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Steady-state, Pre-steady-state, and Single-turnover Kinetic Measurement for DNA Glycosylase Activity
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Alternative steady states in ecological networks.

Yael Fried1, Nadav M Shnerb1, David A Kessler1

  • 1Department of Physics, Bar-Ilan University, Ramat-Gan IL52900, Israel.

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|January 20, 2018
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Summary

This study reveals that the number of stable and uninvadable (SU) states in ecological systems with weak competition grows exponentially with species number. This pattern holds unless the interaction network is asymmetric, where SU states remain constant.

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Area of Science:

  • Theoretical Ecology
  • Mathematical Biology
  • Network Theory

Background:

  • Ecological systems often feature numerous competing species with limited exchange with a larger regional pool.
  • The long-term behavior of these systems is largely determined by their stable and uninvadable (SU) states.
  • The properties of the competition matrix, specifically its mean and variance, influence the quantity of SU states in random competition scenarios.

Purpose of the Study:

  • To investigate the number of stable and uninvadable (SU) states in ecological systems under weak competition and high variance.
  • To establish a mathematical link between ecological stability and network structures in the specified limit.
  • To determine how species richness impacts the number of SU states in such systems.

Main Methods:

  • Utilized a yes-no interaction model to represent species competition.
  • Analyzed the system in the limit of weak competition and large variance.
  • Mapped the problem of counting SU states to identifying maximum cliques in Erdös-Rényi random networks.

Main Results:

  • The number of SU states was shown to be equivalent to the number of maximum cliques in an Erdös-Rényi network.
  • In the weak competition and large variance limit, SU states increase exponentially with the number of species.
  • A notable exception occurs in the asymmetric limit, where the number of SU states remains constant (O(1)).

Conclusions:

  • The findings provide a theoretical framework for understanding ecological stability in complex systems.
  • The exponential growth of SU states highlights potential for rapid diversification or instability depending on network structure.
  • Numerical simulations support the applicability of these results to models with continuous competition distributions.