Many positive sense RNA viruses, especially those infecting plants, are known to experience stringent, stochastic population bottlenecks inside the cells they invade, but exactly how and why these populations become bottlenecked are unclear. A model proposed ten years ago advocates that such bottlenecks are evolutionarily favored because they cause the isolation of individual viral variants in separate cells. Such isolation in turn allows the viral variants to manifest the phenotypic differences they encode. Recently published observations lend mechanistic support to this model, and prompt us to refine the model with novel molecular details. The refined model, designated Bottleneck, Isolate, Amplify, Select (BIAS), postulates that these viruses impose population bottlenecks on themselves by encoding bottleneck-enforcing proteins (BNEPs) that function in a concentration-dependent manner. In cells simultaneously invaded by numerous virions of the same virus, BNEPs reach the bottleneck-ready concentration sufficiently early to arrest nearly all internalized viral genomes. As a result, very few (as few as one) viral genomes stochastically escape to initiate reproduction. Repetition of this process in successively infected cells isolate viral genomes with different mutations in separate cells. This isolation prevents mutant viruses encoding defective viral proteins from hitchhiking on sister genome-encoded products, leading to the swift purging of such mutants. Importantly, genome isolation also ensures viral genomes harboring beneficial mutations accrue the cognate benefit exclusively to themselves, leading to the fixation of such beneficial mutations. Further interrogation of the BIAS hypothesis promises to deepen our understanding of virus evolution, and inspire new solutions to virus disease mitigation.