Abstract
Long-distance migration is a widespread process evolved independently in several animal groups in terrestrial and marine ecosystems. Many factors contribute to the migration process and of primary importance are intra-specific competition and seasonality in the resource distribution. Adaptive migration in direction of increasing fitness should lead to the ideal free distribution (IFD) which is the evolutionary stable strategy of the habitat selection game. We introduce a migration game which focuses on migrating dynamics leading to the IFD for age-structured populations and in time varying habitats, where dispersal is costly. The model predicts migration dynamics between these habitats and the corresponding population distribution. When applied to Atlantic bluefin tunas, it predicts their migration routes and their seasonal distribution. The largest biomass is located in the spawning areas which have also the largest diversity in the age-structure. Distant feeding areas are occupied on a seasonal base and often by larger individuals, in agreement with empirical observations. Moreover, we show that only a selected number of migratory routes emerge as those effectively used by tunas.
Similar content being viewed by others
References
Alerstam T (2001) Detours in bird migration. J Theor Biol 209(3):319–331
Alerstam T, Hedenström A, Åkesson S (2003) Long-distance migration: evolution and determinants. Oikos 103(2):247–260
Aloncle H, Hamre J, Rodriguez-Roda J, Tiews K (1972) Report from the bluefin tuna working group. Observations on the size composition of bluefin tuna catches
Åström M (1994) Travel cost and the ideal free distribution. Oikos 69(3):516–519
Berec M, Křivan V, Berec L (2006) Asymmetric competition, body size, and foraging tactics: testing the ideal free distribution in two competing fish species. Evol Ecol Res 8(5):929– 942
Betini GS, Fitzpatrick MJ, Norris DR (2015) Experimental evidence for the effect of habitat loss on the dynamics of migratory networks. Ecol Lett 18(6):526–534
Block BA, Stevens ED (2001) Tuna: physiology, ecology, and evolution, vol 19. Gulf Professional Publishing
Block BA, Dewar H, Blackwell SB, Williams TD, Prince ED, Farwell CJ, Boustany A, Teo SL, Seitz A, Walli A, Fudge D (2001) Migratory movements, depth preferences, and thermal biology of atlantic bluefin tuna. Science (New York, NY) 293(5533):1310–1314. doi:10.1126/science.1061197
Block BA, Teo SLH, Walli A, Boustany A, Stokesbury MJW, Farwell CJ, Weng KC, Dewar H, Williams TD (2005) Electronic tagging and population structure of Atlantic bluefin tuna. Nature 434(7037):1121–1127. doi:10.1038/nature03463. http://www.ncbi.nlm.nih.gov/pubmed/15858572
Block BA, Jonsen I, Jorgensen S, Winship A, Shaffer SA, Bograd S, Hazen E, Foley D, Breed G, Harrison AL et al (2011) Tracking apex marine predator movements in a dynamic ocean. Nature 475(7354):86–90
Bonte D, Van Dyck H, Bullock JM, Coulon A, Delgado M, Gibbs M, Lehouck V, Matthysen E, Mustin K, Saastamoinen M et al (2012) Costs of dispersal. Biol Rev 87(2):290–312
Chapman JW, Reynolds DR, Wilson K (2015) Long-range seasonal migration in insects: mechanisms, evolutionary drivers and ecological consequences. Ecol Lett 18(3):287–302
Cressman R, Křivan V (2006) Migration dynamics for the ideal free distribution. Am Nat 168(3):384–397
Cury P, Anneville O, Bard F, Fonteneau A, Roy C (1998) Obstinate North Atlantic bluefin tuna (Thunnus thynnus thynnus): an evolutionary perspective to consider spawning migration. Collective volume of scientific papers. ICCAT 50(1):239–247
De Luca G, Mariani P, MacKenzie BR, Marsili M (2014) Fishing out collective memory of migratory schools. J R Soc Interface 11(95):20140043
Dewar H, Graham J (1994) Studies of tropical tuna swimming performance in a large water tunnel-energetics. J Exp Biol 192(1):13–31
Dingle H (2014) Migration: the biology of life on the move. Oxford University Press
Dingle H, Drake VA (2007) What is migration? Bioscience 57(2):113–121
Doney SC, Ruckelshaus M, Emmett Duffy J, Barry JP, Chan F, English CA, Galindo HM, Grebmeier JM, Hollowed AB, Knowlton N et al (2012) Climate change impacts on marine ecosystems. Ann Rev Mar Sci 4:11–37
Dragon AC, Senina I, Titaud O, Calmettes B, Conchon A, Arrizabalaga H, Lehodey P, Jacobson L (2015) An ecosystem-driven model for spatial dynamics and stock assessment of north Atlantic albacore. Can J Fish Aquat Sci 72(999):1–15
