2024/09/04 by Maxime Clenet, François Massol, Jamal Najım · 1 voice
Medicine · Biochemistry, Genetics and Molecular Biology · Computer Science · #Mathematical and Theoretical Epidemiology and Ecology Models #Diffusion and Search Dynamics #Nonlinear Dynamics and Pattern Formation
paper · doi:10.24072/pcjournal.460
openalex publication_date 2024/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
The Lotka-Volterra (LV) model is a simple, robust, and versatile model used to describe large interacting systems such as food webs or microbiomes. The model consists of n coupled differential equations linking the abundances of n different species. We consider a large random interaction matrix with independent entries and a block variance profile. The ith diagonal block represents the intra-community interaction in community i, while the off-diagonal blocks represent the inter-community interactions. The variance remains constant within each block, but may vary across blocks. We investigate the important case of two communities of interacting species, study how interactions affect their respective equilibrium. We also describe equilibrium with feasibility (i.e., whether there exists an equilibrium with all species at non-zero abundances) and the existence of an attrition phenomenon (some species may vanish) within each community. Information about the general case of b communities (b > 2) is provided in the appendix