  Chemo-dynamical N-body simulations are an essential tool for understanding
the formation and evolution of galaxies. As the number of observationally
determined stellar abundances continues to climb, these simulations are able to
provide new constraints on the early star formaton history and chemical
evolution inside both the Milky Way and Local Group dwarf galaxies. Here, we
aim to reproduce the low $\alpha$-element scatter observed in metal-poor stars.
We first demonstrate that as stellar particles inside simulations drop below a
mass threshold, increases in the resolution produce an unacceptably large
scatter as one particle is no longer a good approximation of an entire stellar
population. This threshold occurs at around $10^3\,\rm{M_\odot}$, a mass limit
easily reached in current (and future) simulations. By simulating the Sextans
and Fornax dwarf spheroidal galaxies we show that this increase in scatter at
high resolutions arises from stochastic supernovae explosions. In order to
reduce this scatter down to the observed value, we show the necessity of
introducing a metal mixing scheme into particle-based simulations. The impact
of the method used to inject the metals into the surrounding gas is also
discussed. We finally summarise the best approach for accurately reproducing
the scatter in simulations of both Local Group dwarf galaxies and in the Milky
Way.
