Skip to main content
SpringerLink
Log in
Book cover

The Statistical Physics of Fixation and Equilibration in Individual-Based Models pp 1–9Cite as

Introduction

  • Chapter
  • First Online:

  • 461 Accesses

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

Abstract

In this introduction we discuss the historical use of statistical physics to understand the bio-physical world.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
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

Learn about institutional subscriptions

Notes

  1. 1.

    Ludwig Boltzmann (1844–1906) later derived this result from the kinetic theory of gases [11].

References

  1. T.C. Schelling, Dynamic models of segregation. J. Math. Sociol. 1, 143 (1971)

    Article  Google Scholar 

  2. D. Helbing, B. Tilch, Generalized force model of traffic dynamics. Phys. Rev. E 58, 133 (1998)

    Google Scholar 

  3. J.-P. Bouchaud, Power laws in economics and finance: some ideas from physics. Quant. Finance 1, 105 (2001)

    Google Scholar 

  4. R.N. Mantegna, H.E. Stanley, Introduction to Econophysics: Correlations and Complexity in Finance (Cambridge University Press, Cambridge, 2007)

    MATH  Google Scholar 

  5. J.D. Murray, How the leopard gets its spots. Sci. Am. 258, 80 (1988)

    Google Scholar 

  6. A.M. Turing, The chemical basis of morphogenesis. Philos. Trans. R. Soc. B 237, 37 (1952)

    Google Scholar 

  7. M.C. Cross, H.S. Greenside, Pattern Formation and Dynamics in Non-Equilibrium Systems (Cambridge University Press, Cambridge, 2009)

    Book  MATH  Google Scholar 

  8. J.D. Murray, A pre-pattern formation mechanism for animal coat markings. J. Theor. Biol. 88, 161 (1981)

    Article  MathSciNet  Google Scholar 

  9. J.C. Maxwell, Theory of Heat (Longmans, London, 1871)

    Google Scholar 

  10. J.C. Maxwell, V. Illustrations of the dynamical theory of gases. Part I. On the motions and collisions of perfectly elastic spheres. Philos. Mag. 19, 19 (1860)

    Google Scholar 

  11. L. Boltzmann, Über die Beziehung zwischen dem zweiten Hauptsatze der mechanischen Wärmetheorie und der Wahrscheinlichkeitsrechnung respektive den Sätzen über das Wärmegleichgewicht. Wien. Ber. 76, 373 (1877)

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  13. D. Alonso, A.J. McKane, M. Pascual, Stochastic amplification in epidemics. J. R. Soc. Interface 4, 575 (2007)

    Article  Google Scholar 

  14. M.A. Nowak, Evolutionary Dynamics (Harvard University Press, Cambridge, 2006)

    MATH  Google Scholar 

  15. A.J. McKane, T.J. Newman, Predator-prey cycles from resonant amplification of demographic stochasticity. Phys. Rev. Lett. 94, 218102 (2005)

    Article  ADS  Google Scholar 

  16. R.A. Fisher, On the dominance ratio. Proc. R. Soc. Edinb. 42, 321 (1922)

    Article  Google Scholar 

  17. J.B.S. Haldane, A mathematical theory of natural and artificial selection. V. Selection and mutation. Proc. Cambridge Philos. Soc. 23, 838 (1927)

    Article  ADS  MATH  Google Scholar 

  18. S. Wright, Evolution in Mendelian populations. Genetics 16, 97 (1931)

    Google Scholar 

  19. M. Kimura, On the probability of fixation of mutant genes in a population. Genetics 47, 713 (1962)

    Google Scholar 

  20. T.L. Vincent, J.S. Brown, Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics (Cambridge University Press, Cambridge, 2005)

    Google Scholar 

  21. Cancer Research UK. All cancers combined: Key facts. Cancer Research UK, (2014)

    Google Scholar 

  22. S. Mukherjee, The Emperor of all Maladies: A Biography of Cancer (Fourth Estate, London, 2011)

    Google Scholar 

  23. C. Nordling, A new theory on the cancer-inducing mechanism. Br. J. Cancer 7, 68 (1953)

    Article  Google Scholar 

  24. P. Armitage, R. Doll, The age distribution of cancer and a multi-stage theory of carcinogenesis. Br. J. Cancer 8, 1 (1954)

