Category: Ecology

Summary: Estimating how much within-guild exploitative competition is needed to collapse a generalist-core localized mode in a nested mutualistic network.

Nested mutualistic networks often concentrate their strongest influence on a core of generalist species, and that localization can help organize system-wide responses. This experiment asks when added exploitative competition within each guild becomes strong enough to destroy that core-focused leading mode.

The script constructs dense synthetic nested operators, then increases a competition parameter while carrying the threshold bracket across larger system sizes. By tracking how much of the leading mode remains on the generalist core versus the fringe, it identifies the point where localized mutualistic organization breaks down.

This matters because mutualism and competition are usually analyzed together through stability or feasibility, not through localization of the dominant mode. The experiment therefore turns exploitative pressure into a direct finite-size threshold for loss of nested-core organization.

Method: Dense symmetric eigensolves with iterative deepening and bisection on exploitative competition in synthetic nested mutualistic operators.

What is measured: Critical competition threshold, core mass, fringe mass, leading reactivity, collapsed fraction, and bracket width.