Category: Ecology

Summary: Finding the drift strength at which a favorable refuge stops pinning population growth in a disordered non-Hermitian landscape.

This experiment studies a persistence problem that mixes two ideas usually treated separately: drift-driven delocalization in Hatano-Nelson style operators, and refuge-driven localization in spatial ecology. A compact high-growth refuge can trap the leading growth mode of a population, but increasing directional drift may eventually pull that mode out of the refuge. The central question is where that pinning breakdown occurs as system size grows.

The script builds dense disordered nonlocal persistence operators with a designated refuge region and then bisects the drift parameter to find the threshold where the principal mode is no longer refuge-centered. Iterative deepening pushes the same bracket across larger matrices, allowing the project to estimate a finite-size critical drift rather than a single small-system anecdote.

What makes the experiment useful is the combination of non-Hermitian localization physics with refuge ecology in a dense threshold map. Prior work examined these ingredients separately, but not this specific crossover in a systematic finite-size BOINC sweep.

Method: Dense non-symmetric eigensolve with iterative deepening and bisection on drift strength, at matrix sizes from 128 to 2048.

What is measured: Critical drift threshold, refuge mass fraction, localization score, pinned fraction, leading growth rate, and bracket width.