table 2 ; Additional file 1: Tables S4–S5). Two tight clusters emerged: Geographic and Geomagnetic routes alternated as runner-up in over half of flight segments (50.8–86.7%) with gaps under 20%, while Sun and Magnetoclinic overlapped in 34.5–85.1% of cases with similar moderate margins. In contrast, local wind-aligned routes exhibited independence: their nearest rival appeared in only 36.7–54.5% of cases, and local wind-aligned surpassed that runner-up by up to 41%. This pattern was supported by correlation analysis (Additional file 1: Table S6; Additional file 1: Fig. S5). The strongest associations occurred between strategy pairs that frequently alternated as winner and runner-up. Geographic and Geomagnetic routes showed near-identical predictions, with correlations of r = 0.96–0.97 (DTW/MGD) and r = 1.00 (DIR). Magnetoclinic and Sun strategies were also tightly aligned ( r = 0.95 across DTW and MGD; r = 0.99 in DIR). Correlations between strategies from different clusters—for instance, between Geographic and Magnetoclinic—were consistently lower (MGD/DTW: r = 0.84–0.85). Local wind-aligned, in contrast, showed weak correlations with all other strategies ( r = 0.41–0.45 across metrics), reinforcing its role as a structurally distinct and independently behaving model. Table 2 Runner-up analysis for compass-based strategies (DTW similarity). For each best-fitting strategy, the table shows its most frequent second-best competitor, the proportion of times this competitor occurred (% of flight segments), and the mean improvement of the best strategy over (i) that competitor and (ii) all competitors. Results are given separately for autumn and spring flight segments. Best-Fitting Strategy Top Second-Best Top Second-Best Frequency (%) Mean Improvement Over Top Second-Best Mean Improvement Over All Second-Best Autumn Spring Autumn Spring Autumn Spring GL ML 71.9 84.1 15.7 13.7 15.8 13.3 ML GL 64.3 57.5 18.8 15.0 19.6 14.8 MC SC 78.0 77.1 18.5 18.4 16.7 17.1 SC MC 34.5 55.3 17.0 18.8 14.5 18.6 LW GL 45.8 45.3 25.1 37.8 29.7 36.3 The binomial GLM (n = 1,524) retained season, mean tailwind support, presence of a short pause, great-circle distance, and next-stopover duration as predictors (residual deviance = 2062.9 on 1,518 df; AIC = 2074.9). Segments in autumn were more likely to align with the wind-optimal model than those in spring (OR = 1.61, 95% CI 1.27–2.04, p < 0.001), and the probability increased with tailwind support (per 1 m s⁻¹: OR = 1.08, 95% CI 1.04–1.12, p < 0.001). Segments containing a short pause also had higher odds of wind-optimal classification (OR = 1.41, 95% CI 1.11–1.78, p = 0.005). Model fit was overall relatively low (McFadden’s R² = 0.019). Full details, including coefficient estimates, model selection, collinearity checks, and additional diagnostic evaluations, are provided in Additional file 1: Tables S7–S9. The multinomial GLM (n = 1,524; baseline = geographic) indicated that magnetoclinic assignment was more likely for night departures (OR = 1.75, 95% CI 1.27–2.42, p < 0.001) and less likely in autumn than spring (OR = 0.68, 95% CI 0.49–0.93, p = 0.017). By segment type, the initial leg from the start of migration to the first stopover showed the highest odds of assignment to magnetoclinic, whereas mid-journey segments between stopovers and final legs from a stopover to the destination were less often labelled magnetoclinic (OR = 0.46, 0.34–0.62; and OR = 0.38, 0.25–0.57, respectively). Segments were also more likely to be assigned to local wind rather than geographic under stronger tailwinds (OR = 1.36, 95% CI 1.27–1.45, p < 0.001), weaker crosswinds (OR = 0.77, 0.69–0.87, p < 0.001), when a short pause was present (OR = 2.06, 95% CI 1.28–3.32, p = 0.003), and for intermediate legs between stopovers (OR = 1.56, 95% CI 1.06–2.30, p = 0.026). Model fit was modest (McFadden’s R² = 0.056, multiclass AUC = 0.64, overall accuracy = 39.0%). Full details are provided in Additional file 1: Tables S10–S13. We did not find evidence of repeatability within individual tracks for efficiency benchmarks (wind-optimal vs. great-circle) (R = 0.000, 95% CI: 0.000–0.015; permutation p = 1.00). At the compass level (GL, ML, MC, SC, LW), repeatability was likewise not found (R = 0.000, 95% CI ≤ 0.018), with local wind showing a measurable but very small ICC (R ≈ 0.017, 95% CI: 0.000–0.039; permutation p = 0.023). Discussion By comparing observed flight paths with simulated navigation strategies, we assess how greater white-fronted geese align their movement with alternative compass mechanisms and efficiency benchmarks. At the compass level, three main patterns emerge from our results. First, routes following a geographic loxodrome were most often the closest match to observed trajectories, with magnetoclinic routes generally ranking second. Geomagnetic loxodromes and time-compensated sun compass routes were slightly less frequent but contributed similar shares as the most closely aligned, while the local wind-aligned model was the least common strategy overall. Second, these outcomes resolved into two clear clusters. Geographic and geomagnetic loxodromes frequently alternated as the most similar and second most similar, with only modest differences in similarity. This result is expected where magnetic declination is weak or changes gradually along the flyway, making a constant magnetic bearing coincide with a geographic loxodrome over segment-scale distances [ 33 ]. Magnetoclinic and sun compass routes likewise tended to co-occur as best/runner-up for the same segments, yielding similarly shaped paths via different mechanisms. This supports the view that different compass systems can yield equivalent orientation outcomes, with multiple cues converging on a similar directional reference [ 10 , 62 , 63 ]. Third, these groupings suggest a degree of structural redundancy: several compass rules can produce routes that are difficult to discriminate on the basis of segment-scale trajectories alone, as their mutual differences are often smaller than their collective differences from the observed tracks. The local wind-aligned model was a clear exception, resulting in largely independent routes, which was expected as this mechanism continuously adjusts headings to the instantaneous wind field. At the efficiency level, a larger share of autumn flight segments were most closely aligned with global wind-optimal (WO), whereas spring segments more often matched the great-circle (GC) route. This seasonal split reflects interactions between migration-corridor structure, fuel-use strategies and prevailing winds [ 21 , 23 , 64 ]. In autumn, migration follows a comparatively narrow southwest-bound corridor that repeatedly intersects persistent crosswind bands [ 65 , 66 ]. Maintaining a strict GC course would invite lateral drift, so birds actively adjusted headings to limit drift, producing broad arcs that pulled realised paths toward WO (see Fig. 6 a). This pattern is also consistent with intentional use of supportive tailwinds to save energy and move quickly toward the wintering grounds in autumn [ 21 ]. In spring, the corridor is broader and more heterogeneous, with more dispersed initial bearings. This season included more stopovers, subdividing routes into additional legs and creating more opportunities to depart under favourable local winds [ 3 , 64 ]. Accordingly, local wind-aligned routes were two- to threefold more frequent in spring. With winds more often aligned to the migratory axis [ 65 ], and with denser spring stopovers providing more opportunities to depart under favourable conditions, global wind-optimal detours become less necessary. Birds, therefore, tend to accept modestly suboptimal wind headings to maintain straighter, more direct segment paths, increasing GC matches in spring. Our results point to a navigation system that is flexible and shaped by environmental context. They show that multiple compass options can yield workable headings under the same spatiotemporal conditions [ 62 , 63 ], while seasonal wind regimes and corridor geometry influence whether realised paths prioritise spatial directness or energetic economy [ 21 , 23 , 65 ]. This interpretation is supported by our GLM analysis, which shows that the likelihood of observed routes aligning with wind-efficient paths (local or global) varies with season and wind support. Segments started at night had a higher rate of magnetoclinic assignments, aligning with a light-dependent magnetic compass [ 67 , 68 ]. Segments containing short pauses were more often on wind-efficient routes, consistent with brief halts under unfavourable or turbulent winds or short delays to exploit improved tailwinds [ 2 , 3 , 69 ]. Finally, local-wind alignment was stronger on mid-journey than on initial or terminal legs, matching evidence that winds shape en-route geometry via detours with waypoint choices tracking contemporaneous support [ 70 , 71 ] and models predicting flexible placement and timing of legs to capitalise on support [ 72 , 73 ]. Repeatability was negligible across years and journeys, indicating that neither the assigned efficiency class nor the compass match constitutes a stable, repeatable individual tendency. This pattern aligns with earlier studies reporting low or context-dependent repeatability in migratory routes [ 74 , 75 ]. Low repeatability may arise because changing atmospheric conditions reshape the decision landscape on each leg, with winds periodically favouring different solutions and thus obscuring consistent individual tendencies [ 74 , 75 ]. These patterns reveal a navigation process in greater white-fronted geese that relies on opportunistic adjustments to prevailing conditions, in when they leave and in how they fly, rather than on consistent personal strategies. Although individuals contributed different numbers of segments, the uniformly negligible repeatability suggests that this outcome is unlikely to result from sampling imbalance. Our comparison outcomes depend on several deliberate choices. First, we initialised all compass simulations with the empirically observed departure bearing rather than a population-mean or idealised heading. If a time-compensated sun compass is initialised with an ideal, destination-aware initial direction at mid to high latitudes, it will tend to follow a route that closely tracks the great circle, irrespective of the birds’ actual departure headings. Second, we time-aligned simulations to each observed segment, matching realised ground speeds and short pauses. This reduced artefacts from fixed step lengths or constant speeds and ensured that similarity scores reflected behaviour within a shared space–time and environmental context. Third, we evaluated similarity with three complementary metrics, providing a more robust foundation for interpretation. For instance, directional similarity increased the share of geographic loxodrome assignments by roughly ten percentage points relative to MGD/DTW, illustrating how metric choice could alter biological inference. Our inferences should be interpreted considering several constraints of scope and data. In this study, we compared only a subset of the potential range of navigational strategies, as inference was derived from GPS and globally available environmental data. We did not incorporate other sensory systems implicated in avian navigation, including visual landmarks [ 76 ], polarised light [ 22 ], olfaction [ 77 ], or social information [ 1 ]. Likewise, cognitive processes, including spatial memory [ 78 ], prior experience [ 79 ], and map-like representations [ 80 ] lay beyond the scope of our framework. These unmodelled mechanisms may underlie part of the residual variance not captured by the GLMs. A further challenge lies in defining