Theoretical Population Biology 58, 95106 (2000) Periodic Triggering of an Inducible Gene for Control of a Wild Population S. A. Davis, 1 E. A. Catchpole, and G. R. Fulford 2 School of Mathematics and Statistics, University College, UNSW, Australian Defence Force Academy, Canberra, ACT 2600, Australia Received April 12, 1999 A possible method of control for the management of wild populations consists of continual introgression of an inducible transgene by releasing transgenic individuals, with periodic exposure of the population to a trigger. Exposure to the trigger causes death or sterility in carriers of the transgene, but is otherwise benign. We investigate the effectiveness of various strategies for control. We show that suppression of the population density below any pre- specified level is possible using this technique. At the same time we show that too frequent or too efficient exposure to the trigger can select for non-transgenic genotypes at an intensity such that the population density will be largely unaffected by the trigger. Choices for manage- ment parameters can ensure that the latter scenario is avoided. We show that releasing individuals carrying the transgene at more than one locus facilitates density control. ] 2000 Academic Press Key Wordsy pest control; introgression; transgene; inducible gene; bifurcation. 1. INTRODUCTION Recent developments in genetics have suggested possi- bilities for pest control using inducible genes (Grewe, 1997). Such genes are silent until exposure to a particular compound results in death, if the gene is an inducible fatality gene (IFG), or sterility, if it is an inducible sterility gene (ISG). The spread of an inducible gene through a wild population results in individuals vulnerable to the trigger which induces expression of the gene. This is a species-specific technique because vulnerability is an inherited trait, so if we delineate between species on the basis of reproductive isolation (Mayr, 1942), then only individuals within the species can inherit the trait. As a first step towards control, individuals carrying the inducible gene homozygously are released to mix and breed with the target population. We assume that while the gene is silent there are no differences in survival rates, nor in fecundity rates, between those that carry the trans- gene and those that do not. The gene is thus selectively neutral. Sustained release of transgenic individuals constitutes a crude but sufficient means of spreading a neutral transgene through a wild population (Davis and Fulford, 1999). If the release of transgenics were to be dis- continued, or if there were only a single initial release, then the genotype frequencies would fall into Hardy Weinberg equilibria and, if we were to ignore stochastic effects, remain there. Provided that the release of trans- genics is ongoing the frequency of the neutral transgene will increase. When large proportions of the population carry the gene then the population as a whole is vulnerable to the trigger. Exposure will induce a population collapse, through either a large number of immediate deaths for an IFG or a large reduction in the birth rate in the case of an ISG. If release of transgenics continues as the popula- tion recovers, exposure may be repeated. We illustrate how this can hold a population below any pre-specified density. It follows that if the criterion for control is that doi:10.1006tpbi.2000.1477, available online at http:www.idealibrary.com on 95 0040-580900 K35.00 Copyright ] 2000 by Academic Press All rights of reproduction in any form reserved. 1 Present address: CSIRO, Division of Wildlife and Ecology, P.O. Box 284, Canberra, ACT 601, Australia. 2 Present address: AgResearch, Wallaceville Animal Research Centre, P.O. Box 40063, Upper Hutt, New Zealand.