Characteristic time in quasispecies evolution

Abstract

The time a phenotype takes to achieve a stationary state from an initial condition depends on multiple factors. In particular, it is a function of both its fitness and its mutation rate. We evaluate the average time, referred to as the characteristic time, Tc, that the system takes to reach a final steady state of simple models of populations formed by self-replicative sequences. The dependence of Tc on the mutation rate and on the fitness landscape is also studied. For simple fitness landscapes, e.g. single peak, the characteristic time can be analytically obtained as a function of the system parameters. In this case, Tc for obtaining the quasispecies distribution presents a maximum at a Q-value that depends on the initial conditions and decreases monotonously as the mutation rate tends to zero. For most of the complex landscapes handled in this paper, the characteristic time to achieve the quasispecies distribution picked around the fittest phenotype attains a local minimum for a given mutation rate between 0 and the Q-value at which Tc reaches its local maximum. Thus, in these cases, an optimum value for the mutation rate exists that corresponds to the lowest value of the characteristic time for quasispecies evolution.