Europhys. Lett.
Volume 76, Number 1, October 2006
Page(s) 1 - 7
Section General
Published online 01 September 2006
Europhys. Lett., 76 (1), pp. 1-7 (2006)
DOI: 10.1209/epl/i2006-10224-4

Noisy traveling waves: Effect of selection on genealogies

E. Brunet1, B. Derrida1, A. H. Mueller2 and S. Munier3

1  Laboratoire de Physique Statistique, École Normale Supérieure 24 rue Lhomond, 75231 Paris cedex 05, France
2  Department of Physics, Columbia University - New York, NY 10027, USA
3  Centre de Physique Théorique, Unité mixte de recherche du CNRS (UMR 7644) École Polytechnique - 91128 Palaiseau, France

received 5 July 2006; accepted in final form 2 August 2006
published online 1 September 2006

For a family of models of evolving population under selection, which can be described by noisy traveling-wave equations, the coalescence times along the genealogical tree scale like $\ln^\alpha N$, where N is the size of the population, in contrast with neutral models for which they scale like N. An argument relating this time scale to the diffusion constant of the noisy traveling wave leads to a prediction for $\alpha$ which agrees with our simulations. An exactly soluble case gives trees with statistics identical to those predicted for mean-field spin glasses by Parisi's theory.

02.50.-r - Probability theory, stochastic processes, and statistics.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
89.75.Hc - Networks and genealogical trees.

© EDP Sciences 2006