Host-parasitoid associations in patchy environments.

Studies of insect host-parasitoid interactions have contributed much to the consensus that spatial patchiness is important in the regulation of natural populations. A variety of theoretical models predict that host and parasitoid populations, although unstable in the absence of environmental heterogeneity, may persist at roughly steady overall densities in a patchy environment owing to variation in levels of parasitism from patch to patch. Observed patterns of parasitism, however, have a variety of forms (with variation in attack rates among patches depending directly or indirectly on host density, or showing variation uncorrelated with host density). There is some confusion about the dynamical consequences of these different forms. Here we first show how the dynamical effects of all these forms of environmental heterogeneity can be assessed by a common criterion. This 'CV2 greater than 1 rule' states that the overall population densities will remain roughly steady from generation to generation if the coefficient of variation squared (CV2) of the density of searching parasitoids in the vicinity of each host exceeds approximately unity. By partitioning CV2 into components, we show that both direct and inverse patterns of dependence on host density, and density-independent patterns, all contribute to population regulation in the same way. Second, we show how a maximum-likelihood method can be applied to the kind of field data that are usually available (that is, percentage parasitism versus local host density) to estimate the components of CV2. This analysis indicates that heterogeneity is large enough to stabilize dynamics in 9 of 34 published studies, and that density-independent heterogeneity is the main factor in most cases.