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Heterogeneity and the Dynamics of Host-Parasitoid Interactions [and Discussion]

M. P. Hassell, S. W. Pacala, G. A. Tingley


This paper is concerned with the dynamical effects of spatial heterogeneity in host-parasitoid interactions with discrete generations. We show that the dynamical effects of any pattern of distribution of searching parasitoids in such systems can be assessed within a common, simple framework. In particular, we describe an approximate general rule that the populations of hosts and parasitoids will be regulated if the coefficient of variation squared (CV<latex>$^{2}$</latex>) of the distribution of searching parasitoids is greater than one. This criterion is shown to apply both generally and in several specific cases. We further show that CV<latex>$^{2}$</latex> may be partitioned into a density-dependent component (direct or inverse) caused by the response of parasitoids to host density per patch, and a density independent component. Population regulation can be enhanced as much by density independent as by density-dependent heterogeneity. Thus the dynamical effects of any pattern of distribution of searching parasitoids can be assessed within the same common framework. The paradoxical impact of density-independent heterogeneity on dynamics is especially interesting: the greater the density independence, and thus the more scattered the data of percent parasitism against local host density, the more stable the populations are likely to be. Although a detailed analysis of host-parasitoid interactions in continuous time has yet to be done, evidence does not support the suggestion of Murdoch & Oaten (1989) that non-random parasitism may have quite different effects on the dynamics of continuous-time interactions. There appears to be no fundamental difference in the role of heterogeneity in comparable discrete- or continuous-time interactions. A total of 65 data sets from field studies have been analysed, in which percentage parasitism in relation to local host density have been recorded. In each case, estimated values of CV<latex>$^{2}$</latex> have been obtained by using a maximum likelihood procedure. The method also allows us to partition the CV<latex>$^{2}$</latex> into the density dependent and density-independent components mentioned above. In 18 out of the 65 cases, total heterogeneity was at levels sufficient (if typical of the interactions) to stabilize the interacting populations (i.e. CV<latex>$^{2}$</latex> > 1). Interestingly, in 14 of these it is the host-density-independent heterogeneity that contributes most to the total heterogeneity. Although heterogeneity has often been regarded as a complicating factor in population dynamics that rapidly leads to analytical intractability, this clearly need not necessarily be so. The CV<latex>$^{2}$</latex> > 1 rule explains the consequences of heterogeneity for population dynamics in terms of a simple description of the heterogeneity itself, and provides a rough rule for predicting the effects of different kinds of heterogeneity on population regulation.

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