A dynamical phase transition in a model for evolution with migration

TL;DR

This paper models evolution with migration between habitats and discovers a dynamical phase transition at a critical migration rate, significantly affecting population composition and evolutionary outcomes.

Contribution

It introduces a simple quasispecies model with migration, revealing a phase transition and sensitivity of evolution to small migration rates.

Findings

Divergence of time to steady state at critical migration rate

Above the transition, population dominated by immigrants

Below the transition, coexistence of multiple non-native quasispecies

Abstract

Migration between different habitats is ubiquitous among biological populations. In this Letter, we study a simple quasispecies model for evolution in two different habitats, with different fitness landscapes, coupled through one-way migration. Our model applies to asexual, rapidly evolving organisms such as microbes. Our key finding is a dynamical phase transition at a critical value of the migration rate. The time to reach steady state diverges at this critical migration rate. Above the transition, the population is dominated by immigrants from the primary habitat. Below the transition, the genetic composition of the population is highly non-trivial, with multiple coexisting quasispecies which are not native to either habitat. Using results from localization theory, we show that the critical migration rate may be very small --- demonstrating that evolutionary outcomes can be very sensitive to even a small amount of migration.