    Article  Google Scholar 

  25. J. Fisher, Multiple-mutation theory of carcinogenesis. Nature 181, 651 (1958)

    Article  ADS  Google Scholar 

  26. A.G. Knudson, Mutation and cancer: statistical study of retinoblastoma. Proc. Natl. Acad. Sci. U.S.A. 68, 820 (1971)

    Article  ADS  Google Scholar 

  27. S.H. Moolgavkar, The multistage theory of carcinogenesis and the age distribution of cancer in man. J. Natl. Cancer Inst. 61, 49 (1978)

    Google Scholar 

  28. S.H. Moolgavkar, A.G. Knudson, Mutation and cancer: a model for human carcinogenesis. J. Natl. Cancer Inst. 66, 1037 (1981)

    Google Scholar 

  29. I. Bozic, T. Antal, H. Ohtsuki, H. Carter, D. Kim, S. Chen, R. Karchin, K.W. Kinzler, B. Vogelstein, M.A. Nowak, Accumulation of driver and passenger mutations during tumor progression. Proc. Natl. Acad. Sci. U.S.A. 107, 18545 (2010)

    Article  ADS  Google Scholar 

  30. I. Bozic, J.G. Reiter, B. Allen, T. Antal, K. Chatterjee, P. Shah, Y.S. Moon, A. Yaqubie, N. Kelly, D.T. Le, E.J. Lipson, P.B. Chapman, L.A. Diaz, Jr, B. Vogelstein, M.A. Nowak, Evolutionary dynamics of cancer in response to targeted combination therapy. eLife 2, e00747 (2013)

    Google Scholar 

  31. J. Denes, D. Krewski, An exact representation for the generating function for the Moolgavkar-Venzon-Knudson two-stage model of carcinogenesis with stochastic stem cell growth. Math. Biosci. 131, 185 (1996)

    Article  MATH  Google Scholar 

  32. T. Antal, P. Krapivsky, Exact solution of a two-type branching process: models of tumor progression. J. Stat. Mech. 2011, P08018 (2011)

    Article  Google Scholar 

  33. M.A. Nowak, F. Michor, Y. Iwasa, The linear process of somatic evolution. Proc. Natl. Acad. Sci. U.S.A. 100, 14966 (2003)

    Article  ADS  Google Scholar 

  34. N.L. Komarova, A. Sengupta, M.A. Nowak, Mutation-selection networks of cancer initiation: tumor suppressor genes and chromosomal instability. J. Theor. Biol. 223, 433 (2003)

    Article  MathSciNet  Google Scholar 

  35. A.M. Colman, Game Theory and its Applications in the Social and Biological Sciences (Butterworth-Heinemann, Oxford, 1995)

    Google Scholar 

  36. J.W. Weibull, Evolutionary Game Theory (MIT Press, Cambridge, 1995)

    MATH  Google Scholar 

  37. J. Hofbauer, K. Sigmund, Evolutionary Games and Population Dynamics (Cambridge University Press, Cambridge, 1998)

    Book  MATH  Google Scholar 

  38. H. Gintis, Game Theory Evolving (Princeton University Press, Princeton, 2009)

    MATH  Google Scholar 

  39. W.H. Sandholm, Population Games and Evolutionary Dynamics (MIT Press, Cambridge, 2010)

    MATH  Google Scholar 

  40. R.C. Maclean, I. Gudelj, Resource competition and social conflict in experimental populations of yeast. Nature 441, 498 (2006)

    Article  ADS  Google Scholar 

  41. J. Gore, H. Youk, A. van Oudenaarden, Snowdrift game dynamics and facultative cheating in yeast. Nature 459, 253 (2009)

    Article  ADS  Google Scholar 

  42. R.C. MacLean, A. Fuentes-Hernandez, D. Greig, L.D. Hurst, I. Gudelj, A mixture of “cheats” and “co-operators” can enable maximal group benefit. PLoS Biol. 8, e1000486 (2010)