departure headings. The earliest phase of flight often includes climb, brief manoeuvres, and small reorientations, so a single true initial bearing is difficult to pin down. We therefore initialised simulations with the mean bearing over the first 100 km, which offers a practical, noise-tolerant estimate of departure orientation, while noting that window choice can slightly affect the estimate. Our environmental inputs also introduce a vertical simplification. Winds were extracted at 100 m above ground level because GPS altitude data were often missing or imprecise, preventing robust altitude-resolved annotation. This provided a pragmatic reference level, but it does not capture vertical wind shear or turbulence, thereby simplifying the three-dimensional flight environment. A similar altitude limitation applies to our geomagnetic annotations, though the impact is expected to be smaller at typical flight heights. A promising direction would be to approach migration as a multi-scale process: sub-segments defined by short pauses or directional resets, segments between stopovers, chains of successive legs, and entire trips. Within this framework, turning points are of particular interest because they provide natural opportunities to examine why headings change, whether due to shifting winds [ 36 ], loss or emergence of celestial cues [ 22 ], geomagnetic disturbances [ 20 ], recognition of landmarks [ 76 ], or physiological constraints [ 3 ]. Framing routes as linked chains delineated by such breakpoints connects fine-grained decisions to trip-scale structure. Further extensions might incorporate additional sensory inputs such as visual landmarks, olfaction, acoustic cues, and social interactions, to better capture the multisensory integration known from behavioural and neurobiological studies. Conclusions This study demonstrates that migration routes taken by greater white-fronted geese do not align with a single compass mechanism. Instead, we found evidence that greater white-fronted geese likely employ flexible, context-dependent strategies shaped by wind patterns, corridor structure, and opportunities for reorientation at stopovers. Geographic loxodromes most often were closely aligned with observed segments, with magnetoclinic routes the next most frequent overall. Yet several mechanisms prove difficult to distinguish, particularly the geographic and geomagnetic loxodromes, highlighting a functional redundancy in which different compasses can converge on broadly similar routes at the flight segment scale. Comparing observed routes to efficiency benchmarks, we found a clear seasonal contrast between wind-optimal alignments in autumn and more direct great-circle headings in spring, which highlights how birds balance energetic economy and path straightness in relation to prevailing winds, corridor geometry, and seasonal time pressure. This interpretation is reinforced by our statistical analyses, which supports that alignment with candidate routes varies with environmental context, including season, wind patterns and light regime, and also differs between mid-journey segments and the initial or terminal legs. We further found a lack of individual consistency across journeys, indicating that navigation more likely reflects opportunistic adjustment rather than stable individual traits. Declarations Supplementary Information The online version contains supplementary material available as Additional file 1. Acknowledgements We would like to thank the Dutch Society of Goose catchers for the financial and technical support in catching and tagging the geese in their Dutch and German wintering grounds. Catching geese in the Russian breeding grounds was performed as a collaboration of the Institute of Geography-RAS, Alterra Wageningen-UR, the Institute for Waterbird and Wetlands Research (IWWR) e.V. and the Max Planck Institute for Ornithology. Funding This work forms part of a PhD project funded by the St Andrews Postgraduate Research Widening Access Scholarship (School of Geography & Sustainable Development, University of St Andrews, UK). The funder had no role in study design, data collection, analysis, interpretation, or the decision to submit the article. Data collection was supported by the Lower Saxony Ministry of Food, Agriculture and Consumer Protection and by the ICARUS grant from the German Aerospace Center. Contributions AM conceived the study, designed the simulation framework, led data curation, performed all analyses, produced all visualisations, and wrote the first draft. JAL contributed to methodology, validated analyses, provided supervision, and revised the manuscript. AK provided resources and data curation and revised the manuscript. HK provided resources and revised the manuscript. FBP developed software components, validated analyses, and revised the manuscript. UD contributed to conceptualisation and methodology, provided supervision, revised the manuscript, and handled project administration. All authors read and approved the final manuscript. Availability of data and materials The complete analysis workflow is archived on GitHub (github.com/BEGIN-StAndrews/gwfg-navigation-between-stopovers). Raw GPS data originate from five Movebank studies (IDs 127892189, 408961322, 13183695, 180156318, 44083081) and are available under their original terms. Ethics approval and consent to participate All data collection procedures were carried out in accordance with ethical guidelines of the respective countries. Catching and equipment of birdsind with transmitters were carried out in Russia under the umbrella of a personal permit to Petr Glazov at the Institute of Geography of the Russian Academy of Sciences, in the Netherlands with approval by the Animal Welfare Committee of the Royal Netherlands Academy of Arts and Sciences (DEC NIOO13.14) and in Germany with the permission of the Lower Saxony State Office for Consumer Protection and Food Safety (LAVES; Akt.Z. 33.19-4202-04-15/1956). Consent to Publish declaration Consent to Publish declaration: not applicable. Competing interest The authors declare that they have no competing interests. References Flack A, Aikens EO, Kölzsch A, Nourani E, Snell KRS, Fiedler W, et al. New frontiers in bird migration research. 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J Comp Physiol A. 2022;208:41–67. https://doi.org/10.1007/s00359-021-01529-8 Additional Declarations No competing interests reported. Supplementary Files Additionalfile1.docx Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 30 Jan, 2026 Reviews received at journal 29 Jan, 2026 Reviews received at journal 09 Jan, 2026 Reviewers agreed at journal 10 Dec, 2025 Reviewers agreed at journal 08 Dec, 2025 Reviewers invited by journal 05 Dec, 2025 Editor assigned by journal 15 Nov, 2025 Submission checks completed at journal 15 Nov, 2025 First submitted to journal 10 Nov, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8080422","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":545488516,"identity":"627cbe82-4ee7-4b3f-b602-35af2033fe42","order_by":0,"name":"Ali Moayedi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8klEQVRIiWNgGAWjYFAC5sMPPlRAmBII0QP4tLClGc44A1FNrBYeBWnONlK08E87w2DMOK+ujoH97MHbFRWH7RnYDz9g5jmDW4vE7dwDjwu3HZZg4MlLtjxz5nBiA0+aATPPDTzuup2XYDxz2wEJ+wM5ZpKNbbcTGBhyGJh5PuDWIX87x0Cad06dBAP/G6CWf7ftgQz8WgzAWhqYJRgkQLY03GZskADZgsdhhrfTgIF87LBkg8QbY8uGY/8T2ySeGRycg8f7creTgVFZU8fPwJ9jeLOhJs2enz/54YM3x/B4HwOwMRCIyFEwCkbBKBgFhAEAdmhQbonnEVcAAAAASUVORK5CYII=","orcid":"","institution":"University of St Andrews","correspondingAuthor":true,"prefix":"","firstName":"Ali","middleName":"","lastName":"Moayedi","suffix":""},{"id":545488517,"identity":"aeac80f0-0dc0-4e44-9d6c-9f31ee1b6826","order_by":1,"name":"Jed Long","email":"","orcid":"","institution":"Western University","correspondingAuthor":false,"prefix":"","firstName":"Jed","middleName":"","lastName":"Long","suffix":""},{"id":545488518,"identity":"bf53f416-adb8-49ad-a584-64f7ddfe8a2b","order_by":2,"name":"Andrea Kölzsch","email":"","orcid":"","institution":"Radboud University","correspondingAuthor":false,"prefix":"","firstName":"Andrea","middleName":"","lastName":"Kölzsch","suffix":""},{"id":545488519,"identity":"0b9594c8-2f61-434d-a0f6-5ee5d33f1cd2","order_by":3,"name":"Helmut Kruckenberg","email":"","orcid":"","institution":"Institute for Wetlands and Waterbird Research e.V. (IWWR)","correspondingAuthor":false,"prefix":"","firstName":"Helmut","middleName":"","lastName":"Kruckenberg","suffix":""},{"id":545488520,"identity":"27073c5b-76a8-46c5-9dec-312ada0312c1","order_by":4,"name":"Fernando Benitez-Paez","email":"","orcid":"","institution":"University of St Andrews","correspondingAuthor":false,"prefix":"","firstName":"Fernando","middleName":"","lastName":"Benitez-Paez","suffix":""},{"id":545488521,"identity":"bd2fcf87-93e1-48bb-832e-d1c5f7d48b39","order_by":5,"name":"Urška Demšar","email":"","orcid":"","institution":"University of St Andrews","correspondingAuthor":false,"prefix":"","firstName":"Urška","middleName":"","lastName":"Demšar","suffix":""}],"badges":[],"createdAt":"2025-11-10 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07:59:48","extension":"html","order_by":19,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":203900,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-8080422/v1/f3fdd8ef2defae52af51c9fc.html"},{"id":96153554,"identity":"29f8471c-1e05-4139-a093-a387f9793e57","added_by":"auto","created_at":"2025-11-18 07:59:48","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":249608,"visible":true,"origin":"","legend":"\u003cp\u003eThree modelled routes from the same origin–destination pair (yellow endpoints). Geographic loxodrome (blue): propagated with a fixed bearing to true north, crossing each geographic meridian at a constant angle. Geomagnetic loxodrome (red): propagated with a fixed bearing to magnetic north, crossing each geomagnetic meridian at a constant angle. Great-circle route (green): follows the geodesic arc between the endpoints—the shortest spherical path—and requires continual heading adjustment. Geographic north/meridians in grey, geomagnetic north/meridians in red.\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8080422/v1/0ff7d3e7dfdcba74666eb92c.jpeg"},{"id":96153556,"identity":"90df3d15-fd28-4c6c-852d-107801ab9c4b","added_by":"auto","created_at":"2025-11-18 07:59:48","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":213876,"visible":true,"origin":"","legend":"\u003cp\u003eApparent inclination (I′)during flight as a function of the inclination (I) and the heading (α). Coloured right-angled triangles illustrate the decomposition of the magnetic field: ais the horizontal component along the bird’s course, b the vertical component, and c the resultant indicating the overall field magnitude sensed by the bird.\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8080422/v1/9c32f00911263a825baae0ac.jpeg"},{"id":96153558,"identity":"ccdd37e8-a236-44e1-9679-533f5d6a585d","added_by":"auto","created_at":"2025-11-18 07:59:48","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":243489,"visible":true,"origin":"","legend":"\u003cp\u003eIllustration of a time-compensated sun compass route. The trajectory begins at local sunrise (green circle) and ends at local sunset (green triangle), with headings adjusted continuously to remain locked to the departure sun’s azimuth. All labels are in local time, with waypoints plotted at 3-hour flight intervals. The orange sun arc traces the modelled apparent solar path along the route.