Dynamic-parameter movement models reveal drivers of migratory pace in a soaring bird

Long distance migration can increase lifetime fitness, but can be costly, incurring increased energetic expenses and higher mortality risks. Stopover and other en route behaviors allow animals to rest and replenish energy stores and avoid or mitigate other hazards during migration. Some animals, such as soaring birds, can subsidize the energetic costs of migration by extracting energy from flowing air. However, it is unclear how these energy sources affect or interact with behavioral processes and stopover in long-distance soaring migrants. To understand these behaviors and the effects of processes that might enhance use of flight subsidies, we developed a flexible mechanistic model to predict how flight subsidies drive migrant behavior and movement processes. The novel modelling framework incorporated time-varying parameters informed by environmental covariates to characterize a continuous range of behaviors during migration. This model framework was fit to GPS satellite telemetry data collected from a large soaring and opportunist foraging bird, the golden eagle (Aquila chrysaetos), during migration in western North America. Fitted dynamic model parameters revealed a clear circadian rhythm in eagle movement and behavior, which was directly related to thermal uplift. Behavioral budgets were complex, however, with evidence for a joint migrating/foraging behavior, resembling a slower paced fly-and-forage migration, which could facilitate efficient refueling while still ensuring migration progress. In previous work, ecological and foraging conditions are normally considered to be the key aspects of stopover location quality, but taxa that can tap energy sources from moving fluids to drive migratory locomotion, such as the golden eagle, may pace migration based on both foraging opportunities and available flight subsidies.

Introduction elevation models and weather and atmospheric reanalyses (Bohrer et al., 2012). We 168 followed the Movebank recommendations for interpolation methods; details are below. 169 Movement model 170 We developed a correlated random walk (CRW) movement model to reveal how changes 171 in behavior give rise to the movement paths of migrating eagles. Behavioral models that 172 use a discrete-state switching framework have proven powerful and useful for answering a 173 variety of ecological questions (e.g., Morales et al., 2004;Jonsen et al., 2005;Breed et al., 174 2009;Langrock et al., 2012). For this analysis, however, we chose to use a dynamic, time-175 varying correlation parameter, which represents behavior as a continuum rather than 176 discrete categories, to capture complex behavioral patterns that could occur on multiple 177 temporal and spatial scales (Breed et al., 2012;Auger-Méthé et al., 2017;Jonsen et al., 178 2019). We believe this approach can offer substantial flexibility, as a continuous range of 179 behaviors is more realistic and, as we show, more naturally allows modeling behavior as 180 a function of covariates. 181 The basic form of the model was a first-difference CRW presented by Auger-Méthé 182 et al. (2017), which can take the form: (2) 186 Here, ∆t i = t i − t i−1 represents the time interval between Cartesian coordinate vectors 187 x i and x i−1 for the observed locations of the animal at times t i and t i−1 . Incorporating 188 autocorrelation in behavior, γ i was a random walk, such that 189 γ i |γ i−1 ∼ N γ i−1 , ∆t 2 i σ 2 ν , σ ν > 0.
of movement, and thus behavior, of migrating individuals: estimates of γ i closer to one indicate directionally-persistent, larger-scale migratory movement, while estimates of γ i 193 closer to zero indicate more-tortuous, smaller-scale stopover movement (Breed et al., 2012;194 Auger   (or winter) range with no subsequent return to that range, and the final migration step 243 10 author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/465427 doi: bioRxiv preprint was defined as the step terminating in the apparent winter (or summer) range. This assignment was usually straightforward; however, in some cases there were apparent pre-245 migration staging areas. These were not considered part of migration and excluded from 246 the analysis here.  GDEM;Brandes and Ombalski, 2004;Bohrer et al., 2012). We also introduced wind as 258 a covariate in the behavioral process, as it can influence eagle flight as well as the flight 259 and energy landscape of many birds during migration (Shamoun-Baranes et al., 2017).

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Wind data were bilinearly interpolated from the NCEP NARR u (easterly/zonal) and v 261 (northerly/meridional) components of wind predicted 30 m above ground, from which we 262 calculated the tailwind support z tw , such that z tw ∈ (−∞, ∞) (Safi et al., 2013), where 263 positive values correspond to tailwind and negative values headwind. The bearings used 264 to calculate each z tw,i were the compass bearings required to arrive at x i+1 from x i . 265 We included a time of day interaction in the model because of clear diurnal effects.

