  Underlying physical principles for the high efficiency of excitation energy
transfer in light-harvesting complexes are not fully understood. Notably, the
degree of robustness of these systems for transporting energy is not known
considering their realistic interactions with vibrational and radiative
environments within the surrounding solvent and scaffold proteins. In this
work, we employ an efficient technique to estimate energy transfer efficiency
of such complex excitonic systems. We observe that the dynamics of the
Fenna-Matthews-Olson (FMO) complex leads to optimal and robust energy transport
due to a convergence of energy scales among all important internal and external
parameters. In particular, we show that the FMO energy transfer efficiency is
optimum and stable with respect to the relevant parameters of environmental
interactions and Frenkel-exciton Hamiltonian including reorganization energy
$\lambda$, bath frequency cutoff $\gamma$, temperature $T$, bath spatial
correlations, initial excitations, dissipation rate, trapping rate, disorders,
and dipole moments orientations. We identify the ratio of $\lambda T/\gamma\*g$
as a single key parameter governing quantum transport efficiency, where g is
the average excitonic energy gap.
