Appears in collection : 2022 - T1 - WS3 - Mathematical models in ecology and evolution

A major (if subtle) shift in thinking about ecology and evolution over the past generation has been the growing appreciation of how intertwined adaptation and population dynamics are, and how often they proceed on similar time-scales. This new perspective has been recently thrown into high relief by the need to understand how species may respond to environmental change caused by human activity. It seems certain that a substantial fraction of our planet's current biodiversity will be lost to extinction as species' habitats change at an accelerating rate. Some species, however, may be able to escape that fate by adapting, shifting their geographical ranges, or both. This leads to the questions of when, where and how might adaptation allow species to survive, leading to 'evolutionary rescue'. Some basic answers to those questions come from theory. In this talk I will present recent work on understanding how gene flow, spatial structure and habitat fragmentation affect the probability for evolutionary rescue. I start with a simple analytically tractable model for evolutionary rescue in a two-deme model with gene flow. This model can be analyzed in detail and our main result is a simple condition for when migration facilitates evolutionary rescue, as opposed as no migration. We further investigated the roles of asymmetries in gene flow and/or carrying capacities, and the effects of density regulation and local growth rates on evolutionary rescue. I will also present simulation results of multi-deme models. We find that in many cases spatially structured models can be translated into a simpler island model using an appropriately scaled effective migration rate. Finally, I will discuss continuous space models and highlight analogies to models of evolutionary rescue via modification of the distribution of fitness effects in non-recombining organisms, such as many viral populations.