Stochastic dynamics of adaptive trait and neutral marker driven by eco-evolutionary feedbacks

How the neutral diversity is affected by selection and adaptation is investigated in an eco-evolutionary framework. In our model, we study a finite population in con-tinuous time, where each individual is characterized by a trait under selection and a completely linked neutral marker. Population dynamics are driven by births and deaths, mutations at birth, and competition between individuals. Trait values influ-ence ecological processes (demographic events, competition), and competition gener-ates selection on trait variation, thus closing the eco-evolutionary feedback loop. The demographic effects of the trait are also expected to influence the generation and main-tenance of neutral variation. We consider a large population limit with rare mutation, under the assumption that the neutral marker mutates faster than the trait under selection. We prove the convergence of the stochastic individual-based process to a new measure-valued diffusive process with jumps that we call Substitution Fleming-Viot Process (SFVP). When restricted to the trait space this process is the Trait Substitution Sequence first introduced by Metz et al. (1996). During the invasion of