Using matrix analysis to understand competition in food webs and antimicrobial resistance networks

Abstract Indirect competition is a fundamental mechanism shaping the structure of biological systems, from food webs to antimicrobial resistance (AMR) networks. Translating directed interaction data into a quantitative measure of competition remains a modelling challenge. This paper develops a spectral framework that maps directed bipartite networks into symmetric, positive semidefinite (PSD) competition matrices via the shared-target principle (C=AA⊤). We establish a duality between exploitative competition (consumer overlap) and apparent competition (target overlap) using singular value decomposition (SVD), allowing for a unified spectral analysis of both trophic levels. We further prove that using this data-driven matrix in Lotka–Volterra dynamics guarantees Lyapunov stability at any positive equilibrium, with explicit conditions for global asymptotic stability versus convergence to an equilibrium continuum in the presence of exact guilds. The framework is validated on synthetic AMR strain–gene networks, where we demonstrate that spectral competitive centrality provides a more robust measure of influence than simple gene counts. This approach offers a rigorous, reproducible workflow for converting qualitative interaction structure into quantitative stability predictions.