Particle statistics and population dynamics

We study a master equation system modelling a population dynamics problem in a lattice. The problem is the calculation of the minimum size of a refuge that can protect a population from hostile external conditions, the so-called critical patch size problem. We analyse both cases in which the particles are considered fermions and bosons and show using exact analytical methods that, while the Fermi-Dirac statistics lead to certain extinction for any refuge size, the Bose-Einstein statistics allow survival even for the minimal refuge.