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.
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