Abstract
Many organisms perform regular migrations over long distances. These movements are often related to feeding and reproductive periods and regulated by oceanographic conditions as well as physiological and behavioural traits. Different individual traits and their associated evolutionary constraints will ultimately shape the migratory strategy (and route) of individuals. Optimality theory can provide a framework to assess these inherent trade-offs in individual migrations and identify optimal migration routes in different conditions. Here, we present a model that describes the behavioural trade-off between migration time and energy expenditure and identifies optimal migration routes in realistic ocean conditions. The model explicitly includes a behavioural factor for individual risk management, including risks associated with moving in a stochastic environment. We test this model in three different case studies, one in an idealized theoretical context and two in realistic conditions for sea turtle migrations. We show that behavioural traits can largely influence the optimal routes in long-distance migrations, resulting in major changes in migratory pathways. Further, we assess the ability of the model to infer back behavioural traits given a set of synthetic individual tracks and show relatively good performances. However, further tests are needed to evaluate performances when accurate observations of migrations are used.
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Abrahms B, Hazen EL, Aikens EO, Savoca MS, Goldbogen JA, Bograd SJ, Jacox MG, Irvine LM, Palacios DM, Mate BR (2019) Memory and resource tracking drive blue whale migrations. Proc Natl Acad Sci U S A 116:5582–5587. https://doi.org/10.1073/pnas.1819031116
Åkesson S, Hedenström A (2007) How migrants get there: migratory performance and orientation. Bioscience 57:123–133. https://doi.org/10.1641/B570207
Akesson S, Broderick AC, Glen F, Godley BJ, Luschi P, Papi F, Hays GC (2003) Navigation by green turtles: which strategy do displaced adults use to find Ascension Island? Oikos 103:363–372. https://doi.org/10.1034/j.1600-0706.2003.12207.x
Alerstam T (2001) Detours in bird migration. J Theor Biol 209:319–331. https://doi.org/10.1006/jtbi.2001.2266
Alerstam T (2011) Optimal bird migration revisited. J Ornithol 152:5–23. https://doi.org/10.1007/s10336-011-0694-1
Alerstam T, Lindström Å (1990) Optimal bird migration: the relative importance of time, energy, and safety. In: Bird migration. Springer, Berlin Heidelberg, pp 331–351
Alerstam T, Hedenstrom A, Åkesson S (2003) Long-distance migration: evolution and determinants. Oikos 103:247–260. https://doi.org/10.1034/j.1600-0706.2003.12559.x
Baker AJ, González PM, Piersma T, Niles LJ, de Lima Serrano do Nascimento I, Atkinson PW, Clark NA, Minton CDT, Peck MK, Aarts G (2004) Rapid population decline in red knots: fitness consequences of decreased refuelling rates and late arrival in Delaware Bay. Proc R Soc B Biol Sci 271:875–882. https://doi.org/10.1098/rspb.2003.2663
Bellman R (1954) The theory of dynamic programming. Bull Am Math Soc 60:503–515. https://doi.org/10.1090/S0002-9904-1954-09848-8
Biferale L, Bonaccorso F, Buzzicotti M, Clark di Leoni P, Gustavsson K (2019) Zermelo’s problem: optimal point-to-point navigation in 2D turbulent flows using reinforcement learning. Chaos 29:103138. https://doi.org/10.1063/1.5120370
Bischof R, Loe LE, Meisingset EL, Zimmermann B, van Moorter B, Mysterud A (2012) A migratory northern ungulate in the pursuit of spring: jumping or surfing the green wave? Am Nat 180:407–424. https://doi.org/10.1086/667590
Bloch R, Bruderer B (1982) The air speed of migrating birds and its relationship to the wind. Behav Ecol Sociobiol 11:19–24. https://doi.org/10.1007/BF00297661
