Populations under Periodically and Randomly Varying Growth Conditions

  • M. Markus
  • B. Hess
  • J. Rössler
  • M. Kiwi
Part of the NATO ASI Series book series (NSSA, volume 138)

Abstract

A large number of natural populations result from single generations that do not overlap, so that population growth occurs in discrete steps. The growth of a single species can then be described by an equation of the type
(1)
where we consider the time lapse between two generations as time unity. Examples of this type of poulation are many temperate zone arthropod species with one short-lived adult generation per year [15], bivoltine insects (i.e. insects having a summer and a winter generation [81) and cicadas with adults emerging every 13 years [13].

Keywords

Lyapunov Exponent Step Length Logistic Equation Colorado Potato Beetle Coupling Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    R. Breuer, Geo. 7: 36 - 54 (1985).Google Scholar
  2. [2]
    L.M. Cook, Nature 207: 316 (1965).Google Scholar
  3. [3]
    J.M. Cowley, Phys. Rev. 77: 669 (1950).CrossRefGoogle Scholar
  4. [4]
    J. Davidson and H.F. Andrewartha, J. Anim. Ecol. 17: 193 - 199 (1948).CrossRefGoogle Scholar
  5. [5]
    C. Elton, “Voles, Mice and Lemmings: problems in population dynamics”, Oxford Univ. Press, Oxford (1942).Google Scholar
  6. [6]
    Harwell Subroutine Library, A Catalogue of Subroutines (Theoretical Physics Division, A.E.R.E., Harwell, Great Britain ) (1973).Google Scholar
  7. [7]
    M.P. Hassell, J.H. Lawton and R.M. May, J. Anim. Ecol. 45: 471 - 486 (1976).CrossRefGoogle Scholar
  8. [8]
    M. Kot and W.M. Schaffer, Theor. Popul. Biol. 26: 340 - 360 (1984).CrossRefGoogle Scholar
  9. [9]
    C.J. Krebs, “Ecology: the experimental analysis of distribution and abundance”, 190-200, Harper and Row, New York (1972).Google Scholar
  10. [10]
    A. MacFadyen, “Animal Ecology: Aims and Methods”, 2nd ed., Pitman, London (1963).Google Scholar
  11. [11]
    M. Markus, B. Hess, J. Rössler and M. Kiwi, to be published.Google Scholar
  12. [12]
    K. Matsumoto and I. Tsuda, J. Stat. Phys. 31: 87 - 106 (1983).CrossRefGoogle Scholar
  13. [13]
    R.M. May, Science 186: 645 - 647 (1974).CrossRefGoogle Scholar
  14. [14]
    R.M. May, Nature 261: 459 - 467 (1976).CrossRefGoogle Scholar
  15. [15]
    R.M. May, “Theoretical Ecology. Principles and Applications”, Chapter 2, Blackwell, Oxford (1976).Google Scholar
  16. [16]
    R.M. May and G.F. Oster, Am. Nat. 110: 573 - 599 (1976).CrossRefGoogle Scholar
  17. [17]
    L.F. Olsen, this workshop (1987).Google Scholar
  18. [18]
    W.E. Ricker, J. Fish. Res. Board Canada 11: 559 - 623 (1954).CrossRefGoogle Scholar
  19. [19]
    W.M. Schaffer, Am. Nat. 124: 798 - 820 (1984).CrossRefGoogle Scholar
  20. [20]
    W.M. Schaffer, IMA J. of Math. Applied in Med. and Biol. 2: 221 - 252 (1985).Google Scholar
  21. [21]
    W.M. Schaffer and M. Kot, J. Theor. Biol. 1. 12: 403 - 427 (1985).Google Scholar
  22. [22]
    W.M. Schaffer and M. Kot, Bioscience 35: 342 - 350 (1985).CrossRefGoogle Scholar
  23. [23]
    R. Shaw, Z. Naturforsch 36a: 80 - 112 (1981).Google Scholar

Copyright information

© Springer Science+Business Media New York 1987

Authors and Affiliations

  • M. Markus
    • 1
  • B. Hess
    • 1
  • J. Rössler
    • 2
  • M. Kiwi
    • 3
  1. 1.Max-Planck Institut für ErnährungsphysiologieDortmund 1Germany
  2. 2.Depto. de Fisica Facultad de CienciasUniversidad de ChileSantiagoChile
  3. 3.Facultad de FisicaUniversidad Catolica CasillaSantiagoChile

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