Populations of antigenically diverse pathogens undergoing genetic exchange may be categorized into strains on the basis of a set of principal protective antigens. The extent to which polyvalent vaccines based on these protective antigens can alter the population structure of the pathogen is determined by the degree of cross–protection between strains. In the case where there is no cross–protection, vaccinating against a particular strain will have no effect on the others. As cross–protection increases, the strains containing the antigenic variants included in the vaccine will be diminished in prevalence, and those that do not will increase in prevalence. The rise in prevalence of the latter will become more and more exaggerated as cross–protection increases. However, beyond a critical level of cross–protection, in the absence of vaccination, the steady state of the system is asymmetric in that a certain subset of strains (with non–overlapping repertoires of antigenic variants) will dominate over the others in terms of prevalence. Under these circumstances, a vaccine consisting of the most immunogenic combinations of antigenic variants can cause a dramatic increase in frequency of a subset of rare strains.