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Classification of Systems-I01:26

Classification of Systems-I

Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
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Linear Circuits01:17

Linear Circuits

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Linear time-invariant Systems

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Relative nonlinearity and permanence.

Yun Kang1, Peter Chesson

  • 1Applied Sciences and Mathematics, Arizona State University, Mesa, AZ 85212, USA. : yun.kang@asu.edu

Theoretical Population Biology
|April 17, 2010
PubMed
Summary
This summary is machine-generated.

We introduce uniform invasibility to ensure species coexistence, developing simple conditions for permanent coexistence in discrete-time models. Population fluctuations can undermine coexistence if relative nonlinearity is negative.

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Population Dynamics

Background:

  • The invasibility concept is crucial for understanding species coexistence.
  • Previous models often simplify the conditions for stable coexistence.
  • Discrete-time population models are widely used to study ecological interactions.

Purpose of the Study:

  • To develop a stronger concept of uniform invasibility for species coexistence.
  • To establish easily checked sufficient conditions for permanent coexistence in two-species models.
  • To investigate the impact of population fluctuations on invasion rates and coexistence.

Main Methods:

  • Modification of the invasibility concept to uniform invasibility.
  • Analysis of two-species discrete-time competition and predator-prey models.
  • Generalization of relative nonlinearity to analyze population fluctuations.
  • Derivation of conditions for permanent coexistence.

Main Results:

  • Broad, easily checked sufficient conditions for permanent coexistence were found.
  • Relative nonlinearity determines if population fluctuations affect invasion rates.
  • Negative relative nonlinearity can undermine permanent coexistence due to fluctuations.
  • Permanence is determined by invasibility of fixed points when relative nonlinearity is non-negative.

Conclusions:

  • Permanent coexistence is a more tractable concept with the developed conditions.
  • Population fluctuations can destabilize coexistence, particularly with negative relative nonlinearity.
  • The study provides a framework for analyzing coexistence in complex ecological models.