\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8080422/v1/15bf32e229d2ad40678fc630.jpeg"},{"id":96250656,"identity":"d237ceba-ad50-4940-b704-5420a6d51d5e","added_by":"auto","created_at":"2025-11-19 07:38:49","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":432692,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eComparison of local \u003c/strong\u003ewind‐aligned \u003cstrong\u003eand global wind-optimal trajectories with real wind data. The green line illustrates the local \u003c/strong\u003ewind‐aligned \u003cstrong\u003estrategy, which adjusts its heading at each step to maximise instantaneous tailwind support. The red path results from a global optimisation that accounts for future winds to minimise total travel time to the destination. The blue arrows depict the contemporaneous wind field sampled at three successive time slices (t₁–t₃). The start and destination are marked by an orange circle and triangle, respectively. Within each panel, open circles indicate the current step endpoint, and filled circles denote previously reached positions.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8080422/v1/ed32e264729828dd7e58b9af.jpeg"},{"id":96251901,"identity":"9bdf43f2-c6a3-4a98-a288-27917fc616aa","added_by":"auto","created_at":"2025-11-19 07:40:10","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":837833,"visible":true,"origin":"","legend":"\u003cp\u003eSpring (left) and autumn (right) flight segments of greater white-fronted geese. Lines represent flight segments and points represent departure and arrival locations, along with the stopovers in between.\u003c/p\u003e","description":"","filename":"floatimage5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8080422/v1/dd07529cf98cb330461a6262.jpeg"},{"id":96153559,"identity":"12b4953c-9e90-4f19-b8d1-fcca85a5e394","added_by":"auto","created_at":"2025-11-18 07:59:48","extension":"jpeg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":1116741,"visible":true,"origin":"","legend":"\u003cp\u003eRepresentative flight segments illustrating close alignment with theoretical navigation routes. (a) An autumn flight segment maintains a stable heading near the geographic loxodrome (dark blue), deviating from the shortest path by only a small margin. (b) A spring flight segment follows a trajectory closely matching the local wind-aligned route (bright green), highlighting responsiveness to local airflow. (c) An autumn flight segment traces a broad arc aligned with the global wind-optimal route (green dashed), reflecting an adaptive response to large-scale wind flow. (d) An autumn flight segment matches the great-circle path (dashed red) despite sustained headwinds, prioritising spatial directness. Observed tracks (black) connect consecutive one-hourly fixes; circles mark hourly positions, with filled circles indicating nighttime movement (sun altitude \u0026lt; –6°).\u003c/p\u003e","description":"","filename":"floatimage6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8080422/v1/c08d883d2ca2850bf450b6f4.jpeg"},{"id":96153571,"identity":"2f514a40-aeff-41e7-8070-360b89485fdf","added_by":"auto","created_at":"2025-11-18 07:59:48","extension":"jpeg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":762452,"visible":true,"origin":"","legend":"\u003cp\u003eFlight segment classifications by similarity metric for spring (left) and autumn (right). Panels show (a) MGD—spatial similarity, (b) DTW—spatiotemporal similarity, and (c) DIR—directional similarity. Flight segments are grouped by efficiency benchmark (GC vs WO) and flow into compass strategies; link widths are proportional to frequencies and node labels report the percentage of flight segments assigned to each class.\u003c/p\u003e","description":"","filename":"floatimage7.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8080422/v1/f7caad4ea340bd4a780873b0.jpeg"},{"id":96256962,"identity":"4e8d8b64-613e-4dd8-b190-6bba2a8a638b","added_by":"auto","created_at":"2025-11-19 07:51:07","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5032866,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8080422/v1/09421d7f-1d27-4912-98e7-e11d262183b6.pdf"},{"id":96251752,"identity":"082b3c91-0d4f-4e41-8c55-e46c3a5fcb35","added_by":"auto","created_at":"2025-11-19 07:40:00","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":2253927,"visible":true,"origin":"","legend":"","description":"","filename":"Additionalfile1.docx","url":"https://assets-eu.researchsquare.com/files/rs-8080422/v1/5277a97626b3407b9e9dd1ee.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Navigation Between Stopovers by Greater White-Fronted Geese: Comparing Compass Mechanisms and Efficiency Benchmarks","fulltext":[{"header":"Background","content":"\u003cp\u003eBillions of birds migrate across continents each year, linking breeding and wintering grounds through journeys mostly punctuated by a series of stopovers [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. These stopovers divide the overall trajectory into successive flight segments, each undertaken under a new combination of internal conditions such as fuel reserves and circadian timing, and external factors including wind patterns and light regime [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. As these conditions shift between departures, the navigational choices guiding each segment can differ considerably. However, most studies continue to treat migration as a single continuous process from origin to destination, overlooking how variation among segments shapes the structure of migratory routes [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eTheoretical approaches to avian navigation are often contrasted as globally optimised routes and locally guided compass mechanisms [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Efficiency benchmarks describe theoretical optima such as the great-circle path, which minimises distance, and a global wind-optimal path, which minimises wind-related energetic cost [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. These benchmarks rely on non-local knowledge, including destination geometry or future winds. Compass mechanisms are biologically plausible decision rules based on local cues, including a geographic loxodrome [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], a geomagnetic loxodrome [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e], magnetoclinic orientation [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], a time-compensated sun compass [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e], and local wind-aligned headings [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. However, the navigational strategies that dominate in practice remain unclear [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], likely varying with species and life stage and shifting with environmental conditions, while interpretations are further complicated by heterogeneity in study designs and analyses [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eMigratory navigation occurs within a dynamic environment where the cues that guide orientation fluctuate in their availability and reliability [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. The visibility of celestial references depends on the light regime and cloud cover [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], the magnetic compass itself is light-dependent [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e], and winds continually restructure the energetic cost and stability of candidate routes [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Geomagnetic conditions also fluctuate, and during periods of strong solar activity measured by the planetary Kp index [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e], disturbances in Earth\u0026rsquo;s magnetic field can disrupt orientation [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. These fluctuations mean that the relative advantage of alternative strategies is not constant across a migration\u003c/p\u003e\u003cp\u003eStopovers provide crucial opportunities to refuel, rest, and recalibrate compass systems, preparing birds for the next flight segment [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. At departure, migrants adjust when they leave and which headings they take to balance fuel state and time constraints with prevailing winds and weather [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Individuals with low fuel reserves are less likely to depart and are more likely to leave under tailwinds, whereas time-limited migrants may depart despite sub-optimal winds or adopt drift-aligned headings to maintain progress [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. In greater white-fronted geese (\u003cem\u003eAnser albifrons\u003c/em\u003e), longer spring stopovers and shorter autumn flights further illustrate how seasonal context modifies route choice [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. Each flight segment is influenced by its unique ecological and physiological context. Therefore, if migration is treated as one continuous path, we overlook the important decisions made at intermediate stopovers regarding each segment.\u003c/p\u003e\u003cp\u003eResearch on avian migration advances along three complementary paths. Laboratory experiments isolate orientation under controlled conditions, establishing core sensory capacities, including a stellar and a magnetic compass [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. Field experiments test responses in situ through displacement releases and cue manipulations under natural skies [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. These approaches establish what cues birds can use, but they do not explain how such mechanisms generate sustained routes across dynamic, large-scale environments [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. Route simulations of migratory navigation test whether theoretically specified navigation rules reproduce the large-scale movements observed in tracking data [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. However, the realism of these models depends on behaviourally grounded design and dynamic environmental representation [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e], which remain limited in most existing studies.\u003c/p\u003e\u003cp\u003eMany studies initialise routes from idealised or population-average headings rather than from the empirically observed departure directions of tracked birds, reducing correspondence with individual behaviour [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. Environmental drivers such as wind and geomagnetic fields are often treated as static or averaged conditions, overlooking their strong spatiotemporal variability [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. Moreover, most models represent migration as a single, uninterrupted path, neglecting the adjustments that occur at intermediate stopovers [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. Addressing these limitations requires modelling migration as a sequence of empirically grounded flight segments that capture the environmental variability and behavioural context birds experience between stopovers.\u003c/p\u003e\u003cp\u003eThis study evaluates which routing strategies align most closely with observed GPS tracks of greater white-fronted geese, focusing on flight segments between stopovers. We consider five biologically plausible compass mechanisms: geographic loxodrome, geomagnetic loxodrome, magnetoclinic, time-compensated sun compass, and local wind-aligned headings, alongside two efficiency benchmarks: the great-circle path and a global wind-optimal path. For each segment, simulations are initialised with the empirically observed departure bearing, aligned in time to the corresponding track, and driven by hourly winds and spatiotemporally varying geomagnetic fields. We analyse compass mechanisms and efficiency benchmarks separately, because the former relies on locally available cues during flight whereas the latter assume non-local knowledge of destination geometry or future winds. We then identify the closest matching compass mechanism for each observed leg, evaluate proximity to the two benchmarks, examine how these proximities vary with season and with environmental context, and test whether the resulting patterns recur within individuals across migrations.