Dufour F, Arrizabalaga H, Irigoien X, Santiago J (2010) Climate impacts on albacore and bluefin tunas migrations phenology and spatial distribution. Prog Oceanogr 86(1):283– 290
Facchinei F, Pang JS (2003) Finite-dimensional variational inequalities and complementarity problems, vol 1. Springer Science & Business Media
Fretwell SD, Lucas HL (1969) On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheor 19(1):16–32
Fromentin JM (2009) Lessons from the past: investigating historical data from bluefin tuna fisheries. Fish Fish 10(2):197–216. doi:10.1111/j.1467-2979.2008.00311.x. http://doi.wiley.com/10.1111/j.1467-2979.2008.00311.x
Galuardi B, Lutcavage M (2012) Dispersal routes and habitat utilization of juvenile atlantic bluefin tuna, thunnus thynnus, tracked with mini psat and archival tags. PloS one 7(5):e37,829
Grand TC, Dill LM (1999) Predation risk, unequal competitors and the ideal free distribution. Evol Ecol Res 1:389–409
Hamilton W (1964) The genetical evolution of social behaviour. i
Hawkes LA, Broderick AC, Godfrey MH, Godley BJ et al (2009) Climate change and marine turtles. Endanger Species Res 7(2):137–154
Hays GC, Fossette S, Katselidis KA, Mariani P, Schofield G (2010) Ontogenetic development of migration: Lagrangian drift trajectories suggest a new paradigm for sea turtles. J R Soc Interface 7(50):1319–1327
Hays GC, Christensen A, Fossette S, Schofield G, Talbot J, Mariani P (2014) Route optimisation and solving zermelo’s navigation problem during long distance migration in cross flows. Ecol Lett 17(2):137–143
Henningsson SS, Alerstam T (2005) Barriers and distances as determinants for the evolution of bird migration links: the arctic shorebird system. Proc R Soc B Biol Sci 272(1578):2251–2258
Howard WE (1960) Innate and environmental dispersal of individual vertebrates. Am Midl Nat 152–161
Hugie D, Dill L (1994) Fish and game: a game theoretic approach to habitat selection by predators and prey. J Fish Biol 45:151–169
Hugie DM, Grand TC (1998) Movement between patches, unequal competitors and the ideal free distribution. Evol Ecol 12:1–19
Hunter E, Metcalfe JD, Reynolds JD (2003) Migration route and spawning area fidelity by north sea plaice. Proc R Soc Lond B Biol Sci 270(1529):2097–2103
Jorgensen SJ, Reeb CA, Chapple TK, Anderson S, Perle C, Van Sommeran SR, Fritz-Cope C, Brown AC, Klimley AP, Block BA (2009) Philopatry and migration of pacific white sharks. Proc R Soc Lond B Biol Sci rspb20091155
Kennedy M, Gray RD (1993) Can ecological theory predict the distribution of foraging animals? A critical analysis of experiments on the ideal free distribution. Oikos 158–166
Křivan V, Cressman R, Schneider C (2008) The ideal free distribution: a review and synthesis of the game-theoretic perspective. Theor Popul Biol 73(3):403–425
MacArthur R, Levins R (1964) Competition, habitat selection, and character displacement in a patchy environment. Proc Natl Acad Sci USA 51(6):1207
MacKenzie BR, Myers RA (2007) The development of the northern European fishery for North Atlantic bluefin tuna Thunnus thynnus during 1900–1950. Fish Res 87(2):229–239
MacKenzie BR, Payne MR, Boje J, Høyer JL, Siegstad H (2014) A cascade of warming impacts brings bluefin tuna to Greenland waters. Glob Chang Biol 20(8):2484–2491
Mather FJ, Mason JM, Jones AC (1995) Historical document: life history and fisheries of Atlantic bluefin tuna. Tech. rep., US Dept. of Commerce, National Oceanic and Atmospheric Administration, National Marine Fisheries Service, Miami
Matsumura S, Arlinghaus R, Dieckmann U (2010) Foraging on spatially distributed resources with sub-optimal movement, imperfect information, and travelling costs: departures from the ideal free distribution. Oikos 119(9):1469–1483. doi:10.1111/j.1600-0706.2010.18196.x
McLoughlin PD, Morris DW, Fortin D, Vander Wal E, Contasti AL (2010) Considering ecological dynamics in resource selection functions. J Anim Ecol 79(1):4–12
Milinski M (1979) An evolutionarily stable feeding strategy in sticklebacks1. Z Tierpsychol 51(1):36–40
Mobæk R, Mysterud A, Egil Loe L, Holand Ø, Austrheim G (2009) Density dependent and temporal variability in habitat selection by a large herbivore; an experimental approach. Oikos 118(2):209–218
