  We investigate the ground state of a few-body Bose-Fermi mixture in a
one-dimensional harmonic trap with varying interaction strengths and mass
ratio. A bunching-antibunching crossover of the bosonic species for increasing
interspecies' repulsion is observed within our fully correlated
\textit{ab~initio} studies. Interestingly, this crossover is suppressed if the
bosonic repulsion exceeds a critical value which strongly depends on the mass
ratio. In order to unveil the physical origin of this crossover, we employ
different levels of approximations: while a species mean-field approach can
account for the antibunching, only the inclusion of the interspecies
correlations can lead to the bunching. We show that these correlations
effectively create an induced bosonic interaction, which in turn elucidates the
occurrence of the bosonic bunching. Finally, we derive a two-site extended
Bose-Hubbard model which reveals the low-energy physics of the bosons for the
case of much heavier fermions.
