We consider a model of a population of fixed size N undergoing selection.
Each individual acquires beneficial mutations at rate μN​, and each
beneficial mutation increases the individual's fitness by sN​. Each
individual dies at rate one, and when a death occurs, an individual is chosen
with probability proportional to the individual's fitness to give birth. Under
certain conditions on the parameters μN​ and sN​, we show that the
genealogy of the population can be described by the Bolthausen-Sznitman
coalescent. This result confirms predictions of Desai, Walczak, and Fisher
(2013), and Neher and Hallatschek (2013).Comment: 54 page