Equadiff 82 pp 215-245 | Cite as

Deterministic and stochastic models for the dynamics of animal populations

  • U. Halbach
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1017)

Keywords

Population Dynamic Deterministic Model Stochastic Simulation Intrinsic Rate Natural Increase 
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.
    G.A. BECUS, (1980): Stochastic predator-prey relationships. Lect. Notes Pure Appl. Math. 58, 171–195.MathSciNetMATHGoogle Scholar
  2. 2.
    K. BEUTER, C. WISSEL & U. HALBACH, (1981): Correlation and spectral analyses of the dynamics of a controlled rotifer population. In: D.G. CHAPMAN & V.F. GALUCCI (Eds.): Quantitative Population Dynamics (Statistical Ecology Series 13), 61–82.Google Scholar
  3. 3.
    C. BIRCH, (1948): The intrinsic rate of natural increase of an insect population. J. Anim. Ecol. 17, 15–26.CrossRefGoogle Scholar
  4. 4.
    L.M. COOK, (1965): Oscillations in the simple logistic growth model. Nature (Lond.), 207, 316.CrossRefGoogle Scholar
  5. 5.
    L.J. DUBLIN & A.J. LOTKA, (1925): On the true rate of natural increase. J. Amer. Statist. Ass. 20, 305–339.Google Scholar
  6. 6.
    W.T. EDMONDSON, (1968): A graphical model for evaluating the use of egg ratio for measuring birth and death rates. Oecologia 1, 1–37.CrossRefGoogle Scholar
  7. 7.
    F.C. EVANS & E.F. SMITH, (1952): The intrinsic rate of natural increase of the human louse Pediculus humanus L. Amer. Nat. 86, 229–310.CrossRefGoogle Scholar
  8. 8.
    J.W. FORRESTER, (1971): World Dynamics. Cambridge, Mass.Google Scholar
  9. 9.
    D. GIRKE & U. HALBACH, (1982): A new population model: Computer simulation using different time lags for birth and death rate. Ber. Ökol. Aussenst. Schlüchtern 11 (in press).Google Scholar
  10. 10.
    B.S. GOH, (1980): Stability of some multispecies population models. Lect. Notes Pure Appl. Math. 58, 209–216.MathSciNetMATHGoogle Scholar
  11. 11.
    U. HALBACH, (1970): Influence of temperature on the population dynamics of the rotifer Brachionus calyciflorus PALLAS. Oecologia 4, 176–207.CrossRefGoogle Scholar
  12. 12.
    U. HALBACH, (1973): Life table data and population dynamics of the rotifer Brachionus calyciflorus PALLAS as influenced by periodically oscillating temperature. In: W. WIESER (Ed.): Effects of Temperature on Ectothermic Organisms. Springer-Verlag, Berlin-Heidelberg-New York, 217–228.CrossRefGoogle Scholar
  13. 13.
    U. HALBACH, (1974): Modelle in der Biologie. Naturwiss. Rundschau 27, 3–15.Google Scholar
  14. 14.
    U. HALBACH, (1975): Methoden der Populationsökologie. Verh. Ges. Ökol., Erlangen 1974, 1–24.Google Scholar
  15. 15.
    U. HALBACH, (1976): Populations-und synökologische Modelle in der Ornithologie. J. Ornithol. 117, 279–296.CrossRefGoogle Scholar
  16. 16.
    U. HALBACH, (1978a): Problems of ecosystem research as exemplified by limnology. Verh. Dtsch.Zool. Ges. 1977, 41–66.Google Scholar
  17. 17.
    U. HALBACH, (1978b): Populationdynamik planktischer Rotatorien. Verh. Ges. Ökol. Kiel 1977, 173–183.Google Scholar
  18. 18.
    U. HALBACH, (1979a): The ecological niche and derived concepts. Abh. Geb. Vogelkunde 6, 53–65.Google Scholar
  19. 19.
    U. HALBACH, (1979b): Introductory remarks: Strategies in population research exemplified by rotifer population dynamics. In: U. HALBACH & J. JACOBS (Eds.): Population Ecology. Fortschr. Zool. 25, 1–27.Google Scholar
  20. 20.
    U. HALBACH, (1979c): Modelle und Modellvorstellungen in der Biologie. Handbuch d. prakt. und exper. Schulbiologie 1/1, 61–112.Google Scholar
  21. 21.
    U. HALBACH, (1979d): Computer sagt Bevölkerungsentwicklung voraus. Mathematische Modelle für Schwankungen der Individuendichte. Umschau 79(11), 341–346.Google Scholar
  22. 22.
    U. HALBACH, (1982a): Population dynamics of rotifers and its consequences for ecotoxicology. Hydrobiologia (in press).Google Scholar
  23. 23.
    U. HALBACH, (1982b): Population ecology of rotifers as a bioassay tool for ecotoxicological tests in aquatic environments. Ecotoxicology and Environmental Safety (in press).Google Scholar
  24. 24.
    U. HALBACH & H.-J. BURKHARDT (1972): Are simple time-lags responsible for cyclic variation of population density? A comparison of laboratory population dynamics with computer simulations. Oecologia 9, 215–222.CrossRefGoogle Scholar
