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Red queen dynamics in specific predator-prey systems.

Terence Harris1, Anna Q Cai

  • 1School of Mathematics and Statistics, University of New South Wales, Sydney, Australia, t.harris@student.unsw.edu.au.

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Predator-prey dynamics were compared in discrete and continuous strategy spaces. Constant prey switching in discrete models stabilizes the system and reduces predator diversity via extinction.

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Area of Science:

  • Ecology
  • Evolutionary Game Theory
  • Mathematical Biology

Background:

  • Predator-prey interactions are fundamental to ecosystem stability.
  • Understanding strategy dynamics is crucial for ecological modeling.
  • Discrete and continuous models offer different perspectives on biological systems.

Purpose of the Study:

  • To compare predator-prey system dynamics across discrete and continuous strategy spaces.
  • To investigate the impact of prey switching on system stability.
  • To analyze the effect of strategy space on predator diversity.

Main Methods:

  • Mathematical modeling of predator-prey interactions.
  • Comparison of average strategies in discrete versus continuous models.
  • Analysis of the stabilizing effects of constant prey switching.

Main Results:

  • Average strategies in discrete and continuous cases were found to be equivalent.
  • Constant prey switching in discrete models demonstrated a stabilizing effect.
  • Extinction of predator types was observed, reducing overall diversity.

Conclusions:

  • Discrete and continuous models yield similar average strategies in this predator-prey system.
  • Prey switching is a key factor in stabilizing discrete predator-prey dynamics.
  • Ecological strategies can lead to reduced biodiversity through competitive exclusion.