Ratio-dependent parasitism with Trissolcus basalis (Wollaston) (Hymenoptera: Scelionidae) on egg rafts of Nezara viridula (Linnaeus) (Hemiptera: Pentatomidae): effect of experimental variables and compatibility of 'ratio' and 'Holling' models

Abstract Egg rafts of Nezara viridula were exposed to the parasitoid wasp Trissolcus basalis in experimental arenas to establish the relationship of the rates of attack and parasitism to various combinations of arena size, parasitoid density, host density and parasitoid-to-host ratio. Arena sizes were varied in the ratio 1:9:63, with the largest having a search area of 1.44 m². Parasitoid and host densities were varied over a 27-fold range. The parasitoid-to-host ratios used were 1:1, 3:1 and 6:1. Finding time was related to a constant factor (flight propensity), rather than to the difficulty of finding (density of hosts). Initial attack rates were therefore related only to parasitoid numbers (or density), even at the lower densities and ratios. Parasitism rates (a function of attack rate per host) were thus also strongly related to parasitoid to host ratio, regardless of densities used and arena sizes. Even reducing host density, while keeping time and parasitoid density constant, increased the parasitism rate. A ratio model for parasitism rate was therefore compatible with the data but the more explicit Holling 'disc' equation was also compatible because handling time was sufficiently large to make it sensitive to the ratio of parasitoids to hosts for the densities used. We conclude that the two models would predict different results if the density of host egg rafts was in a range below one per square metre.     

Use of the score test as a goodness-of-fit measure of the covariance structure in genetic analysis of longitudinal data

Model selection is an essential issue in longitudinal data analysis since many different models have been proposed to fit the covariance structure. The likelihood criterion is commonly used and allows to compare the fit of alternative models. Its value does not reflect, however, the potential improvement that can still be reached in fitting the data unless a reference model with the actual covariance structure is available. The score test approach does not require the knowledge of a reference model, and the score statistic has a meaningful interpretation in itself as a goodness-of-fit measure. The aim of this paper was to show how the score statistic may be separated into the genetic and environmental parts, which is difficult with the likelihood criterion, and how it can be used to check parametric assumptions made on variance and correlation parameters. Selection of models for genetic analysis was applied to a dairy cattle example for milk production.