  We develop and apply the multi-layer multi-configuration time-dependent
Hartree method for bosons, which represents an ab initio method for
investigating the non-equilibrium quantum dynamics of multi-species bosonic
systems. Its multi-layer feature allows for tailoring the wave function ansatz
in order to describe intra- and inter-species correlations accurately and
efficiently. To demonstrate the beneficial scaling and the efficiency of the
method, we explore the correlated tunneling dynamics of two species with
repulsive intra- and inter-species interactions, to which a third species with
vanishing intra-species interaction is weakly coupled. The population
imbalances of the first two species can feature a temporal equilibration and
their time-evolution significantly depends on the coupling to the third
species. Bosons of the first and of the second species exhibit a bunching
tendency, whose strength can be influenced by their coupling to the third
species.