\u003c/p\u003e"},{"header":"Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003eGPS Tracking Data and Preprocessing\u003c/h2\u003e\n \u003cp\u003eWe analysed high-resolution GPS tracking data from 122 adult greater white-fronted geese, collected between 2014 and 2024 across five coordinated studies (see Data Availability). Birds were captured either on the breeding grounds at Kolguyev Island, Russia, or at wintering sites in the Netherlands and Germany [\u003cspan class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e37\u003c/span\u003e]. Each was equipped with a 35 g GPS/GPRS neckband transmitter (madebytheo) programmed to record timestamped coordinates at intervals of 1\u0026ndash;30 minutes (median: 5 minutes). The dataset spans both migration seasons and a broad flyway corridor, capturing variation in compass orientation across space, time, and diel phases in a species that migrates day and night [\u003cspan class=\"CitationRef\"\u003e21\u003c/span\u003e].\u003c/p\u003e\n \u003cp\u003eTo maintain positional accuracy, we retained only GPS fixes with low horizontal error (\u0026le;\u0026thinsp;30 m) and sufficient satellite connections (\u0026ge;\u0026thinsp;4). Outliers were removed when they fell outside the expected spatial bounds (40\u0026ndash;85\u0026deg; N, 0\u0026ndash;120\u0026deg; E), exhibited unrealistic speeds (\u0026gt;\u0026thinsp;45 m s⁻\u0026sup1;), or formed systematic trajectory anomalies. Finally, to avoid within-flock duplication, we ensured that only one bird per flock was included in the analyses.\u003c/p\u003e\n\u003c/div\u003e\n\u003ch3\u003eStopover Detection and Flight-Segment Delineation\u003c/h3\u003e\n\u003cp\u003eWe identified stopovers as periods of limited movement, defined by explicit spatial and temporal constraints while allowing for small within-period excursions [\u003cspan class=\"CitationRef\"\u003e38\u003c/span\u003e]. We first scanned for sequences of temporally contiguous fixes that exceeded a duration threshold. For each candidate period, we fitted a minimum enclosing disk to 95% of locations nearest to the median centre and retained the period as a stopover if the resulting cluster remained within 30 km for at least 48 hours, consistent with established criteria for migratory geese [\u003cspan class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e37\u003c/span\u003e]. This approach mirrors density-based residence region methods, which reduce spatial noise by excluding peripheral fixes before boundary estimation [\u003cspan class=\"CitationRef\"\u003e39\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003eFlight segments were defined as uninterrupted movements between consecutive stopovers, from the first post-departure fix to the last pre-arrival fix. We retained only segments within the migration windows (1 March\u0026ndash;31 May for spring; 15 August\u0026ndash;15 November for autumn; K\u0026ouml;lzsch et al., 2019) and excluded segments with data gaps\u0026thinsp;\u0026gt;\u0026thinsp;2 h. To distinguish migratory transit from localised repositioning, we required a net displacement\u0026thinsp;\u0026ge;\u0026thinsp;150 km [\u003cspan class=\"CitationRef\"\u003e40\u003c/span\u003e], on the premise that shorter movements may reflect stopover switching due to predation, habitat loss, or competition [\u003cspan class=\"CitationRef\"\u003e3\u003c/span\u003e]. To standardise temporal resolution and mitigate the influence of irregular sampling intervals, all retained flight segments were resampled at hourly intervals via linear interpolation.\u003c/p\u003e\n\u003ch3\u003eSimulation framework\u003c/h3\u003e\n\u003cp\u003eWe simulated seven alternative routes for each observed flight segment: five compass-based strategies\u0026mdash;geographic loxodrome (GL), geomagnetic loxodrome (ML), magnetoclinic (MC), time-compensated sun compass (SC), and local wind-aligned route (LW)\u0026mdash;and two efficiency benchmarks: the wind-optimal route (WO) and the great-circle route (GC). All simulations began at the same departure point and time as the corresponding empirical segment, ensuring alignment in origin, timing, and duration under the experienced environmental conditions. For compass-based strategies, initial bearings were set to the observed departure direction, calculated as the mean heading over the first 100 km from the stopover centre. We advanced the simulation using the observed displacement magnitudes from the track, while directions were given by the navigational rule under test. Details of each simulated strategy are listed in Additional file 1: Table \u003cspan class=\"InternalRef\"\u003eS1\u003c/span\u003e.\u003c/p\u003e\n\u003ch3\u003eGeographic Loxodrome Route\u003c/h3\u003e\n\u003cp\u003eThe geographic loxodrome (GL), or rhumb-line route, models orientation along a constant azimuth relative to geographic (true) north (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). This approach reflects navigation based on celestial rotation cues, such as star trails or the solar arc, which provide a fixed reference to Earth\u0026rsquo;s rotational axis and have been proposed as biologically plausible in migratory birds [\u003cspan class=\"CitationRef\"\u003e8\u003c/span\u003e]. Under this strategy, the initial bearing is maintained unchanged relative to true north, and positions are projected along the resulting rhumb‐line path.\u003c/p\u003e\n\u003ch3\u003eGeomagnetic Loxodrome Route\u003c/h3\u003e\n\u003cp\u003eThe geomagnetic loxodrome route (ML) assumes a constant bearing relative to magnetic north, consistent with experimental evidence for a magnetic compass in birds [\u003cspan class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e41\u003c/span\u003e] (see Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). This strategy was simulated by preserving the initial magnetic azimuth and converting it dynamically to geographic headings at each step using local geomagnetic declination, producing a magnetic rhumb-line path. Declination values were interpolated in time and space from precomputed hourly rasters (10 \u0026times; 10 km) generated from satellite geomagnetic data using the MagGeo tool [\u003cspan class=\"CitationRef\"\u003e42\u003c/span\u003e], capturing both secular variation and transient disturbances that static and gridded world geomagnetic models fail to capture [\u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e]. Geomagnetic storm exposure was then defined for each flight segment using the maximum planetary Kp index during its duration, with Kp\u0026thinsp;\u0026gt;\u0026thinsp;5 marking disturbed conditions [\u003cspan class=\"CitationRef\"\u003e19\u003c/span\u003e].\u003c/p\u003e\n\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n \u003ch2\u003eMagnetoclinic Route\u003c/h2\u003e\n \u003cp\u003eThe magnetoclinic route (MC) assumes birds maintain a constant apparent inclination (often termed the apparent dip) during flight (Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e). The apparent inclination is defined as the angle between the movement vector and the local geomagnetic field [\u003cspan class=\"CitationRef\"\u003e11\u003c/span\u003e]. We set this constant at departure based on the initial heading and local field and updated headings hourly to preserve it as conditions changed, using the simulation framework described by \u0026Aring;kesson \u0026amp; Bianco [\u003cspan class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e36\u003c/span\u003e]. Magnetic inputs (declination, inclination) were spatiotemporally interpolated from the same precomputed hourly rasters (10 \u0026times; 10 km) generated from satellite geomagnetic data via the MagGeo tool [\u003cspan class=\"CitationRef\"\u003e42\u003c/span\u003e].\u003c/p\u003e\n\u003c/div\u003e\n\u003ch3\u003eTime-Compensated Sun Compass Route\u003c/h3\u003e\n\u003cp\u003eThe time-compensated sun compass (SC) enables birds to navigate by referencing the sun\u0026rsquo;s azimuth against an internal circadian clock [\u003cspan class=\"CitationRef\"\u003e43\u003c/span\u003e]. In the clock-synchronous mode, the internal clock is reset to local solar time, producing a constant compass bearing and a geographic loxodrome [\u003cspan class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e34\u003c/span\u003e]. In the departure-time‐locked mode, the clock remains fixed at its calibration phase, causing a progressive mismatch between local time and internal time as the bird moves across longitudes [\u003cspan class=\"CitationRef\"\u003e44\u003c/span\u003e] (Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e). This mismatch progressively distorts the perceived solar azimuth, producing systematic curvature in the route, often approximating a great-circle path at mid and high latitudes [\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e44\u003c/span\u003e]. Seasonal changes in solar declination also shift the azimuth of reference events (e.g., sunrise, sunset), requiring explicit correction [\u003cspan class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e33\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003eIn our simulations, each flight segment was assigned a calibration sun based on departure light conditions\u0026mdash;sunrise for daytime departures, sunset for night, or solar midnight/noon in polar-light regimes. Headings were then updated hourly from the initial direction according to:\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\" style=\"width: 573px; height: 82.798px;\" width=\"573\" height=\"82.798\"\u003e\u003c/p\u003e\n\u003cp\u003eHere, \u0026theta;\u003csub\u003es\u003c/sub\u003e(\u0026phi;,\u0026lambda;) is the azimuth of the chosen solar event at position (\u0026phi;,\u0026lambda;), and \u0026omega;\u003csub\u003eref\u003c/sub\u003e is the solar angular velocity at departure [\u003cspan class=\"CitationRef\"\u003e44\u003c/span\u003e]. The solar-geometry correction accounts for seasonal/latitudinal changes in the calibration sun\u0026rsquo;s azimuth between the current and departure positions, while the clock-drift correction represents the accumulated shift in perceived solar position due to longitudinal displacement, scaled by Earth\u0026rsquo;s 15\u003csup\u003e∘\u003c/sup\u003eh\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e rotation.\u003c/p\u003e\n\u003ch3\u003eLocal Wind-aligned Route\u003c/h3\u003e\n\u003cp\u003eThe local wind-aligned route (LW) models a navigation strategy in which birds continually adjust their heading to maximise instantaneous tailwind support by aligning with the prevailing wind direction (Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e). Unlike global wind‐optimal paths, which minimise energy or time costs across the entire flight segment [\u003cspan class=\"CitationRef\"\u003e7\u003c/span\u003e], this approach is a greedy, locally optimal heuristic, consistent with observations that birds select favourable winds at departure [\u003cspan class=\"CitationRef\"\u003e2\u003c/span\u003e], and adjust headings to exploit them during flight [\u003cspan class=\"CitationRef\"\u003e45\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e46\u003c/span\u003e]. In the simulation, hourly headings were set to the wind direction at the simulated position and time, obtained from the ERA5 reanalysis (100 m above ground level) at hourly resolution [\u003cspan class=\"CitationRef\"\u003e47\u003c/span\u003e].