Quantifying stochastic introgression processes with hazard rates

Introgression is the permanent incorporation of genes from one population into another through hybridization and backcrossing. It can have large environmental consequences, such as the spread of insecticide or herbicide resistant genes, the escape of transgenes from genetically modified crops, and the invasion of exotic genes into new habitats. Introgression usually involves strong random components, such as rare hybridization and backcrossing events, and demographic variation in reproduction and survival. Most introgression studies ignore these random effects, and consequently fail to accurately assess the risk of introgression. This paper presents a methodology for quantifying stochastic introgression processes, based on multitype branching process models. We derive a quantity called the hazard rate, which can be used to investigate how the risk of introgression depends on crop management and life history.