Skip to main content
SpringerLink
Log in

Conclusions

  • Chapter
  • First Online:
The Influence of Demographic Stochasticity on Population Dynamics

Part of the book series: Springer Theses ((Springer Theses))

  • 561 Accesses

Abstract

This thesis has investigated the role of stochasticity in population systems. The central message is that despite the fact that the noise is a small, random effect, it can lead to complex, self-organised behaviours which do not emerge in a description in which the noise is absent.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. R. Benzi, A. Sutera, A. Vulpiani, J. Phys. A 14, 453 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  2. R. Benzi, G. Parisi, A. Sutera, A. Vulpiani, Tellus 34, 10 (1982)

    Article  ADS  Google Scholar 

  3. A.S. Pikovsky, J. Kurths, Phys. Rev. Lett. 78, 775 (1997)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  4. B. Lindner, J. Garcia-Ojalvo, A. Neiman, L. Schimansky-Geier, Phys. Rep. 392, 321 (2004)

    Article  ADS  Google Scholar 

  5. A. Raj, A. van Oudenaarden, Cell 135, 216 (2008)

    Article  Google Scholar 

  6. M. Thattai, A. van Oudenaarden, PNAS 98, 8614 (2001)

    Article  ADS  Google Scholar 

  7. M.B. Elowitz, A.J. Levine, E.D. Siggia, P.S. Swain, Science 297, 1183 (2002)

    Article  ADS  Google Scholar 

  8. M. Kimura, The Neutral Theory of Molecular Evolution (Cambridge University Press, Cambridge, 1984)

    Google Scholar 

  9. G.D. Schuler, M.S. Boguski, E.A. Stewart, L.D. Stein, G. Gyapay, K. Rice, R.E. White, P.C. Rodriguez-Tomé, A. Aggarwal, E. Bajorek et al., Science 274, 540 (1996)

    Google Scholar 

  10. L. Ridolfi, P. D‘Odorico, F. Laio, Noise-Induced Phenomena in the Environmental Sciences (Cambridge University Press, Cambridge, 2011)

    Google Scholar 

  11. C.W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, 4th edn. (Springer, New York, 2009)

    Google Scholar 

  12. N.G. van Kampen, Stochastic Processes in Physics and Chemistry, 3rd edn. (Elsevier Science, Amsterdam, 2007)

    Google Scholar 

  13. T. Rogers, A. McKane, A. Rossberg, Eur. Phys. Lett. 97, 40008 (2012)

    Article  ADS  Google Scholar 

  14. D. Remondini, E. Giampieri, A. Bazzani, G. Castellani, A. Maritan, Physica A 392, 336 (2013)

    Article  ADS  Google Scholar 

  15. W. Horsthemke, R. Lefever, Noise-Induced Transitions (Springer, Berlin, 1984)

    MATH  Google Scholar 

  16. A.J. McKane, T. Biancalani, T. Rogers, Bull. Math. Biol. (2013)

    Google Scholar 

  17. R. Kubo, K. Matsuo, K. Kitahara, J. Stat. Phys. 9, 51 (1973)

    Article  ADS  Google Scholar 

  18. H. Gang, Phys. Rev. A 36, 5782 (1987)

    Article  ADS  Google Scholar 

  19. M.I. Dykman, E. Mori, J. Ross, P.M. Hunt, J. Chem. Phys. 100, 5735 (1994)

    Article  ADS  Google Scholar 

  20. M. Mobilia, M. Assaf, Eur. Phys. Lett. 91, 10002 (2010)

    Article  ADS  Google Scholar 

  21. D.A. Kessler, N.M. Shnerb, J. Stat. Phys. 127, 861 (2007)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  22. B. Meerson, P.V. Sasorov, Phys. Rev. E 78, 60103 (2008)