\u003c/p\u003e\n\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\n \u003ch2\u003eGlobal Wind-Optimal Route\u003c/h2\u003e\n \u003cp\u003eThe global wind-optimal route (WO) is the first efficiency benchmark, modelling the path that minimises total travel time (as a proxy for energy cost) between origin and destination by exploiting the spatial and temporal structure of winds (Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e). Based on control theory and optimal path planning [\u003cspan class=\"CitationRef\"\u003e7\u003c/span\u003e], it represents a theoretical upper bound on time savings achievable through perfect wind use. Studies indicate that such flow-aware movement is mathematically tractable and consistent with detours that enhance migratory efficiency [\u003cspan class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e48\u003c/span\u003e]. Graph-based algorithms such as Dijkstra, A*, and isochrone routing can approximate these paths efficiently; however, their reliance on static or simplified wind fields limits performance under dynamic conditions [\u003cspan class=\"CitationRef\"\u003e49\u003c/span\u003e]. In contrast, dynamic programming is widely used in aviation and maritime navigation to solve minimum-time routing under spatiotemporally varying fields, reliably producing globally optimal solutions [\u003cspan class=\"CitationRef\"\u003e50\u003c/span\u003e].\u003c/p\u003e\n \u003cp\u003eFollowing established approaches in aviation and maritime optimisation [\u003cspan class=\"CitationRef\"\u003e50\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e51\u003c/span\u003e], we implemented a dynamic programming framework to compute wind-optimal trajectories between each segment\u0026rsquo;s observed departure and arrival points (Additional file 1: Fig. \u003cspan class=\"InternalRef\"\u003eS1\u003c/span\u003e). The search space was represented as a time‐expanded graph constrained to a fixed‐width corridor centred on the great‐circle bearing but allowing lateral detours up to half the great‐circle distance. The corridor was discretised into hourly time slices, with candidate positions (nodes) spaced at 10 km intervals perpendicular to the main axis. For each potential transition between nodes, travel time was calculated as the great‐circle distance divided by wind‐adjusted ground speed, estimated by adding a constant airspeed of 15 m s⁻\u0026sup1; [\u003cspan class=\"CitationRef\"\u003e52\u003c/span\u003e] to the wind support component, projected onto the transition bearing. To capture within‐step variability in wind, vectors were evaluated at the spatiotemporal midpoint of each transition, improving ground‐speed estimates under dynamic conditions [\u003cspan class=\"CitationRef\"\u003e53\u003c/span\u003e]. The dynamic programming algorithm then evaluated all feasible transitions in a forward pass and reconstructed the minimum‐time route through backtracking.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\n \u003ch2\u003eGreat-Circle Route\u003c/h2\u003e\n \u003cp\u003eThe great-circle (GC) route, or orthodrome, represents the shortest geodesic path between two points on a sphere (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). Unlike compass-based strategies that maintain a fixed bearing, it requires continual adjustment of heading to follow the minimal-distance arc [\u003cspan class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e]. As it defines the lower bound on distance, the great-circle route is widely used as an efficiency benchmark in avian navigation [\u003cspan class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e34\u003c/span\u003e].\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\n \u003ch2\u003eRoute Summary Measures\u003c/h2\u003e\n \u003cp\u003eFor each flight segment, we calculated key descriptive statistics summarising its geometry, timing, and environmental context. These measures provided the quantitative basis for later comparisons with simulated routes and for assessing seasonal differences in segment properties. Segment duration was defined as the elapsed time between the first post-departure and last pre-arrival fix. Cumulative travel distance was calculated as the sum of successive step lengths. To measure path directness, we calculated the straightness index as the ratio of the great-circle distance to the cumulative distance. Each flight segment was also annotated with the maximum planetary Kp index recorded during its duration, to quantify exposure to geomagnetic disturbances. In addition, we measured solar altitude at departure and classified departures as nocturnal when the sun was more than 6\u0026deg; below the horizon, a threshold corresponding to civil twilight and widely used in avian movement studies.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\n \u003ch2\u003eRoute Similarity Measures\u003c/h2\u003e\n \u003cp\u003eA rigorous, quantitative comparison between simulated and empirical flight paths is essential for assessing the plausibility of candidate navigation mechanisms in migrating birds [\u003cspan class=\"CitationRef\"\u003e31\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e]. Traditional approaches based solely on endpoint proximity or qualitative visual agreement [\u003cspan class=\"CitationRef\"\u003e36\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e54\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e55\u003c/span\u003e] cannot determine whether two routes share fine-scale spatiotemporal structure or consistent directional tendencies along their entire course [\u003cspan class=\"CitationRef\"\u003e56\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e57\u003c/span\u003e]. Trajectory-similarity analysis, using distance-based measures such as Dynamic Time Warping (DTW), Fr\u0026eacute;chet distance, or the Longest Common Subsequence (LCSS), provides a formal means of detecting such correspondences [\u003cspan class=\"CitationRef\"\u003e56\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e58\u003c/span\u003e], with metrics falling broadly into three complementary classes: spatial similarity, spatio-temporal similarity, and directional similarity.\u003c/p\u003e\n \u003cp\u003eTo represent each of these dimensions, we applied three corresponding metrics to every flight segment. Spatial similarity was quantified as the median point-wise geodesic distance (MGD) between temporally matched fixes [\u003cspan class=\"CitationRef\"\u003e59\u003c/span\u003e]. Spatio-temporal alignment was quantified using Dynamic Time Warping (DTW) on fix coordinate sequences, accommodating differences in pacing, sampling rate, or stop duration [\u003cspan class=\"CitationRef\"\u003e60\u003c/span\u003e]. Directional consistency (DIR), a key aspect of navigational behaviour, was measured as the cosine similarity between successive heading vectors derived from consecutive fix positions [\u003cspan class=\"CitationRef\"\u003e61\u003c/span\u003e]. For definitions and expected ranges, see Additional file 1: Table S2.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\n \u003ch2\u003eStatistical Analyses\u003c/h2\u003e\n \u003cp\u003eRoute-similarity scores quantify correspondence between simulated strategies and observed segments, yet they leave open the relationships among strategies, the conditions under which certain patterns emerge, and the extent to which individuals behave consistently across migrations. We therefore applied statistical analyses to reveal the environmental structure and behavioural consistency underlying these similarities, moving beyond spatial correspondence toward ecological interpretation.\u003c/p\u003e\n \u003cp\u003eEach flight segment was assigned to its closest-matching simulated route using the three trajectory-similarity metrics described above. We then computed pairwise Pearson correlations between segment-level similarity scores to quantify structural overlap among compass-based strategies. For each segment, we also identified the most frequent runner-up strategy and calculated the mean margin in similarity score between the winner and this competitor, providing a measure of decision margin.\u003c/p\u003e\n \u003cp\u003eWe fitted a generalised linear model to assess environmental and temporal correlates of which efficiency benchmark was closest. The dependent variable was a binary indicator of whether the closest matching efficiency benchmark to an observed flight segment was the wind-optimal route (coded 1) or the great-circle route (coded 0). The independent variables we considered were: season (spring; autumn), mean tailwind support (m s⁻\u0026sup1;), mean crosswind (m s⁻\u0026sup1;), geomagnetic-storm exposure during the segment (storm: Kp\u0026thinsp;\u0026ge;\u0026thinsp;5; no storm: Kp\u0026thinsp;\u0026lt;\u0026thinsp;5), light regime at departure (day; night), great-circle distance (km), segment duration (h), segment type (origin\u0026ndash;stopover; stopover\u0026ndash;stopover; stopover\u0026ndash;destination), presence of a short pause (yes; no), and durations of the preceding and following stopovers (h). Model selection was performed via stepwise comparison of additive models using the Akaike Information Criterion (AIC). Collinearity among predictors was assessed, but no variables required removal (all variance inflation factors\u0026thinsp;\u0026lt;\u0026thinsp;3). Model adequacy was assessed using residual deviance, AIC, pseudo-R\u0026sup2; (McFadden\u0026rsquo;s, Tjur\u0026rsquo;s), and standard diagnostic checks (residuals, discrimination, calibration, influence).\u003c/p\u003e\n \u003cp\u003eWe also fitted a multinomial generalised linear model to examine factors associated with compass-based route choice, distinguishing among five navigation types: geographic (reference), geomagnetic, magnetoclinic, sun, and local wind-aligned. The same set of candidate predictors used in the efficiency model was included, and the final additive structure was selected through stepwise comparison using the AIC. Collinearity checks confirmed that all adjusted variance inflation factors were below 3, and overall model adequacy was evaluated using standard measures of explanatory strength and predictive performance.\u003c/p\u003e\n \u003cp\u003eFinally, we assessed within-individual repeatability for the efficiency benchmark (wind-optimal vs great-circle) and for the compass choices (GL, ML, MC, SC, LW; one-vs-rest). Analyses were restricted to individuals with at least two flight segments. For each binary outcome, we fitted a generalised linear mixed model with individual ID included as a random intercept, and computed repeatability (intra-class correlation, ICC) on the latent (logit) scale. Uncertainty was quantified using parametric bootstrap confidence intervals (B\u0026thinsp;=\u0026thinsp;1000) and permutation-based p-values (P\u0026thinsp;=\u0026thinsp;1000).\u003c/p\u003e\n\u003c/div\u003e"},{"header":"Results","content":"\u003cp\u003eWe identified 1524 migratory flight segments from 122 individuals, consisting of 1137 spring and 387 autumn flight segments. Spring and autumn migration routes broadly overlapped along the Baltic\u0026ndash;Barents\u0026ndash;Kara corridor, though notable differences in spatial extent and path geometry were observed. Autumn flights tended to follow narrower, straighter routes, while spring routes showed more variable orientations and detours over eastern Europe (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). These patterns are reflected in summary statistics of flight segment properties, such as straightness, duration, and directional spread (Additional file 1: Table S3).