Module 5: Migration & Navigation
Every autumn, perhaps three million raptors move from the Palearctic to sub-Saharan Africa, streaming through a small number of narrow land bridges where soaring thermals terminate abruptly at the sea. This module develops the aerodynamic, sensory and geographical underpinnings of raptor migration in quantitative terms: the glide-polar and MacCready speed-to-fly theory that governs inter-thermal glide speed; the cognitive map built from sun, magnetic, and landmark cues; and the energetics and stochasticity of trans-water crossings. We focus on three flagship Palearctic migrants — Aquila nipalensis (steppe eagle), Clanga clanga (greater spotted eagle) and C. pomarina (lesser spotted eagle) — whose Rift Valley routes total some 12 000 km round-trip.
1. The Migratory Raptors
Of the ~350 species of diurnal raptors, about 60 are long-distance migrants. The flagship Palearctic-African migrants include:
- Aquila nipalensis (steppe eagle) — breeding from Russia to Mongolia, wintering in the African Rift Valley and the Arabian Peninsula; ~6000 km one-way.
- Clanga pomarina (lesser spotted eagle) — Eastern-European breeder wintering in Southern Africa; the longest-distance migrant of the genus.
- Clanga clanga (greater spotted eagle) — slightly larger, less obligately migratory; individuals cross the Bosphorus and Levantine flyway.
- Pernis apivorus (European honey buzzard) — famous for its thermal-soaring dependency and bottleneck concentrations at Gibraltar.
- Circus harriers, Circaetus gallicus (short-toed snake eagle), and the New-World Buteo swainsoni (Swainson’s hawk).
Movement is strongly seasonal and tied to thermal season. Adult steppe eagles often travel 200–400 km per day during peak migration by alternating climbs and glides, accumulating altitude in each thermal and then sacrificing it over many kilometres of inter-thermal glide.
Bottleneck sites
Thermals are driven by solar heating of dry land and collapse over water. Migrating raptors therefore concentrate at narrow land bridges:
- Bosphorus (Turkey): 15–20 km strait; hundreds of thousands of broad-winged raptors pass in autumn.
- Bab-el-Mandeb (Red Sea entrance):30 km; the primary land-connection between East Africa and Eurasia for Steppe-eagle-class migrants.
- Gibraltar: 14 km; Western European autumn funnel; Clanga rare but Pernis, Buteo, and Circaetus abundant.
- Veracruz (“river of raptors”):Gulf-coast Mexico, bottleneck for Buteo, Ictinia, and Swainson’s hawk; annual counts exceed 5 million.
2. Thermal Soaring and MacCready Theory
The glider analogue of raptor soaring was formalised by MacCready (1958) for competition sailplane pilots and adapted to birds by Pennycuick (1972, 1975, 1989). An eagle alternates between two phases: (A) climbing spirally in a thermal updraught of vertical velocity \( w_t \), and (B) gliding inter-thermal along a glide polar that trades speed for sink rate.
Glide polar
At airspeed \( V \), the bird’s vertical sink rate is:
\[ w_s(V) \;=\; \frac{1}{2}\rho\, C_{D0}\, S\, V^3 \cdot \frac{1}{mg} \;+\; \frac{2(mg)}{\pi e\, \text{AR}\, \rho\, S}\cdot\frac{1}{V} \]
The two terms represent parasitic (form) drag and induced (lift-dependent) drag. The minimum sink rate occurs at \( V_{\min\,s} \); the best glide ratio at a slightly higher \( V_{\max\,L/D} \).
MacCready speed-to-fly
For a cycle of climb rate \( w_t \) followed by glide at \( V \) with sink \( w_s(V) \), the average ground speed is:
\[ V_{\text{xc}}(V) \;=\; V \cdot \frac{w_t}{w_t + w_s(V)} \]
Maximising yields the MacCready condition \( V^* \frac{dw_s}{dV}(V^*) = w_s(V^*) + w_t \), equivalent to drawing the tangent from \( (0, +w_t) \) to the glide polar.
