  Demographic (shot) noise in population dynamics scales with the square root
of the population size. This process is very important, as it yields an
absorbing state at zero field, but simulating it, especially on spatial
domains, is a non-trivial task. Here we compare the results of two
operator-splitting techniques suggested for simulating the corresponding
Langevin equation, one by Pechenik and Levine (PL) and the other by Dornic,
Chat\'e and Mu\~noz (DCM). We identify an anomalously strong bias toward the
active phase in the numerical scheme of DCM, a bias which is not present in the
alternative scheme of PL. This bias strongly distorts the phase diagram
determined via the DCM procedure for the range of time-steps used in such
simulations. We pinpoint the underlying cause in the inclusion of the
diffusion, treated as an on-site decay with a constant external source, in the
stochastic part of the algorithm. Treating the diffusion deterministically is
shown to remove this unwanted bias while keeping the simulation algorithm
stable, thus a hybrid numerical technique, in which the DCM approach to
diffusion is applied but the diffusion is simulated deterministically, appears
to be optimal.
