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Invasion exponents in biological networks

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  • Demetrius, Lloyd
  • Gundlach, Volker Matthias
  • Ochs, Gunter

Abstract

This article is concerned with the characterization of invasion exponents in biological networks defined by a population of replicating elements: molecules, cells, higher organisms. We show that the outcome of competition between an invader and a resident population is a stochastic process, determined by the rate at which a population returns to its steady state after a random perturbation in the parameters that characterize the replicating elements. This return rate is defined by the macroscopic parameter evolutionary entropy, a measure of the diversity of the interaction between the individuals in the population. We also show that the evolutionary stability of a population, that is the invulnerability of a resident to the introduction of an invader competing for the available resources, are given by extremal states of entropy. These results which pertain to networks of interacting molecules, cells and higher organisms, are generalizations of results established for demographic networks, that is populations of replicating organisms parametrized by the ages at which they reproduce and die.

Suggested Citation

  • Demetrius, Lloyd & Gundlach, Volker Matthias & Ochs, Gunter, 2009. "Invasion exponents in biological networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(5), pages 651-672.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:5:p:651-672
    DOI: 10.1016/j.physa.2008.10.048
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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Demetrius, Lloyd A. & Wolf, Christian, 2022. "Directionality theory and the second law of thermodynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 598(C).
    2. Germano, Fabrizio, 2022. "Entropy, directionality theory and the evolution of income inequality," Journal of Economic Behavior & Organization, Elsevier, vol. 198(C), pages 15-43.

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