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Invasions in a four-species fractured cyclic ecological system.

E Y Siegfried1, A Bayliss1, V A Volpert1

  • 1Department of Engineering Sciences & Applied Mathematics, Northwestern University, Evanston, 60208, Illinois, USA; Institute for Theory and Mathematics in Biology, NSF-Simons National, Chicago, 60610, Illinois, USA.

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This study examines invasion dynamics in four-species ecological communities. Fracturing an alliance impacts invasion success, particularly under balanced or strong competition, affecting species coexistence.

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Asymptotic analysisBiological invasionsCyclic ecosystemsFractured alliancesPiecewise linear approximations

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Population Dynamics

Background:

  • Cyclic ecological communities exhibit complex competitive interactions.
  • Interspecies competition can dominate intraspecies competition, leading to alliance formation.
  • Alliance fracturing due to internal factors can alter community dynamics.

Purpose of the Study:

  • To analyze the invasion problem in a four-species cyclic community.
  • To determine standstill conditions when an alliance is fractured.
  • To investigate the impact of fracturing on standstill in balanced and strong competition regimes.

Main Methods:

  • Reduced the invasion problem to a traveling wave problem.
  • Analyzed standstill conditions (zero traveling wave speed).
  • Employed coordinate transformation for balanced competition and linearization for strong competition.

Main Results:

  • Identified conditions for standstill in a fractured four-species cyclic community.
  • Demonstrated the role of fracturing in influencing standstill conditions.
  • Showcased distinct behaviors in balanced versus strong competition regimes.
  • Validated analytical findings through numerical computations.

Conclusions:

  • Alliance fracturing significantly influences invasion dynamics and species coexistence.
  • Standstill conditions are critically dependent on the balance between interspecies and intraspecies competition.
  • Mathematical modeling provides insights into complex ecological community stability.