  The occupation fraction of massive black holes (MBHs) in dwarf galaxies
offers interesting insights into initial black hole seeding mechanisms and
their mass assembly history, though disentangling these two effects remains
challenging. Using the {\sc Romulus} cosmological simulations we examine the
impact of environment on the occupation fraction of MBHs in low mass galaxies.
Unlike most modern cosmological simulations, {\sc Romulus} seeds MBHs based on
local gas properties, selecting dense ($n>3$ cm$^{-3}$), pristine
($Z<3e-4Z_{\odot}$), and rapidly collapsing regions in the early Universe as
sites to host MBHs without assuming anything about MBH occupation as a function
of galaxy stellar mass, or halo mass, {\it a priori}. The simulations predict
that dwarf galaxies with M$_{\star}<10^9$ M$_{\odot}$ in cluster environments
are $\sim2$ times more likely to host a MBH compared to those in the field. The
predicted occupation fractions are remarkably consistent with those of nuclear
star clusters. Across cluster and field environments, dwarf galaxies with
earlier formation times are more likely to host a MBH. While the MBH occupation
function is similar between cluster and field environments at high redshift
($z>3$), a difference arises as late-forming dwarfs -- which do not exist in
the cluster environment -- begin to dominate in the field and pull the MBH
occupation fraction down for low mass galaxies. Additionally, prior to in-fall
some cluster dwarfs are similar to progenitors of massive, isolated galaxies,
indicating that they might have grown to higher masses had they not been
impeded by the cluster environment. While the population of MBHs in dwarf
galaxies is already widely understood to be important for understanding MBH
formation, this work demonstrates that environmental dependence is important to
consider as future observations search for low mass black holes in dwarf
galaxies.
