Category: Ecology

Summary: Testing whether a coherent low-rank mutualistic core first suppresses and then later restores localized reactivity in heterogeneous May community matrices.

May-style random community models are often used to study stability and reactivity in complex ecosystems, but structured mutualism can reorganize those responses in ways that simple disorder does not. This experiment asks whether adding a coherent low-rank mutualistic core changes the stable-but-reactive window nonmonotonically, first delocalizing amplification and then creating a re-localized outlier-like mode on the core.

The script builds dense ecological interaction matrices with controlled connectance, heterogeneity, and core strength, then computes reactive and unstable spectral properties on the GPU. It summarizes how wide the reactive window is, how much reactive mass falls on the mutualistic core, and how localized the dominant mode becomes as the core is strengthened.

That allows the experiment to separate two effects that are often conflated: whether mutualism shifts stability boundaries at all, and whether it concentrates amplification onto a special subset of species. The resulting map is aimed at the geometry of ecological response, not only the sign of the leading eigenvalue.

Method: GPU spectral analysis of heterogeneous May community matrices with an added low-rank mutualistic core, swept over species counts, connectance, heterogeneity, and core strength.

What is measured: Reactive-window width, reactive and unstable localization, core reactive mass, core unstable mass, leading spectral values, and whether reactivity appears before instability.