An open question in epidemiology is why transmission is often overdispersed, meaning that most new infections are driven by few infected individuals. For example, around 10\% of COVID-19 cases cause 80\% of new COVID-19 cases. This overdispersion in pathogen transmission is likely driven by intrinsic biological heterogeneity among hosts, i.e. variability in SARS-CoV-2 viral loads. However, host heterogeneity could also indirectly increase transmission dispersion by driving pathogen adaptation. Specifically, transmission variation among hosts could drive pathogen specialization to highly-infectious hosts. Adaptation to rare, highly-infectious hosts could amplify transmission dispersion by simultaneously decreasing transmission from common, less-infectious hosts. This study considers whether increased transmission dispersion can be, in part, an emergent property of parasite adaptation to heterogeneous host populations. We develop a mathematical model using a Price equation framework to address this question that follows the epidemiological and evolutionary dynamics of a general host-parasite system. The results predict that parasite adaptation to heterogeneous host populations drives high transmission dispersion early in epidemics. Further, parasite adaptation can maintain increased transmission dispersion at endemic equilibria as long as virulence differs between hosts in a heterogeneous population. More broadly, this study provides a framework for predicting how parasite adaptation determines transmission dispersion for emerging and re-emerging infectious disease.