Critical patch size under Allee-effect growth on graphs

Establish survival thresholds and critical habitat size for the discrete diffusion model on graphs with sink vertices when the local growth term exhibits an Allee effect, by characterizing how the spectral survival condition based on the principal Dirichlet eigenvalue changes relative to the logistic-growth setting analyzed in the paper.

Background

The analysis in the paper focuses on logistic-type growth and shows that survival in large Erdős–Rényi habitats is governed by the principal Dirichlet eigenvalue of the Laplacian submatrix on non-sink vertices, yielding sharp thresholds. The authors point out that other growth terms, specifically Allee-effect dynamics, are an open direction.

An Allee effect alters the reaction term and may modify the relationship between reaction-to-diffusion parameters and spectral thresholds, motivating a distinct analysis.