The transmission dynamics of viruses in a replicating cell population is investigated, assuming that viral mutants differ in their efficiencies of horizontal and vertical transmission. As a genetic result we find that competition between such different viral strategies need not select for increasing basic reproductive rates. We illustrate evolutionary trajectories that lead to increased viral latency even at the expense of lower basic reproductive rates and lower equilibrium abundance. In some cases oscillations in the prevalence of different mutants are obtained.