  Background: The accumulation of deleterious mutations of a population
directly contributes to the fate as to how long the population would exist.
Muller's ratchet provides a quantitative framework to study the effect of
accumulation. Adaptive landscape as a powerful concept in system biology
provides a handle to describe complex and rare biological events. In this
article we study the evolutionary process of a population exposed to Muller's
ratchet from the new viewpoint of adaptive landscape which allows us estimate
the single click of the ratchet starting with an intuitive understanding.
  Methods: We describe how Wright-Fisher process maps to Muller's ratchet. We
analytically construct adaptive landscape from general diffusion equation. It
shows that the construction is dynamical and the adaptive landscape is
independent of the existence and normalization of the stationary distribution.
We generalize the application of diffusion model from adaptive landscape
viewpoint.
  Results: We develop a novel method to describe the dynamical behavior of the
population exposed to Muller's ratchet, and analytically derive the decaying
time of the fittest class of populations as a mean first passage time. Most
importantly, we describe the absorption phenomenon by adaptive landscape, where
the stationary distribution is non-normalizable. These results suggest the
method may be used to understand the mechanism of populations evolution and
describe the biological processes quantitatively.
