It is commonly believed that influenza epidemics arise through the incremental accumulation of viral mutations, culminating in a novel antigenic type that is able to escape host immunity. Successive epidemic strains therefore become increasingly antigenically distant from a founding strain. Here, we present an alternative explanation where, because of functional constraints on the defining epitopes, the virus population is characterized by a limited set of antigenic types, all of which may be continuously generated by mutation from preexisting strains and other processes. Under these circumstances, influenza outbreaks arise as a consequence of host immune selection in a manner that is independent of the mode and tempo of viral mutation. By contrast with existing paradigms, antigenic distance between epidemic strains does not necessarily accumulate with time in our model, and it is the changing profile of host population immunity that creates the conditions for the emergence of the next influenza strain rather than the mutational capabilities of the virus.