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Muller's ratchet with overlapping generations

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Metzger,  Jakob J.
Department of Nonlinear Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Eule,  Stephan
Department of Nonlinear Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Metzger, J. J., & Eule, S. (2013). Muller's ratchet with overlapping generations. PLoS Computational Biology, 9(11): e1003303. doi:10.1371/journal.pcbi.1003303.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-0F99-D
Abstract
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.