Branching processes models for evolutionary rescue

Environmental change, if severe, can cause a population to decline in size and ultimately drive it extinct unless the population rapidly adapts to the new conditions. If the population adapts and recovers, we speak of evolutionary rescue. For evolutionary rescue to occur, it is not sufficient that well-adapted types are present in the population or appear during population decline. They also need to escape stochastic loss and establish in the population. An important mathematical tool to calculate the establishment probability of novel genetic variants is provided by branching process theory.
In the first part of the talk, I will present models of evolutionary rescue in an ecological context and discuss how environmental and genetic factors influence the probability of evolutionary res- cue. In the second part, I will turn to a situation where rescue is undesired: the evolution of drug resistance under drug pressure. How do we need to design treatment strategies to minimise the risk of resistance evolution?