Minimum-power vs. maximum-range speed
The mechanical flight power (Pennycuick 1989) is the sum of parasitic, induced, and profile contributions:
\[ P(V) \;=\; \tfrac{1}{2}\rho C_{D0} S V^3 \;+\; \frac{2(mg)^2}{\pi b^2 \rho V} \;+\; P_{\text{pro}} \]
The minimum-power speed \( V_{\text{mp}} \) is where \( dP/dV = 0 \); the maximum-range speed \( V_{\text{mr}} \) is where \( d(P/V)/dV = 0 \) and corresponds to the tangent from the origin to the power curve. For Clanga pomarina (2.2 kg), \( V_{\text{mp}} \approx 10 \) m/s and \( V_{\text{mr}} \approx 14 \) m/s.
Slope-glide uplift and sky-sampling
In hilly terrain, ridges generate deflection uplift that eagles exploit as an auxiliary lift source (sky-sampling during slope-soar; Bohrer et al. 2012). The “river of raptors” at Veracruz is driven by these ridge-lift sources through the coastal plain. Strouhal frequency of flap-soar alternation in long-distance migrants (St = fA/U) falls in the 0.2–0.4 range characteristic of efficient flapping flight (Taylor et al. 2003).
Thermal climb-and-glide cycle
3. Navigation: Magnetic, Sun, and Landmark Compasses
A migrating raptor leaves its natal territory and accurately finds a wintering area it has never seen. The answer to “how?” is a hierarchical navigation system drawing on at least three compasses — magnetic, solar, and landmark — integrated onto an underlying cognitive map.
Magnetic compass: radical-pair mechanism
Wiltschko & Wiltschko (1972) first demonstrated that migrating European robins respond to the inclination of the magnetic field rather than its polarity. Three decades of work identified the retinal flavoprotein cryptochrome (Cry4 in birds) as the light-activated sensor. Upon blue-light excitation, a flavin– tryptophan electron transfer creates a short-lived radical pair whose singlet/ triplet recombination probability depends on the external magnetic field:
\[ \Phi_S(\theta) \;=\; \Phi_{S,0} + \Delta\Phi \cdot \bigl(3\cos^2\theta - 1\bigr) \]
where \( \theta \) is the angle between the magnetic field and the molecular axis. The signal is visuo-topographic: birds see the field as a pattern overlaid on the visual scene (Hein et al. 2011; Hiscock et al. 2016).
Sun compass with time compensation
Kramer (1952) demonstrated that birds use the sun’s azimuth, corrected by the internal circadian clock. The sun-compass correction is:
\[ \psi_{\text{heading}} \;=\; \alpha_{\text{sun}}(t) \;-\; \Omega\,(t - t_{\text{ref}}) \]
with \( \Omega = 15^\circ\) per hour on average (not exact — the sun’s azimuthal motion depends on latitude and season). Circadian phase-shift experiments predictably rotate the selected heading.
Landmark recalibration at night-roost
Night-roost sites along the flyway — traditional forests at the edge of mountain ranges, or prominent coastal promontories — provide visual reference points that recalibrate the magnetic heading estimate. Grüter & Leadbeater (2014) model this as a Bayesian update:
\[ p(x_t \mid z_t) \;\propto\; p(z_t \mid x_t)\, p(x_t \mid z_{1:t-1}) \]
with the landmark likelihood \( p(z_t \mid x_t) \) sharper than the magnetic compass likelihood, so that nightly observations dominate the posterior heading estimate.
GPS telemetry: from VHF to Argos
Viitala et al. (1995) pioneered the use of small VHF transmitters on birds of prey to reveal UV markings on rodent urine trails (a vole-hunting cue). Modern studies use Argos/GPS transmitters (20–80 g) mounted as backpack harnesses, producing sub-kilometre positional fixes at 10–30 minute intervals. The result is an unprecedented picture of individual-level migration: Meyburg et al. (2017) documented the flyway of a single lesser spotted eagle across 9 calendar years and 70 000 km of cumulative flight.
