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Coexistence of productive and non-productive populations by fluctuation-driven spatio-temporal patterns

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  • Behar, Hilla
  • Brenner, Naama
  • Louzoun, Yoram

Abstract

Cooperative interactions, their stability and evolution, provide an interesting context in which to study the interface between cellular and population levels of organization. Here we study a public goods model relevant to microorganism populations actively extracting a growth resource from their environment. Cells can display one of two phenotypes — a productive phenotype that extracts the resources at a cost, and a non-productive phenotype that only consumes the same resource. Both proliferate and are free to move by diffusion; growth rate and diffusion coefficient depend only weakly phenotype. We analyze the continuous differential equation model as well as simulate stochastically the full dynamics. We find that the two sub-populations, which cannot coexist in a well-mixed environment, develop spatio-temporal patterns that enable long-term coexistence in the shared environment. These patterns are purely fluctuation-driven, as the corresponding continuous spatial system does not display Turing instability. The average stability of coexistence patterns derives from a dynamic mechanism in which the producing sub-population equilibrates with the environmental resource and holds it close to an extinction transition of the other sub-population, causing it to constantly hover around this transition. Thus the ecological interactions support a mechanism reminiscent of self-organized criticality; power-law distributions and long-range correlations are found. The results are discussed in the context of general pattern formation and critical behavior in ecology as well as in an experimental context.

Suggested Citation

  • Behar, Hilla & Brenner, Naama & Louzoun, Yoram, 2014. "Coexistence of productive and non-productive populations by fluctuation-driven spatio-temporal patterns," Theoretical Population Biology, Elsevier, vol. 96(C), pages 20-29.
    • Handle: RePEc:eee:thpobi:v:96:y:2014:i:c:p:20-29
    DOI: 10.1016/j.tpb.2014.06.002
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    1. Jeff Gore & Hyun Youk & Alexander van Oudenaarden, 2009. "Snowdrift game dynamics and facultative cheating in yeast," Nature, Nature, vol. 459(7244), pages 253-256, May.
    2. Hauert, Christoph & Wakano, Joe Yuichiro & Doebeli, Michael, 2008. "Ecological public goods games: Cooperation and bifurcation," Theoretical Population Biology, Elsevier, vol. 73(2), pages 257-263.
    3. Elhanati, Yuval & Schuster, Stefan & Brenner, Naama, 2011. "Dynamic modeling of cooperative protein secretion in microorganism populations," Theoretical Population Biology, Elsevier, vol. 80(1), pages 49-63.
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    1. Stojkoski, Viktor & Karbevski, Marko & Utkovski, Zoran & Basnarkov, Lasko & Kocarev, Ljupco, 2021. "Evolution of cooperation in networked heterogeneous fluctuating environments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).

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