Bacterial range expansions on a growing front: Roughness, Fixation, and Directed Percolation

Abstract

Directed Percolation (DP) is a classic model for nonequilibrium phase transitions into a single absorbing state (fixation). It has been extensively studied by analytical and numerical techniques in diverse contexts. Recently, DP has appeared as a generic model for the evolutionary/ecological dynamics of competing bacterial populations. Range expansion -- the stochastic reproduction of bacteria competing for space to be occupied by their progeny -- leads to a fluctuating and rough growth front, which is known from experiment and simulation to affect the underlying critical behavior of the DP transition. In this work, we employ symmetry arguments to construct a pair of non-linear stochastic partial differential equations describing the co-evolution of surface roughness with the composition field of DP. Macroscopic manifestations (phenomenology) of these equations on growth patterns and genealogical tracks of range expansion are discussed; followed by a renormalization group analysis of possible scaling behaviors at the DP transition.

arXiv comment13+9 pages, 5+5 figures, 1 table

References in corpus (26)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Universality classes in nonequilibrium lattice systems
• Genetic drift at expanding frontiers promotes gene segregation
• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Genetic Demixing and Evolutionary Forces in the One-Dimensional Stepping Stone Model
• A KPZ Cocktail- Shaken, not stirred: Toasting 30 years of kinetically roughened surfaces
• Two-Loop Renormalization Group Analysis of the Burgers-Kardar-Parisi-Zhang Equation
• The Field Theory Approach to Percolation Processes
• Selective sweeps in growing microbial colonies
• Driven Depinning in Anisotropic Media
• Competition and cooperation in one-dimensional stepping stone models
• Phase ordering and roughening on growing films
• Radial Domany-Kinzel Models with Mutation and Selection
• Range Expansion with Mutation and Selection: Dynamical Phase Transition in a Two-Species Eden Model
• Asymmetric Mutualism in Two- and Three-Dimensional Range Expansions
• Effects of turbulent mixing on the nonequilibrium critical behaviour
• Weak and strong dynamic scaling in a one-dimensional driven coupled-field model: Effects of kinematic waves
• Renormalization Group: Applications in Statistical Physics
• Nonequilibrium critical dynamics of the relaxational models C and D
• Fixation Probabilities in Weakly Compressible Fluid Flows
• Interplay between phase ordering and roughening on growing films
• Ordering Phenomena on Growing Films
• Active-to-absorbing state phase transition in the presence of fluctuating environments: Weak and strong dynamic scaling
• Symmetries and scaling in generalised coupled conserved Kardar-Parisi-Zhang equations
• Active to absorbing state phase transition in the presence of a fluctuating environment: Feedback and universality
• Frequency-Dependent Selection at Rough Expanding Fronts

Cited by in corpus (10)

• Slow expanders invade by forming dented fronts in microbial colonies
• The Kardar-Parisi-Zhang model of a random kinetic growth: effects of a randomly moving medium
• Population Extinction on a Random Fitness Seascape
• Effects of turbulent environment on the surface roughening: The Kardar-Parisi-Zhang model coupled to the stochastic Navier-Stokes equation
• Shape of population interfaces as an indicator of mutational instability in coexisting cell populations
• BLUES iteration applied to nonlinear ordinary differential equations for wave propagation and heat transfer
• Epidemic processes with vaccination and immunity loss studied with the BLUES function method
• Specialization at an expanding front
• Geometrically Regulating Evolutionary Dynamics in Biofilms
• Branching structure of genealogies in spatially growing populations and its implications for population genetics inference