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Researchers developed a stochastic mathematical framework to explain boom-bust population dynamics where species grow rapidly, overshoot their carrying capacity due to slow environmental feedback, and sometimes face complete extinction. The model, based on individual organisms and incorporating environmental noise, identifies a threshold behavior where populations either experience a "boom" or go extinct before expansion, and characterizes a transition between excitable regimes (where populations are absorbed after one bust) and persistent regimes (where populations reach metastable states). This transition depends on noise strength and the ratio between environmental and population growth timescales.
Why it matters
This framework provides theoretical tools for predicting and potentially managing sudden population collapses in invasive species, understanding plant succession patterns, modeling microbial community dynamics, and informing cancer treatment strategies where the goal is tumor elimination. The model fills a gap left by deterministic approaches that cannot capture finite-time extinction events driven by environmental feedback.
arXiv:2601.20670v2 Announce Type: replace
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 noise strength and the ratio of environmental-to-population timescales. This framework provides a theoretical basis for understanding irreversible transitions in invasive species, plant succession, microbial dynamics, and the elimination of cancerous tumors.
Source: Noise-induced excitability: bloom, bust and extirpation in autotoxic population dynamics