Interaction network structures in competitive ecosystems.

We present a numerical analysis of local community assembly through weak migration from a regional species pool. At equilibrium, the local community consists of a subset ("clique") of species from the regional community. Our analysis, based on numerical integration of the generalized Lotka-Volterra equations, reveals that the interaction networks of these cliques exhibit nontrivial architectures. Specifically, we demonstrate a pronounced nested structure of the clique interaction matrix in the case of symmetric interactions and a hyperuniform structure seen in asymmetric communities. For a local community to be stable, its composition must meet two requirements: first, it must be feasible on its own, such that internal competition does not lead to species extinction. Second, it must be resistant against invasion by species from the regional community. We show that the nestedness property, although it slightly compromises feasibility, is essential to ensure noninvadability and, thus, characterizes communities with symmetric interactions. In the case of asymmetric interactions, achieving a nested structure is challenging; therefore, the local community at any given moment is hyperuniform, ensuring feasibility but making it invasion-prone. As a result, the dynamics of systems with strong asymmetric interactions is unstable.