Transgenes in plants affect life history traits including seed survival and germination. With stochastic matrix models we predict population-level consequences of transgene induced life history changes. We assess systematically which changes in life history traits, resulting from genetic modification, may increase the risk of invasion and persistence of feral crops or increase fitness in case of introgression from arable fields into conspecific, feral populations. We apply our method to feral populations of oilseed rape. Like many annual weeds, oilseed rape depends critically on disturbance; in undisturbed habitats it is generally outcompeted by perennials. The associated inherent variability and unpredictability render deterministic models inappropriate. With a stochastic matrix model we study population growth rate, elasticities and quasi-extinction times. Our results indicate that changes in survival in the seed bank impact population growth and persistence most. Less important are dormancy, fecundity and seedling survival. The predicted distribution of extinction times is highly skewed, with some patches persisting for decades.