Reaching agreement in competitive microbial systems

Abstract

We study distributed agreement in microbial distributed systems under stochastic population dynamics and competitive interactions. Motivated by recent applications in synthetic biology, we examine how the presence and absence of direct competition among microbial species influences their ability to reach majority consensus . In this problem, two species are designated as input species, and the goal is to guarantee that eventually only the input species which had the highest initial count prevails. We show that direct competition dynamics reach majority consensus with high probability even when the initial gap between the species is small, i.e., Ω (√(nlog n)) , where n is the initial population size. In contrast, we show that absence of direct competition is not robust: solving majority consensus with constant probability requires a large initial gap of Ω (n) . To corroborate our analytical results, we use simulations to show that these consensus dynamics occur within practical biological time scales.

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BibTeX RIS

BibTeX

@article{andaur2026reaching,
  title = {{Reaching agreement in competitive microbial systems}},
  author = {Victoria Andaur and Janna Burman and Matthias Függer and Bilal Manssouri and Thomas Nowak and Joel Rybicki},
  journal = {Natural Computing},
  year = {2026},
  month = jun,
  doi = {10.1007/s11047-026-10070-z},
  eprint = {2103.07450},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05774166v1},
  note = {CC BY 4.0},
}

RIS

TY  - JOUR
TI  - Reaching agreement in competitive microbial systems
AU  - Victoria Andaur
AU  - Janna Burman
AU  - Matthias Függer
AU  - Bilal Manssouri
AU  - Thomas Nowak
AU  - Joel Rybicki
PY  - 2026
DA  - 2026/06/12
JO  - Natural Computing
DO  - 10.1007/s11047-026-10070-z
UR  - https://hal.science/hal-05774166v1
AB  - We study distributed agreement in microbial distributed systems under stochastic population dynamics and competitive interactions. Motivated by recent applications in synthetic biology, we examine how the presence and absence of direct competition among microbial species influences their ability to reach majority consensus . In this problem, two species are designated as input species, and the goal is to guarantee that eventually only the input species which had the highest initial count prevails. We show that direct competition dynamics reach majority consensus with high probability even when the initial gap between the species is small, i.e., Ω (√(nlog n)) , where n is the initial population size. In contrast, we show that absence of direct competition is not robust: solving majority consensus with constant probability requires a large initial gap of Ω (n) . To corroborate our analytical results, we use simulations to show that these consensus dynamics occur within practical biological time scales.
SN  - 1567-7818
SN  - 1572-9796
ER  -

Abstract

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