Extinction transition in stochastic population dynamics in a random, convective environment

TL;DR

This paper investigates how random environmental factors and directional bias affect population extinction in a stochastic model, revealing novel critical behaviors and phases distinct from symmetric cases.

Contribution

It introduces an asymmetric variant of the contact process with quenched disorder, showing new extinction transition behaviors and phases influenced by environmental randomness and bias.

Findings

Critical population drifts with finite or vanishing velocity depending on asymmetry.

Dynamical quantities exhibit multiscaling and non-self-averaging at the transition.

A Griffiths phase appears below the transition with non-universal power-law decay.

Abstract

Motivated by modeling the dynamics of a population living in a flowing medium where the environmental factors are random in space, we have studied an asymmetric variant of the one-dimensional contact process, where the quenched random reproduction rates are systematically greater in one direction than in the opposite one. The spatial disorder turns out to be a relevant perturbation but, according to results of Monte Carlo simulations, the behavior of the model at the extinction transition is different from the (infinite randomness) critical behavior of the disordered, symmetric contact process. Depending on the strength $a$ of the asymmetry, the critical population drifts either with a finite velocity or with an asymptotically vanishing velocity as $x(t)\sim t^{\mu(a)}$, where $\mu(a)<1$. Dynamical quantities are non-self-averaging at the extinction transition; the survival probability, for instance, shows multiscaling, i.e. it is characterized by a broad spectrum of effective exponents. For a sufficiently weak asymmetry, a Griffiths phase appears below the extinction transition, where the survival probability decays as a non-universal power of the time while, above the transition, another extended phase emerges, where the front of the population advances anomalously with a diffusion exponent continuously varying with the control parameter.