Cultural adaptation is one means by which conservationists may help populations adapt to threats. A learned behavior may protect an individual from a threat, and the behavior can be transmitted horizontally (within generations) and vertically (between generations), rapidly conferring population-level protection. Although possible in theory, it remains unclear whether such manipulations work in a conservation setting; what conditions are required for them to work; and how they might affect the evolutionary process. We examined models in which a population can adapt through both genetic and cultural mechanisms. Our work was motivated by the invasion of highly toxic cane toads (Rhinella marina) across northern Australia and the resultant declines of endangered northern quolls (Dasyurus hallucatus), which attack and are fatally poisoned by the toxic toads. We examined whether a novel management strategy in which wild quolls are trained to avoid toads can reduce extinction probability. We used a simulation model tailored to quoll life history. Within simulations, individuals were trained and a continuous evolving trait determined innate tendency to attack toads. We applied this model in a population viability setting. The strategy reduced extinction probability only when heritability of innate aversion was low (<20%) and when trained mothers trained >70% of their young to avoid toads. When these conditions were met, genetic adaptation was slower, but rapid cultural adaptation kept the population extant while genetic adaptation was completed. To gain insight into the evolutionary dynamics (in which we saw a transitory peak in cultural adaptation over time), we also developed a simple analytical model of evolutionary dynamics. This model showed that the strength of natural selection declined as the cultural transmission rate increased and that adaptation proceeded only when the rate of cultural transmission was below a critical value determined by the relative levels of protection conferred by genetic versus cultural mechanisms. Together, our models showed that cultural adaptation can play a powerful role in preventing extinction, but that rates of cultural transmission need to be high for this to occur.