Competition in ecosystems has been one of the major topics where physics can contribute to understanding of biological problems. Recent experiments have shown that two neutral bacteria strains spontaneously segregate from a well-mixed state on an agar plate [1], which suggests importance of interplay between competition and spatial patterns. Moreover, another study has suggested relevance of universal scaling laws developed in statistical physics [2]. In addition, microfluidic devices with anisotropic geometry such as a channel with open ends enable quantitative and long-time observation of bacterial population [3] and add new aspects to bacterial competition problems.

To study competition between two neutral strains in anisotropic channel systems, we construct a simple three-dimensional lattice model, which allows us to investigate large-scale statistical properties of the problems [4]. In its simplest version only with self-replication of cells, we find that the two strains form stripe patterns along the channel. The formed lanes are gradually rearranged, with increasing length scales in the two-dimensional cross-sectional plane. Remarkably, it turns out that the spatiotemporal evolution of lanes can be characterized by logarithmically slow coarsening, which is characteristic of the two-dimensional voter model [5] (and also known as critical behavior of the generalized voter class for absorbing-state transitions [6]).

We also generalize the model by introducing mutation and killing of bacteria. We find a phase transition from a monopolistic phase, where lanes along the channel are coarsened until the system is dominated by one of the two strains, to a mixed phase without lane structure. In the presentation, we will show the numerical results and theoretical accounts based on continuum equations, which we obtain by applying a mean field approximation.

[1] O. Hallatschek et al, PNAS 104, 19926 (2007).

[2] L. Mcnally et al, Nat. Commun. 8, 14371 (2017).

[3] G. Velve-Casquillas et al, Nano Today 5, 28 (2010).

[4] T. Shimaya and Kazumasa A. Takeuchi, arXiv:1804.09895

[5] I. Dornic et al, PRL 87, 045701 (2001).

[6] O. Al Hammal et al, PRL 94, 230601 (2005).