none. We examine a spatially explicit 'case model' for the interaction between the lycaenid butterfly, Maculinea rebeli, and its specialist parasitoid, Ichneumon eumerus. This butterfly lives in small, closed populations, rarely numbering over a few thousand individuals, and the parasitoid is found at only a small subset of butterfly-harbouring sites. We explore how parasitoid searching intensity and behaviour, and host refuges from parasitism affect the dynamics of the host-parasitoid couple. In the absence of explicit host refuges, the parasitoid persists only for a very restricted range of search rates and searching behaviours. Absolute refuges to parasitism, modelled as a cue-threshold phenomenon in the elicitation of intensive search for the host, expand the persistence conditions. We link these results to the more general problem of what inferences can be drawn concerning the association between population-level variation in the distribution of parasitism and the population dynamics of the system. The parasitoid's persistence depends importantly on heterogeneity in the vulnerability of the host caterpillars to encounter with parasitoids. Although the host's persistence is also enhanced by such heterogeneity, it is actually intraspecific competition within ant nests that dominates host dynamics. Deductions of the stabilizing power of parasitoids from measures of spatial heterogeneity in parasitism will be spurious without information about the respective density-dependent influences of the parasitoid and other limitation factors affecting the host.