  We present an analytical model for the cosmological evolution of the FRII
source population. Based on an earlier model for the intrinsic radio luminosity
- linear size evolution of these objects, we construct theoretical source
samples. The source distributions in the radio power - linear size plane of
these samples are then compared with that of an observed flux-limited sample.
We find that the source parameters determining the radio luminosity of FRII
objects can not be independent of each other. The best-fitting models predict
the jet power to be correlated either with the life time of the source or with
the shape of the density distribution of the source environment. The latter
case is consistent with the observed tendency of the most luminous radio
sources at high redshift to be located in richer and more extended environments
than their low redshift counterparts. We also find evidence for a class of FRII
sources distinctly different from the main population. These sources are
extremely old and/or are located in very underdense environments. The
luminosity function of FRII sources resulting from the model is in good
agreement with previous results for high luminosity sources. The apparent
luminosity evolution of the radio luminosity function is not reproduced because
of the high flux limit of the used comparison sample. The cosmological
evolution of the median linear size of FRII sources is found to be mild.
