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Prey Selection, Vertical Migrations and the Impacts of Harvesting Upon the Population Dynamics of a Predator-Prey System

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Abstract

A model is developed to describe the interaction between a predator and two prey types located in different regions. Conditions for stability and persistence are analysed. The effects of harvesting the predators are investigated by making the predator mortality rate habitat dependent. Results demonstrate that for any given set of parameter values there is a value of the intrinsic preference of the predator for each prey type at which the system undergoes a Hopf bifurcation. Above this critical value the system evolves towards a stable equilibrium, whereas below it, stable limit cycles arise by Hopf bifurcations. Simulations demonstrate that the presence of demographic stochasticity may destabilise oscillatory populations, thereby causing population extinctions. An application of the model to the foraging behaviour of North Sea cod is described. It is shown that if the preferred prey is more productive, it is likely that the equilibrium will be stable, whereas if the less preferred prey is more productive, populations are likely to display cycles and in the stochastic case become extinct. As cod fishing mortality is increased, the point of bifurcation and region of parameter space for which the system is unstable decreases. An increased understanding of how cod behave may enable fish stocks to be managed more successfully, for example by indicating where marine reserves should be placed.

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Authors and Affiliations

  1. Marine Spatial Ecology Lab, School of Biosciences, Hatherly Laboratory, University of Exeter, Prince of Wales Road, Exeter, Devon, EX4 4PS, UK

    Helen J. Edwards

  2. Department of Biology, University of York, Heslington, York, YO10 5YW, UK

    Calvin Dytham & Jonathan W. Pitchford

  3. Centre for Environment, Fisheries and Aquaculture Science, Lowestoft Laboratory, Pakefield Road, Lowestoft, Suffolk, NR33 0HT, UK

    David Righton

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  1. Helen J. Edwards
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  2. Calvin Dytham
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  3. Jonathan W. Pitchford
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  4. David Righton
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Correspondence to Helen J. Edwards.

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Edwards, H.J., Dytham, C., Pitchford, J.W. et al. Prey Selection, Vertical Migrations and the Impacts of Harvesting Upon the Population Dynamics of a Predator-Prey System. Bull. Math. Biol. 69, 1827–1846 (2007). https://doi.org/10.1007/s11538-007-9194-0

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  • DOI: https://doi.org/10.1007/s11538-007-9194-0

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