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Nonlinear Competition Avoidance Favors Coexistence in Spatially Structured Microbial Populations

Mattia Mattei1, David Soriano-Paños1,2, and Alex Arenas1,3

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PRX Life 4, 043011 – Published 5 November, 2026

DOI: https://doi.org/10.1103/4t9n-nvgc

Abstract

Bacteria regulate their motility through a variety of mechanisms, including quorum sensing and other density-dependent responses mediated by diffusible signals. While nonlinear density-dependent motility is well known in active-matter theory to generate nonequilibrium spatial patterns, its consequences for the coexistence of growing, interacting species remain less explored. Here we develop a minimal spatially structured model for two strongly competing species in which local demographic interactions are coupled to an escape response: Each species increases its motility nonlinearly (sigmoidal) with the local abundance of its competitor. We show that this sigmoidal motility regulation promotes optimal spatial self-organization and can sustain long term coexistence via segregation, even in parameter regimes that yield competitive exclusion in well-mixed Lotka-Volterra dynamics. On two-dimensional lattices, the interplay between demographic competition and density-dependent motility generates a range of emergent patterns, including regimes in which the weaker competitor counterintuitively has higher total abundance. Overall, our results identify nonlinear, competitor-induced motility as a fundamental mechanism capable of sustaining coexistence in competing microbial populations.

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PRX Life 4, 043011– Published 5 November, 2026
  • Received 20 January 2026
  • Accepted 30 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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