To delay resistance development to Bacillus thuringiensis (Bt) plants expressing their own insecticide, the application of the Insect Resistance Management strategy called “High Dose/Refuge Strategy” (HD/R) is recommended by the US Environmental Protection Agency (US EPA). This strategy was developed for Bt plants expressing one toxin. Presently, however, new Bt plants that simultaneously express two toxins are on the market. We used a mathematical model to evaluate the efficiency of the HD/R strategy for both these Bt toxins. As the current two-toxin Bt plants do not express two new Cry toxins but reuse one toxin already in use with a one-toxin plant, we estimated the spread of resistance when the resistance alleles are not rare. This study assesses: (i) whether the two toxins have to be present in high concentration, and (ii) the impact of the relative size of the refuge zone on the evolution of resistance and population density. We concluded that for Bt plants expressing one toxin, a high concentration is an essential condition for resistance management. For the pyramided Bt plants, one toxin could be expressed at a low titer if the two toxins are used for the first time, and a small refuge zone is acceptable.

Early View (EV): 1-EV contagion between populations of susceptible hosts and vectors through the use of transmission kernels (Keeling et al. 2001).In both ecology and epidemiology, the use of mechanistic models generally requires a detailed understanding of key life-history parameters. Some of these can be inferred from historical invasions or epidemics through inverse modelling in which ranges of parameter values are tested to identify values that optimize the fit of the model to the observed data. But when the number of parameters increases, the volume of parameter space to be explored becomes high and the search for optimal combinations of parameters is thus computationally intensive. In contrast, empirical statistical models characterize the spatio-temporal patterns of invasions in order to quantify some of their key features (e.g. rate of spread, correlation between date of first invasion and external The spread of invading organisms has historically attracted considerable attention. Interest has often focused on characterizing geographical patterns of spread, and with it, the speed of invasion (Hengeveld 1989, Bosch et al. 1992. One of the first mechanistic (mathematical) models describing invasion spread was proposed by Skellam (1951); this reaction-diffusion model coupled exponential growth with diffusive movement of invader populations. Several subsequent mathematical formulations built upon this model by accounting for elements such as a limited carrying capacity, different dispersal kernels (e.g. fat-tailed dispersal kernels; Kot et al. 1996), modes of dispersion (e.g. stratified dispersal; Shigesada and Kawasaki 1997), or the incorporation of density-dependent processes (e.g. Allee effect; Lewis and Kareiva 1993 Invading species rarely spread homogeneously through a landscape and invasion patterns typically display irregular frontal boundaries as the invasion progresses through space. Those irregular patterns are generally produced by local environmental factors that may slow or accelerate movement of the frontal boundary. While there is an abundant literature on species distribution modelling methods that quantify local suitability for species establishment, comparatively few studies have examined methods for measuring the local velocity of invasions that can then be statistically analysed in relation to spatially variable environmental factors. Previous studies have used simulations to compare different methods for estimating the overall rate of spread of an invasion. We adopted a similar approach of simulating invasions that resemble two real casestudies, both in terms of their spatial resolution (i.e. considering the size of one cell as one km) and their spatial extent ( 600 000 km²). Simulations were sampled to compare how different methods used to measure local spread rate, namely the neighbouring, nearest distance and Delaunay methods, perform for spatio-temporal comparisons. We varied the assessment using three levels of complexity of the spatio-temporal pattern of invasion, three sample siz...

On the market since 1996, genetically modified plants expressing an insecticidal toxin (Cry toxin stemmed from Bacillus thuringiensis) target several lepidopteran and coleopteran pests. In this study, we assessed the impact of two varieties of Bt maize producing different toxins (Cry1Ab or Cry1Fa, respectively) on the biology of a storage pest: Plodia interpunctella (Hübner) (Lepidoptera: Pyralidae). The Indianmeal moths were susceptible to both toxins but showed an escape behavior only from Cry1Fa. The weight of females issued from larvae reared on Cry1Ab increased with increasing toxin concentration, but adults of both sexes reared on Cry1Fa had decreased weight. Both toxins increased development time from egg to adult regardless of sex and had no impact on the male adult lifespan. Finally, we recorded a time lag between metamorphosis from the non-Bt and the Bt diets, which increased proportionally to Cry concentration in the Bt diet.

The “High Dose/Refuge” strategy (HD/R) is the currently recommended Insect Resistance Management strategy (IRM) to limit resistance development to Bacillus thuringiensis (Bt) plants. This strategy requires planting a “refuge zone” composed of non-Bt plants suitable for the target insect and in close proximity to a “Bt zone” expressing a high toxin concentration. One of the main assumptions is that enough susceptible adults mate with resistant insects. However, previous studies have suggested that the high toxin concentration produced by Bt plants induces slower insect development, creating an asynchrony in emergence between the refuge and the Bt zone and leading to assortative mating between adults inside each zone. Here, we develop a deterministic model to estimate the impact of toxin concentration, emergence asynchrony and refuge zone size on the effectiveness of the HD/R strategy. We conclude that emergence asynchrony only affects resistance when toxin concentration is high and resistance is recessive. Resistance develops more rapidly and survival of susceptible insects is higher at lower toxin concentration, but in such situations, resistance is insensitive to emergence asynchrony.

Current strategies to control classical scrapie remove animals at risk of scrapie rather than those known to be infected with the scrapie agent. Advances in diagnostic tests, however, suggest that a more targeted approach involving the application of a rapid live test may be feasible in future. Here we consider the use of two diagnostic tests: recto-anal mucosa-associated lymphatic tissue (RAMALT) biopsies; and a blood-based assay. To assess their impact we developed a stochastic age- and prion protein (PrP) genotype-structured model for the dynamics of scrapie within a sheep flock. Parameters were estimated in a Bayesian framework to facilitate integration of a number of disparate datasets and to allow parameter uncertainty to be incorporated in model predictions. In small flocks a control strategy based on removal of clinical cases was sufficient to control disease and more stringent measures (including the use of a live diagnostic test) did not significantly reduce outbreak size or duration. In medium or large flocks strategies in which a large proportion of animals are tested with either live diagnostic test significantly reduced outbreak size, but not always duration, compared with removal of clinical cases. However, the current Compulsory Scrapie Flocks Scheme (CSFS) significantly reduced outbreak size and duration compared with both removal of clinical cases and all strategies using a live diagnostic test. Accordingly, under the assumptions made in the present study there is little benefit from implementing a control strategy which makes use of a live diagnostic test.