On the Mechanistic Derivation of Various Discrete-Time Population Models

Original Paper

Abstract

We present a derivation of various discrete-time population models within a single unifying mechanistic context. By systematically varying the within-year patterns of reproduction and aggression between individuals we can derive various discrete-time population models. These models include classical examples such as the Ricker model, the Beverton--Holt model, the Skellam model, the Hassell model, and others. Some of these models until now lacked a good mechanistic interpretation or have been derived in a different context. By using this mechanistic approach, the model parameters can be interpreted in terms of individual behavior.

Keywords

Beverton–Holt model Discrete-time population model Hassell model Ricker model Skellam model 

References

  1. Beverton, R.J.H., Holt, S.J., 1957. On the dynamics of exploited fish populations. Fisheries Investigations, Series 2, vol. 19. H. M. Stationery Office, London.Google Scholar
  2. Brännström, Å., Sumpter, D.J.T., 2005. The role of competition and clustering in population dynamics. Proc. R. Soc. Lond. Ser. B 272, 2065–2072.CrossRefGoogle Scholar
  3. Geritz, S.A.H., Kisdi, É., 2004. On the mechanistic underpinning of discrete-time population models with complex dynamics. J. Theor. Biol. 228, 261–269.CrossRefMathSciNetGoogle Scholar
  4. Hassell, M.P., 1975. Density-dependence in single-species populations. J. Anim. Ecol. 44, 283–295.CrossRefGoogle Scholar
  5. Johansson, A., Sumpter, D.J.T., 2003. From local interactions to population dynamics in site-based models of ecology. Theor. Popul. Biol. 64, 497–517.MATHCrossRefGoogle Scholar
  6. Ricker, W.E., 1954. Stock and recruitment. J. Fish. Res. Bd. Can. 11, 559–623.Google Scholar
  7. Skellam, J.G., 1951. Random dispersal in theoretical populations. Biometrika 38, 196–218.MATHMathSciNetGoogle Scholar
  8. Sumpter, D.J.T., Broomhead, D.S., 2001. Relating individual behaviour to population dynamics. Proc. R. Soc. Lond. Ser. B 268, 925–932.CrossRefGoogle Scholar
  9. Thieme, H.R.T., 2003. Mathematics in Population Biology. Princeton University Press, Princeton, NJ.MATHGoogle Scholar

Copyright information

© Society for Mathematical Biology 2006

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TurkuTurkuFinland
  2. 2.Department of Mathematics and StatisticsRolf Nevanlinna Institute, University of HelsinkiHelsinkiFinland

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