AI Insight
This theoretical study investigates the conditions under which large multispecies ecosystems, modeled by generalized Lotka-Volterra equations, remain feasible (i.e., all species maintain positive population abundances) versus experiencing extinctions. Using random matrix theory, the author demonstrates that species abundances follow a Gaussian distribution at equilibrium in the weakly interacting regime, and that feasibility breaks down before dynamical stability as the number of species grows. The study derives an analytical formula for the probability of exactly n species going extinct and proposes a single-parameter scaling law governing extinction patterns, with results validated through numerical simulations.
Why it matters
Understanding the mathematical conditions that trigger species extinctions in complex ecosystems could inform conservation strategies and help predict tipping points in biodiversity loss under environmental pressures such as habitat fragmentation or climate change.
arXiv:2511.04327v2 Announce Type: replace
Abstract: 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.
Source: Feasibility and Single Parameter Scaling of Extinctions in Large Ecological Communities