Morris DW (1987a) Spatial scale and the cost of density-dependent habitat selection. Evol Ecol 1(4):379–388
Morris DW (1987b) Tests of density-dependent habitat selection in a patchy environment. Ecol Monogr:270–281
Morris DW (1989) Density-dependent habitat selection: testing the theory with fitness data. Evol Ecol 3(1):80–94
Morris DW (1996) Coexistence of specialist and generalist rodents via habitat selection. Ecology:2352–2364
Morris DW (2011) Adaptation and habitat selection in the eco-evolutionary process. Proc Biol Sci R Soc 278 (1717):2401–2411. doi:10.1098/rspb.2011.0604. http://www.ncbi.nlm.nih.gov/pubmed/21613295
Mullon C (2013) Network economics of marine ecosystems and their exploitation. CRC Press
Murray DW (1932) Tunny (Thunnus thynnus l.) in the north sea. J Conseil 7(2):251–254
Olafsdottir D, Ingimundardottir T (2003) Age-size relationship for bluefin tuna (Thunnus thynnus) caught during feeding migrations to the northern Atlantic. Col Vol Sci Pap ICCAT 55(3):1254– 1260
Overholtz W (2006) Estimates of consumption of Atlantic herring (Clupea harengus) by bluefin tuna (Thunnus thynnus) during 1970–2002: an approach incorporating uncertainty. J Northwest Atl Fish Sci 36:55–63
Pan J, Nagurney A (1994) Using Markov chains to model human migration in a network equilibrium framework. Math Comput Model 19(11):31–39
Rijnsdorp AD, Peck MA, Engelhard GH, M¨ollmann C, Pinnegar JK (2009) Resolving the effect of climate change on fish populations. ICES J Mar Sci 66(7):1570–1583
Rose GA (1993) Cod spawning on a migration highway in the north-west Atlantic. Nature 366(6454):458–461
Rosenzweig ML (1981) A theory of habitat selection. Ecology 62(2):327–335
Rosenzweig ML, Abramsky Z (1985) Detecting density-dependent habitat selection. Am Nat:405–417
Safina C, Klinger DH (2008) Collapse of bluefin tuna in the western Atlantic. Conserv Biol 22(2):243–246
Sandholm WH (2010) Population games and evolutionary dynamics. MIT Press
Schreiber SJ (2012) The evolution of patch selection in stochastic environments. Am Nat 180(1):17–34
Scott R, Marsh R, Hays GC (2014) Ontogeny of long distance migration. Ecology 95(10):2840–2850
SCRS (2012) Report of the 2012 Atlantic bluefin tuna stock assessment session. Tech. Rep. SCI-033 / 2012, ICCAT
Shaw AK, Couzin ID (2013) Migration or residency? The evolution of movement behavior and information usage in seasonal environments. Am Nat 181(1):114–124
Simon M, Fromentin JM, Bonhommeau S, Gaertner D, Brodziak J, Etienne MP (2012) Effects of stochasticity in early life history on steepness and population growth rate estimates: an illustration on Atlantic bluefin tuna. PloS one 7(10):e48,583
Sutherland WJ, Parker GA (1985) Distribution of unequal competitors. In: Sibly R M, Smith R H (eds) Behavioural ecology. Blackwell, Oxford, pp 255–273
Svärdson G (1949) Competition and habitat selection in birds. Oikos 1(2):157–174
Taylor CM, Norris DR (2010) Population dynamics in migratory networks. Theor Ecol 3(2):65–73
Tiews K (1978) On the disappearance of bluefin tuna in the north sea and its ecological implications for herring and mackerel. Rapports et Proces-Verbaux des Reunions (Denmark)
Tregenza TOM, Thompson DJ (1998) Unequal competitor ideal free distribution in fish? Evol Ecol 12:655–666
Vanderlaan AS, Hanke AR, Chassé J, Neilson JD (2014) Environmental influences on Atlantic bluefin tuna (Thunnus thynnus) catch per unit effort in the southern gulf of st. lawrence. Fish Oceanogr 23(1):83–100
Walli A, Teo SL, Boustany A, Farwell CJ, Williams T, Dewar H, Prince E, Block BA (2009) Seasonal movements, aggregations and diving behavior of Atlantic bluefin tuna (Thunnus thynnus) revealed with archival tags. PLoS One 4(7):e6151
Walther GR, Post E, Convey P, Menzel A, Parmesan C, Beebee TJ, Fromentin JM, Hoegh-Guldberg O, Bairlein F (2002) Ecological responses to recent climate change. Nature 416(6879):389–395
Ware D (1978) Bioenergetics of pelagic fish: theoretical change in swimming speed and ration with body size. J Fish Board Can 35(2):220–228
Wecker SC (1963) The role of early experience in habitat selection by the prairie deer mouse, Peromyscus maniculatus bairdi. Ecol Monogr 33(4):307–325
Westberry T, Behrenfeld M, Siegel D, Boss E (2008) Carbon-based primary productivity modeling with vertically resolved photoacclimation. Glob Biogeochem Cycles 22(2):GB2024
