%0 Book Section %1 statphys23_0203 %A Park, S.C. %A Krug, J. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K asexually clonal dispersion fixation index interference model organisms reproducing statphys23 topic-10 wright-fisher %T Clonal interference in large populations %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=203 %X The common forces shaping the evolution of biological organisms on earth are mutation, selection, and genetic drift arising from sampling noise in the reproduction process. A decent theory of evolution should incorporate all three features. In addition, the possible effects of recombination must be taken into account. If there is no recombination, as in asexually reproducing organisms such as bacteria or viruses, beneficial mutations which appear almost at the same time compete against each other for fixation, which is not the case in organisms with recombination. This phenomenon is referred to as clonal interference (CI). The theory of CI developed by Gerrish and Lenski (GL) in a seminal paper 1 is based on two crucial assumptions - the absence of multiple mutations and the independence of genetic drift and CI - which are both expected to become invalid in very large populations. To assess the range of validity of the GL theory, we studied the Wright-Fisher model of non-overlapping discrete generations with multiplicative fitnesses numerically for finite populations, and analytically in the deterministic limit of infinite population size. We found that when the population size is very large, the GL theory deviates significantly from the simulation results. In particular, the prediction of Gerrish 2 for the reduction of the index of dispersion (the ratio of the variance to the mean) of the number of fixed mutations in the CI regime is not compatible with our findings. We show that, for large populations, a distinction has to be made between the number of substitution events and the number of fixed mutations, and we predict the limiting values of the index of dispersion for these two quantities. Moreover, our simulations partly explain why the GL theory, despite it shortcomings, has provided a reasonable interpretation of microbial evolution experiments. 1) P.J. Gerrish and R.E. Lenski, Genetica 102/103, 127 (1998).\\ 2) P.J. Gerrish, Nature 413, 299 (2001).

@incollection{statphys23_0203, abstract = {The common forces shaping the evolution of biological organisms on earth are mutation, selection, and genetic drift arising from sampling noise in the reproduction process. A decent theory of evolution should incorporate all three features. In addition, the possible effects of recombination must be taken into account. If there is no recombination, as in asexually reproducing organisms such as bacteria or viruses, beneficial mutations which appear almost at the same time compete against each other for fixation, which is not the case in organisms with recombination. This phenomenon is referred to as clonal interference (CI). The theory of CI developed by Gerrish and Lenski (GL) in a seminal paper [1] is based on two crucial assumptions - the absence of multiple mutations and the independence of genetic drift and CI - which are both expected to become invalid in very large populations. To assess the range of validity of the GL theory, we studied the Wright-Fisher model of non-overlapping discrete generations with multiplicative fitnesses numerically for finite populations, and analytically in the deterministic limit of infinite population size. We found that when the population size is very large, the GL theory deviates significantly from the simulation results. In particular, the prediction of Gerrish [2] for the reduction of the index of dispersion (the ratio of the variance to the mean) of the number of fixed mutations in the CI regime is not compatible with our findings. We show that, for large populations, a distinction has to be made between the number of substitution events and the number of fixed mutations, and we predict the limiting values of the index of dispersion for these two quantities. Moreover, our simulations partly explain why the GL theory, despite it shortcomings, has provided a reasonable interpretation of microbial evolution experiments. 1) P.J. Gerrish and R.E. Lenski, Genetica {\bf 102/103}, 127 (1998).\\ 2) P.J. Gerrish, Nature {\bf 413}, 299 (2001).}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Park, S.C. and Krug, J.}, biburl = {https://www.bibsonomy.org/bibtex/2bbc272dca5f8de34942ac1005a4c3653/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {a9bb82b0791f06df786cce40fd13d3bd}, intrahash = {bbc272dca5f8de34942ac1005a4c3653}, keywords = {asexually clonal dispersion fixation index interference model organisms reproducing statphys23 topic-10 wright-fisher}, month = {9-13 July}, timestamp = {2007-06-20T10:16:14.000+0200}, title = {Clonal interference in large populations}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=203}, year = 2007 }