  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 analize both cases in which the particles are
considered fermions and bosons and show using exact analitical methods that,
while the Fermi-Dirac statistics leads to certain extinction for any refuge
size, the Bose-Eistein statistics allows survival even for the minimal refuge.