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This also helped reduce zero inflation, particularly for thermal uplift, which often decays 267 to zero after sunset due to heat flux and atmospheric boundary layer dynamics. To 268 introduce the interaction, we used a dummy variable z 0 , such that z 0,i = 0 when t i fell 269 after sunset but before sunrise and z 0,i = 1 when t i fell after sunrise but before sunset.

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This assumed behavior was not dependent on the covariates at night, which is sensible 271 author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/465427 doi: bioRxiv preprint given observed diurnal behavioral cycles. Sunrise and sunset times local to each GPS 272 point were calculated in R with the 'sunriset' function in the package 'maptools' (R 273 Core Team, 2016;Bivand and Lewin-Koh, 2016). The final overall formulation of the 274 behavioral process for the full model was: The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/465427 doi: bioRxiv preprint dently with five chains of 300,000 HMC iterations, including a 200,000 iteration warm-up 300 phase, and retaining every tenth sample. Convergence to the posterior distribution was 301 checked with trace plots, effective sample sizes, posterior plots of parameters, and Gelman 302 diagnostics (R) for each model fit. 303 We compared candidate models with leave-one-out cross-validation approximated by  For five migration tracks, we did not consider the null model converged to the posterior 321 (e.g.,R > 1.01), but in all cases the full model showed strong evidence of convergence.

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The five migrations for which the null model did not converge were excluded from formal 323 model selection. Note that these five failed convergences were out of a total of 248 fits of 324 the candidate model formulations across migration tracks. 325 13 author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/465427 doi: bioRxiv preprint Median (interquartile range) departure and arrival dates were 5 March (4.5 d) and 27 327 March (6.4 d) in the spring and 29 September (11.7 d) and 16 November (15.5 d) in the 328 fall. On average, eagles encountered similar orographic uplift in spring and fall but more 329 intense thermal uplift and tailwind in the spring (Table 1).

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The model revealed that eagles changed their behavior on multiple scales. First, 331 there were very strong daily rhythms in behavior during migration, with birds migrating   (Table 2). While there were differences in some environmental 353 14 author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/465427 doi: bioRxiv preprint covariates) indicate that there was little to no difference in effect of flight subsidies on 355 behavior between spring and fall ( Fig. 4, Table S1). Positive coefficients on the thermal 356 uplift covariate indicate that increasing thermal uplift resulted in more highly-correlated 357 displacements, or migratory movements. Despite that, there were some migration bouts 358 not associated with great thermal uplift (Figs. 1 & 2). Coefficients close to zero for 359 orographic uplift and tailwind indicate that, in general, they were not strong drivers of 360 directionally-persistent movements, though they were probably occasionally used by birds 361 for short movements when these subsidies were available.

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Based on the model selection, the best-fitting formulation of the environmental drivers 363 of the behavioral process was variable across individuals. However, in almost all cases, 364 some form of flight subsidy was used and there was little difference between the spring 365 and fall seasons in the pattern of subsidy use ( Table 2). The high variability across 366 individuals (Table S1) was likely due to differing weather patterns and thus subsidy 367 sources encountered and/or used by each eagle as migrations were not synchronous (in 368 time or space) across individuals. In addition, inter-individual variation was much larger 369 than any difference attributable to demographic variables; we found no evidence that 370 difference in sex nor age explained patterns of flight subsidy use during migration. Note, 371 though, that all eagles included in this analysis were in adult plumage, so strong age 372 effects would not necessarily be expected.

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Here, we develop and demonstrate how dynamic parameter CRW models fit to GPS data 375 reveal the effects of variable flight subsides available along migration routes. Use of these 376 subsidies gives rise to diverse patterns in the movement of a long-distance soaring migrant.

