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DY: Fachverband Dynamik und Statistische Physik

DY 32: Statistical Physics in Biological Systems III (organised by BP)

DY 32.8: Talk

Thursday, March 17, 2011, 12:30–12:45, ZEU 260

A dynamical phase transition in a model for evolution with migration — •Bartlomiej Waclaw, Rosalind Allen, and Martin Evans — Department of Physics & Astronomy, University of Edinburgh, JCMB, The King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, United Kingdom

Migration between different habitats is ubiquitous among biological populations. Here I will discuss a simple model for evolution of asexual organisms in two different habitats coupled by one-way migration as well as mutations. This gives rise to clusters of closely related genotypes (quasispecies). The habitats are assumed to have different fitness landscapes, i.e., organisms which are well-adapted in the primary habitat are likely to be maladapted in the secondary habitat. The model undergoes a dynamical phase transition: at a critical value of the migration rate, the time to reach the steady state diverges. Above the transition, the population is dominated by immigrants from the primary habitat. Below the transition, the genetic composition of the population is highly non-trivial, with multiple coexisting "quasispecies" which are not native to either habitat. Using results from localization theory, I will show that the critical migration rate may be very small --- demonstrating that evolutionary outcomes can be very sensitive to even a small amount of migration.