  25. 25.
    U. HALBACH & I. FRIZ, (1978): Bei welcher Individuendichte stoppt eine Bevölkerungsexplosion? Ber. Ökol. Aussenstelle Schlüchtern 1, 107–127.Google Scholar
  26. 26.
    U. HALBACH & G. HALBACH-KEUP, (1974): Quantitative relations between phytoplankton and the population dynamics of the rotifer Brachionus calyciflorus PALLAS. Results of laboratory experiments and field studies. Arch. Hydrobiol. 73, 273–309.Google Scholar
  27. 27.
    U. HALBACH et al. (1981a): Population dynamics of rotifers as rotifers as bioassay tool for toxic effects of organic pollutants. Verh. Intern. Verein. Limnol. 21, 1147–1152.Google Scholar
  28. 28.
    U. HALBACH et al. (1981b): The population dynamics of rotifers as bioassay for sublethal ecotoxicological effects exemplified with pentachlorophenol (PCP). Verh. Ges. Ökol., Berlin 1980, 261–267.Google Scholar
  29. 29.
    T.G. HALLAM, (1980): Persistence in Lotka-Volterra models of food chains and competition. Lect. Notes Pure Appl. Math. 58, 1–12.MathSciNetMATHGoogle Scholar
  30. 30.
    J.F. HANEY, M. BRAUER & G. NÜRNBERG, (1982): Cerenkov Counting: A useful method for determining feeding, egestion, and excretion rates of zooplankton. Limnol. & Oceanogr. (in press).Google Scholar
  31. 31.
    A. HASTINGS, (1980): Population dynamics in patchy environments. Lect. Notes Pure Appl. Math. 58, 217–224.MathSciNetMATHGoogle Scholar
  32. 32.
    D. VON HOLST, (1974): Soozialer Stress bei Tier und Mensch. Verh. Ges. Ökol., Saarbrücken 1973, 97–106.Google Scholar
  33. 33.
    E. HUTCHINSON, (1948): Circular causal systems in ecology. Ann. N.Y. Acad. Sci. 50, 221–246.CrossRefGoogle Scholar
  34. 34.
    E. HUTCHINSON, (1954): Theoretical notes on oscillating populations. J. Wildlife Mgmt. 18, 107–109.CrossRefGoogle Scholar
  35. 35.
    H. KAUSER, (1975): Dynamics of populations and properties of single individuals. Verh. Ges. Ökol., Erlangen 1974, 25–38.Google Scholar
  36. 36.
    N. LEIMEROTH, (1980): Respiration of different stages and energy budgets of juvenile Brachionus calyciflorus. Hydrobiologia 73, 195–197.CrossRefGoogle Scholar
  37. 37.
    P.H. LESLIE & T. PARK, (1949): The intrinsic rate of natural increase of Tribolium castaneum HERBST. Ecology 30, 469–477.CrossRefGoogle Scholar
  38. 38.
    R.M. MAY, (1974): Stability and complexity in model ecosystems. Monographs in Population Biology 6, 2nd Edition. Princeton, New Jersey.Google Scholar
  39. 39.
    R.M. MAY, (1976): Theoretical Ecology — Principals and Applications. Oxford.Google Scholar
  40. 40.
    D.H. MEADOWS et al., (1972): The Limits of Growth. New York.Google Scholar
  41. 41.
    A.J. NICHOLSON, (1954): An outline of the dynamics of animal populations. Austr. J. Zool. 2, 9–65.CrossRefGoogle Scholar
  42. 42.
    A. PARISE, (1966): Ciclo sessuale e dinamica popolazioni di Euchlanis (Rotatoria) in condizioni sperimentali. Arch. Oceanogr. Limnol. 16, 387–411.Google Scholar
  43. 43.
    R. PEARL & S.A. GOULD, (1936): Human Biology 8, 399–511.Google Scholar
  44. 44.
    I. RECHENBERG, (1973): Evolutionsstrategie. Stuttgart-Bad Cannstatt.Google Scholar
  45. 45.
    C. RORRES, (1980): Optimal age-specific harvesting policy for a continuous time-population model. Lect. Notes Pure Appl. Math. 58,239–254.MathSciNetMATHGoogle Scholar
  46. 46.
    A. SEITZ & U. HALBACH, (1973): How is the population density regulated? Experimental studies on rotifers and computer simulations. Naturwiss. 60, 51.CrossRefGoogle Scholar
  47. 47.
    P.J. WANGERSKY & W.J. CUNNINGHAM, (1957): Time lag in population models. Cold Spr. Harb. Symp. Quant. Biol. 22, 329–338.CrossRefGoogle Scholar
  48. 48.
    C. WISSEL, K. BEUTER & U. HALBACH, (1981): Correlation functions for the evaluation of repeated time series with fluctuations. ISEM Journal 3, 11–29.Google Scholar
  49. 49.
    D.J. WOLLKIND, A. HASTINGS & J.A. LOGAN, (1980): Models involving differential equations appropriate for describing a temperature dependent predatorprey mite ecosystem on apples. Lect. Notes Pure Appl. Math. 58,255–277.MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • U. Halbach
    • 1
  1. 1.Ecology Group, Department of BiologyJohann Wolfgang Goethe - UniversitätFrankfurt am MainWest Germany

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