Several studies have shown that classical results of microparasite evolution could not extend to the case where the host species shows an important spatial structure. Rabbit haemorrhagic disease virus (RHDV), responsible for rabbit haemorrhagic disease (RHD), which recently emerged in rabbits, has strains within a wide range of virulence, thus providing an interesting example of competition between strains infecting a host species with a metapopulation structure. In addition, rabbits may show a genetic diversity regarding RHDV susceptibility. In the present paper we use the example of the rabbit-RHDV interaction to study the competition between strains of a same microparasite in a host population that is both spatially and genetically structured. Using metapopulation models we show that the evolution of the microparasite is guided by a trade-off between its capacity to invade subpopulations potentially infected by other strains and its capacity to persist within the subpopulation. In such a context, host genetic diversity acts by reducing the number of hosts susceptible to each strain, often favouring more persistent-and generally less virulent-strains. We also show that even in a stochastic context where host genes regularly go locally extinct, the microparasite pressure helps maintain the genetic diversity in the long term while reinforcing gene loss risk in the short term. Finally, we study how different demographic and epidemiologic parameters affect the coevolution between the rabbit and RHDV.