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Elephant-seal movements: Modelling migration

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Selected Works of David Brillinger

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Abstract

Elephant seals migrate over vast areas of the eastern Nonh Pacific Ocean between rookeries in southern California and distant northern foraging areas. Several models of particle movement were evaluated and a model for great-circle motion found to give reasonable results for the movement of an adult female. This model takes specific account of the fact that the movement is on the surface of a sphere and that the animal is apparently heading toward a particular destination. The parameters of the motion were estimated. Such a great-circle path of migration may imply that these seals have the ability to assess their position with respect to some global or celestial cues, allowing them to continually adjust their course and achieve the most direct geodesic route between origin and destination of migration. But the navigational mechanism actually used by these seals to accomplish such feats is as yet unknown.

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Reference

  • Able, K.P. (1996). The debate over olfactory navigation by homing pigeons. J. Exp. Biol., 199, 121-124.

    Google Scholar 

  • Anderson-Sprecher, R. (1954). Robust estimates of wildlife location using telemetry data . Biometrics. 50, 406-410.

    Article  Google Scholar 

  • Anderson-Sprecher, R., and Lcdoltcr, J. (1991). State -space analysis of wildlife telemetry data. J. Amer. Suui s. Assoc., X6, 596-602.

    Article  Google Scholar 

  • Basawa, l.V ., and Ran, B.L.S.P. (19XO). Statistical Inference for Stochastic Processes . Academic Press . New York.

    Google Scholar 

  • Bengtson, J.L., and Stewart, B.S. (1992). Diving and haulout paucrns of crahcatcr seals in the Weddell Sea, Antarctica during March 19XO. Polar BioI., 12,635-644.

    Google Scholar 

  • Bester. M.N., and Pansegrouw, H.M. (1992). Ranging behaviour of southern elephant seal cows from Marion Island . South African J. Sci ., 88, 574-575.

    Google Scholar 

  • Bhattacharya, R.N., and Waymire, E. (1990). Stocha stic Processes with Applications. Wiley, New York.

    Google Scholar 

  • Bril, G. (1995). Foreca sting hurrican e tracks using the Kalman Iiltcr, Environmetrics, 6, 7-10.

    Article  Google Scholar 

  • Brillingcr, D.R. (1997). A particle migrating randomly on a sphere. J. Theoret. Probab .. 10.429-443.

    Article  MathSciNet  Google Scholar 

  • Brillinger, D.R. (1998). Some examples of random process environmental data analysis. Handbook of Statistics, Vo/. 17. North-Holland, Amsterdam. To appear

    Google Scholar 

  • Brillinger, D.R., and Stewart, B.S. ( 1996). Elephant seal movements: some frequency based studies , Brazilian J. Probab . Statist .. 10. 15- 33.

    Google Scholar 

  • Brillingcr. D.R.. and Stewart. B.S. (1997 ). Elephant seal movements: Dive types and their sequences. Modelling Longitudinal and Sp atially Correlated Data (T.G . Gregoire. D.R. Brillingcr. PJ . Digglc, E. Russek-Cohe. W.G. Warren . R.D. Wolfinge r, eds.y; Lecture NOles in Statistics 122, Springer-Verlag. New York, 275-288

    Google Scholar 

  • Brink . K.H.• Beardsley, R.C., Niilcr, P.P., Abbott. M.• Huycr, A.. Ramp. S.. Stanton. T.. and Stuart, D. (1991). Sta tistical properties of ncar-surface !low in the California coastal transition zone , J. Geoph vs. Res. 96. 14693- 14706.

    Google Scholar 

  • Burgicrc, P. (1993). Thcorc rnc de limite ce ntrale pour un cstirnatcur non pararnct riquc de la variance d'un process us de diffusion muhidimensionelle. Ann. In.H. H. Poincare Probab . Stl11i.VI.• 29. 357-389.

    Google Scholar 

  • Chandrase khar, S. (1943 ). Stochastic problems in physic s and astronomy. Rev. Modem Phys ., I5. I- 89.

    Google Scholar 

  • Cleveland. W.S.. Grosse . E.• and Shyu, W.M. (1990). local regression models. Statistical Models in S (J.M. Cham hers and TJ. Hastic, eds.), Wadsworth. Pacific Grove . Ca lif.. 300-376.

