Extinction rate fragility in population dynamics

TL;DR

This paper investigates how small parameter changes can cause exponential shifts in population extinction rates, revealing a fragile dependence linked to nonanalytic barrier height variations, with implications for epidemiological models.

Contribution

It introduces the concept of extinction rate fragility, providing analytical conditions and demonstrating this phenomenon in the SIS epidemiological model.

Findings

Extinction rate can change exponentially with small parameter variations.

Fragility is linked to nonanalytic dependence of barrier height on parameters.

Analytical results agree with simulation data.

Abstract

Population extinction is a rare event which requires overcoming an effective barrier. We show that the extinction rate can be fragile: a small change in the system parameters leads to an exponentially strong change of the rate, with the barrier height depending on the parameters nonanalytically. General conditions of the fragility are established. The fragility is found in one of the best-known models of epidemiology, the SIS model. The analytical expressions are compared with simulations.