Dynamics of fixation of advantageous mutations

We investigate the process of fixation of advantageous mutations in an asexual population. We assume that the effect of each beneficial mutation is exponentially distributed with mean value omega(med) = 1/beta. The model also considers that the effect of each new deleterious mutation reduces the fitness of the organism independent on the previous number of mutations. We use the branching process formulation and also extensive simulations to study the model. The agreement between the analytical predictions and the simulational data is quite satisfactory. Surprisingly, we observe that the dependence of the probability of fixation P-fix on the parameter omega(med) is precisely described by a power-law relation, P-fix similar to omega(med). The exponent gamma is an increasing function of the rate of deleterious mutations U, whereas the probability P-fix is a decreasing function of U. The mean value omega(fix) of the beneficial mutations which reach ultimate fixation depends on U and omega(med). The ratio omega(fix)/omega(med) increases as we consider higher values of mutation value U in the region of intermediate to large values of omega(med), whereas for low omega(med) we observe the opposite behavior. (C) 2004 Elsevier B.V. All rights reserved.