  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, $P_{fix} \sim \omega_{med}^{\gamma}$. The
exponent $\gamma$ is an increase 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.
