Feasibility and Single Parameter Scaling of Extinctions in Large Ecological Communities
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909050653900800 |
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| author | Jacquod, Philippe |
| author_facet | Jacquod, Philippe |
| contents | Multispecies ecosystems modelled by generalized Lotka-Volterra equations exhibit stationary population abundances, where large number of species often coexist. Understanding the precise conditions under which this is at all feasible and what triggers species extinctions is a key, outstanding problem in theoretical ecology. Using standard methods of random matrix theory, I show that distributions of species abundances are Gaussian at equilibrium, in the weakly interacting regime. One consequence is that feasibility is generically broken before stability, for large enough number of species. I further derive an analytical expression for the probability that $n=0,1,2,...$ species go extinct and conjecture that a single-parameter scaling law governs species extinctions. These results are corroborated by numerical simulations in a wide range of system parameters. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_04327 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Feasibility and Single Parameter Scaling of Extinctions in Large Ecological Communities Jacquod, Philippe Populations and Evolution Adaptation and Self-Organizing Systems Biological Physics Multispecies ecosystems modelled by generalized Lotka-Volterra equations exhibit stationary population abundances, where large number of species often coexist. Understanding the precise conditions under which this is at all feasible and what triggers species extinctions is a key, outstanding problem in theoretical ecology. Using standard methods of random matrix theory, I show that distributions of species abundances are Gaussian at equilibrium, in the weakly interacting regime. One consequence is that feasibility is generically broken before stability, for large enough number of species. I further derive an analytical expression for the probability that $n=0,1,2,...$ species go extinct and conjecture that a single-parameter scaling law governs species extinctions. These results are corroborated by numerical simulations in a wide range of system parameters. |
| title | Feasibility and Single Parameter Scaling of Extinctions in Large Ecological Communities |
| topic | Populations and Evolution Adaptation and Self-Organizing Systems Biological Physics |
| url | https://arxiv.org/abs/2511.04327 |