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.