ENVIRONMENTAL HETEROGENEITY AND THE STABILITY OF HOST PARASITOID INTERACTIONS

1. Spatial heterogeneity has long been recognized as a potentially powerful stabilizing force in host-parasitoid interactions. Most previous work has emphasized heterogeneity in the rate of attacks experienced by individual hosts. In contrast, we highlight the potential importance of spatial heterogeneity in demographic parameters other than the rate of parasitism. 2. Following the model structure explored by Hassell & May (1973) in which hosts and parasitoids are distributed across patches according to fixed distribution rules, we show that, in the absence of heterogeneity in the rate of parasitism, spatial variability in other demographic parameters has no effect on population stability. 3. Spatial heterogeneity in demographic parameters may, however, interact with heterogeneous attack rates to augment or, conversely, destroy stability. This is illustrated from a generalized proportional refuge model in which a fixed fraction of hosts escape parasitism each generation, and refuge hosts have a different growth rate from exposed hosts. We show that the system may be stable even if hosts have high average rates of increase, provided that those hosts with the higher rates of increase are differentially afflicted by parasitism. 4. The generality of this conclusion is assessed by numerical studies of a two-patch model in which the host and/or parasitoid show partial rather than complete mixing between patches in each generation. We show that such partially coupled refuges are most likely to be stabilizing if they are 'sinks', with relatively low host growth rates. Moreover, and a unique feature emerging from these partially coupled models, heterogeneity in the number of adult female parasitoids produced per parasitized host can be sufficient by itself to stabilize the system. 5. These theoretical results suggest that a fruitful direction for empirical work is to document the patterns of covariance among attack rates, host rates of increase and parasitoid emergence rates.