Berlin 2012 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 9: Statistical Physics of Biological Systems II (with BP, talks from BP)
DY 9.1: Talk
Monday, March 26, 2012, 15:00–15:15, H 1058
The probability of parallel evolution — •Joachim Krug1, Ivan G. Szendro1, Martijn F. Schenk2,3, and J. Arjan G.M. de Visser3 — 1Institut für Theoretische Physik, Universität zu Köln, Germany — 2Institut für Genetik, Universität zu Köln, Germany — 3Laboratory for Genetics, Wageningen University, Netherlands
The question whether evolutionary processes are repeatable is of central importance in evolutionary biology and continues to be vigorously debated. In a simple version of this problem introduced by Orr, one considers a situation where n beneficial mutations are available to an organism and asks for the probability P that the same mutation is fixed in two replicate populations. When the fitness values are drawn from a distribution that belongs to the Gumbel domain of attraction, Orr showed that P=2/(n+1), about twice the neutral expectation 1/n that would apply if all mutations were equally likely to fix. Motivated by recent experiments that observed a heavy-tailed distribution of fitness effects in an antibiotic resistance gene, we extend Orr’s analysis to distributions of selection coefficients s of Pareto form, f(s) ∼ s−(α+1). Using an approach from the statistical physics of disordered systems, we show that the probability of parallel evolution is dramatically enhanced when α < 2, with P ∼ n−(2−α) for 1 < α < 2 and P = const. for α < 1. We also briefly address the influence of population size on the probability of parallel evolution.