  We study the matter and velocity divergence power spectra in a f(R) gravity
theory and their time evolution measured from several large-volume N-body
simulations with varying box sizes and resolution. We find that accurate
prediction of the matter power spectrum in f(R) gravity places stronger
requirements on the simulation than is the case with LCDM, because of the
nonlinear nature of the fifth force. Linear perturbation theory is shown to be
a poor approximation for the f(R) models, except when the chameleon effect is
very weak. We show that the relative differences from the fiducial LCDM model
are much more pronounced in the nonlinear tail of the velocity divergence power
spectrum than in the matter power spectrum, which suggests that future surveys
which target the collection of peculiar velocity data will open new
opportunities to constrain modified gravity theories. A close investigation of
the time evolution of the power spectra shows that there is a pattern in the
evolution history, which can be explained by the properties of the
chameleon-type fifth force in f(R) gravity. Varying the model parameter |f_R0|,
which quantifies the strength of the departure from standard gravity, mainly
varies the epoch marking the onset of the fifth force, as a result of which the
different f(R) models are in different stages of the same evolutionary path at
any given time
