Calculation of the relative density and the crossing time through the fitness barrier in an asymmetric sharply-peaked landscape

摘要

We have calculated the relative density and crossing time through the fitness barrier by switching on an asymmetric sharply-peaked landscape, from the initial state which is the quasispecies in a sharply-peaked landscape. It is found that the increment of the relative density with the reversal sequence is a linearly increasing function of time unless a new stationary state in an asymmetric sharply-peaked landscape is reached. It is also found that the relative density with the reversal sequence at the new stationary state X-L(*) is in inverse proportion to the asymmetric parameter when the asymmetric L parameter is greater than the saturation asymmetric parameter. We have derived the approximate formulae for the relaxation time, the saturation asymmetric parameter, and the relative density with the reversal sequence X-L(*) which nicely fit computer simulation L results. It is found that the crossing time diverges at the critical fitness parameter in the asymmetric sharply-peaked landscape, in contrast with the symmetric sharply-peaked landscape where the crossing time scales as a power law in the fitness parameter. It is also found that the critical fitness parameter decreases as the asymmetric parameter and sequence length increase.