Can natural enemies enforce geographical range Limits?

We develop a simple mathematical model to investigate the question as to wh ether a specialised consumer san be responsible for creating a range limit in the population of its dynamic resource. The model is most attuned for pa rasitoid-host relationships, but the central results should apply to a broa d range of systems. Specifically, at the beginning of each simulation host and parasitoid populations are distributed at random along a string of patc hes. In each discrete generation and for each patch, host and parasitoid po pulations grow and interact, and then a constant fraction of those remainin g disperses one sr more patch distances in either direction according to a geometric distribution. We iterate the model 200 generations, and in any ge neration for any patch, either host and/or parasitoid can go locally extinc t if its population falls below a threshold density. We find that a special ised parasitoid can enforce a limit, and it is even more likely to fragment its host population. The two most important conditions for parasitoid-enfo rced range limits are: 1) the theoretical host equilibrium density in the p resence 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 discussi ng our findings for specialist and generalist natural enemies, and the rele vance of our study to the wealth of investigations on the causes of geograp hical range limits.