The emergence of multiple new SARS-CoV-2 variants, characterized to varying degrees by increased infectivity, higher virulence and evasion of vaccine and infection-induced immunologic memory, has hampered international efforts to contain the virus . While it is generally believed that these variants first develop in single individuals with poor immunologic control of the virus, the factors governing variant predominance in the population remain poorly characterized . Here we present a mathematical framework for variant emergence accounting for the highly variable number of people secondarily infected by individuals with SARS-CoV-2 infection . Our simulations suggest that threatening new variants probably develop within infected people fairly commonly, but that most die out and do not achieve permanence in the population . Variants that predominate are more likely to be associated with higher infectiousness, but also the occurrence of a super-spreader event soon after introduction into the population.