t$ turns positive, while the expected number of fixed mutants, shown in Figure \[figure:figNmutants\]b, increases.

![\[figure:figNmutants\] a: Expected increase in fitness due to introduction of mutants as a function of time between their introduction. b: Expected number of fixed mutants (panel b) as a function of $\Delta t$ ($s_{1}=0.1$, $s_{2}=0.5$, $u=0.0$, $N=1000$, for a and batt). Solid line in panel (a) is expected result according to fixation probabilities given by Eq. (\[tanh-ansatz\]).](Figure6.eps){width="10cm"}

Discussion
==========

The rate of adaptation of a non-recombining chromosome or asexual population is a non-trivial quantity that depends on details of the fitness distribution of mutations. Beneficial mutations often take a long time to dominate in a population, and compete against each other in the background of deleterious mutations. The probability of fixation of any one mutation depends on the time of their introduction, stochastic drift, and the prevalent mutation rate. A good understanding of the rate of adaptation of asexuals is important in molecular phylogeny, because it influences the speed of the assumed molecular clock [@KuhnerFelsenstein1994]. Since successive fixation events determine the branchings in the phylogenetic tree, a stochastic analysis of the fixation probability of competing mutations can provide insight into models of evolution used for 