Wilson S, Lutcavage M, Brill R, Genovese M, Cooper A, Everly A (2005) Movements of bluefin tuna (thunnus thynnus) in the northwestern Atlantic ocean recorded by pop-up satellite archival tags. Mar Biol 146(2):409–423
Acknowledgments
Authors wish to thank the participants to the conference “Dispersal and competition of populations and communities in spatially heterogeneous environments,” Lausanne, Switzerland, 4–8 August 2014 for inspiring some of this work. PM received support from Otto Mønsted Fond and was supported by the European Union Seventh Framework Programme project EURO-BASIN (ENV.2010.2.2.1-1) under grant agreement nr. 264933. This work was partly conducted while VK was a Sabbatical Fellow at the Mathematical Biosciences Institute, an Institute sponsored by the National Science Foundation under grant DMS 0931642. Support provided by the Institute of Entomology (RVO:60077344) is acknowledged.
Author information
Authors and Affiliations
Corresponding author
Appendix: Model calibration for Atlantic bluefin tuna
Appendix: Model calibration for Atlantic bluefin tuna
Migration costs
The time needed to migrate between two habitats regulates the cost of migration in fish population since the energy consumed will be higher the longer is the migration time. The power rate consumed while swimming at an optimal speed (P) is:
where w is the mass of the fish, while the estimates for allometric constants α 0 and η assume fish swimming in a turbulent regime (i.e., high Reynolds number) (Ware 1978), Table 4).
We can assume that during migration fish swim at the optimal speed (U ∗) at which the total energy expenditure per unit distance is minimized. Using an allometric function for the metabolic costs M = α 1 w γ, a general form of U ∗ can be derived by an optimisation procedure relating the swimming cost to the total cost of moving (metabolic cost plus power output):
where α 1 and γ are allometric constants for fish metabolism (Table 4). This results in an allometric scaling for the optimal swimming speed as:
In tuna, the exponent β has been found to range between 1.4<β < 2.8 (Dewar and Graham 1994) and we assume β = 2.1, which provides swimming speeds in the range reported for several tuna species (1.2 − 2.4 body length per second) (Block and Stevens 2001). Thus we obtain a scaling U ∗≈w 0.06.
Demography
Uncertainties exist on the definition of demographic parameters for the bluefin tuna population (Simon et al. 2012). In our model, the young-of-the-year stage (0–1 years) excludes the egg phase and does not have reproductive potential while at juvenile stage (1–5 years), a small fraction is mature for reproduction. The reproductive maturity increases up to 50 % at the adult stage (5–10 years) while mature (10–20) and old (20–35) stages are fully reproductive but the latter has a lower survival rate. Those rates are consistent with observed maturity at age data for western and eastern Atlantic bluefin tuna (SCRS 2012) and are used to define the values of r k . Moreover, the value survival (q) and growth (g) values used in the Leslie matrix are consistent with reported values for the yearly mortality rates (SCRS 2012) and provide a realistic bluefin tuna age-structure (Fig. 7) with a maximum population growth rate (0.15) that is in the range of previous estimates (Simon et al. 2012). Finally, we constrain the global bluefin tuna population using a given total carrying capacity K t and assume a density dependent function on the spawning factor s.
Extended sensitivity analyses
At low spawning intensity and high migration costs (Fig. 8g), only the spawning areas are occupied. Decreasing habitat selection costs allows tuna to migrate in adjacent feeding areas (G and C) but reduce the total biomass and increase fluctuations in the migration behaviour (Fig. 8a, d). On the other hand, at high spawning and low migration costs (Fig. 8a, b), the biomass reaches the total carrying capacity over few months, and all habitats are occupied although at different levels of biomass.
Rights and permissions
About this article
Cite this article
Mariani, P., Křivan, V., MacKenzie, B.R. et al. The migration game in habitat network: the case of tuna. Theor Ecol 9, 219–232 (2016). https://doi.org/10.1007/s12080-015-0290-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12080-015-0290-8