  We present a study of the trends in luminosity, linear size, spectral index,
and redshift of classical double radio sources from three complete samples
selected at successively fainter low radio-frequency flux-limits. We have been
able to decouple the effects of the tight correlation between redshift and
luminosity (inherent in any single flux-limited sample) which have hitherto
hindered interpretation of the relationships between these four source
properties. The major trends found are that (i) spectral indices increase with
linear size, (ii) rest-frame spectral indices have a stronger dependence on
luminosity than on redshift except at high (GHz) frequencies, and that (iii)
the linear sizes are smaller at higher redshifts. We reproduce the observed
dependences in a model for radio sources (born throughout cosmic time according
to a radio-source birth function) whose lobes are fed with a
synchrotron-emitting population (whose energy distribution is governed by
compact hotspots), and which suffer inverse Compton, synchrotron and adiabatic
expansion losses. In simulating the basic observed dependences, we find that
there is no need to invoke any systematic change in the environments of these
objects with redshift if the consequences of imposing a survey flux-limit on
our simulated datasets are properly included in the model. We present evidence
that for a radio survey there is an unavoidable `youth--redshift degeneracy',
even though radio sources are short-lived relative to the age of the Universe;
it is imperative to take this into account in studies which seemingly reveal
correlations of source properties with redshift such as the `alignment effect'.
