Noise-induced excitability: bloom, bust and extirpation in autotoxic population dynamics
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866916046317813760 |
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| author | Moreno-Spiegelberg, Pablo Aguilar, Javier |
| author_facet | Moreno-Spiegelberg, Pablo Aguilar, Javier |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20670 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Noise-induced excitability: bloom, bust and extirpation in autotoxic population dynamics Moreno-Spiegelberg, Pablo Aguilar, Javier Populations and Evolution Statistical Mechanics Adaptation and Self-Organizing Systems 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. |
| title | Noise-induced excitability: bloom, bust and extirpation in autotoxic population dynamics |
| topic | Populations and Evolution Statistical Mechanics Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2601.20670 |