We found a formula that predicts the exact moment a species will go extinct just by looking at the shape of where they live.
April 2, 2026
Original Paper
The Critical Patch Size Problem in Random Graphs
arXiv · 2604.00624
The Takeaway
Using a new spectral theory, researchers found that the survival of a population is governed by a single mathematical number—a 'sharp threshold' that determines if a habitat is viable. This formula can be used to predict extinction events in fragmented forests or even determine how electrical signals persist or fade within the complex networks of the human brain.
From the abstract
The problem of {\it critical patch size} -- a threshold condition for population persistence -- is investigated in the context of discrete habitats, modeled as graphs with a distinguished subset of vertices acting as sinks. These sinks impose boundary-like constraints analogous to Dirichlet conditions in continuous domains. The population proliferates locally at the vertices and diffuse across the network through the graph Laplacian. In the sinks the population cannot survive. The Dirichlet eige