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Behavioral changes occur continuously as available subsidies shift across space and time as 378 migration proceeds. These key driving mechanisms underlie emergent movement paths, 379 yet such processes are often hidden in the discrete satellite observations available. Our 380 15 author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/465427 doi: bioRxiv preprint behavior, and those changes in behavior to the observed movement paths, revealing time 382 series of behaviors more complex than individuals simply apportioning time between 383 migration and stopover.  Table S1). Intense thermal uplift was often associated with the peaks in daily migration 426 bouts (Fig. 1). The larger magnitude of the thermal uplift effect, relative to orographic 427 uplift, was somewhat surprising, as many individuals in our sample followed the Rocky  In spring, eagles used subsidies to drive a migration that allows timely arrival on the 461 breeding grounds, consistent with a time minimization strategy. In the fall, flight was 462 subsidized to minimize net energy use, which emerged as a much more diverse behavioral 463 repertoire during a slower fall migration ( Fig. 3; Miller et al., 2016). The more rapid and author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/465427 doi: bioRxiv preprint direct flight punctuated by bouts of tortuous, stopover-like movement in the spring (Fig.   465 3), suggest eagles pause, refuel, and/or perhaps wait for better migration conditions. This 466 aligns some with a net energy maximization strategy (Hedenström, 1993;Miller et al., 467 2016), despite the need for timely arrival on the breeding grounds to avoid fitness costs 468 (Both and Visser, 2001).
The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/465427 doi: bioRxiv preprint our modeling framework aligned with the movement ecology paradigm (Nathan et al., 522 2008); it used the observed data-GPS locations, rather than a derived metric-and a 523 theoretical movement process to infer behavior from movement patterns along tracks on 524 a spectrum ranging from stopped to rapid, directionally-persistent movement.

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Our analyses, however, showed that eagles still tended to continue along their mi-526 gration route during periods of movement most resembling stopover, but with reduced 527 movement rate and directional persistence (Figs. 1-3). This pattern suggests a joint mi-528 gration/opportunistic foraging behavior that resembles fly-and-forage migration (Strand-529 berg and Alerstam, 2007;Åkesson et al., 2012;Klaassen et al., 2017), which is consistent 530 with observations of en route hunting behavior of golden eagles by Dekker (1985). Such 531 behavior could be used to maintain balance between time expenses and energy intake, as 532 it allows simultaneous migration progress and foraging.

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This pattern does not fall very well within the "stopover" paradigm (Gill, 2007;New-534 ton, 2008), however, as true stops during the migrations we observed were rare, except 535 for expected nightly stops. Rather, migrants seemed to change their pace-either by 536 slowing down, moving more tortuously, or both-but still generally moved toward their 537 migratory destination (Figs. 1-3). Thus, instead of a discrete behavioral framework, 538 whereby migrants switch between two migratory phases (migration and stopover) with 539 very different movement and behavioral properties, we propose that for certain taxa, 540 including some and perhaps many soaring migrants, as well some migrating species in 541 other fluid environments such as fishes and marine mammals, a continuous alternative 542 framework "migratory pacing" may be more appropriate and a natural way to interpret 543 en route migratory behavior and movement dynamics. Soaring birds, even when energy 544 reserves are relatively depleted, likely can still make steady progress toward a migratory 545 goal when flight subsidies are available. Flapping migrants, on the other hand, would not 546 be able to achieve this as readily due in part to the greater energy demands for sustained 547 flight, and would require more regular refueling stopovers where migration progress is 548 temporarily completely arrested. Both opportunism in foraging and use of energetic sub-549 sidies are likely key characters of fly-and-forage behavior and the ability to change pace 550 author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/465427 doi: bioRxiv preprint of migration without actually stopping, as they relax the need for individuals to stopover 551 in specific, food-rich habitats, which are required by most migrants with less flexibility 552 in food and that lack the morphological specialization to maximally exploit the energetic 553 subsidies available in moving fluids (Piersma, 2007;Gill, 2007).

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Our model results revealed seasonal variability in migratory pacing by golden eagles.

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The tendency for eagles to exhibit movements matching fly-and-forage behavior, and 556 pace their migrations more slowly was most apparent during fall migration. In contrast, 557 spring migration was usually composed of much more punctuated events of slower-paced 558 movements but these were still extended over space (Fig. 3), indicating the eagles pace 559 their migration and employ a mixed behavioral strategy to some extent in spring as well.

