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Coexistence and extinction for two competing species in patchy environments.

Chang-Yuan Cheng1, Kuang-Hui Lin, Chih-Wen Shih

  • 1Department of Applied Mathematics, National Pingtung University, Pingtung, Taiwan 900.

Mathematical Biosciences and Engineering : MBE
|March 14, 2019
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Summary

This study examines competing species diffusion in a two-patch environment. Depending on birth rate variations and diffusion speed, either coexistence or species extinction occurs, with the higher-average-birth-rate species often dominating.

Keywords:
competing speciesdispersal rateglobal dynamicsmonotone dynamicspatchy environmentspatial heterogeneity

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Area of Science:

  • Mathematical Biology
  • Ecology
  • Theoretical Ecology

Background:

  • Investigates a two-species competition model with diffusion across two patches.
  • Builds upon prior work examining scenarios where u-species has a higher average birth rate than v-species.

Purpose of the Study:

  • Analyzes global dynamics and bifurcations for a modified model where v-species has a higher average birth rate than u-species.
  • Explores how variations in birth rates and diffusion rates influence species coexistence and extinction.

Main Methods:

  • Mathematical modeling of competing species diffusion.
  • Analysis of global dynamics and bifurcations.
  • Investigating stability switches of semitrivial equilibria.

Main Results:

  • Identified two distinct dynamic scenarios based on relative birth rate variations.
  • Demonstrated that the v-species (higher average birth rate) prevails in fast diffusion environments.
  • Observed that in slow diffusion, either coexistence or extinction of v-species occurs, with u-species potentially dominating.

Conclusions:

  • The interplay between birth rate heterogeneity and diffusion rates critically determines the outcome of interspecific competition.
  • Stability switches in equilibria are contingent on the magnitude of average birth rate variations.
  • Ecological outcomes are sensitive to diffusion speed, leading to different dominance or coexistence patterns.