  We study the evolution of a collection of individuals subject to Brownian
diffusion, reproduction and disappearance. In particular, we focus on the case
where the individuals are initially prepared at equilibrium within a confined
geometry. Such systems are widespread in physics and biology and apply for
instance to the study of neutron populations in nuclear reactors and the
dynamics of bacterial colonies, only to name a few. The fluctuations affecting
the number of individuals in space and time may lead to a strong patchiness,
with particles clustered together. We show that the analysis of this peculiar
behaviour can be rather easily carried out by resorting to a backward formalism
based on the Green's function, which allows the key physical observables,
namely, the particle concentration and the pair correlation function, to be
explicitly derived.
