Radial Domany-Kinzel Models with Mutation and Selection

TL;DR

This paper investigates how radial expansion influences evolutionary dynamics in spatial models of asexual organisms, revealing that inflation enhances the survival of advantageous mutants and alters critical transition behaviors.

Contribution

It introduces a generalized off-lattice Domany-Kinzel model for radial expansions and analyzes how inflation affects genetic drift, mutant survival, and phase transitions.

Findings

Inflation causes genetic demixing to cease after a finite time.

Advantageous mutants have increased survival probability due to inflation.

Radial expansion modifies directed percolation transition properties.

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 $t^* = R_0/v$, 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.