Parasitism in patchy environments: inverse density dependence can be stabilizing

There are now many examples in the literature where the spatial distribution of per cent parasitism by insect parasitoids is either directly or inversely dependent on host density per patch. While it is well known that direct density dependent relationships can contribute markedly to the stability of a host-parasitoid interaction, inverse relationships have been more-or-less ignored. Using difference equation models, the dynamics of host-parasitoid interactions are described where parasitism per patch varies across the range from direct to inversely density dependent. These models demonstrate for a variety of host distributions that inverse relationships can also strongly promote stability.