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During spring, hibernating mammalian prey would be minimally available, leaving car-561 rion, along with a few non-migratory and -hibernating species (e.g., ptarmigan Lagopus 562 spp. and hare Lepus spp.), as major food sources, which could help explain the more 563 punctuated bouts of slower-pacing. Alternatively, individuals could have been slowed by 564 poor weather conditions (Rus et al., 2017). Scavenging large ungulate carcasses would be 565 extremely rewarding in terms of energy accumulation. Much of the carrion we used suc-566 cessfully to capture eagles was large ungulate (e.g., moose Alces alces), strongly suggesting 567 that the population we sampled uses carcasses during migration. The bimodal distribu-568 tion for the behavioral parameter γ in fall shows that eagles tended to budget daytime 569 behaviors approximately equally between rapid, directed and slower-paced movements 570 (Fig. 3); the high frequency and range of intermediate values are, again, evidence for the 571 more complex fly-and-forage and pacing dynamic, rather than eagles simply switching 572 between stopover and migration. This behavioral complexity might be biologically im-573 portant, allowing eagles to arrive on winter home ranges in better condition compared to 574 migration strategies that do not incorporate en route foraging opportunity. In contrast 575 to fall, daytime movements in the spring were typically faster-paced (i.e. larger-scale and 576 directionally-persistent; Fig. 3), consistent with a time minimization strategy, where ea-577 gles need to partition time more in favor of migration progress to ensure timely arrival on 578 breeding grounds (Hedenström, 1993;Alerstam, 2011;Miller et al., 2016). We thus see in 579 22 author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/465427 doi: bioRxiv preprint along the continuum between time minimization and net energy maximization strategies 581 (Alerstam, 2011;Miller et al., 2016). A migrant's pace would be expected to depend 582 upon their energetic demands, energetic subsidies available from the environment, and 583 the importance of arriving at the migration terminus in a timely fashion (Nathan et al., .

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Implications & conclusions 586 We developed and applied a movement model with time-varying parameters to help reveal 587 the mechanisms underlying the migration of a long-distance soaring migrant that relies 588 on incredibly dynamic flight subsidies. We found that variation in flight subsidies gives 589 rise to changes in migrant behavior with thermal uplift seemingly most important. While 590 these findings might be expected given previous phenomenological work (e.g., Duerr et al., 591 2012;Lanzone et al., 2012;Katzner et al., 2015;Vansteelant et al., 2015;Miller et al., 2016;592 Shamoun- Baranes et al., 2016;Rus et al., 2017), we were able to show how meteorology 593 is a mechanism driving changes in movement patterns and thus behavior.

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In the behavioral budgets of migrating golden eagles, we identified an expected daily 595 rhythm, as well as evidence for behavioral dynamics that would allow nearly simulta-596 neous foraging and migration, which is greater complexity than the traditional stopover 597 paradigm allows. Migratory pacing, facilitated by fly-and-forage behavior, expands the 598 traditional notion of stopover, whereby a bird migrates until resting and refueling is re-599 quired, at which point it stops for a brief period in specific habitat suitable for efficient 600 foraging (Gill, 2007;Newton, 2008). This advance was enabled by incorporating time- The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/465427 doi: bioRxiv preprint 10.1007/s13253-017-0283-8. The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/465427 doi: bioRxiv preprint author/funder. All rights reserved. No reuse allowed without permission.
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The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/465427 doi: bioRxiv preprint Figure 4 Table S1: Estimates of environmental covariate effects on golden eagle behavior and movements during migrations. Parameter estimates are from the correlated random walk model with full behavioral process, including and intercept (β 0 ) orographic uplift (β ou ), thermal uplift (β tu ), and tailwind support (β tw ) as predictors. Top model is the best fitting candidate of the behavioral process resulting from an approximate leave-one-out cross-validation model selection procedure.  (Vehtari etal., 2016); all models within two looic of the top model listed in order of fit (separated by /); -indicates null did not converge d oro + therm + twind Figure S1: Posterior plots of variance components of the correlated random walk model with orographic uplift, thermal uplift, and tailwind support as behavioral predictors for the spring track of golden eagle 135423. Curves are approximately Gaussian, indicating the model was well behaved and likely converged to the posterior. Figure S2: Interpolated thermal uplift as a function of latitude during spring migration. Hue corresponds to individual. Curves are from the individual level of a Bayesian hierarchical Gamma regression. The 95% Bayesian credible interval for the latitude coefficient was −0.040 < β lat < −0.015, strong evidence for a decreasing trend in thermal uplift with increasing latitude. 47 author/funder. All rights reserved. No reuse allowed without permission.
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