  We compare the recently introduced multi-state mapping approach to surface
hopping (MASH) with the F\"orster and Redfield theories of excitation energy
transfer. Whereas F\"orster theory relies on weak coupling between
chromophores, and Redfield theory assumes the electronic excitations to be
weakly coupled to fast chromophore vibrations, MASH is free from any
perturbative or Markovian approximations. We illustrate this with an example
application to the rate of energy transfer in a Frenkel-exciton dimer, showing
that MASH interpolates correctly between the opposing regimes in which the
F\"orster and Redfield results are reliable. We then compare the three methods
for a realistic model of the Fenna-Matthews-Olson complex with a structured
vibrational spectral density and static disorder in the excitation energies. In
this case there are no exact results for comparison so we use MASH to assess
the validity of F\"orster and Redfield theories. We find that F\"orster theory
is the more accurate of the two on the picosecond timescale, as has been shown
previously for a simpler model of this particular light-harvesting complex. We
also explore various ways to sample the initial electronic state in MASH and
find that they all give very similar results for exciton dynamics.
