Phytoplankton:virus interactions are important factors in aquatic nutrient cycling and community succession. The number of viral progeny resulting from an infection of a cell critically influences the propagation of infection and concomitantly the dynamics of phytoplankton populations. Host nucleotide content may be the resource limiting viral particle assembly. We present evidence for a strong linear correlation between measured viral burst sizes and viral burst sizes predicted from the host DNA content divided by the viral genome size, across a diversity of phytoplankton:viral pairs. An analysis of genome sizes therefore supports predictions of taxon-specific phytoplankton population density thresholds beyond which viral proliferation can trim populations or terminate phytoplankton blooms. We present corollaries showing that host:virus interactions may place evolutionary pressure towards genome reduction of both phytoplankton hosts and their viruses.