Journal of Mathematical Biology

, Volume 28, Issue 6, pp 609–643

A size dependent predator-prey interaction: who pursues whom?

  • A. M. De Roos
  • J. A. J. Metz
  • E. Evers
  • A. Leipoldt
Article

DOI: 10.1007/BF00160229

Cite this article as:
De Roos, A.M., Metz, J.A.J., Evers, E. et al. J. Math. Biol. (1990) 28: 609. doi:10.1007/BF00160229

Abstract

We investigate the properties of an (age, size) -structured model for a population of Daphnia that feeds on a dynamical algal food source. The stability of the internal equilibrium is studied in detail and combined with numerical studies on the dynamics of the model to obtain insight in the relation between individual behaviour and population dynamical phenomena. Particularly the change in the (age, size)-relation with a change in the food availability seems to be an important behavioural mechanism that strongly influences the dynamics. This influence is partly stabilizing and partly destabilizing and leads to the coexistence of a stable equilibrium and a stable limit cycle or even coexistence of two stable limit cycles for the same parameter values. The oscillations in this case are characterized by drastic changes in the size-structure of the population during a cycle. In addition the model exhibits the usual predator-prey oscillations that characterize Lotka-Volterra models.

Key words

Predator-prey interaction Size-structured population dynamics Behavioural mechanisms Dynamical phenomena 

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • A. M. De Roos
    • 1
  • J. A. J. Metz
    • 2
  • E. Evers
    • 2
  • A. Leipoldt
    • 2
  1. 1.Department of Biological SciencesUniversity of CalgaryCalgaryCanada
  2. 2.Institute of Theoretical BiologyLeiden UniversityLeidenThe Netherlands

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