Extinction, Persistence, and Evolution

Part of the Mathematics and Biosciences in Interaction book series (MBI)


Extinction can occur for many reasons. We have a closer look at the most basic form, extinction of populations with stable but insufficient reproduction. Then we move on to competing populations and evolutionary suicide.


Branching process extinction survival population dynamics evolution 


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  1. 1.
    T.R. Malthus, An Essay on the Principle of Population, as it Affects the Future Improvement of Society, with Remarks on the Speculations of Mr Godwin, M. Condorcet and Other Writers. John Murray, London, 1798.Google Scholar
  2. 2.
    F. Galton, Problem 4001: On the extinction of surnames. Educational Times 26 (1873), 17.Google Scholar
  3. 3.
    C. Darwin, On the Origin of Species by Means of Natural Selection or the Preservation of Favoured Races in the Struggle for Life. John Murray, London, 1859.Google Scholar
  4. 4.
    D. Raup, Extinction: Bad Genes or Bad Luck? NW. W. Norton & Company, USA, 1991.Google Scholar
  5. 5.
    J.B.S. Haldane, The Causes of Evolution. Longmans Green, London, 1932.Google Scholar
  6. 6.
    K. Parvinen, Evolutionary suicide. Acta Biotheor. 53 (2005), 241–264.CrossRefGoogle Scholar
  7. 7.
    P. Jagers, F.C. Klebaner, and S. Sagitov, On the path to extinction. Proc. Natl. Acad. Sci. USA 104 (2007), 6107–6111.CrossRefMathSciNetGoogle Scholar
  8. 8.
    P. Haccou, P. Jagers, and V.A. Vatutin, Branching Processes. Variation, Growth, and Extinction of Populations, volume 5 of Cambridge Studies in Adaptive Dynamics. Cambridge University Press, UK, 2005.Google Scholar
  9. 9.
    F. Galton and H.W. Watson, On the probability of extinction of families. EJ. Anthropol. Inst. 4 (1874), 138–144.Google Scholar
  10. 10.
    J.B.S. Haldane, A mathematical theory of natural and artificial selection, Part V: Selection and mutation. Proceed. of the Cambridge Phil. Soc. 23 (1927), 838–844.zbMATHGoogle Scholar
  11. 11.
    F.H. Steffensen, Om sandsyndligheden for at afkommet uddør. Matematisk Tidskrift B (1930), 19–23.Google Scholar
  12. 12.
    C.C. Heyde and E. Seneta, I.J. Bienaym´e, Statistical Theory Anticipated. Springer- Verlag, New York, 1977.Google Scholar
  13. 13.
    P. Fahlbeck, Sveriges adel, statistisk unders¨okning ¨ofver de˚a riddarhuset introducerade ¨atterna, I and II (The Swedish Nobility, a Statistical Investigation of the Families of the House of Nobility). Gleerups, Sweden, 1898, 1902.Google Scholar
  14. 14.
    J.M. Keynes, A Tract on Monetary Reform. MacMillan, London, 1923.Google Scholar
  15. 15.
    P. Jagers and F. Klebaner, Random variation and concentration effects in PCR. J. Theor. Biol. 224 (2003), 299–304.CrossRefMathSciNetGoogle Scholar
  16. 16.
    F.C. Klebaner, S. Sagitov, V.A. Vatutin, P. Haccou, and P. Jagers, Stochasticity in the adaptive dynamics of evolution: the bare bones (to appear), invited submission. J. Biol. Dynamics.Google Scholar
  17. 17.
    S. Janson, Large deviation inequalities for sums of indicator variables (1994), technical report, Dep. Mathematics, Uppsala University 34.Google Scholar
  18. 18.
    F.C. Klebaner and J. Lazar, On the quasi-stationary distribution in randomly perturbed dynamical systems with a single attracting point. In R.Wilson, D. PraMurthy, and S. Osaki (eds.), Proc. 2nd Australia-Japan Workshop on Stochastic Models in Engineering, Technology, and Management, 348–354, The University of Queensland, Australia, 1996.Google Scholar
  19. 19.
    S.A.H. Geritz, ´E. Kisdi, G. Meszena, and J.A.J. Metz, Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree. Evol. Ecol. 12 (1998), 35–57.Google Scholar
  20. 20.
    F.B. Christiansen and V. Loeschcke, Evolution and intraspecific exploitative Competition. 1. One-Locus theory for small additive gene effects. Theor. Popul. Biol. 18 (1980), 297–313.Google Scholar
  21. 21.
    M. Gyllenberg and K. Parvinen, Necessary and sufficient conditions for evolutionary suicide. Bull. Math. Biol. 63 (2001), 981–993.CrossRefGoogle Scholar

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© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Mathematical SciencesChalmers University of Technology and the University of GothenburgGothenburgSweden

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