Extinction transitions in correlated external noise

TL;DR

This paper investigates how long-range correlated external noise influences extinction phase transitions, revealing that positive correlations accelerate typical population decay but slow ensemble decay, with critical behavior linked to fractional random walks.

Contribution

It demonstrates that positively correlated environmental noise amplifies extinction effects and establishes a connection to fractional random walks through extensive simulations.

Findings

Positively correlated noise accelerates typical population decay.

Correlations slow down the decay of the ensemble average.

Mean extinction time grows slower than a power law with population size.

Abstract

We analyze the influence of long-range correlated (colored) external noise on extinction phase transitions in growth and spreading processes. Uncorrelated environmental noise (i.e., temporal disorder) was recently shown to give rise to an unusual infinite-noise critical point [Europhys. Lett. 112, 30002 (2015)]. It is characterized by enormous density fluctuations that increase without limit at criticality. As a result, a typical population decays much faster than the ensemble average which is dominated by rare events. Using the logistic evolution equation as an example, we show here that positively correlated (red) environmental noise further enhances these effects. This means, the correlations accelerate the decay of a typical population but slow down the decay of the ensemble average. Moreover, the mean time to extinction of a population in the active, surviving phase grows slower than a power law with population size. To determine the complete critical behavior of the extinction transition, we establish a relation to fractional random walks, and we perform extensive Monte-Carlo simulations.