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Solution Equilibrium and Saturation

Imagine adding a small amount of sugar to a glass of water, stirring until all the sugar has dissolved, and then adding a bit more. You can repeat this process until the sugar concentration of the solution reaches its natural limit, a limit determined primarily by the relative strengths of the solute-solute, solute-solvent, and solvent-solvent attractive forces. You can be certain that you have reached this limit because, no matter how long you stir the solution, undissolved sugar remains. The...
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Experimental Protocol for Manipulating Plant-induced Soil Heterogeneity
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Dynamical phase coexistence: a simple solution to the "savanna problem".

Federico Vazquez1, Cristóbal López, Justin M Calabrese

  • 1IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos, CSIC-UIB, E-07122 Palma de Mallorca, Spain. federico@pks.mpg.de

Journal of Theoretical Biology
|February 16, 2010
PubMed
Summary
This summary is machine-generated.

Dynamical phase coexistence explains how trees and grasses stably coexist in savannas. This ecological model shows long-term stability despite environmental fluctuations and system size.

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Area of Science:

  • Theoretical Ecology
  • Mathematical Modeling
  • Ecosystem Dynamics

Background:

  • The savanna problem highlights the difficulty in explaining stable coexistence of trees and grasses.
  • Savannas exhibit significant spatiotemporal variability, posing challenges for ecological models.

Purpose of the Study:

  • To introduce dynamical phase coexistence as a solution to the savanna problem.
  • To model the robust coexistence of trees and grasses in savanna ecosystems.

Main Methods:

  • A modified contact process (CP) model incorporating varying environmental conditions and tree age.
  • Analysis of system fluctuations between woodland and grassland phases.

Main Results:

  • The model demonstrates a stable phase with dynamically coexisting woodland and grassland patches.
  • Mean time to tree extinction scales as a power-law with system size, reaching millions of years.
  • Local tree interactions affect spatial distribution but not dynamical coexistence.

Conclusions:

  • Dynamical phase coexistence provides a robust mechanism for savanna stability.
  • The model's findings are potentially applicable to other complex systems in physics, biology, and social sciences.