Although the hypothesis that nestedness determines mutualistic ecosystem dynamics is accepted in general, results of some recent data analyses and theoretical studies have begun to cast doubt on the impact of nestedness on ecosystem stability. However, definite conclusions have not yet been reached because previous studies are mainly based on numerical simulations. Therefore, we reveal a mathematical architecture in the relationship between ecological mutualistic networks and local stability based on spectral graph analysis. In particular, we propose a theoretical method for estimating the dominant eigenvalue (i.e., spectral radius) of quantitative (or weighted) bipartite networks by extending spectral graph theory, and provide a theoretical prediction that the heterogeneity of node degrees and link weights primarily determines the local stability; on the other hand, nestedness additionally affects it. Numerical simulations demonstrate the validity of our theory and prediction. This study emphasizes the importance of ecological network heterogeneity in ecosystem dynamics, and it enhances our understanding of structure–stability relationships.
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