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Hydra effects in stable food chain models.

Debprasad Pal1, Bapan Ghosh2, Tapan Kumar Kar3

  • 1Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Botanic Garden, Howrah 711103, West Bengal, India; Department of Mathematics, Bethune College, 181, Bidhan Sarani, Kolkata 700006, West Bengal, India.

Bio Systems
|August 23, 2019
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Summary

The hydra effect, where increased mortality boosts population size, was studied in food chains. This research found the hydra effect can occur in prey and predator populations within stable ecological models.

Keywords:
Dynamical systemFood chainHarvestingHydra effectPopulation dynamicsStability

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Theoretical Ecology

Background:

  • The hydra effect is a paradoxical ecological phenomenon where increased mortality can lead to population growth.
  • Understanding population dynamics is crucial for applied ecology, including fishery management and pest control.

Purpose of the Study:

  • To propose and analyze a dynamical system model of a food chain exhibiting the hydra effect.
  • To investigate how increasing mortality rates impact targeted species' populations in stable steady states.
  • To explore the occurrence of the hydra effect in multi-trophic systems.

Main Methods:

  • Development of a Rosenzweig-MacArthur food chain model with logistic prey growth and Holling type II functional responses.
  • Modeling a 'pure predator system' where predator per capita growth rate is density-independent.
  • Analysis of system stability under varying mortality rates and harvesting pressures.

Main Results:

  • The hydra effect was observed at stable states in prey (4-trophic system), the first predator (5-trophic system), and both prey and second predator (6-trophic system).
  • The model demonstrated that the unique stable steady state can remain stable even under harvesting of different trophic levels.
  • Unlike some ratio-dependent systems, harvesting did not necessarily induce instability preventing the hydra effect at stable states in this model.

Conclusions:

  • The study contributes to understanding population interactions and the conditions under which the hydra effect manifests in food chains.
  • Findings have implications for fishery management and biological pest control strategies by clarifying population responses to mortality.
  • The proposed model provides a framework for further research into paradoxical effects in ecological systems.