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The Use Of Potential Functions In Modelling Animal Movement

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Part of the book series: Selected Works in Probability and Statistics ((SWPS))

Summary

Potential functions are a physical science concept often used in modelling the motion of particles and planets. In the work of this paper potential function based models are considered for the movement of free-ranging elk in a large, fenced ex- perimental forest. Equations of motion are set down and the parameters involved are estimated nonparametrically. The question of whether a potential function is plausible for describing the elk motion is considered. The conclusion is that it is not possible to reject this hypothesis for the data set and estimates considered.

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Reference

  1. Banon, G. and Nguyen , H. T . (1981). Recurs ive est imat ion in diffusion model. SIAM J. Cont rol and Optimizat ion 19 676-685.

    Google Scholar 

  2. Bertrand, P. (1998). Comparison de l'err eur quadratique moyenne integree pour differents est imate urs du coefficient de diffusion d'un processus . C. R . A cad. S ci. Paris 327 399-404 .

    Google Scholar 

  3. Bhattacharya, R. N. and Waymire, E. (1990). Stochastic Pro cesses with Applications. Wiley, New York .

    Google Scholar 

  4. Brillinger , D. R. and Stewart , B. S. (1998) . Elephant seal movements: modelling migrat ion . Canadian 1. Sta tisti cs 26 431-443 .

    Google Scholar 

  5. Burgiere, P. (1993) . Theoreme de limite centrale pour un estimateur non pararnetriquc de la variance d'un pro cessus diffusion multidimcnsionelle. Annales de l 'lnstitut Henri Poin car e, S ection B, Calcul des Probabilities et Statist iqu e 29 357-389.

    Google Scholar 

  6. Clark, J . D. , Dunn, J . E., Smith, K. G. (1993) . A multivari at e model of female black bear hab it at use for geographic information system . J01lr. Wild. J1;[anaqe. 57 519-526.

    Google Scholar 

  7. Cleveland , ' V. S. , Grosse, E. an d Shyu, W. :M. (1992) . Local regression models. Pp. 309-376 in Statistica l Models in S (Eds . .T . jVI. Chambers and T . .T . Hasti e) . Pacific Grove , Wadswo rt h.

    Google Scholar 

  8. Dohnal , G. (1987) . On est imating t he diffusion coefficient J ournal of A pplie d Probability 24 105-114.

    MathSciNet  MATH  Google Scholar 

  9. Dunn, .T. E. an d Brisbin , 1. L. (1985) . Characterization of the multivari ate Ornst ein- Uhlenb eck diffusion process in the context of home ran ge analysis. Sta tist ical T heory and Dat a Analy sis. K. Matusit a [ed.]. Elsevier Science Publishers B.V. North-Holland. 181-205.

    Google Scholar 

  10. Dunn , J . ~~ . and Gipson, P. S. (1977). Analysis of radio telemetry data in studi es of home range. Biometr ics 33 85-101.

    Article  MATH  Google Scholar 

  11. Efron ,B. an d Tibshirani, R. J . (1993) . An I ntrodu cti on to the B oot st rap . Chapman and Hall , New York .

    Google Scholar 

  12. Findholdt, S. 1,., J ohnson, B. K., Bryant , L. D. and Thomas, J . W. (1996) . Corrections for positi on bias of a LORAN-C radi o-t elemetry system using DGPS. Northw est Sci enc e 70 273-280.

    Google Scholar 

  13. Genon-Catalot , V., Lar edo , C., Pi card , D. (1992) . Nonparametric est imat ion of the diffusion coefficient by wavelets methods . Sc an din avian Journal of St at ist ic s 19 317-335.

    MathSciNet  MATH  Google Scholar 

  14. Hastic, T. J. and Tibshirani, R..J. (1990). Generalize d Linear Models . Chapman and Hall, London .

    Google Scholar 

  15. Heyde, C.C. (1994) . A quasi-likelihoo d approach to est imating paramete rs in diffusion- typ e processes. Essays in Honour of Takacs. Journal of Applied Probability, 31A 283-290.

    Google Scholar 

  16. Karlin, S. and Taylor , H.M . (1981) . A Second Course in St ochast ic Process es. Academi c, New York [17] Kloeden , P. E. and Pl at en , E. (1995) . Num erical Solution of Stoc hast ic Differential E quat ions. Springer , New York .

    Google Scholar 

  17. Moorcroft , P. R. , Lewis, M. A. and Crabt ree, R. 1. (1999) . Home range analysis using a mechani sti c home range model. Ecology 80 1656-1665.

    Article  Google Scholar 

  18. [1 9] Nelson , E. (1967). Dynamical Theo ri es of Brownian Motion. Princeton U. Press, Princeton.

    Google Scholar 

  19. Preisler , H. K. an d Akers, P. (1995) . Autoregressive-typ e models for th e analysis of bark beetle tracks. Biometrics 51 259-267.

    Article  Google Scholar 

  20. Preisler , B. K., Brillingcr , D. R., Ager , A. A. and Kie, ;J. G. (1999) . Analysis of animal movement using telemet ry and GIS data . Pro c. ASA S ection on St atist ics and th e Environment.

    Google Scholar 

  21. Prohorov, Yu. V. and Rozanov , Yu. A. (1969) . Probability T heor y. Spri ngerVerlag, New York.

    Google Scholar 

  22. Rowland , M. M ., Bryan t , L. D., J ohnson , B. K. , Noyes, J . B ., 'Wisdom, M. J . an d Thomas , .T. W. (1997). The St arke y Project : Histo ry , Facilit ies, and Data Collection Meth ods for Ungulat e Research. Technical Report PNW-GTR-396, Forest Service, USDA.

    Google Scholar 

  23. Sorensen, M. (1997) . Estimat ing fun ctions for discret ely observed diffusions: a review. Pp . 305-326 in Se lected Proceedings oj th e S ymposium on Estimating Functions. Eds. Basawa , 1. V, Godambe, V. P. and Tay lor , R. L. Vol. 32 Lecture Notes. Institute of Mathemati cal St atistics, Hayward .

    Google Scholar 

  24. Spivak , M. (1965) . Calculus on Manifolds. Benjamin , New York .

    Google Scholar 

  25. Stewart , J . (1991) . Cal culus, E arly Transcendentals. Brooks/Cole, Pacific Grove.

    Google Scholar 

  26. Turchin, P. (1998) . Qllantitative A na lysis of Mo vem ent. Sinauer, Sunderland ,

    Google Scholar 

  27. MA.

    Google Scholar 

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Brillinger, D.R., Preisler, H.K., Ager, A.A., Kie, J.G. (2012). The Use Of Potential Functions In Modelling Animal Movement. 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_22

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