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Pursuit-evasion predator-prey waves in two spatial dimensions.

V N Biktashev1, J Brindley, A V Holden

  • 1Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, United Kingdom.

Chaos (Woodbury, N.Y.)
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Summary

This study explores population dynamics with species taxis, revealing novel wave behaviors in two dimensions. These findings introduce a new mechanism for complex spatiotemporal activity in ecological models.

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Theoretical Ecology

Background:

  • Population dynamics models often use diffusion to describe species spread.
  • Taxis, or directed movement towards or away from stimuli, can significantly alter spatial dynamics.
  • Previous work identified unique wave phenomena in one-dimensional models with taxis.

Purpose of the Study:

  • To investigate novel spatial patterns and wave behaviors in a two-dimensional population dynamics model incorporating taxis.
  • To identify new mechanisms of spatiotemporal activity arising from predator-prey interactions and taxis.
  • To compare and contrast these phenomena with those observed in simpler reaction-diffusion systems.

Main Methods:

  • Simulations of a spatially distributed population dynamics model.
  • Incorporation of taxis (gradient-following behavior) alongside or instead of diffusion.
  • Analysis of wave propagation, reflection, and pattern formation in two spatial dimensions.

Main Results:

  • Observed unusual spiral meander patterns.
  • Identified partial wave reflection and swelling wave tips.
  • Discovered wave end attachment leading to self-supporting complex spatiotemporal activity.

Conclusions:

  • Taxis introduces complex behaviors in two-dimensional population dynamics not seen in standard reaction-diffusion models.
  • The identified mechanisms offer new insights into self-organizing spatial structures in ecological systems.
  • This model provides a framework for understanding emergent complexity driven by directed species movement.