A dynamical phase transition in a model for evolution with migration
A dynamical phase transition in a model for evolution with migration
- Event time: 1:00pm
- Event date: 21st March 2011
- Speaker: Dr Bartlomiej Waclaw (School of Physics & Astronomy, University of Edinburgh)
- Location: Room 2511, James Clerk Maxwell Building (JCMB) James Clerk Maxwell Building Peter Guthrie Tait Road Edinburgh EH9 3FD GB
Event details
Biological dispersal---the movement of organisms between habitats---is a ubiquitous phenomenon with important and wide-ranging consequences. In the natural environment, organisms expand their ranges, colonise new habitats, and can undergo speciation if they become spatially isolated. Therefore, dispersal plays a key role in determining spatial and temporal patterns of genetic diversity. It has been pointed out recently, that migration from a favourable habitat to an unfavourable one can explain the genetics of some pathogenic microbes and viruses. However, despite its importance, a general understanding of how migration affects mutation-selection balance in microbial systems is lacking. In particular, one would like to know how migration changes the proportions of different genotypes in the evolving population. Here I will discuss a simple model for evolution of asexual organisms in two different habitats, with different fitness landscapes, coupled through one-way migration. The key finding is a dynamical phase transition at a critical value of the migration rate. The time to reach steady state diverges at this critical migration rate. 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 quasi-species 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.
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This is a weekly series of informal talks given primarily by members of the institute of condensed matter and complex systems, but is also open to members of other groups and external visitors. The aim of the series is to promote discussion and learning of various topics at a level suitable to the broad background of the group. Everyone is welcome to attend..