Category: Ecology

Summary: Finding the dispersal rate that causes refuge-protected populations to delocalize into hostile habitat.

This experiment investigates spatial population persistence in heterogeneous landscapes. When organisms have a protected refuge surrounded by hostile habitat, dispersal between patches determines whether the population stays localized in the refuge or spreads (and potentially collapses) into the hostile background.

The experiment constructs random heterogeneous persistence operators and bisects the exchange strength to find the critical threshold where the leading eigenmode transitions from refuge-localized to delocalized. This maps the finite-size boundary between population persistence and extinction in spatially structured habitats.

Prior work on principal-eigenvalue persistence criteria exists, but this dense finite-size threshold map for refuge-exchange delocalization has not been published.

Method: Dense eigensolve (np.linalg.eigvalsh) on symmetric operators with iterative deepening. System sizes N=64 to 2048, bisection on exchange leakage.

What is measured: Critical exchange threshold, participation ratio on refuge sites, delocalization transition sharpness.