Radial Domany-Kinzel Models with Mutation and Selection

Abstract

We study the effect of spatial structure, genetic drift, mutation, and selective pressure on the evolutionary dynamics in a simplified model of asexual organisms colonizing a new territory. Under an appropriate coarse-graining, the evolutionary dynamics is related to the directed percolation processes that arise in voter models, the Domany-Kinzel (DK) model, contact process, etc. We explore the differences between linear (flat front) expansions and the much less familiar radial (curved front) range expansions. For the radial expansion, we develop a generalized, off-lattice DK model that minimizes otherwise persistent lattice artifacts. With both simulations and analytical techniques, we study the survival probability of advantageous mutants, the spatial correlations between domains of neutral strains, and the dynamics of populations with deleterious mutations. "Inflation" at the frontier leads to striking differences between radial and linear expansions. For a colony with initial radius $R_0$ expanding at velocity $v$, significant genetic demixing, caused by local genetic drift, only occurs up to a finite time $t^{\ast }=R_0/v$, after which portions of the colony become causally disconnected due to the inflating perimeter of the expanding front. As a result, the effect of a selective advantage is amplified relative to genetic drift, increasing the survival probability of advantageous mutants. Inflation also modifies the underlying directed percolation transition, introducing novel scaling functions and modifications similar to a finite size effect. Finally, we consider radial range expansions with deflating perimeters, as might arise from colonization initiated along the shores of an island.

24 pages, 21 figures

References in corpus (11)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Genetic drift at expanding frontiers promotes gene segregation
• Universal scaling behavior of non-equilibrium phase transitions
• Genetic Demixing and Evolutionary Forces in the One-Dimensional Stepping Stone Model
• Selective sweeps in growing microbial colonies
• A Quantitative Test of Population Genetics Using Spatio-Genetic Patterns in Bacterial Colonies
• On the area under a continuous time Brownian motion till its first-passage time
• Systems with two symmetric absorbing states: relating the microscopic dynamics with the macroscopic behavior
• Range Expansion with Mutation and Selection: Dynamical Phase Transition in a Two-Species Eden Model
• The struggle for space: Viral extinction through competition for cells
• Crossover scaling in the Domany-Kinzel cellular automaton

Cited by in corpus (21)

• Asymmetric Mutualism in Two- and Three-Dimensional Range Expansions
• Survival Probabilities at Spherical Frontiers
• Clonal interference and Muller's ratchet in spatial habitats
• Kardar-Parisi-Zhang Interfaces with Inward Growth
• Fractal aggregation of active particles
• Evolutionary Dynamics with Fluctuating Population Sizes and Strong Mutualism
• Range Expansion of Heterogeneous Populations
• Convection shapes the trade-off between antibiotic efficacy and the selection for resistance in spatial gradients
• Bacterial range expansions on a growing front: Roughness, Fixation, and Directed Percolation
• Evolution of populations expanding on curved surfaces
• Universal constraint on nonlinear population dynamics
• Scale invariant growth processes in expanding space
• Critical Fitness Collapse in Three-Dimensional Spatial Population Genetics
• Shape of population interfaces as an indicator of mutational instability in coexisting cell populations
• Rare beneficial mutations cannot halt Muller's ratchet in spatial populations
• Short-Range Migration Can Alter Evolutionary Dynamics in Solid Tumors
• Interacting Particle Systems in Time-Dependent Geometries
• Assortative clustering in a one-dimensional population with replication strategies
• Survival in Branching Cellular Populations
• Pinned, locked, pushed, and pulled traveling waves in structured environments
• Branching structure of genealogies in spatially growing populations and its implications for population genetics inference