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Journal of Mathematical Biology

, Volume 64, Issue 1–2, pp 341–360 | Cite as

The hydra effect in predator–prey models

  • Michael Sieber
  • Frank M. Hilker
Article

Abstract

The seemingly paradoxical increase of a species population size in response to an increase in its mortality rate has been observed in several continuous-time and discrete-time models. This phenomenon has been termed the “hydra effect”. In light of the fact that there is almost no empirical evidence yet for hydra effects in natural and laboratory populations, we address the question whether the examples that have been put forward are exceptions, or whether hydra effects are in fact a common feature of a wide range of models. We first propose a rigorous definition of the hydra effect in population models. Our results show that hydra effects typically occur in the well-known Gause-type models whenever the system dynamics are cyclic. We discuss the apparent discrepancy between the lack of hydra effects in natural populations and their occurrence in this standard class of predator–prey models.

Keywords

Consumer–resource models Gause-type model Population cycles Allee effect Mean population density Population extinction 

Mathematics Subject Classification (2000)

92D25 92D40 34C60 34D05 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of Mathematics and Computer Science, Institute of Environmental Systems ResearchUniversity of OsnabrückOsnabrückGermany
  2. 2.Department of Mathematical Sciences, Centre for Mathematical BiologyUniversity of BathBathUK

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