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DY: Fachverband Dynamik und Statistische Physik

DY 36: Statistical Physics in Biological Systems IV (organised by BP)

DY 36.10: Vortrag

Donnerstag, 17. März 2011, 16:30–16:45, ZEU 260

A Non-Equillibrium Phase Transition in Expanding Populations — •Jan-Timm Kuhr and Erwin Frey — Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München

Recently, expanding bacterial populations found much attention in both experimental and theoretical work [1]. These “range expansions” have interesting statistical properties, as constant genetic re-sampling from a small population at the expanding front induces strong fluctuations. The influence of non-neutral mutations on the dynamics is less well studied. Here, we introduce an extension of the Eden model [2], including mutations. Using Monte Carlo simulations, we analyze the interplay of kinetic surface roughening, mutations and selection at the front. While beneficial mutations always take over the front eventually, for detrimental mutations one finds two generic cases: if rare, mutant sectors are independent and wild types prevail. If mutants spawn more frequently, sectors coalesce and wild types are soon lost in the bulk. Between these regimes one finds self-affine patterns, and we identify a non-equilibrium phase transition. We measure critical exponents near this transition, and find universal scaling behavior for this model of evolution in expanding populations.

[1] O. Hallatschek and D. Nelson, Life at the front of an expanding population. Evolution, 64, 193-206, (2010) – [2] M. Eden, A two-dimensional growth process, Proc. of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, 4, 223-239, (1960)