Category: Ecology

Summary: Finding the omnivory level that destabilizes trophically coherent food webs.

This experiment maps the critical omnivory threshold in ecological food webs. Trophic coherence (species eating from one trophic level) promotes stability, but omnivory (species eating across multiple levels) disrupts it. The open question is: exactly how much omnivory leakage causes a coherent food-web community matrix to transition from stable to unstable?

The experiment constructs random trophically coherent Jacobian matrices of increasing size, then bisects the omnivory leakage parameter to find where the leading eigenvalue crosses zero — the point where the ecosystem becomes reactively unstable.

Prior work studied omnivory and food-web stability separately, but this dense finite-size spectral threshold map for the omnivory-driven instability transition has not been published.

Method: Dense eigensolve (np.linalg.eigvals) on non-symmetric Jacobians with iterative deepening. System sizes N=64 to 2048, bisection on omnivory leakage.

What is measured: Critical omnivory leakage threshold, leading eigenvalue real part, stability transition sharpness.