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eTo illustrate the diversity of observed navigation behaviours before formal classification, we first present examples of real flight segments that are closely aligned with the navigation mechanisms previously identified. One autumn flight segment (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea) closely follows the geographic loxodrome, maintaining a stable heading over a 1057 km flight and deviating from the shortest path by only 37 km. Another flight segment (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eb) shows a wind-aligned orientation response, curving northeast shortly after departure and tracking local wind structure rather than a fixed heading. The resulting 1626 km route was nearly 300 km longer than the shortest available path, highlighting an adaptive, wind-responsive course. Additional examples for the remaining compass strategies are provided in Additional file 1: Figs. S2\u0026ndash;S4. The next autumn flight segment (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ec) traced a broad arc that closely followed the global wind-optimal route, reflecting an adaptive response to large-scale wind patterns and a strategy that traded additional distance for improved ground speed and energetic efficiency. In contrast, another autumn flight segment (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ed) exemplifies a close match to the great-circle route, diverging from both wind-optimal and compass-based strategies. A brief pause early in the flight likely marked a key decision point, after which the bird committed to a spatially direct course. Despite sustained headwinds averaging \u0026minus;\u0026thinsp;4.48 m s⁻\u0026sup1;, it maintained a prolonged, uninterrupted flight of 952 km, indicating a strong preference for spatial efficiency over wind support.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eWe found evidence of structured and seasonally divergent patterns at both the efficiency and compass levels (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e). When routes were compared to the two efficiency benchmarks, results showed a clear seasonal shift: in autumn, a majority of flight segments aligned best with the global wind-optimal (WO) model (54.5\u0026ndash;55.3% across DTW and MGD), whereas in spring more flight segments aligned with the great-circle (GC) route (56.1\u0026ndash;59.6% across all three metrics). The geographic loxodrome (GL) was the compass strategy identified as the closest match with the largest share of flight segments in both autumn (42.1\u0026ndash;52.7%) and in spring (30.0\u0026ndash;40.5%). GL\u0026rsquo;s dominance is stronger under directional similarity, by roughly ten percentage points. Magnetoclinic (MC) routes were consistently the second most frequent mechanism identified as the closest match in both seasons (19.1\u0026ndash;21.4% in autumn; 21.9\u0026ndash;25.3% in spring). Assignments to the remaining compass strategies were less frequent. Geomagnetic loxodromes (ML) and sun compass (SC) models were each associated with roughly 10\u0026ndash;16% of flight segments across seasons. Local wind-aligned (LW) strategies, while the least common in autumn (5.7\u0026ndash;7.8%), were more common as the closest match in spring (12.7\u0026ndash;18.0%).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eWe next compared best-fitting strategies with their most frequent runner-up to evaluate how closely strategies overlap and compete for classification (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e2\u003c/span\u003e; Additional file 1: Tables S4\u0026ndash;S5). Two tight clusters emerged: Geographic and Geomagnetic routes alternated as runner-up in over half of flight segments (50.8\u0026ndash;86.7%) with gaps under 20%, while Sun and Magnetoclinic overlapped in 34.5\u0026ndash;85.1% of cases with similar moderate margins. In contrast, local wind-aligned routes exhibited independence: their nearest rival appeared in only 36.7\u0026ndash;54.5% of cases, and local wind-aligned surpassed that runner-up by up to 41%. This pattern was supported by correlation analysis (Additional file 1: Table S6; Additional file 1: Fig. S5). The strongest associations occurred between strategy pairs that frequently alternated as winner and runner-up. Geographic and Geomagnetic routes showed near-identical predictions, with correlations of \u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.96\u0026ndash;0.97 (DTW/MGD) and \u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.00 (DIR). Magnetoclinic and Sun strategies were also tightly aligned (\u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.95 across DTW and MGD; \u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.99 in DIR). Correlations between strategies from different clusters\u0026mdash;for instance, between Geographic and Magnetoclinic\u0026mdash;were consistently lower (MGD/DTW: \u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.84\u0026ndash;0.85). Local wind-aligned, in contrast, showed weak correlations with all other strategies (\u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.41\u0026ndash;0.45 across metrics), reinforcing its role as a structurally distinct and independently behaving model.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eRunner-up analysis for compass-based strategies (DTW similarity). For each best-fitting strategy, the table shows its most frequent second-best competitor, the proportion of times this competitor occurred (% of flight segments), and the mean improvement of the best strategy over (i) that competitor and (ii) all competitors. Results are given separately for autumn and spring flight segments.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"8\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eBest-Fitting Strategy\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eTop Second-Best\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003eTop Second-Best Frequency (%)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e\u003cp\u003eMean Improvement Over Top Second-Best\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e\u003cp\u003eMean Improvement Over All Second-Best\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eAutumn\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eSpring\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eAutumn\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eSpring\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eAutumn\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c8\"\u003e\u003cp\u003eSpring\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGL\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eML\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e71.9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e84.1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e15.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e13.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e15.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e13.3\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eML\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eGL\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e64.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e57.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e18.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e15.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e19.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e14.8\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMC\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSC\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e78.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e77.1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e18.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e18.4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e16.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e17.1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSC\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMC\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e34.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e55.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e17.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e18.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e14.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e18.6\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLW\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eGL\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e45.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e45.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e25.1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e37.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e29.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e36.3\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe binomial GLM (n\u0026thinsp;=\u0026thinsp;1,524) retained season, mean tailwind support, presence of a short pause, great-circle distance, and next-stopover duration as predictors (residual deviance\u0026thinsp;=\u0026thinsp;2062.9 on 1,518 df; AIC\u0026thinsp;=\u0026thinsp;2074.9). Segments in autumn were more likely to align with the wind-optimal model than those in spring (OR\u0026thinsp;=\u0026thinsp;1.61, 95% CI 1.27\u0026ndash;2.04, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001), and the probability increased with tailwind support (per 1 m s⁻\u0026sup1;: OR\u0026thinsp;=\u0026thinsp;1.08, 95% CI 1.04\u0026ndash;1.12, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001). Segments containing a short pause also had higher odds of wind-optimal classification (OR\u0026thinsp;=\u0026thinsp;1.41, 95% CI 1.11\u0026ndash;1.78, p\u0026thinsp;=\u0026thinsp;0.005). Model fit was overall relatively low (McFadden\u0026rsquo;s R\u0026sup2; = 0.019). Full details, including coefficient estimates, model selection, collinearity checks, and additional diagnostic evaluations, are provided in Additional file 1: Tables S7\u0026ndash;S9.\u003c/p\u003e\u003cp\u003eThe multinomial GLM (n\u0026thinsp;=\u0026thinsp;1,524; baseline\u0026thinsp;=\u0026thinsp;geographic) indicated that magnetoclinic assignment was more likely for night departures (OR\u0026thinsp;=\u0026thinsp;1.75, 95% CI 1.27\u0026ndash;2.42, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001) and less likely in autumn than spring (OR\u0026thinsp;=\u0026thinsp;0.68, 95% CI 0.49\u0026ndash;0.93, p\u0026thinsp;=\u0026thinsp;0.017). By segment type, the initial leg from the start of migration to the first stopover showed the highest odds of assignment to magnetoclinic, whereas mid-journey segments between stopovers and final legs from a stopover to the destination were less often labelled magnetoclinic (OR\u0026thinsp;=\u0026thinsp;0.46, 0.34\u0026ndash;0.62; and OR\u0026thinsp;=\u0026thinsp;0.38, 0.25\u0026ndash;0.57, respectively). Segments were also more likely to be assigned to local wind rather than geographic under stronger tailwinds (OR\u0026thinsp;=\u0026thinsp;1.36, 95% CI 1.27\u0026ndash;1.45, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001), weaker crosswinds (OR\u0026thinsp;=\u0026thinsp;0.77, 0.69\u0026ndash;0.87, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001), when a short pause was present (OR\u0026thinsp;=\u0026thinsp;2.06, 95% CI 1.28\u0026ndash;3.32, p\u0026thinsp;=\u0026thinsp;0.003), and for intermediate legs between stopovers (OR\u0026thinsp;=\u0026thinsp;1.56, 95% CI 1.06\u0026ndash;2.30, p\u0026thinsp;=\u0026thinsp;0.026). Model fit was modest (McFadden\u0026rsquo;s R\u0026sup2; = 0.056, multiclass AUC\u0026thinsp;=\u0026thinsp;0.64, overall accuracy\u0026thinsp;=\u0026thinsp;39.0%). Full details are provided in Additional file 1: Tables S10\u0026ndash;S13.