1302.3439 (Jakob J. Metzger et al.)

Muller's ratchet with overlapping generations    [PDF]

Jakob J. Metzger, Stephan Eule

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 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 show numerically that the formulation with overlapping generations leads to similar results as the standard model with non-overlapping generations and the diffusion approximation in the regime where the ratchet clicks frequently. For parameter values closer to the rare clicking regime, however, we find that the rate of Muller's ratchet strongly depends on the microscopic reproduction model.

View original: http://arxiv.org/abs/1302.3439