Models for the introgression of a transgene into a wild population within a stochastic environment, with applications to pest control

Several forms of control are currently under consideration for pest species in Australia. Perhaps the most novel makes use of either an inducible fatality gene (IFG) or an inducible sterility gene (ISG). The transgene is integrated into the genome of target populations by periodically releasing transgenic animals. When high proportions of the population carry the transgene then the gene may be induced to reduce abundance. A fundamental feasibility issue is how much time and effort is required before the proportion of the population carrying the transgene reaches values close to 1. It is shown that the speed of introgression may be underestimated if models do not allow for year-to-year variability in natural processes, such as the number of young arising from natural breeding or the number of adults surviving to breed. Furthermore, the improvements in speed of introgression due to variability are magnified for species with lower lifespans. We include, as specific examples, application of the model to common carp (Cyprinus carpio) and mosquitofish (Gambusia affinis), which are major freshwater pests in Australia.