Bacteriophages are the most numerous entities in the biosphere. Despite this numerical dominance, the genetic structure of bacteriophage populations is poorly understood. Here we present a biogeography study involving 25 novel bacteriophages from the Cystoviridae clade, a group characterized by a double stranded RNA genome divided into three segments. Previous laboratory manipulation has found that when multiple Cystoviruses infect a single host cell, they undergo (i) rare intrasegment recombination events, and (ii) frequent genetic reassortment between segments. Analyzing linkage disequilibrium within segments, we find no evidence of intrasegment recombination in wild populations, consistent with (i). An extensive analysis of linkage disequilibrium between segments supports frequent reassortment, on a time scale similar to the genomic mutation rate. The absence of linkage disequilibrium within this group of phage is consistent with expectations for a completely sexual population, despite that some segments have more than 50% nucleotide divergence at four-fold degenerate sites. This extraordinary rate of genetic exchange between highly unrelated individuals is unprecedented in any taxa. We discuss our results in light of the biological species concept applied to viruses.