Noise-induced excitability: bloom, bust and extirpation in autotoxic population dynamics

TL;DR

This paper introduces a stochastic model to analyze boom-bust-extinction dynamics in populations influenced by environmental feedback, revealing noise-driven thresholds and transitions between transient and persistent regimes.

Contribution

It develops a novel stochastic framework based on individual-based models to capture finite-time extinctions and regime transitions in population dynamics.

Findings

Identification of noise-driven, threshold-like behavior in population extinction.

Characterization of a transition between excitable and persistent regimes.

Demonstration of how environmental-to-population timescale ratios influence dynamics.

Abstract

Species populations often modify their environment as they grow. When environmental feedback operates more slowly than population growth, the system can undergo boom-bust dynamics, where the population overshoots its carrying capacity and subsequently collapses. In extreme cases, this collapse leads to total extinction. While deterministic models typically fail to capture these finite-time extinction events, we propose a stochastic framework, derived from an individual-based model, to describe boom-bust-extirpation dynamics. We identify a noise-driven, threshold-like behavior where, depending on initial conditions, the population either undergoes a "boom" or is extirpated before the expansion occurs. Furthermore, we characterize a transition between an excitable regime, where most trajectories are captured by the absorbing state immediately after the first bust, and a persistent regime, where most populations reach a metastable state. We show that this transition is governed by the diffusion strength and the ratio of environmental-to-population timescales. This framework provides a theoretical basis for understanding irreversible transitions in invasive species, plant succession, and microbial dynamics.