  We seek to develop an essentially analytical model for the evolution of
Fanaroff-Riley Class II radio galaxies as they age individually and as their
numbers vary with cosmological epoch. Such modeling is required in order to
probe in more detail the impact of radio galaxies on the growth of structures
in the universe, which appears likely to have been quite significant at z > 1.
In this first paper of a series we compare three rather sophisticated
analytical models for the evolution of linear size and lobe power of FR II
radio galaxies, those of Kaiser, Dennett-Thorpe & Alexander (1997), Blundell,
Rawlings & Willott (1999), and Manolakou & Kirk (2002). We perform
multi-dimensional Monte Carlo simulations in order to compare the predictions
of each model for radio powers, sizes, redshifts and spectral indices with
data. The observational samples used here are the low frequency radio surveys,
3CRR, 6CE and 7CRS, which are flux-limited and complete. We search for and
describe the best parameters for each model, after doing statistical tests on
them. We find that no existing model can give acceptable fits to all the
properties of the surveys considered, although the Kaiser, Dennett-Thorpe &
Alexander (1997) model gives better overall results than do the Manolakou &
Kirk (2002) or Blundell, Rawlings & Willott (1999) models for most of the tests
we performed. We suggest ways in which these models may be improved.
