Fitting host-parasitoid models with CV² > 1 using hierarchical generalized linear models

The powerful general Pacala-Hassell host-parasitoid model for a patchy environment, which allows host density–dependent heterogeneity (HDD) to be distinguished from between-patch, host density–independent heterogeneity (HDI), is reformulated within the class of the generalized linear model (GLM) family. This improves accessibility through the provision of general software within well–known statistical systems, and allows a rich variety of models to be formulated. Covariates such as age class, host density and abiotic factors may be included easily. For the case where there is no HDI, the formulation is a simple GLM. When there is HDI in addition to HDD, the formulation is a hierarchical generalized linear model. Two forms of HDI model are considered, both with between-patch variability: one has binomial variation within patches and one has extra-binomial, overdispersed variation within patches. Examples are given demonstrating parameter estimation with standard errors, and hypothesis testing. For one example given, the extra-binomial component of the HDI heterogeneity in parasitism is itself shown to be strongly density dependent.

Multiple attractors of host-parasitoid models with integrated pest management strategies: eradication, persistence and outbreak

Host-parasitoid models including integrated pest management (IPM) interventions with impulsive effects at both fixed and unfixed times were analyzed with regard to host-eradication, host-parasitoid persistence and host-outbreak solutions. The host-eradication periodic solution with fixed moments is globally stable if the host's intrinsic growth rate is less than the summation of the mean host-killing rate and the mean parasitization rate during the impulsive period. Solutions for all three categories can coexist, with switch-like transitions among their attractors showing that varying dosages and frequencies of insecticide applications and the numbers of parasitoids released are crucial. Periodic solutions also exist for models with unfixed moments for which the maximum amplitude of the host is less than the economic threshold. The dosages and frequencies of IPM interventions for these solutions are much reduced in comparison with the pest-eradication periodic solution. Our results, which are robust to inclusion of stochastic effects and with a wide range of parameter values, confirm that IPM is more effective than any single control tactic.

The effect of spatial scale on interactions between two weevils and their parasitoid

1. The effect of spatial scale on the interactions between three hymenopteran parasitoids and their weevil hosts was investigated. The parasitoid Mesopolobus incultus (Walker) parasitised Gymnetron pascuorum Gyll.; the parasitoids Entodon sparetus (Walker) and Bracon sp. parasitised Mecinus pyraster Herbst. Both of these weevils develop inside the seedhead of Plantago lanceolata L. but occupy different niches. Seedheads were sampled annually from 162 plants at each of two experimental sites consisting of a series of habitat patches of two distinct sizes. Data were analysed from three site-years. 2. Parasitoid densities at each site-year were closely related to the abundance of their respective weevil hosts. The overall proportion of hosts parasitised was more variable for M. incultus than for E. sparetus and Bracon sp. 3. Changes in spatial scale affected the variability of parasitoid densities. For M. incultus, there was generally a greater degree of additional heterogeneity for all increases of scale; for E. sparetus, this was true only at the largest scales; for Bracon sp., all components of variance were negative. 4. The rate of parasitism was related to host density in different ways at different spatial scales. Mesopolobus incultus exhibited inverse density dependence at the finest (seedhead) scale, direct density dependence at the intermediate (plant) scale, and density independence at the large (habitat area 729 m2) scale. Entodon sparetus showed no response to variation in host density at any spatial scale. Bracon sp. showed direct density dependence only at the intermediate and largest scales. 5. Parasitoids E. sparetus and Bracon sp. seemed able to detect more than one M. pyraster individual in seedheads with multiple host occupancy; a greater incidence of conspecific parasitoids than expected emerged from such seedheads.