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Resurrection of Dormant Daphnia magna: Protocol and Applications
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Persistence in fluctuating environments.

Sebastian J Schreiber1, Michel Benaïm, Kolawolé A S Atchadé

  • 1Department of Evolution and Ecology and the Center for Population Biology, University of California, Davis, CA 95616, USA. sschreiber@ucdavis.edu

Journal of Mathematical Biology
|June 10, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces a new mathematical theory for population coexistence, showing that environmental noise can either help or hinder species interactions. The findings are crucial for understanding ecological community dynamics and biodiversity.

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Area of Science:

  • Population Biology
  • Mathematical Ecology
  • Theoretical Ecology

Background:

  • Coexistence of interacting populations (plants, animals, viruses) is vital in population biology.
  • Biotic interactions and environmental fluctuations significantly influence population coexistence.
  • Existing theories often focus on deterministic systems, with less emphasis on stochastic influences.

Purpose of the Study:

  • To develop a mathematical theory for population coexistence under both deterministic and stochastic conditions.
  • To extend the nonlinear theory of permanence to stochastic difference and differential equations.
  • To provide a robust criterion for predicting species coexistence in ecological communities.

Main Methods:

  • Developed a mathematical theory extending nonlinear permanence theory to stochastic systems.
  • Defined a coexistence condition based on weighted average invasion rates across stationary distributions.
  • Analyzed the impact of noise and perturbations on population dynamics and coexistence criteria.

Main Results:

  • Established a novel coexistence condition requiring positive weighted invasion rates for all population sub-collections.
  • Demonstrated that populations converge to a unique stationary distribution when the coexistence condition is met with sufficient noise.
  • Showed the coexistence criterion is robust to small perturbations in model functions.
  • Illustrated that environmental noise can enhance or inhibit coexistence in rock-paper-scissor dynamics.
  • Found stochastic mortality rate variations do not affect coexistence criteria in Lotka-Volterra models.
  • Indicated random forcing can promote genetic diversity in exploitative interactions.

Conclusions:

  • The developed theory provides a unified framework for understanding population coexistence under deterministic and stochastic forces.
  • Environmental noise plays a complex role in ecological communities, with effects dependent on interaction dynamics and demographic correlations.
  • The findings have implications for predicting biodiversity and community stability in fluctuating environments.