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Host coexistence in a model for two host-one parasitoid interactions.

Valentina Clamer1, Andrea Pugliese2, Davide Liessi3

  • 1Department of Mathematics, University of Trento, Trento, Italy.

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|January 2, 2017
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Summary

This study explores host-parasitoid models. Density-dependent mortality can allow two host species to coexist with a parasitoid, while density-independent mortality prevents it.

Keywords:
Characteristic multipliersDelay differential equationsHost–parasitoid modelNumerical bifurcationPeriodic solutionsSpecies coexistence

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Area of Science:

  • Ecology
  • Population Dynamics
  • Biological Control

Background:

  • Host-parasitoid interactions are crucial in ecological systems.
  • Previous models by Murdoch et al. (1987) provide a foundation.
  • Understanding coexistence dynamics is key for pest management.

Purpose of the Study:

  • To investigate the coexistence dynamics of a two-host, one-parasitoid system.
  • To determine conditions favoring coexistence under density-dependent and independent mortality.
  • To explore the role of oscillatory dynamics in promoting coexistence.

Main Methods:

  • Building upon a continuous-time host-parasitoid model.
  • Analyzing dynamics with fixed larval stage duration.
  • Employing numerical bifurcation analysis.

Main Results:

  • Explicit conditions for equilibrium coexistence found with density-dependent host mortality.
  • Equilibrium coexistence is impossible with density-independent host mortality.
  • Oscillatory dynamics in one host-parasitoid system favor coexistence, even without density-dependence.

Conclusions:

  • Density-dependence is critical for stable equilibrium coexistence in this model.
  • Parasitoid models with oscillatory dynamics show potential for biological control.
  • Periodic solutions can facilitate host coexistence.