Abstract
BackgroundThe accumulation of deleterious mutations of a population directly contributes to the fate as to how long the population would exist, a process often described as Muller's ratchet with the absorbing phenomenon. The key to understand this absorbing phenomenon is to characterize the decaying time of the fittest class of the population. Adaptive landscape introduced by Wright, a re-emerging powerful concept in systems biology, is used as a tool to describe biological processes. To our knowledge, the dynamical behaviors for Muller's ratchet over the full parameter regimes are not studied from the point of the adaptive landscape. And the characterization of the absorbing phenomenon is not yet quantitatively obtained without extraneous assumptions as well.MethodsWe describe how Muller's ratchet can be mapped to the classical Wright-Fisher process in both discrete and continuous manners. Furthermore, we construct the adaptive landscape for the system analytically from the general diffusion equation. The constructed adaptive landscape is independent of the existence and normalization of the stationary distribution. We derive the formula of the single click time in finite and infinite potential barrier for all parameters regimes by mean first passage time.ResultsWe describe the dynamical behavior of the population exposed to Muller's ratchet in all parameters regimes by adaptive landscape. The adaptive landscape has rich structures such as finite and infinite potential, real and imaginary fixed points. We give the formula about the single click time with finite and infinite potential. And we find the single click time increases with selection rates and population size increasing, decreases with mutation rates increasing. These results provide a new understanding of infinite potential. We analytically demonstrate the adaptive and unadaptive states for the whole parameters regimes. Interesting issues about the parameters regions with the imaginary fixed points is demonstrated. Most importantly, we find that the absorbing phenomenon is characterized by the adaptive landscape and the single click time without any extraneous assumptions. These results suggest a graphical and quantitative framework to study the absorbing phenomenon.
Highlights
The accumulation of deleterious mutations of a population directly contributes to the fate as to how long the population would exist, a process often described as Muller’s ratchet with the absorbing phenomenon
We study the dynamical behaviors by investigating the position and adaptiveness of all fixed points
We have not found any study of Muller ratchet for the fixed points to give a complete description
Summary
The accumulation of deleterious mutations of a population directly contributes to the fate as to how long the population would exist, a process often described as Muller’s ratchet with the absorbing phenomenon. The key to understand this absorbing phenomenon is to characterize the decaying time of the fittest class of the population. The characterization of the absorbing phenomenon is not yet quantitatively obtained without extraneous assumptions as well. Muller’s ratchet proposed in 1964 is that the genome of an asexual population accumulates deleterious mutations in an irreversible manner. In order to assess the relevance of Muller’s ratchet, it is necessary to determine the rate (or the time) for the accumulation of deleterious mutations [10]. It has been a long interest to develop a suitable and quantitative theory for the ratchet mechanism and the incidental absorbing phenomenon
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