Regensburg 2007 – wissenschaftliches Programm

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BP: Fachverband Biologische Physik

BP 1: Evolutionary and Population Dynamics

BP 1.4: Vortrag

Montag, 26. März 2007, 11:00–11:15, H43

Stationary population distribution of quasispecies in fitness landscapes with multiple peaks — •Andrea Wolff and Joachim Krug — Universität zu Köln, Institut für theoretische Physik, Köln, Deutschland

We investigate the long time behaviour of the quasispecies model, as introduced by M. Eigen in 1971, in permutation invariant fitness landscapes. Examples include the multiplicative single peak Fujiyama landscape and a landscape with two peaks of different heights and widths. In the latter case, the competition between the two peaks leads to a first order ’selection transition’ at which the population shifts discontinuously from one peak to the other. In contrast to the well-known delocalization transition occuring at the error threshold, the mutation rate at the selection transition does not scale with the sequence length N as µ ∝ 1/N. As a consequence, recently developed functional integral methods for estimating the largest eigenvalue of the evolution matrix in the limit N → ∞ cannot be applied. Here we use direct diagonalization techniques to examine the nature of the selection transition and to find the correct scaling behaviour of the mutation rate with the sequence length.