Bacterial range expansions on a growing front: Roughness, fixation, and directed percolation

Area of Science:

• Statistical Physics
• Non-equilibrium Phase Transitions
• Mathematical Biology

Background:

• Directed percolation (DP) is a fundamental model for nonequilibrium phase transitions into a single absorbing state.
• DP has recently been recognized as a generic model for the evolutionary and ecological dynamics of competing bacterial populations.
• Bacterial range expansion, characterized by a fluctuating and rough growth front, is known to impact the critical behavior of DP transitions.

Purpose of the Study:

• To develop a theoretical framework describing the interplay between surface roughness and directed percolation in bacterial range expansion.
• To investigate the macroscopic phenomenology and scaling behaviors associated with this coevolutionary process.

Main Methods:

• Symmetry arguments were used to construct a pair of nonlinear stochastic partial differential equations.
• The equations model the coevolution of surface roughness and the composition field in DP.
• Renormalization group analysis was applied to study scaling behaviors.

Main Results:

• A theoretical model was established to describe the coupled dynamics of surface roughness and DP.
• The study discusses macroscopic manifestations on growth patterns and genealogical tracks.
• Potential scaling behaviors at the DP transition were analyzed.

Conclusions:

• The developed nonlinear stochastic partial differential equations provide a new framework for understanding DP in biological systems.
• This work bridges concepts from statistical physics and mathematical biology, offering insights into bacterial competition dynamics.
• The findings contribute to the understanding of how physical phenomena like surface roughness influence evolutionary and ecological processes.