Geometric Insights into evolutionary rescue dynamics in a two-deme model

Understanding evolutionary rescue mechanisms in fragmented populations is crucial in the context of rapidly changing environments. This study employs analytical derivations and simulations within a two-deme metapopulation model using Fisher's geometric model framework. We explore the impacts of abrupt environmental changes on two subpopulations that lead to distinct phenotypic optima. We determine the probability density of distances between these optima through analytical derivations. This enables us to calculate the intersection volume of the rescue domains of two subpopulations in the phenotypic space. This approach also allows us to assess the fixation probability of mutations that concurrently rescue both subpopulations and identify the domain of one-step rescue mutations. Our findings reveal that the likelihood of joint evolutionary rescue diminishes with increasing dimensionality of the phenotypic space, posing significant challenges for species with complex trait configurations. The study underscores the importance of genetic variation due to de novo mutations, local adaptation, and migration rates. These insights enhance our understanding of the factors that govern the adaptive potential of fragmented populations in response to severe environmental disturbances.