We examine birth--death processes with state dependent transition
probabilities and at least one absorbing boundary. In evolution, this describes
selection acting on two different types in a finite population where
reproductive events occur successively. If the two types have equal fitness the
system performs a random walk. If one type has a fitness advantage it is
favored by selection, which introduces a bias (asymmetry) in the transition
probabilities. How long does it take until advantageous mutants have invaded
and taken over? Surprisingly, we find that the average time of such a process
can increase, even if the mutant type always has a fitness advantage. We
discuss this finding for the Moran process and develop a simplified model which
allows a more intuitive understanding. We show that this effect can occur for
weak but non--vanishing bias (selection) in the state dependent transition
rates and infer the scaling with system size. We also address the Wright-Fisher
model commonly used in population genetics, which shows that this stochastic
slowdown is not restricted to birth-death processes.Comment: 8 pages, 3 figures, accepted for publicatio
