Self-organized criticality in complex model ecosystems
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908697554321408 |
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| author | de Pirey, Thibaut Arnoulx |
| author_facet | de Pirey, Thibaut Arnoulx |
| contents | We show that spatial extensions of many-species population dynamics models, such as the Lotka-Volterra model with random interactions we focus on in this work, generically exhibit scale-free correlation functions of population sizes in the limit of an infinite number of species. Using dynamical mean-field theory, we describe the many-species system in terms of single-species dynamics with demographic and environmental noises. We show that the single-species model features a random mass term, or equivalently a random space-time averaged growth rate, poising some species very close to extinction. This introduces a hierarchy of ever larger correlation times and lengths as the extinction threshold is approached. In turn, every species, even those far from extinction, are coupled to these near-critical fields which combine to make fluctuations of population sizes generically scale-free. We argue that these correlations are described by exponents derived from those of directed percolation in spatial dimension $d=3$, but not in lower dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06961 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Self-organized criticality in complex model ecosystems de Pirey, Thibaut Arnoulx Statistical Mechanics Disordered Systems and Neural Networks Populations and Evolution We show that spatial extensions of many-species population dynamics models, such as the Lotka-Volterra model with random interactions we focus on in this work, generically exhibit scale-free correlation functions of population sizes in the limit of an infinite number of species. Using dynamical mean-field theory, we describe the many-species system in terms of single-species dynamics with demographic and environmental noises. We show that the single-species model features a random mass term, or equivalently a random space-time averaged growth rate, poising some species very close to extinction. This introduces a hierarchy of ever larger correlation times and lengths as the extinction threshold is approached. In turn, every species, even those far from extinction, are coupled to these near-critical fields which combine to make fluctuations of population sizes generically scale-free. We argue that these correlations are described by exponents derived from those of directed percolation in spatial dimension $d=3$, but not in lower dimensions. |
| title | Self-organized criticality in complex model ecosystems |
| topic | Statistical Mechanics Disordered Systems and Neural Networks Populations and Evolution |
| url | https://arxiv.org/abs/2512.06961 |