Block BA, Jonsen ID, Jorgensen SJ, Winship AJ, Shaffer SA, Bograd SJ, Hazen EL, Foley DG, Breed GA, Harrison AL, Ganong JE, Swithenbank A, Castleton M, Dewar H, Mate BR, Shillinger GL, Schaefer KM, Benson SR, Weise MJ, Henry RW, Costa DP (2011) Tracking apex marine predator movements in a dynamic ocean. Nature 475:86–90. https://doi.org/10.1038/nature10082
Both C, Van Turnhout CAM, Bijlsma RG et al (2010) Avian population consequences of climate change are most severe for long-distance migrants in seasonal habitats. Proc R Soc B Biol Sci 277:1259–1266. https://doi.org/10.1098/rspb.2009.1525
Bryson AE, Ho Y-C (1975) Applied optimal control
Byron CJ, Burke BJ (2014) Salmon Ocean migration models suggest a variety of population-specific strategies. Rev Fish Biol Fish 24:737–756. https://doi.org/10.1007/s11160-014-9343-0
Cardona L, Martins S, Uterga R, Marco A (2017) Individual specialization and behavioral plasticity in a long-lived marine predator. J Exp Mar Bio Ecol 497:127–133. https://doi.org/10.1016/j.jembe.2017.09.021
Carmel Y, Ben-Haim Y (2005) Info-gap robust-satisficing model of foraging behavior: do foragers optimize or satisfice? Am Nat 166:633–641. https://doi.org/10.1086/491691
Carr A (1987) New perspectives on the pelagic stage of sea turtle development new perspectives on the pelagic stage of sea turtle development. Conserv Biol 1:103–121
Carr A, Goodman D (1970) Ecologic implications of size and growth in Chelonia. Copeia 783:783. https://doi.org/10.2307/1442334
Cerritelli G, Bianco G, Santini G, Broderick AC, Godley BJ, Hays GC, Luschi P, Åkesson S (2019) Assessing reliance on vector navigation in the long-distance oceanic migrations of green sea turtles. Behav Ecol 30:68–79. https://doi.org/10.1093/beheco/ary166
Clapham PJ, Mayo CA (1987) Reproduction and recruitment of individually identified humpback whales, Megaptera novaeangliae , observed in Massachusetts Bay, 1979–1985. Can J Zool 65:2853–2863. https://doi.org/10.1139/z87-434
Cole ST, Wortham C, Kunze E, Owens WB (2015) Eddy stirring and horizontal diffusivity from Argo float observations: Geographic and depth variability. 1–9. https://doi.org/10.1002/2015GL063827.Received
Comincioli V (2010) Biomatematica: interazioni tra le scienze della vita e la matematica
Dalleau M, Kramer-Schadt S, Gangat Y et al (2019) Modeling the emergence of migratory corridors and foraging hot spots of the green sea turtle. Ecol Evol ece3.5552. https://doi.org/10.1002/ece3.5552
De Luca G, Mariani P, MacKenzie BR, Marsili M (2014) Fishing out collective memory of migratory schools. J R Soc Interface 11:20140043. https://doi.org/10.1098/rsif.2014.0043
Dingle H (2014) Migration: the biology of life on the move. Second Edition
Dvijotham K, Todorov E (2011) A unifying framework for linearly solvable control. In: Proceedings of the twenty-seventh conference annual conference on uncertainty in artificial intelligence (UAI-11). AUAI Press, Corvallis, Oregon, pp 179–186
Fagan WF, Lewis MA, Auger-Méthé M, Avgar T, Benhamou S, Breed G, LaDage L, Schlägel UE, Tang WW, Papastamatiou YP, Forester J, Mueller T (2013) Spatial memory and animal movement. Ecol Lett 16:1316–1329. https://doi.org/10.1111/ele.12165
Gauthreaux SAJ (1991) The flight behavior of migrating birds in changing wind fields: radar and visual analyses. Am Zool 31:187–204. https://doi.org/10.1093/icb/31.1.187
Girard C, Sudre J, Benhamou S, Roos D, Luschi P (2006) Homing in green turtles Chelonia mydas: oceanic currents act as a constraint rather than as an information source. Mar Ecol Prog Ser 322:281–289. https://doi.org/10.3354/meps322281
Hays GC (2017) Ocean currents and marine life. Curr Biol 27:R470–R473. https://doi.org/10.1016/j.cub.2017.01.044
Hays GC, Åkesson S, Broderick AC et al (2001) The diving behaviour of green turtles undertaking oceanic migration to and from Ascension Island: dive durations, dive profiles and depth distribution. J Exp Biol 204:4093–4098
