The intensity dependence of picosecond kinetics in the light-harvesting antenna of the photosynthetic bacterium Rhodospirillum rubrum is studied at 77 K. By changing either the average excitation intensity or the pulse intensity we have been able to discriminate singlet-singlet and singlet-triplet annihilation. It is shown that the kinetics of both annihilation types are well characterized by the concept of percolative excitation dynamics leading to the time-dependent annihilation rates. The time dependence of these two types of annihilation rates is qualitatively different, whereas the dependencies can be related through the same adjustable parameter-a spectral dimension of fractal-like structures. The theoretical dependencies give a good fit to the experimental kinetics if the spectral dimension is equal to 1.5 and the overall singlet-singlet annihilation rate is close to the value obtained at room temperature. The percolative transfer is a consequence of spectral inhomogeneous broadening. The effect is more pronounced at lower temperatures because of the narrowing of homogeneous spectra.