Tempo and mode in quasispecies evolution

Abstract

Evolutionary dynamics in an uncorrelated rugged fitness landscape is studied in the framework of Eigen's molecular quasispecies model. We consider the case of strong selection, which is analogous to the zero temperature limit in the equivalent problem of directed polymers in random media. In this limit the population is always localized at a single temporary master sequence σ * (t), and we study the statistical properties of the evolutionary trajectory which σ * (t) traces out in sequence space. Numerical results for binary sequences of length N = 10 and exponential and uniform fitness distributions are presented. Evolution proceeds by intermittent jumps between local fitness maxima, where high lying maxima are visited more frequently by the trajectories. The probability distribution for the total time T required to reach the global maximum shows a T −2 -tail, which is argued to be universal and to derive from near-degenerate fitness maxima. The total number of jumps along any given trajectory is always small, much smaller than predicted by the statistics of records for random longranged evolutionary jumps. * Permanent address.

Quasispecies evolution in general mean-field landscapes

“…I shall describe the evolutionary dynamics in the "thermodynamic limit" introduced in refs. [10,11], which is close in spirit to the strong selection limit considered by Krug [12] to treat the transient in quasispecies evolution as a form of extremal dynamics.…”

High power, 1060-nm diode laser with an asymmetric hetero-waveguide

“…the free trajectory with the largest slope (with respect to the time axis) becomes the rightmost trajectory-was studied recently [21,27]. It was estimated that its pdf has a power-law tail p(T e ) ∼ T −2 e .…”

Characteristic time in quasispecies evolution

“…Most of the models in which this problem has been examined are stochastic in nature. In this context different times have been defined, for instance, the searching time and fixation time (Traulsen et al, 2007;Gokhale et al, 2009;Stich et al, 2007;Stich and Manrubia, 2011), the evolution time (Krug and Karl, 2003) the adaptation time (Stich et al, 2007), the crossover time, the jump time, the residence time and the tunneling time (Jain and Krug, 2007;Krug, 2002).…”