    Article  Google Scholar 

  43. X.-Y. Li, C. Pietschke, S. Fraune, P.M. Altrock, T.C.G. Bosch, A. Traulsen, Which games are growing bacterial populations playing? J. R. Soc. Interface 12, 20150121 (2015)

    Article  Google Scholar 

  44. P. Ashcroft, P.M. Altrock, T. Galla, Fixation in finite populations evolving in fluctuating environments. J. R. Soc. Interface 11, 20140663 (2014)

    Article  Google Scholar 

  45. P. Ashcroft, A. Traulsen, T. Galla, When the mean is not enough: calculating fixation time distributions in birth-death processes. Phys. Rev. E 92, 042154 (2015)

    Article  ADS  Google Scholar 

  46. Y. Iwasa, F. Michor, M.A. Nowak, Stochastic tunnels in evolutionary dynamics. Genetics 166, 1571 (2004)

    Article  Google Scholar 

  47. M.A. Nowak, F. Michor, N.L. Komarova, Y. Iwasa, Evolutionary dynamics of tumor suppressor gene inactivation. Proc. Natl. Acad. Sci. U.S.A. 101, 10635 (2004)

    Article  ADS  Google Scholar 

  48. Y. Iwasa, F. Michor, N.L. Komarova, M.A. Nowak, Population genetics of tumor supressor genes. J. Theor. Biol. 233, 15 (2005)

    Article  MathSciNet  Google Scholar 

  49. F. Michor, Y. Iwasa, Dynamics of metastasis suppressor gene inactivation. J. Theor. Biol. 241, 676 (2006)

    Article  MathSciNet  Google Scholar 

  50. S.R. Proulx, The rate of multi-step evolution in Moran and Wright-Fisher populations. Theor. Popul. Biol. 80, 197 (2011)

    Article  MATH  Google Scholar 

  51. H. Haeno, Y.E. Maruvka, Y. Iwasa, F. Michor, Stochastic tunneling of two mutations in a population of cancer cells. PLoS ONE 8, e65724 (2013)

    Article  ADS  Google Scholar 

  52. M. Assaf, B. Meerson, Extinction of metastable stochastic populations. Phys. Rev. E 81, 021116 (2010)

    Article  ADS  Google Scholar 

  53. I. Lohmar, B. Meerson, Switching between phenotypes and population extinction. Phys. Rev. E 84, 051901 (2011)

    Article  ADS  Google Scholar 

  54. O. Gottesman, B. Meerson, Multiple extinction routes in stochastic population models. Phys. Rev. E 85, 021140 (2012)

    Article  ADS  Google Scholar 

  55. O.A. van Herwaarden, J. Grasman, Stochastic epidemics: major outbreaks and the duration of the endemic period. J. Math. Biol. 33, 581 (1995)

    Article  MATH  Google Scholar 

  56. A. Kamenev, B. Meerson, Extinction of an infectious disease: a large fluctuation in a nonequilibrium system. Phys. Rev. E 77, 061107 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  57. M.I. Dykman, I.B. Schwartz, A.S. Landsman, Disease extinction in the presence of random vaccination. Phys. Rev. Lett. 101, 078101 (2008)

    Article  ADS  Google Scholar 

  58. A.J. Black, A.J. McKane, WKB calculation of an epidemic outbreak distribution. J. Stat. Mech. 2011, P12006 (2011)

    Article  Google Scholar 

  59. L. Billings, L. Mier-Y-Teran-Romero, B. Lindley, I.B. Schwartz, Intervention-based stochastic disease eradication. PLoS ONE 8, e70211 (2013)

    Article  ADS  Google Scholar 

  60. A.J. Black, A. Traulsen, T. Galla, Mixing times in evolutionary games. Phys. Rev. Lett. 109, 028101 (2012)

    Article  ADS  Google Scholar 

  61. C.H. Waddington, The Strategy of the Genes (Allen and Unwin, London, 1957)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Integrative Biology, ETH Zürich, Zürich, Switzerland

    Peter Ashcroft

Authors
  1. Peter Ashcroft
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Peter Ashcroft .

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Ashcroft, P. (2016). Introduction. In: The Statistical Physics of Fixation and Equilibration in Individual-Based Models. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-41213-9_1

Download citation

Publish with us

Policies and ethics

Search

Navigation