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DY: Fachverband Dynamik und Statistische Physik

DY 46: Stochastic Dynamics of Growth Processes in Biological and Social Systems (joint session SOE/BP)

DY 46.8: Vortrag

Freitag, 4. April 2014, 11:45–12:00, GÖR 226

Clonal interference and Muller’s ratchet in spatial habitats — Jakub Otwinowski¹ and •Joachim Krug² — ¹Biology Department, University of Pennsylvania, Philadelphia, USA — ²Institute for Theoretical Physics, University of Cologne, Cologne, Germany

Competition between independently arising beneficial mutations is enhanced in spatial populations due to the linear rather than exponential growth of the clones. The resulting fitness dynamics is analogous to a surface growth process, where new layers nucleate and spread stochastically, leading to the build up of scale-invariant roughness. This scenario differs qualitatively from the standard view of adaptation in that the speed of adaptation becomes independent of population size while the fitness variance does not, in apparent violation of Fisher’s fundamental theorem. Here we exploit recent progress in the understanding of surface growth processes to obtain precise results for the universal, non-Gaussian shape of the fitness distribution for one-dimensional habitats. We then consider a version of the model where all mutations are deleterious, that is, a spatial version of Muller’s ratchet. Based on an analogy to models of nonequilibrium wetting, we show that the system displays a phase transition related to directed percolation. The transition is governed by the ratio U/s², where U denotes the deleterious mutation rate and s the selection coefficient of mutations. For U/s² > 1 the speed of the ratchet remains finite in the limit of infinite habitat size.