Hays GC, Åkesson S, Broderick AC, Glen F, Godley BJ, Papi F, Luschi P (2003) Island-finding ability of marine turtles. Proc R Soc London Ser B Biol Sci 270:S5–S7. https://doi.org/10.1098/rsbl.2003.0022
Hays GC, Christensen A, Fossette S, Schofield G, Talbot J, Mariani P (2014a) Route optimisation and solving Zermelo’s navigation problem during long distance migration in cross flows. Ecol Lett 17:137–143. https://doi.org/10.1111/ele.12219
Hays GC, Mortimer JA, Ierodiaconou D, Esteban N (2014b) Use of long-distance migration patterns of an endangered species to inform conservation planning for the World’s largest marine protected area. Conserv Biol 28:1636–1644. https://doi.org/10.1111/cobi.12325
Hedenström A (2003) Optimal migration strategies in animals that run: a range equation and its consequences. Anim Behav 66:631–636. https://doi.org/10.1006/anbe.2003.2234
Horton TW, Holdaway RN, Zerbini AN, Hauser N, Garrigue C, Andriolo A, Clapham PJ (2011) Straight as an arrow: humpback whales swim constant course tracks during long-distance migration. Biol Lett 7:674–679. https://doi.org/10.1098/rsbl.2011.0279
Howard RA, Matheson JE (1972) Risk-sensitive Markov decision processes. Manag Sci 18:356–369. https://doi.org/10.1287/mnsc.18.7.356
Hulthén K, Chapman BB, Nilsson PA, Hansson LA, Skov C, Brodersen J, Vinterstare J, Brönmark C (2017) A predation cost to bold fish in the wild. Sci Rep 7:3–7. https://doi.org/10.1038/s41598-017-01270-w
Itô K (1951) On a formula concerning stochastic differentials. Nagoya Math J 3:55–66. https://doi.org/10.1017/s0027763000012216
Jørgensen C, Ernande B, Fiksen Ø, Dieckmann U (2006) The logic of skipped spawning in fish. Can J Fish Aquat Sci 63:200–211. https://doi.org/10.1139/f05-210
Lagarias JC, Reeds JA, Wright MH, Wright PE (1998) Convergence properties of the Nelder--Mead simplex method in low dimensions. SIAM J Optim 9:112–147. https://doi.org/10.1137/S1052623496303470
Lennox RJ, Chapman JM, Souliere CM, Tudorache C, Wikelski M, Metcalfe JD, Cooke SJ (2016) Conservation physiology of animal migration. Conserv Physiol 4:1–15. https://doi.org/10.1093/conphys/cov072
Luschi P, Hays GC, Del Seppia C et al (1998) The navigational feats of green sea turtles migrating from Ascension Island investigated by satellite telemetry. Proc Biol Sci 265:2279–2284. https://doi.org/10.1098/rspb.1998.0571
Luschi P, Hays GC, Papi F (2003) A review of long-distance movements by marine turtles , and the possible role of ocean currents. Oikos 103:293–302. https://doi.org/10.1034/j.1600-0706.2003.12123.x
MATLAB (2016) version 9.1 (R2016b) The MathWorks Inc., Natick, Massachusetts
McLaren JD, Shamoun-Baranes J, Dokter AM et al (2014) Optimal orientation in flows: providing a benchmark for animal movement strategies. J R Soc Interface 11:20140588. https://doi.org/10.1098/rsif.2014.0588
Metcalfe JD, Hunter E, Buckley AA (2006) The migratory behaviour of North Sea plaice: currents, clocks and clues. Mar Freshw Behav Physiol 39:25–36. https://doi.org/10.1080/10236240600563404
Mueller T, O’Hara RB, Converse SJ et al (2013) Social learning of migratory performance. Science (80- ) 341:999–1002. https://doi.org/10.1126/science.1237139
Øksendal B (2003) Stochastic differential equations. Springer, Berlin Heidelberg, Berlin, Heidelberg
Painter KJ, Hillen T (2015) Navigating the flow: individual and continuum models for homing in flowing environments. J R Soc Interface 12:20150647. https://doi.org/10.1098/rsif.2015.0647
Painter KJ, Plochocka AZ (2019) Efficiency of island homing by sea turtles under multimodal navigating strategies. Ecol Model 391:40–52. https://doi.org/10.1016/j.ecolmodel.2018.10.025
Prange HD (1976) Energetics of swimming of a sea turtle. J Exp Biol 64:1–12