4. Energy Budgets and Bottleneck Decisions
Soaring is energetically cheap, typically 2–4 times the basal metabolic rate. Flapping flight over water is 20–30 times basal. Therefore the ecological currency that drives bottleneck routing is energy, not distance: a 2000 km land route that can be soared is cheaper than a 500 km direct water crossing that forces powered flight.
Energy budget over a crossing
For a steppe eagle making a direct crossing of width \( d \) with wind speed \( u(t) \) (positive tailwind):
\[ E_{\text{crossing}} \;=\; \int_0^{T} \Big[ P_{\text{flap}}(V_{\text{air}}) \;-\; \rho_\text{air}\, \dot{u}\, (\text{weather})\Big]\,dt \]
With stochastic wind modelled as an Ornstein–Uhlenbeck process around a mean, the crossing success probability becomes a function of the initial fat reserve, the mean wind, and the crossing length. Sharp thresholds emerge: below a critical fat reserve, all crossings fail.
Broad-front vs. narrow-front
When thermal availability is strong and fat reserves are high, some individuals choose a broad-front water crossing rather than the narrow-front land bypass. The equilibrium proportion of broad-front migrants is an evolutionarily stable strategy determined by the distribution of wind regimes and the cost of the detour.
5. Climate Change and Vulture Cross-Link
Both et al. (2006) documented that spring arrival dates for several European long-distance migrants have advanced by 10–15 days over the past four decades, matching the earlier green-up of temperate spring. Mismatch between predator arrival and prey availability is a well-documented driver of population decline in some species (e.g., Pernis apivorus in the Netherlands). Stopover habitat loss — particularly drying of the Sahelian stopover zone south of the Sahara — represents a second, independent pressure.
Vulture migration
Old World vultures (Gyps, Aegypius) are among the highest- soaring long-distance movers on the planet. Gyps rueppellii (Rüppell’s griffon) holds the bird altitude record at 11,274 m, a collision altitude inferred from the ingestion of one such vulture by a commercial aircraft over Côte d’Ivoire (Laybourne 1974). Their cross-continent movements follow the same MacCready glide-and-thermal template as accipitrid eagles and share many bottleneck sites (Bildstein 2006).
6. Flapping-Soar Alternation and Gait Transitions
Long-distance migrants must switch between pure gliding, thermal-soaring, and powered flapping as conditions dictate. The transition is not continuous: at a given wing loading, flapping below some minimum speed becomes energetically wasteful, and at speeds above the maximum-range speed flapping is again inefficient. The resulting gait-transition diagram has been formalised by Rayner (1979) and refined for raptors by Tobalske (2007).
Strouhal number of flap-soar
During flap-and-glide, the wingbeat has characteristic amplitude \( A \) and frequency \( f \); the non-dimensional Strouhal number is:
\[ \text{St} \;=\; \frac{f \cdot A}{U} \]
Taylor, Nudds & Thomas (2003) showed that flying and swimming animals cluster tightly around \( 0.2 \le \text{St} \le 0.4 \), an optimum set by the propulsive efficiency of oscillating aerofoils. Steppe-eagle flapping migration fits squarely in this band.
Wing loading and aspect ratio
Wing loading \( W/S \) (weight over wing area) and aspect ratio \( \text{AR} = b^2/S \) determine the shape of the glide polar. Aquila nipalensis has a relatively high wing loading (~80 N/m²) and a moderate aspect ratio (~6.5) — trade-offs that favour fast gliding and strong-thermal soaring over dead-low-speed manoeuvring. By contrast Clanga pomarina has lower wing loading (~55 N/m²) and similar AR, allowing it to climb in weaker thermals — a decisive advantage on the autumn crossing of the Bosphorus, where thermals collapse earliest in the afternoon.
