We develop a simple mathematical model to investigate the question as to whether a specialised consumer can be responsible for creating a range limit in the population of its dynamic resource. The model is most attuned for parasitoid-host relationships, but the central results should apply to a broad range of systems. Specifically, at the beginning of each simulation host and parasitoid populations are distributed at random along a string of patches. In each discrete generation and for each patch, host and parasitoid populations grow and interact, and then a constant fraction of those remaining disperses one or more patch distances in either direction according to a geometric distribution. We iterate the model 200 generations, and in any generation for any patch, either host and/or parasitoid can go locally extinct if its population falls below a threshold density. We find that a specialised parasitoid can enforce a limit, and it is even more likely to fragment its host population. The two most important conditions for parasitoid-enforced range limits are: 1) the theoretical host equilibrium density in the presence of the parasitoid be very small at sites eliminated from the host's range, and 2) the parasitoid disperses at high rates. We close by discussing our findings for specialist and generalist natural enemies, and the relevance of our study to the wealth of investigations on the causes of geographical range limits.