Complex noise in diffusion-limited reactions of replicating and competing species

TL;DR

This paper derives exact Langevin equations for quasispecies dynamics with complex noise, revealing how spatio-temporal fluctuations depend on diffusion and amplification time scales in reaction systems.

Contribution

It introduces a novel derivation of Langevin equations with complex noise for replicating species, including numerical methods for simulation.

Findings

Complex noise causes significant density fluctuations.

Fluctuations are suppressed only when diffusion is much faster than amplification.

Spatio-temporal fluctuations depend on the ratio of diffusion to amplification time scales.

Abstract

We derive exact Langevin-type equations governing quasispecies dynamics. The inherent multiplicative noise has both real and imaginary parts. The numerical simulation of the underlying complex stochastic partial differential equations is carried out employing the Cholesky decomposition for the noise covariance matrix. This noise produces unavoidable spatio-temporal density fluctuations about the mean field value. In two dimensions, the fluctuations are suppressed only when the diffusion time scale is much smaller than the amplification time scale for the master species.