Skip to main content
SpringerLink
Log in

Dynamical inference of hidden biological populations

  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

Population fluctuations in a predator-prey system are analyzed for the case where the number of prey could be determined, subject to measurement noise, but the number of predators was unknown. The problem of how to infer the unmeasured predator dynamics, as well as the model parameters, is addressed. Two solutions are suggested. In the first of these, measurement noise and the dynamical noise in the equation for predator population are neglected; the problem is reduced to a one-dimensional case, and a Bayesian dynamical inference algorithm is employed to reconstruct the model parameters. In the second solution a full-scale Markov Chain Monte Carlo simulation is used to infer both the unknown predator trajectory, and also the model parameters, using the one-dimensional solution as an initial guess.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N.C. Stenseth, Science 269, 1061 (1995)

    Article  ADS  Google Scholar 

  2. J.L. Aron, I.B. Schwartz, J. Theor. Biol. 110, 665 (1984)

    Article  MathSciNet  Google Scholar 

  3. P. Turchin, I. Hanski, American Naturalist 149, 842 (1997)

    Article  Google Scholar 

  4. E.L. Ionides, C. Breto, A.A. King, Proc. Nat. Acad. Sci. 103, 18438 (2006)

    Article  ADS  Google Scholar 

  5. S. Cauchemez, N.M. Ferguson, J. R. Soc. Interface 5, 885 (2008), 10.1098/rsif.2007.1292

    Article  Google Scholar 

  6. I. Hanski, H. Henttonen, E. Korpimaäki, L. Oksanen, P. Turchin, Ecology 82, 1505 (2001)

    Article  Google Scholar 

  7. P. Turchin, S.P. Ellner, Ecology 81(11), 3099 (2000)

    Google Scholar 

  8. NERC Centre for Population Biology, Imperial College (1999), The Global Population Dynamics Database, http://www.sw.ic.ac.uk/cpb/cpb/gpdd.htm

  9. K. Visscher, M.J. Schnitzer, S.M. Block, Nature 400, 184 (1999)

    Article  ADS  Google Scholar 

  10. J. Christensen-Dalsgaard, Rev. Mod. Phys. 74, 1073 (2002)

    Article  ADS  Google Scholar 

  11. R. Meyer, N. Christensen, Phys. Rev. E 62, 3535 (2000)

    Article  ADS  Google Scholar 

  12. C. Calder, M. Lavine, P. Müller, J.S. Clark, Ecology 84, 1395 (2003)

    Article  Google Scholar 

  13. V.N. Smelyanskiy, D.G. Luchinsky, A. Stefanovska, P.V.E. McClintock, Phys. Rev. Lett. 94, 098101 (4) (2005)

    Article  ADS  Google Scholar 

  14. V.N. Smelyanskiy, D.G. Luchinsky, D.A. Timucin, A. Bandrivskyy, Phys. Rev. E 72, 026202 (12) (2005)

    Article  ADS  Google Scholar 

  15. D.G. Luchinsky, V.N. Smelyanskiy, M. Millonas, P.V.E. McClintock, in Noise in Complex Systems and Stochastic Dynamics III, edited by L.B. Kish, K. Lindenberg, Z. Gingl (2005), Vol. 5845 of Proc. of SPIE, Conf. on Noise in Complex Systems and Stochastic Dynamics III May 24–26, 2005, Austin, TX. SPIE, Bellingham, (2005), pp. 173–181

    Chapter  Google Scholar 

  16. O. Gilg, I. Hanski, B. Sittler, Science 302, 866 (2003)

    Article  ADS  Google Scholar 

  17. K. Laine, H. Henttonen, Oikos 40 (3), 407 (1983)

    Article  Google Scholar 

  18. H.U. Voss, J. Timmer, J. Kurths, Int. J. Bifurc. and Chaos 14, 1905 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  19. C.W. Tidd, L.F. Olsen, W.M. Schaffer, Proc. R. Soc. London B 254 (1341), 257 (1993)

    Article  ADS  Google Scholar 

  20. R. Meyer, N. Christensen, Phys. Rev. E 65, 016206 (2001)

    Article  ADS  Google Scholar 

  21. D.G. Luchinsky, V.N. Smelyanskiy, J. Smith, in Unsolved Problems of Noise and Fluctuations, edited by L. Reggiani, C. Pennetta, V. Akimov, E. Alfinito, M. Rosini (2005), Vol. 800 of AIP Conference Proceedings, pp. 539–545, 4th International Conference on Unsolved Problems of Noise and Fluctuations in Physics, Biology and High Technology June 06-10, 2005 Gallipoli, ITALY

  22. R. Graham, Tracts in Modern Physics (Springer-Verlag, New York, 1973), Vol. 66, chap. Quantum Statistics in Optics and Solid-State Physics

    Google Scholar 

  23. E. Gozzi, Phys. rev. D 28 (8), 1922 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  24. W.R. Gilks, S. Richardson, D.J. Spiegelhalter, Markov Chain Monte Carlo in Practice (Chapman and Hall, New York, 1996)

    MATH  Google Scholar 

  25. W.K. Hastings, Biometrika 57, 97 (1970)

    Article  MATH  Google Scholar 

  26. V.V. Osipov, D.G. Luchinsky, V.N. Smelyanskiy, D.A. Timucin, AIAA 2007-5823 (2007), 43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 8–11 July 2007, Cincinnati, OH

Download references

Author information

Authors and Affiliations

  1. NASA Ames Research Center, Mail Stop 269-2, Moffett Field, CA, 94035, USA

    D. G. Luchinsky & V. N. Smelyanskiy

  2. Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK

    D. G. Luchinsky & P. V. E. McClintock

  3. Mission Critical Technologies Inc., 2041 Rosecrans Ave. Suite 225, El Segundo, CA, 90245, USA

    D. G. Luchinsky & M. Millonas

Authors
  1. D. G. Luchinsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. N. Smelyanskiy
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Millonas
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. P. V. E. McClintock
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. G. Luchinsky.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Luchinsky, D.G., Smelyanskiy, V.N., Millonas, M. et al. Dynamical inference of hidden biological populations. Eur. Phys. J. B 65, 369–377 (2008). https://doi.org/10.1140/epjb/e2008-00340-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2008-00340-5

PACS

Search

Navigation