Distribution of the fittest individuals and the rate of Muller's ratchet in a model with overlapping generations.
Muller's ratchet is a paradigmatic model for the accumulation of deleterious mutations in a population of finite size. A click of the ratchet occurs when all individuals with the least number of deleterious mutations are lost irreversibly due to a stochastic fluctuation. In spite of the simplicity of the model, a quantitative understanding of the process remains an open challenge. In contrast to previous works, we here study a Moran model of the ratchet with overlapping generations. Employing an approximation which describes the fittest individuals as one class and the rest as a second class, we obtain closed analytical expressions of the ratchet rate in the rare clicking regime. As a click in this regime is caused by a rare, large fluctuation from a metastable state, we do not resort to a diffusion approximation but apply an approximation scheme which is especially well suited to describe extinction events from metastable states. This method also allows for a derivation of expressions for the quasi-stationary distribution of the fittest class. Additionally, we confirm numerically that the formulation with overlapping generations leads to the same results as the diffusion approximation and the corresponding Wright-Fisher model with non-overlapping generations.
Max Planck Institute for Dynamics and Self-Organization (MPIDS), Göttingen, Germany ; Institute for Nonlinear Dynamics, Department of Physics, University of Göttingen, Göttingen, Germany.
Jakob J
JJ
Metzger
Stephan
S
Eule
D019295:Computational Biology; D019143:Evolution, Molecular; D056084:Genetic Fitness / Q000235:genetics*; D008957:Models, Genetic; D009154:Mutation / Q000235:genetics*; D012641:Selection, Genetic / Q000235:genetics*