An individual-based model for the Lenski experiment, and the deceleration of the relative fitness

Vortrag von Prof. Dr. Noemi Kurt

Sprecher eingeladen von: Prof. Dr. Jean Bertoin

Datum: 14.03.18  Zeit: 17.15 - 19.00  Raum: Y27H12

The Lenski experiment investigates the long-term evolution of bacterial populations. Its design allows the direct comparison of the reproductive fitness of an evolved strain with its founder ancestor. It was observed by Wiser et al. (2013) that the mean fitness over time increases sublinearly, a behaviour which in the biological literature is commonly attributed to effects like clonal interference or epistasis. In this talk we present an individual-based probabilistic model that captures essential features of the design of the Lenski experiment. We assume that each beneficial mutation increases the individual reproduction rate by a fixed amount, which corresponds a priori to the absence of epistasis. Using an approximation by near-critical Galton-Watson processes, we prove that under some assumptions on the model parameters which exclude clonal interference, the relative fitness process derived from the microscopic model converges, after suitable rescaling, in the large population limit to a power law function. This is joint work with Adrián González Casanova, Anton Wakolbinger, and Linglong Yuan.