Schott FA, McCreary JP (2001) The monsoon circulation of the Indian Ocean. Prog Oceanogr 51:1–123. https://doi.org/10.1016/S0079-6611(01)00083-0
Scott R, Marsh R, Hays GC (2014) Ontogeny of long distance migration. Ecology 95:2840–2850. https://doi.org/10.1890/13-2164.1
Sequeira AMM, Rodríguez JP, Eguíluz VM, Harcourt R, Hindell M, Sims DW, Duarte CM, Costa DP, Fernández-Gracia J, Ferreira LC, Hays GC, Heupel MR, Meekan MG, Aven A, Bailleul F, Baylis AMM, Berumen ML, Braun CD, Burns J, Caley MJ, Campbell R, Carmichael RH, Clua E, Einoder LD, Friedlaender A, Goebel ME, Goldsworthy SD, Guinet C, Gunn J, Hamer D, Hammerschlag N, Hammill M, Hückstädt LA, Humphries NE, Lea MA, Lowther A, Mackay A, McHuron E, McKenzie J, McLeay L, McMahon CR, Mengersen K, Muelbert MMC, Pagano AM, Page B, Queiroz N, Robinson PW, Shaffer SA, Shivji M, Skomal GB, Thorrold SR, Villegas-Amtmann S, Weise M, Wells R, Wetherbee B, Wiebkin A, Wienecke B, Thums M (2018) Convergence of marine megafauna movement patterns in coastal and open oceans. Proc Natl Acad Sci 115:3072–3077. https://doi.org/10.1073/pnas.1716137115
Shaffer SA, Tremblay Y, Weimerskirch H, Scott D, Thompson DR, Sagar PM, Moller H, Taylor GA, Foley DG, Block BA, Costa DP (2006) Migratory shearwaters integrate oceanic resources across the Pacific Ocean in an endless summer. Proc Natl Acad Sci U S A 103:12799–12802. https://doi.org/10.1073/pnas.0603715103
Shamoun-Baranes J, Leyrer J, van Loon E, Bocher P, Robin F, Meunier F, Piersma T (2010) Stochastic atmospheric assistance and the use of emergency staging sites by migrants. Proc R Soc B Biol Sci 277:1505–1511. https://doi.org/10.1098/rspb.2009.2112
Smith RJ, Moore FR (2005) Arrival timing and seasonal reproductive performance in a long-distance migratory landbird. Behav Ecol Sociobiol 57:231–239. https://doi.org/10.1007/s00265-004-0855-9
Stamation KA, Croft DB, Shaughnessy PD, Waples KA (2007) Observations of humpback whales (Megaptera novaeangliae) feeding during their southward migration along the coast of southeastern New South Wales, Australia: identification of a possible supplemental feeding ground. Aquat Mamm 33:165–174. https://doi.org/10.1578/AM.33.2.2007.165
Sundström LF, Petersson E, Höjesjö J, Johnsson JI, Järvi T (2004) Hatchery selection promotes boldness in newly hatched brown trout (Salmo trutta): implications for dominance. Behav Ecol 15:192–198. https://doi.org/10.1093/beheco/arg089
Thomson KA, Ingraham WJ, Healey MC et al (1992) The influence of ocean currents on latitude of landfall and migration speed of sockeye salmon returning to the Fraser River. Fish Oceanogr 1:163–179. https://doi.org/10.1111/j.1365-2419.1992.tb00035.x
Weinrich M (1998) Early experience in habitat choice by humpback whales (Megaptera novaeangliae). J Mammal 79:163–170. https://doi.org/10.2307/1382851
Whittle P (1990) Risk-sensitive optimal control. Wiley
Wolf M, van Doorn GS, Leimar O, Weissing FJ (2007) Life-history trade-offs favour the evolution of animal personalities. Nature 447:581–584. https://doi.org/10.1038/nature05835
Zermelo E (1931) Über das Navigationsproblem bei ruhender oder veranderlicher Windverteilung. ZAMM 11:114–124
Acknowledgements
We thank Susanne Åkesson and Paolo Luschi for discussions on turtle migrations that motivated the analyses presented in the manuscript. We also thank two anonymous reviewers for their constructive comments enabling us to improve the manuscript.
Funding
This work was supported by the Centre for Ocean Life, a VKR Centre of excellence funded by the Villum Foundation.
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Pinti, J., Celani, A., Thygesen, U.H. et al. Optimal navigation and behavioural traits in oceanic migrations. Theor Ecol 13, 583–593 (2020). https://doi.org/10.1007/s12080-020-00469-4
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DOI: https://doi.org/10.1007/s12080-020-00469-4