    Google Scholar 

  • Delong. R.L.. Stewa rt, B.S.. and Hill, R.D. ( 1992). Documenting migrations of northern elephant sea ls using day length. Marine Mamma l Sci. R. 155-1 59.

    Google Scholar 

  • Ding le. H. ( 1996). Migration: The Biology of Life on the Move . Ox ford Univ . Press, Oxford,

    Google Scholar 

  • Dillman. A.H., and Quin, T.P. (1996). Homing in Pacific salmon: Mechanisms and eco logica l basis. 1. Exp . Bioi. 199. R3-91.

    Google Scholar 

  • Dohn al, G. ( 19R7). On estimating the diffusion coe fficient. J. App l. Probab ., 24. 105- 114.

    Google Scholar 

  • Dunn. J.E.. and Brisbin . I.L. ( 19R5). Characterizatio n of the multi vari ate Oms tcin-Uhlcnbcck di ffusion process in the context of home range analysis. Statistical Theory and Dl11a Analysis (K. Matusita, ed .i. Elsevie r, Amsterdam, IR1-205.

    Google Scholar 

  • Dunn. J.E., and Gipson. P.S. ( 1977). Analysis of radio tele metry data in studies of home range. Biometrics. 33. R5-10 1.

    Google Scholar 

  • Gcnon-Catalot, V.• Laredo. C.. and Picard. D. ( 1992). Non-parametric estimation of the di ffusion coeff icient by wavelets methods. Scand. J. Statist. 19. 3 17-335.

    Google Scholar 

  • Hadclcr , K.P., de Mou oni, P.• and Schumaker. K. ( 19RO). Dyna mic models for animal orientation. J. Math . Bioi. 10.307-332.

    Google Scholar 

  • Heyde. c.c. (1994 ). A quasi-li kelihood approach 10 estimating paramete rs in diffu sion-type processes. J. Appl. Probab.. 31A. 2R3-290.

    Google Scholar 

  • Kareiva, P.M.. and Shigesad a, N. (19R3). Analyzing insect movement as a co rrelated random walk. Oecologiu (Berlin). 56. 234-238.

    Google Scholar 

  • Karlin . S.. and Taylor. H.M. (l 9RI). A Second Cours e in Stochastic Processes. Academic Press. New York.

    Google Scholar 

  • Kend all . D.G. (1974). Pole-seeking Brownian motion and bird navigation. J. Roy. Statist. Soc, Ser. B, 36.

    Google Scholar 

  • 365-417 .

    Google Scholar 

  • Levin. S.A. ( 19R6). Random walk mode ls of movement and thei r imp lications. Mathematical Ecology (T.G . Hallam and S. Levin, eds.). Springer -Verlag. Berl in. 149-1 54.

    Google Scholar 

  • Lohmann. KJ .. and Lohmann. C.M .F. (1996) . Orien tation and open -sea naviga tion in sea turt les. J. Exp . Bioi. 199, 73-R 1.

    Google Scholar 

  • Malik. F.. Brill ingcr, D.. and Vale. R.D. (1994). High-re solut ion tracking of microtubule motil ity driven by a single kinesin motor. Proc. Nail. Acad. Sci. U.S.A . 9 1. 4584-4588.

    Google Scholar 

  • McConnell . BJ.• and Fedak. M.A. ( 1996). Movemen ts in so uthern elephant seals. Canad. J. Zoo l. 74. 14X51496.

    Google Scholar 

  • McCull och. C.E.. and Cain. M.L. ( 19X9). Analyzin g discrete movement data as a correlated random walk. Ecology, 7. 383-3X8.

    Google Scholar 

  • Moore. M. ( 1985). Modell ing iceberg motion : A multiple lime series approach. Canad. J. Statist. 13. XX-93.

    Google Scholar 

  • Niwa, H. (1996). Newt onian dynamical approach to fish schoo ling. J. Theoret. Bioi.. IXI, 47-63.

    Google Scholar 

  • Oksc ndal, B. (1995). Stocha stic Differen tia l Equations. Fourth Edition, Spri nger-Verlag. New York.

