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

Hilla Behar, Naama Brenner, Yoram Louzoun

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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.

Original languageEnglish
Pages (from-to)20-29
Number of pages10
JournalTheoretical Population Biology
StatePublished - Sep 2014

Bibliographical note

Funding Information:
This research is supported in part by the Israel Binational Science Foundation personal grant (NB) (grant number 1566/11 ).


  • Coexistence
  • Microbial cooperation
  • Microorganism population
  • Spatio-temporal patterns
  • Stochastic processes


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