Distribution of the Fittest Individuals and the Rate of Muller's Ratchet in a Model with Overlapping Generations

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.

Clonal interference and Mullerʼs ratchet in spatial habitats

“…the probability of fixation of an additional deleterious mutation in this class is exponentially small. Detailed analysis shows that under condition (4) the rate of Muller's ratchet is also exponentially small in N [21, 23,25], whereas for n 0 |s| < 1 the fitness of the population declines continuously, and a description in terms of a traveling wave in fitness space, similar to that used in the context of adaptation (s > 0), is applicable [11]. Importantly, for a given set of mutation parameters (U d , s) the slow ratchet condition (4) is always attained for large populations, which implies that the fitness decline effectively ceases for N → ∞.…”

Mitochondrial complementation: a possible neglected factor behind early eukaryotic sex

“…Muller's ratchet, the irreversible accumulation of deleterious mutations in asexual genomes, is typically studied by tracking the dynamics of the loss of the least‐mutated class – that is to say, by focusing on the number of mutations, not their identity (e.g. in mitochondria: Bergstrom & Pritchard, ; Metzger & Eule, ; Christie & Beekman, ; Radzvilavičius et al ., ; though see Gordo et al ., ; for a model of neutral genetic diversity in a ratchet setting). However, a mutational class (i.e.…”

Evolutionary algorithms and synthetic biology for directed evolution: commentary on “on the mapping of genotype to phenotype in evolutionary algorithms” by Peter A. Whigham, Grant Dick, and James Maclaurin

“… When the population size is too small, some individuals who may yet contribute to optimality are simply squeezed out (especially in mutation-only organisms); this is known as Muller’s ratchet (e.g. [ 6 – 8 ]). Weak mutation and strong selection (see [ 9 – 14 ]) is common in many ecosystems, and traps individuals and populations in local minima (or maxima) from which neutral evolution cannot help them escape.…”

“…When the population size is too small, some individuals who may yet contribute to optimality are simply squeezed out (especially in mutation-only organisms); this is known as Muller’s ratchet (e.g. [ 6 – 8 ]).…”