  We study the interplay between two environmental influences on excited state
energy transfer in photosynthetic light harvesting complexes, namely,
vibrationally assisted energy transfer (VAET) and environment-assisted quantum
transport (ENAQT), considering a dimeric chromophore donor-acceptor model as a
prototype for larger systems. We demonstrate how the basic features of the
excitonic energy transfer are influenced by these two environments, both
separately and together, with the environment being fully quantum in the case
of VAET and treated in the Haken-Strobl-Reineker classical limit in the case of
ENAQT. Our results reveal that in the weak noise regime, the presence of a
classical noise source is detrimental to the energy transfer that is resonantly
assisted by the exciton-vibration interactions intrinsic to VAET. In the strong
noise regime we reproduce all the features of ENAQT including the turnover into
a Zeno regime where energy transfer is suppressed, and VAET is insignificant.
