title: Coexistence of productive and non-productive populations by fluctuation-driven spatio-temporal patterns.
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.
authors: Department of Mathematics and Gonda Brain Research Center, Bar-Ilan University, Ramat Gan, Israel. Electronic address: hilla.behar2@gmail.com.
authors: Hilla
authors: H
authors: Behar
authors: Department of Chemical Engineering and Network Biology Research Lab, Technion, Haifa, Israel. Electronic address: nbrenner@tx.technion.ac.il.
authors: Naama
authors: N
authors: Brenner
authors: Department of Mathematics and Gonda Brain Research Center, Bar-Ilan University, Ramat Gan, Israel. Electronic address: louzouy@math.biu.ac.il.
authors: Yoram
authors: Y
authors: Louzoun
mesh_terms: D004463:Ecology; D008827:Microbiological Phenomena; D008962:Models, Theoretical; D013269:Stochastic Processes
keywords: Coexistence; Microbial cooperation; Microorganism population; Spatio-temporal patterns; Stochastic processes