7. Juvenile Dispersal and Natal Homing
Unlike songbirds, raptors do not inherit the migration route genetically in a vector-and-distance sense. Young steppe eagles appear to rely heavily on following experienced conspecifics during their first southbound migration, a social inheritance confirmed by Perrins et al. (2018) in a Turkish-release study. Juveniles released outside the migration period followed inexperienced paths and suffered high mortality.
Natal philopatry and gene flow
Despite the long migrations, most populations show strong natal philopatry — individuals return to within 50 km of their hatch site (Newton 1979). This creates a population-genetic texture where mtDNA haplotypes are geographically structured along the breeding range despite the 12 000 km annual round-trip.
\[ F_{ST} \;=\; \frac{\sigma_d^2}{2 \sigma_d^2 + N_e \, \sigma_m^2} \]
with dispersal variance \( \sigma_d^2 \) and migratory drift \( \sigma_m^2 \); steppe eagles show significant \( F_{ST} \) between Russian and Mongolian breeding clusters despite sharing African wintering grounds.
Simulation 1: Thermal-Soaring Glide-Polar Optimisation
A quantitative MacCready optimisation for a steppe-eagle glide polar: computing optimal inter-thermal airspeed as a function of thermal strength, the minimum-power and maximum-range speeds of the power curve, and the cross-country speed integrated over a realistic Rayleigh distribution of thermal strengths.
Click Run to execute the Python code
Code will be executed with Python 3 on the server
Simulation 2: Trans-Mediterranean Crossing with Wind and Energy Budget
Monte-Carlo simulation of a 500-km direct water crossing vs. a 2000-km land-based soaring detour for a lesser spotted eagle, with stochastic Ornstein–Uhlenbeck wind, energy-budget tracking, and the emergent success-probability surface as a function of initial fat reserve.
Click Run to execute the Python code
Code will be executed with Python 3 on the server
Key References
• MacCready, P. B. (1958). “Optimum airspeed selector.” Soaring, March, 10–11.
• Pennycuick, C. J. (1972). “Soaring behaviour and performance of some East African birds.” Ibis, 114, 178–218.
• Pennycuick, C. J. (1989). Bird Flight Performance: A Practical Calculation Manual. Oxford University Press.
• Kerlinger, P. (1989). Flight Strategies of Migrating Hawks. University of Chicago Press.
• Bildstein, K. L. (2006). Migrating Raptors of the World: Their Ecology and Conservation. Cornell University Press.
• Wiltschko, W. & Wiltschko, R. (1972). “Magnetic compass of European robins.” Science, 176, 62–64.
• Hiscock, H. G. et al. (2016). “The quantum needle of the avian magnetic compass.” Proc. Natl. Acad. Sci. USA, 113, 4634–4639.
• Viitala, J., Korpimaki, E., Palokangas, P. & Koivula, M. (1995). “Attraction of kestrels to vole scent marks visible in ultraviolet light.” Nature, 373, 425–427.
• Meyburg, B.-U., Meyburg, C. & Franck-Neumann, F. (2017). “Why do lesser spotted eagles (Clanga pomarina) from central Europe usually return in autumn via the Middle East?” Journal of Ornithology, 158, 387–397.
• Bohrer, G. et al. (2012). “Estimating updraft velocity components over large spatial scales: contrasting migration strategies of golden eagles and turkey vultures.” Ecology Letters, 15, 96–103.
• Both, C., Bouwhuis, S., Lessells, C. M. & Visser, M. E. (2006). “Climate change and population declines in a long-distance migratory bird.” Nature, 441, 81–83.
• Laybourne, R. C. (1974). “Collision between a vulture and an aircraft at an altitude of 37,000 feet.” Wilson Bulletin, 86, 461–462.
• Taylor, G. K., Nudds, R. L. & Thomas, A. L. R. (2003). “Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency.” Nature, 425, 707–711.