This paper describes a new numerical technique for investigating the cosmological implications of radio source counts. Using all the available observational data, it is shown that the counts of radio sources are consistent with evolutionary cosmologies in which the properties of a class of powerful radio sources, tentatively identified with quasi-stellar sources, evolve with epoch. From the satisfactory models, it is found that: (1) the local ρ ( P ) luminosity function may be derived; (2) the mode of evolution of these powerful sources with epoch may be determined; and (3) the universe is isotropic to a redshift of at least 4. The models may be readily compared with future observations as they become available.