    Article  ADS  Google Scholar 

  23. J. Ohkubo, N. Shnerb, D.A. Kessler, J. Phys. Soc. Jpn. 77, 044002 (2007)

    Article  ADS  Google Scholar 

  24. T. Biancalani, T. Rogers, A.J. McKane, Phys. Rev. E 86, 010106(R) (2012)

    Article  ADS  Google Scholar 

  25. J. Pasteels, J.L. Deneubourg, S. Goss, EXS 54, 155 (1987)

    Google Scholar 

  26. A. Kirman, Q. J. Econ. 108, 137 (1993)

    Article  Google Scholar 

  27. J.L. Deneubourg, S. Goss, Ethol. Ecol. Evol. 1, 295 (1989)

    Article  Google Scholar 

  28. G.S. Becker, J. Polit. Econ. 99, 1109 (1991)

    Article  Google Scholar 

  29. D.S. Scharfstein, J.C. Stein, Am. Econ. Rev. 80, 465 (1990)

    Google Scholar 

  30. C. Detrain, J.L. Deneubourg, Phys. Life Rev. 3, 162 (2006)

    Article  ADS  Google Scholar 

  31. J.D. Murray, Math. Biol., vol. 2, 3rd edn. (Springer, Berlin, 2008)

    Google Scholar 

  32. T.C. Butler, N. Goldenfeld, Phys. Rev. E 80, 030902(R) (2009)

    Article  ADS  Google Scholar 

  33. P.K. Maini, T.E. Woolley, R.E. Baker, E.A. Gaffney, S.S. Lee, Interface Focus 2, 487 (2012)

    Article  Google Scholar 

  34. T.C. Butler, N. Goldenfeld, Phys. Rev. E 84, 011112 (2011)

    Article  ADS  Google Scholar 

  35. T. Biancalani, T. Galla, A.J. McKane, Phys. Rev. E 84, 026201 (2011)

    Article  ADS  Google Scholar 

  36. T. Biancalani, D. Fanelli, F. Di Patti, Phys. Rev. E 81, 046215 (2010)

    Article  ADS  Google Scholar 

  37. M. Scott, F. Poulin, H. Tang, Proc. R. Soc. A 467, 718 (2011)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  38. S.A. Levin, L.A. Segel, Nature 259, 659 (1976)

    Article  ADS  Google Scholar 

  39. D. Fanelli, A.J. McKane, Phys. Rev. E 82, 21113 (2010)

    Article  ADS  Google Scholar 

  40. T.E. Woolley, R.E. Baker, E.A. Gaffney, P.K. Maini, Phys. Rev. E 84, 021915 (2011)

    Article  ADS  Google Scholar 

  41. T.E. Woolley, R.E. Baker, E.A. Gaffney, P.K. Maini, Phys. Rev. E 84, 046216 (2011)

    Article  ADS  Google Scholar 

  42. T.C. Butler, M. Benayounc, E. Wallace, W. van Drongelenc, N. Goldenfeld, J. Cowane, PNAS 109, 606 (2012)

    Article  ADS  Google Scholar 

  43. T.E. Woolley, R.E. Baker, E.A. Gaffney, P.K. Maini, S. Seirin-Lee, Phys. Rev. E 85, 51914 (2012)

    Article  ADS  Google Scholar 

  44. I. Hanski, Metapopulation Ecology (Oxford University Press, New York, 1999)

    Google Scholar 

  45. J.A. Bonachela, M.A. Muñoz, S.A. Levin, J. Stat. Phys. 148, 723 (2012)

    Google Scholar 

  46. L. Trefethen, A. Trefethen, S. Reddy, T. Driscoll, Science 261, 578 (1993)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  47. L.N. Trefethen, M. Embree, Spectra and Pseudospectra (Princeton University Press, Princeton, 2005)

    MATH  Google Scholar 

  48. M.G. Neubert, H. Caswell, Ecology 78, 653 (1997)

    Article  Google Scholar 

  49. M.G. Neubert, H. Caswell, J.D. Murray, Math. Biosci. 175, 1 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  50. M. Asllani, T. Biancalani, arXiv, 1305.7318v1 (2013)

    Google Scholar 

  51. H.G. Othmer, L.E. Scriven, J. Theor. Biol. 32, 507 (1971)

    Article  Google Scholar 

  52. H. Nakao, A.S. Mikhailov, Nat. Phys. 6, 544 (2010)

    Article  Google Scholar 

  53. P.N. McGraw, M. Menzinger, Phys. Rev. E 77, 31102 (2008)

    Article  ADS  Google Scholar 

  54. M. Asslani, F.D. Patti, D. Fanelli, Phys. Rev. E 86, 046105 (2012)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, University of Illinois at Urbana–Champaign, Urbana, IL, USA

    Tommaso Biancalani

Authors
  1. Tommaso Biancalani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tommaso Biancalani .

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Biancalani, T. (2014). Conclusions. In: The Influence of Demographic Stochasticity on Population Dynamics. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-07728-4_6

Download citation

Publish with us

Policies and ethics

Search

Navigation