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Background: The accumulation of deleterious mutations of a populationdirectly contributes to the fate as to how long the population would exist, aprocess often described as Muller's ratchet with the absorbing phenomenon. Thekey to understand this absorbing phenomenon is to characterize the decayingtime of the fittest class of the population. Adaptive landscape introduced byWright, a re-emerging powerful concept in systems biology, is used as a tool todescribe biological processes. To our knowledge, the dynamical behaviors forMuller's ratchet over the full parameter regimes are not studied from the pointof the adaptive landscape. And the characterization of the absorbing phenomenonis not yet quantitatively obtained without extraneous assumptions as well.  Results: We describe the dynamical behavior of the population exposed toMuller's ratchet in all parameters regimes by adaptive landscape. The adaptivelandscape has rich structures such as finite and infinite potential, real andimaginary fixed points. We give the formula about the single click time withfinite and infinite potential. And we find the single click time increases withselection rates and population size increasing, decreases with mutation ratesincreasing. These results provide a new understanding of infinite potential. Weanalytically demonstrate the adaptive and unadaptive states for the wholeparameters regimes. Interesting issues about the parameters regions with theimaginary fixed points is demonstrated. This can help understand the biologicalmeaning of the critical points such as the intersection points of regimes. Mostimportantly, we find that the absorbing phenomenon is characterized by theadaptive landscape and the single click time without any extraneousassumptions. These results suggest a graphical and quantitative framework tostudy the absorbing phenomenon.

Absorbing Phenomena and Escaping Time for Muller's Ratchet in Adaptive Landscape