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

Abstract

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.

Spatial patterns of Trybliographa rapae parasitism of Delia radicum larvae in oilseed rape and cauliflower

“…When applied to field data, μ describes the host density‐dependent heterogeneity of parasitism and non‐zero values of μ are symptomatic of a parasitoid response to host density (Pacala and Hassell 1991). We obtained estimates of μ from generalized linear modelling of the equation (Perry et al. 2000): using S‐Plus (Insightful Corp. 2005), where a is a nuisance parameter and E ( p i ) is expected p i .…”

Host selection is not expressed for underground hosts in a pupal parasitoid

“…However, the variability in parasitism risk can also emerge through host preference of parasitoids in a single patch when host preference by parasitoids acts on intraspecific host variability (Okuyama, 2019). Although studies that quantify within‐species variability in parasitism risk among hosts typically assume such variability due to host preference is absent (Pacala et al, 1990; Perry et al, 2000), proper description of host preference is important in identifying variability in parasitism risk among hosts and its broad implications.…”

Gall size determines the structure of theRabdophaga strobiloideshost–parasitoid community

“…An accurate characterisation of community dynamics therefore requires either the unrealistic assumption that the final distribution of parasitoids reflects the distribution of attacks, or knowledge of the attacks themselves. Some numerical methods have been developed to estimate the distribution of attacks based on the resulting mortality patterns (Pacala et al ., 1990; Perry et al ., 2000). These methods, however, have not been widely adopted, likely due to the complexity of the numerical calculations involved.…”