Population extinction in a time-modulated environment

TL;DR

This paper studies how periodic environmental changes can significantly accelerate population extinction by analyzing a stochastic model with time-dependent parameters, using advanced mathematical techniques.

Contribution

It introduces a perturbative approach to quantify how environmental modulation affects population extinction times in a stochastic model.

Findings

Environmental modulation can exponentially reduce extinction time.

Theoretical methods accurately predict the impact of modulation.

Different regimes of modulation frequency have distinct effects.

Abstract

The extinction time of an isolated population can be exponentially reduced by a periodic modulation of its environment. We investigate this effect using, as an example, a stochastic branching-annihilation process with a time-dependent branching rate. The population extinction is treated in eikonal approximation, where it is described as an instanton trajectory of a proper reaction Hamiltonian. The modulation of the environment perturbs this trajectory and synchronizes it with the modulation phase. We calculate the corresponding change in the action along the instanton using perturbation techniques supported by numerical calculations. The techniques include a first-order theory with respect to the modulation amplitude, a second-order theory in the spirit of the Kapitsa pendulum effect, and adiabatic theory valid for low modulation frequencies.