    Google Scholar 

  • Okubo, A. (I9RO). Diffusion and Ecological Prob lems : Mathematical Mode ls. Springe r-Verlag . New York.

    Google Scholar 

  • Perrin , M.F. ( 192R). Mouvcrncnt brow nicn de rota tion . Ann. Em il' Norm. Sup .. 45, I- 5 1.

    Google Scholar 

  • Preisler, H.K., and Akers. R.P. (1995). Autoregressive- type models for the analysis of bark bee tle trucks. Biometrics . 5 I . 259- 267.

    Google Scholar 

  • Stewart. B.S. (1996). Uncommon commuters . Natur. Hist.• 105. 5X-63.

    Google Scholar 

  • Stewart. B.S.. and Delong. R.L. (1995). Double migratio ns of the nort hern elephant seal. 1. Mummalogy 76 . 196-205.

    Google Scholar 

  • Stewart. B.S.. and Huller. H.R. ( 1993). Miroung a angustirostris. Mammalian Species. 449 . 1- 10.

    Google Scholar 

  • Stewart. B.S.• Leatherwo od. S.. Yochcm, P. K., and Heide-Jorgen sen, M.P. (19X9). Satel lite telemetry of loca tions and dive durations of a free-ranging harb or sea l iPhoca vitulinu richardsi i in the So uthern

    Google Scholar 

  • Ca lifornia Bight. Marine Mammal Sci . 5. 361-375.

    Google Scholar 

  • Stewart. B.S.. Yochcm , P.K.. Huber, H.R.. DeLong. R.L. , Jameson. RJ., Sydcrnan, W.. Allen. S.U.. and LeBoeuf, BJ. (1994). History and present status of the northern elephant seal population. Elephant

    Google Scholar 

  • Seals: Population Ecology. Behaviour and Physiology (BJ. LeBoeuf and R.M. Laws, eds.t. University of California Press . Los Angeles. 29-48.

    Google Scholar 

  • Wagner. H. (1986) . Flight performance and visual control of Ilight of the free Ilying houselly. Philos. Trans. Roy. Soc. London Ser. B, 312, 581-595.

    Article  Google Scholar 

  • Wehner, R., Michel, B.. and Antonsen. P. (1996). Visual navigation in insects: Coupling of egocentric and geocentric information. J. Exp. Bioi. 199, 129-140.

    Google Scholar 

  • Wchrhahn, C; Poggio, T., and Bulthoff, H. (1982). Tracking and chasing in houseflies. Bioi. Cvbernet. 45, 123-130.

    Article  Google Scholar 

  • Wcindlcr, P.• Wiltschko, R., and Wiltschko, W. (1996). Magnetic information affects the stellar orientation of young birds . Nature, 383. 158-160.

    Google Scholar 

  • Wiltschko, W., and Wiltschko, R. (1996). Magnetic orientation in birds . J. Exp. Bioi, 199,29-38.

    Google Scholar 

  • Yosida, K. (1949). Brownian motion on the surface of the 3-sphere. Ann . Math . Statis.. 20, 292-296.

    Article  MathSciNet  Google Scholar 

  • Zwicrs, F.W. (1985) . Estimating the probability of collision between an iceberg and a fixed marine structure. Canad. J. Statist., 13,94-105.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. University of California, Berkeley (D.R.B., B.R.S.), Berkeley, CA, USA

    David R. Brillinger

  2. Hubbs-Sea World Research Institute (B.R.S.), Berkeley, CA, USA

    Brent S. Stewart

Authors
  1. David R. Brillinger
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  2. Brent S. Stewart
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Editor information

Editors and Affiliations

  1. , Department of Statistics, University of Washington, Box 354322, Seattle, 98195-4322, Washington, USA

    Peter Guttorp

  2. Dept. Statistics, University of California, Evans Hall 367, Berkeley, 94720-3860, California, USA

    David Brillinger

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Brillinger, D.R., Stewart, B.S. (2012). Elephant-seal movements: Modelling migration. In: Guttorp, P., Brillinger, D. (eds) Selected Works of David Brillinger. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1344-8_23

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