Abstract
Introgression is the permanent incorporation of genes from the genome of one population into another. This can have severe consequences, such as extinction of endemic species, or the spread of transgenes. Quantification of the risk of introgression is an important component of genetically modified crop regulation. Most theoretical introgression studies aimed at such quantification disregard one or more of the most important factors concerning introgression: realistic genetical mechanisms, repeated invasions and stochasticity. In addition, the use of linkage as a risk mitigation strategy has not been studied properly yet with genetic introgression models. Current genetic introgression studies fail to take repeated invasions and demographic stochasticity into account properly, and use incorrect measures of introgression risk that can be manipulated by arbitrary choices. In this study, we present proper methods for risk quantification that overcome these difficulties. We generalize a probabilistic risk measure, the so-called hazard rate of introgression, for application to introgression models with complex genetics and small natural population sizes. We illustrate the method by studying the effects of linkage and recombination on transgene introgression risk at different population sizes.