\u003c/p\u003e\u003cp\u003eWe did not find evidence of repeatability within individual tracks for efficiency benchmarks (wind-optimal vs. great-circle) (R\u0026thinsp;=\u0026thinsp;0.000, 95% CI: 0.000\u0026ndash;0.015; permutation p\u0026thinsp;=\u0026thinsp;1.00). At the compass level (GL, ML, MC, SC, LW), repeatability was likewise not found (R\u0026thinsp;=\u0026thinsp;0.000, 95% CI\u0026thinsp;\u0026le;\u0026thinsp;0.018), with local wind showing a measurable but very small ICC (R\u0026thinsp;\u0026asymp;\u0026thinsp;0.017, 95% CI: 0.000\u0026ndash;0.039; permutation p\u0026thinsp;=\u0026thinsp;0.023).\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eBy comparing observed flight paths with simulated navigation strategies, we assess how greater white-fronted geese align their movement with alternative compass mechanisms and efficiency benchmarks. At the compass level, three main patterns emerge from our results. First, routes following a geographic loxodrome were most often the closest match to observed trajectories, with magnetoclinic routes generally ranking second. Geomagnetic loxodromes and time-compensated sun compass routes were slightly less frequent but contributed similar shares as the most closely aligned, while the local wind-aligned model was the least common strategy overall. Second, these outcomes resolved into two clear clusters. Geographic and geomagnetic loxodromes frequently alternated as the most similar and second most similar, with only modest differences in similarity. This result is expected where magnetic declination is weak or changes gradually along the flyway, making a constant magnetic bearing coincide with a geographic loxodrome over segment-scale distances [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. Magnetoclinic and sun compass routes likewise tended to co-occur as best/runner-up for the same segments, yielding similarly shaped paths via different mechanisms. This supports the view that different compass systems can yield equivalent orientation outcomes, with multiple cues converging on a similar directional reference [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e62\u003c/span\u003e, \u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e63\u003c/span\u003e]. Third, these groupings suggest a degree of structural redundancy: several compass rules can produce routes that are difficult to discriminate on the basis of segment-scale trajectories alone, as their mutual differences are often smaller than their collective differences from the observed tracks. The local wind-aligned model was a clear exception, resulting in largely independent routes, which was expected as this mechanism continuously adjusts headings to the instantaneous wind field.\u003c/p\u003e\u003cp\u003eAt the efficiency level, a larger share of autumn flight segments were most closely aligned with global wind-optimal (WO), whereas spring segments more often matched the great-circle (GC) route. This seasonal split reflects interactions between migration-corridor structure, fuel-use strategies and prevailing winds [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e, \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e64\u003c/span\u003e]. In autumn, migration follows a comparatively narrow southwest-bound corridor that repeatedly intersects persistent crosswind bands [\u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e65\u003c/span\u003e, \u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e66\u003c/span\u003e]. Maintaining a strict GC course would invite lateral drift, so birds actively adjusted headings to limit drift, producing broad arcs that pulled realised paths toward WO (see Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea). This pattern is also consistent with intentional use of supportive tailwinds to save energy and move quickly toward the wintering grounds in autumn [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. In spring, the corridor is broader and more heterogeneous, with more dispersed initial bearings. This season included more stopovers, subdividing routes into additional legs and creating more opportunities to depart under favourable local winds [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e64\u003c/span\u003e]. Accordingly, local wind-aligned routes were two- to threefold more frequent in spring. With winds more often aligned to the migratory axis [\u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e65\u003c/span\u003e], and with denser spring stopovers providing more opportunities to depart under favourable conditions, global wind-optimal detours become less necessary. Birds, therefore, tend to accept modestly suboptimal wind headings to maintain straighter, more direct segment paths, increasing GC matches in spring.\u003c/p\u003e\u003cp\u003eOur results point to a navigation system that is flexible and shaped by environmental context. They show that multiple compass options can yield workable headings under the same spatiotemporal conditions [\u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e62\u003c/span\u003e, \u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e63\u003c/span\u003e], while seasonal wind regimes and corridor geometry influence whether realised paths prioritise spatial directness or energetic economy [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e, \u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e65\u003c/span\u003e]. This interpretation is supported by our GLM analysis, which shows that the likelihood of observed routes aligning with wind-efficient paths (local or global) varies with season and wind support. Segments started at night had a higher rate of magnetoclinic assignments, aligning with a light-dependent magnetic compass [\u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e67\u003c/span\u003e, \u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e68\u003c/span\u003e]. Segments containing short pauses were more often on wind-efficient routes, consistent with brief halts under unfavourable or turbulent winds or short delays to exploit improved tailwinds [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e69\u003c/span\u003e]. Finally, local-wind alignment was stronger on mid-journey than on initial or terminal legs, matching evidence that winds shape en-route geometry via detours with waypoint choices tracking contemporaneous support [\u003cspan citationid=\"CR70\" class=\"CitationRef\"\u003e70\u003c/span\u003e, \u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e71\u003c/span\u003e] and models predicting flexible placement and timing of legs to capitalise on support [\u003cspan citationid=\"CR72\" class=\"CitationRef\"\u003e72\u003c/span\u003e, \u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e73\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eRepeatability was negligible across years and journeys, indicating that neither the assigned efficiency class nor the compass match constitutes a stable, repeatable individual tendency. This pattern aligns with earlier studies reporting low or context-dependent repeatability in migratory routes [\u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e74\u003c/span\u003e, \u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e75\u003c/span\u003e]. Low repeatability may arise because changing atmospheric conditions reshape the decision landscape on each leg, with winds periodically favouring different solutions and thus obscuring consistent individual tendencies [\u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e74\u003c/span\u003e, \u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e75\u003c/span\u003e]. These patterns reveal a navigation process in greater white-fronted geese that relies on opportunistic adjustments to prevailing conditions, in when they leave and in how they fly, rather than on consistent personal strategies. Although individuals contributed different numbers of segments, the uniformly negligible repeatability suggests that this outcome is unlikely to result from sampling imbalance.\u003c/p\u003e\u003cp\u003eOur comparison outcomes depend on several deliberate choices. First, we initialised all compass simulations with the empirically observed departure bearing rather than a population-mean or idealised heading. If a time-compensated sun compass is initialised with an ideal, destination-aware initial direction at mid to high latitudes, it will tend to follow a route that closely tracks the great circle, irrespective of the birds\u0026rsquo; actual departure headings. Second, we time-aligned simulations to each observed segment, matching realised ground speeds and short pauses. This reduced artefacts from fixed step lengths or constant speeds and ensured that similarity scores reflected behaviour within a shared space\u0026ndash;time and environmental context. Third, we evaluated similarity with three complementary metrics, providing a more robust foundation for interpretation. For instance, directional similarity increased the share of geographic loxodrome assignments by roughly ten percentage points relative to MGD/DTW, illustrating how metric choice could alter biological inference.\u003c/p\u003e\u003cp\u003eOur inferences should be interpreted considering several constraints of scope and data. In this study, we compared only a subset of the potential range of navigational strategies, as inference was derived from GPS and globally available environmental data. We did not incorporate other sensory systems implicated in avian navigation, including visual landmarks [\u003cspan citationid=\"CR76\" class=\"CitationRef\"\u003e76\u003c/span\u003e], polarised light [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e], olfaction [\u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e77\u003c/span\u003e], or social information [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Likewise, cognitive processes, including spatial memory [\u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e78\u003c/span\u003e], prior experience [\u003cspan citationid=\"CR79\" class=\"CitationRef\"\u003e79\u003c/span\u003e], and map-like representations [\u003cspan citationid=\"CR80\" class=\"CitationRef\"\u003e80\u003c/span\u003e] lay beyond the scope of our framework. These unmodelled mechanisms may underlie part of the residual variance not captured by the GLMs.\u003c/p\u003e\u003cp\u003eA further challenge lies in defining departure headings. The earliest phase of flight often includes climb, brief manoeuvres, and small reorientations, so a single true initial bearing is difficult to pin down. We therefore initialised simulations with the mean bearing over the first 100 km, which offers a practical, noise-tolerant estimate of departure orientation, while noting that window choice can slightly affect the estimate.\u003c/p\u003e\u003cp\u003eOur environmental inputs also introduce a vertical simplification. Winds were extracted at 100 m above ground level because GPS altitude data were often missing or imprecise, preventing robust altitude-resolved annotation. This provided a pragmatic reference level, but it does not capture vertical wind shear or turbulence, thereby simplifying the three-dimensional flight environment. A similar altitude limitation applies to our geomagnetic annotations, though the impact is expected to be smaller at typical flight heights.