  We consider the evolution of non-thermal dark matter perturbations in models
which contain both Weakly Interacting Massive Particles (WIMPs) and axions.
Using constraints from existing observations we examine the percentage of WIMPs
and axions that may comprise the cosmological dark matter budget in models with
an Early Matter Dominated Epoch (EMDE) -- where entropy production is
important. After carefully tracking the thermal evolution of the various
species by solving the Boltzmann equations, we consider the enhancement of
perturbations that may have led to early structure formation for axions and
WIMPs. We investigate the impact of enhanced perturbations on the parameter
space of both species, after imposing existing constraints from indirect
detection experiments. Given these constraints we establish the feasibility of
axions to form miniclusters in the early universe in EMDEs for a given
percentage of allowed WIMPs. We find that EMDEs with low reheat temperatures
near the BBN limit are preferred for axion minicluster formation. When the EMDE
is caused by string moduli, the WIMP contribution to the relic density is set
by the moduli branching to dark matter at the level of $\lesssim
\mathcal{O}(10^{-4})$.
