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Multiple invasion speeds in a two-species integro-difference competition model.

Bingtuan Li1

  • 1Department of Mathematics, University of Louisville, Louisville, KY, 40292, USA. bing.li@louisville.edu.

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|January 18, 2018
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Summary

Invasion dynamics of two competing species were analyzed. The species with a faster invasion speed can establish its own traveling wave, with speeds analytically determined for competitive scenarios.

Keywords:
CompetitionIntegro-difference equationLinear determinacySpreading speed

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Area of Science:

  • Mathematical Biology
  • Ecological Modeling
  • Invasion Biology

Background:

  • Understanding interspecific competition is crucial for predicting species coexistence and distribution.
  • Invasion dynamics, particularly how competing species establish in new environments, are complex and influenced by multiple factors.

Purpose of the Study:

  • To analyze an integro-difference competition model for two species consecutively invading a habitat.
  • To determine the conditions under which invading species can establish traveling waves and to analytically derive their speeds.

Main Methods:

  • Utilized an integro-difference competition model.
  • Employed mathematical analysis based on linear determinacy and novel techniques.
  • Investigated scenarios of one species invading a rival's wave and bidirectional spatial expansion.

Main Results:

  • The species with a larger invasion speed can establish a traveling wave into open space.
  • Analytical determination of boundary movement speeds is possible under specific competitive conditions.
  • The model predicts multiple invasion speeds, including the possibility of dual waves for a single species or distinct speeds in opposite directions for each species.

Conclusions:

  • Invasion speed is a critical factor in determining the establishment and propagation of competing species.
  • The mathematical framework allows for precise prediction of invasion speeds and wave dynamics.
  • Complex invasion patterns, including multiple distinct wave speeds, can arise from simple competitive interactions.