\u003c/p\u003e\u003cp\u003eA promising direction would be to approach migration as a multi-scale process: sub-segments defined by short pauses or directional resets, segments between stopovers, chains of successive legs, and entire trips. Within this framework, turning points are of particular interest because they provide natural opportunities to examine why headings change, whether due to shifting winds [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e], loss or emergence of celestial cues [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e], geomagnetic disturbances [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e], recognition of landmarks [\u003cspan citationid=\"CR76\" class=\"CitationRef\"\u003e76\u003c/span\u003e], or physiological constraints [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Framing routes as linked chains delineated by such breakpoints connects fine-grained decisions to trip-scale structure. Further extensions might incorporate additional sensory inputs such as visual landmarks, olfaction, acoustic cues, and social interactions, to better capture the multisensory integration known from behavioural and neurobiological studies.\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eThis study demonstrates that migration routes taken by greater white-fronted geese do not align with a single compass mechanism. Instead, we found evidence that greater white-fronted geese likely employ flexible, context-dependent strategies shaped by wind patterns, corridor structure, and opportunities for reorientation at stopovers. Geographic loxodromes most often were closely aligned with observed segments, with magnetoclinic routes the next most frequent overall. Yet several mechanisms prove difficult to distinguish, particularly the geographic and geomagnetic loxodromes, highlighting a functional redundancy in which different compasses can converge on broadly similar routes at the flight segment scale. Comparing observed routes to efficiency benchmarks, we found a clear seasonal contrast between wind-optimal alignments in autumn and more direct great-circle headings in spring, which highlights how birds balance energetic economy and path straightness in relation to prevailing winds, corridor geometry, and seasonal time pressure. This interpretation is reinforced by our statistical analyses, which supports that alignment with candidate routes varies with environmental context, including season, wind patterns and light regime, and also differs between mid-journey segments and the initial or terminal legs. We further found a lack of individual consistency across journeys, indicating that navigation more likely reflects opportunistic adjustment rather than stable individual traits.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eSupplementary Information\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe online version contains supplementary material available as Additional file 1.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe would like to thank the Dutch Society of Goose catchers for the financial and technical support in catching and tagging the geese in their Dutch and German wintering grounds. Catching geese in the Russian breeding grounds was performed as a collaboration of the Institute of Geography-RAS, Alterra Wageningen-UR, the Institute for Waterbird and Wetlands Research (IWWR) e.V. and the Max Planck Institute for Ornithology.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work forms part of a PhD project funded by the St Andrews Postgraduate Research Widening Access Scholarship (School of Geography \u0026amp; Sustainable Development, University of St Andrews, UK). The funder had no role in study design, data collection, analysis, interpretation, or the decision to submit the article. Data collection was supported by the Lower Saxony Ministry of Food, Agriculture and Consumer Protection and by the ICARUS grant from the German Aerospace Center.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eContributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAM conceived the study, designed the simulation framework, led data curation, performed all analyses, produced all visualisations, and wrote the first draft. JAL contributed to methodology, validated analyses, provided supervision, and revised the manuscript. AK provided resources and data curation and revised the manuscript. HK provided resources and revised the manuscript. FBP developed software components, validated analyses, and revised the manuscript. UD contributed to conceptualisation and methodology, provided supervision, revised the manuscript, and handled project administration. All authors read and approved the final manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and materials\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe complete analysis workflow is archived on GitHub (github.com/BEGIN-StAndrews/gwfg-navigation-between-stopovers). Raw GPS data originate from five Movebank studies (IDs 127892189, 408961322, 13183695, 180156318, 44083081) and are available under their original terms.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics approval and consent to participate\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll data collection procedures were carried out in accordance with ethical guidelines of the respective countries. Catching and equipment of birdsind with transmitters were carried out in Russia under the umbrella of a personal permit to Petr Glazov at the Institute of Geography of the Russian Academy of Sciences, in the Netherlands with approval by the Animal Welfare Committee of the Royal Netherlands Academy of Arts and Sciences (DEC NIOO13.14) and in Germany with the permission of the Lower Saxony State Office for Consumer Protection and Food Safety (LAVES; Akt.Z. 33.19-4202-04-15/1956).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent to Publish declaration\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eConsent to Publish declaration: not applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eFlack A, Aikens EO, K\u0026ouml;lzsch A, Nourani E, Snell KRS, Fiedler W, et al. 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Animal Behaviour. 2004;67:189\u0026ndash;204. https://doi.org/10.1016/j.anbehav.2003.06.007\u003c/li\u003e\n\u003cli\u003eMouritsen H, Heyers D, G\u0026uuml;nt\u0026uuml;rk\u0026uuml;n O. The Neural Basis of Long-Distance Navigation in Birds. Annual Review of Physiology. 2016;78:133\u0026ndash;54. https://doi.org/10.1146/annurev-physiol-021115-105054\u003c/li\u003e\n\u003cli\u003eWiltschko R, Wiltschko W. Avian Navigation: A Combination of Innate and Learned Mechanisms. Advances in the Study of Behavior. 2015;47:229\u0026ndash;310. https://doi.org/10.1016/bs.asb.2014.12.002\u003c/li\u003e\n\u003cli\u003eLohmann KJ, Goforth KM, Mackiewicz AG, Lim DS, Lohmann CMF. Magnetic maps in animal navigation. J Comp Physiol A. 2022;208:41\u0026ndash;67. https://doi.org/10.1007/s00359-021-01529-8\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"movement-ecology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"move","sideBox":"Learn more about [Movement Ecology](http://movementecologyjournal.biomedcentral.com/)","snPcode":"40462","submissionUrl":"https://submission.nature.com/new-submission/40462/3","title":"Movement Ecology","twitterHandle":"@BioMedCentral","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Avian migration, compass orientation, movement ecology, navigation strategies, route planning, Anser albifrons","lastPublishedDoi":"10.21203/rs.3.rs-8080422/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8080422/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eBackground\u003c/h2\u003e\u003cp\u003eLong-distance migration in many birds proceeds as a series of chained flight segments between stopovers, each undertaken under shifting winds, light conditions, and geomagnetic contexts. Yet, most analyses still model journeys as continuous paths across entire trips, applying global optima or fixed compass rules and overlooking leg-specific variations. This obscures how conditions at departure reshape headings and route geometry at the segment scale, where decisions are made.\u003c/p\u003e\u003ch2\u003eMethods\u003c/h2\u003e\u003cp\u003eWe analysed 1524 flight segments (2014\u0026ndash;2024) from 122 GPS-tagged greater white-fronted geese (\u003cem\u003eAnser albifrons\u003c/em\u003e). For each segment, we simulated five biologically plausible compass mechanisms (geographic and geomagnetic loxodromes, magnetoclinic route, time-compensated sun compass, local wind-aligned route) and two efficiency benchmarks (great-circle route, global wind-optimal route). Simulations were initialised with the observed departure bearing, time-aligned to each track, and driven by data on hourly winds and spatiotemporally varying geomagnetic fields. Similarity between observed and simulated routes was quantified using median geodesic distance, dynamic time warping and directional consistency. We then modelled environmental correlates of closest matched routes and tested within-individual repeatability across journeys.\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e\u003cp\u003eEfficiency benchmarks showed seasonal structure. In autumn, segments most often matched the global wind-optimal path. In spring, segments more frequently matched the great-circle route. Across seasons, the geographic loxodrome was the most frequent compass match, with magnetoclinic routes commonly second. Geographic and geomagnetic loxodromes often alternated as winner and runner-up with small margins, which indicates structural redundancy. Local wind-aligned routes were least common overall but occurred more often in spring. Alignment patterns varied with tailwind support, departure light regime, short pauses en route and segment position (initial, mid-journey, terminal). No within-individual repeatability was detected for either efficiency class or compass assignment.\u003c/p\u003e\u003ch2\u003eConclusions\u003c/h2\u003e\u003cp\u003eOur results support a multi-cue, context-sensitive navigation process with functional redundancy among compass options and seasonal differences in efficiency alignment. Decisions made at stopovers reshape subsequent legs, arguing for segment-focused modelling to understand how environmental conditions translate into realised routes.\u003c/p\u003e","manuscriptTitle":"Navigation Between Stopovers by Greater White-Fronted Geese: Comparing Compass Mechanisms and Efficiency Benchmarks","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-18 07:59:43","doi":"10.21203/rs.3.rs-8080422/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-01-30T14:23:09+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-01-29T17:26:23+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-01-09T12:59:03+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"244747625278031606029747585074930385682","date":"2025-12-10T20:43:17+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"49648582234250507213618311535953520790","date":"2025-12-08T18:29:47+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-12-05T11:30:52+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-11-15T10:35:23+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-11-15T10:35:02+00:00","index":"","fulltext":""},{"type":"submitted","content":"Movement Ecology","date":"2025-11-10T20:22:34+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"movement-ecology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"move","sideBox":"Learn more about [Movement Ecology](http://movementecologyjournal.biomedcentral.com/)","snPcode":"40462","submissionUrl":"https://submission.nature.com/new-submission/40462/3","title":"Movement Ecology","twitterHandle":"@BioMedCentral","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"ee641a36-5681-4185-ab92-122b6950b4e5","owner":[],"postedDate":"November 18th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-05-14T16:53:30+00:00","versionOfRecord":[],"versionCreatedAt":"2025-11-18 07:59:43","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8080422","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8080422","identity":"rs-8080422","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}