Dynamic Mutation–Selection Balance as an Evolutionary Attractor

Abstract

The vast majority of mutations are deleterious and are eliminated by purifying selection. Yet in finite asexual populations, purifying selection cannot completely prevent the accumulation of deleterious mutations due to Muller's ratchet: once lost by stochastic drift, the most-fit class of genotypes is lost forever. If deleterious mutations are weakly selected, Muller's ratchet can lead to a rapid degradation of population fitness. Evidently, the long-term stability of an asexual population requires an influx of beneficial mutations that continuously compensate for the accumulation of the weakly deleterious ones. Hence any stable evolutionary state of a population in a static environment must involve a dynamic mutation-selection balance, where accumulation of deleterious mutations is on average offset by the influx of beneficial mutations. We argue that such a state can exist for any population size N and mutation rate U and calculate the fraction of beneficial mutations, e, that maintains the balanced state. We find that a surprisingly low e suffices to achieve stability, even in small populations in the face of high mutation rates and weak selection, maintaining a well-adapted population in spite of Muller's ratchet. This may explain the maintenance of mitochondria and other asexual genomes. P URIFYING selection maintains well-adapted genotypes in the face of deleterious mutations ). Yet in asexual populations, random genetic drift in the most-fit class of individuals will occasionally lead to its irreversible extinction, a process known as Muller's ratchet (Muller 1964;Felsenstein 1974). The repetitive action of the ratchet leads to the accumulation of deleterious mutations, despite the action of purifying selection. This ratchet effect has been extensively analyzed (Gessler 1995;Charlesworth and Charlesworth 1997; Gordo and Charlesworth 2000a,b; and has been observed in experiments (Chao 1990;Duarte et al. 1992;Andersson and Hughes 1996;Zeyl et al. 2001) and in nature (Rice 1994;Lynch 1996;Howe and Denver 2008). In small populations when deleterious mutation rates are high or selection pressures are weak, the ratchet can proceed quickly, causing rapid degradation of asexual genomes Lynch et al. , 1995. Hence Muller's ratchet has been described as a central problem for the maintenance of asexual populations such as mitochondria (Loewe 2006). Avoiding this mutational catastrophe is thought to be a major benefit of sex and recombination (see Barton and Charlesworth 1998 and De Visser and Elena 2007 for reviews).However, new studies indicate that natural and laboratory asexual populations do not always melt down as predicted. For example, recently showed that even very small laboratory populations of phage with high mutation rates tend toward fitness plateaus. In addition, a recent comparison of human, chimpanzee, and rhesus Y chromosomes demonstrated that after an initial period of degradation following the halt of recombination, gene loss in the human Y chromosome effectively stopped (Hughes et al. 2...

Tug-of-war between driver and passenger mutations in cancer and other adaptive processes

“…Occasionally, however, the population may acquire several new highly advantageous traits for this new environment, allowing it to rapidly expand its size and avert extinction. Both its evolutionary parameters (18) and behavior (38) mirror our model. Our mathematical framework further explains why these populations sometimes adapt, yet often fail.…”

“…Although the role of deleterious mutations in cancer is largely unknown, their effects on natural populations have been extensively studied in genetics (16)(17)(18). The accumulation of deleterious mutations can cause population extinction by Muller's ratchet and mutational meltdown (16,19).…”

Coalescence and genetic diversity in sexual populations under selection

“…We simulate the lattermost using a model with recurrent mutations such that the population settles into a dynamic equilibrium where the fixation of beneficial mutations is roughly canceled out by that of deleterious mutations (33). The predictions for neutral diversity, LD, and the SFS match the simulation results very well.…”

Genomic mutation rates that neutralize adaptive evolution and natural selection

“…Under these more realistic conditions, the fitness decline due to Muller's ratchet can be cancelled out or even reversed by beneficial mutations, resulting in unchanging or increasing fitness. The effect of beneficial mutations on Muller's ratchet has been explored previously [47][48][49]; these studies focused on how the effects and relative fractions of beneficial versus deleterious mutations would affect the adaptation rate and whether that rate was positive or negative. In this study, we focus on how the genomic mutation rate affects the progress of adaptive evolution and the effectiveness of natural selection.…”

“…Increasing the mutation rate, however, will often cause a subsequent increase in fitness variance, in turn increasing the mutation rate required to satisfy (2.1). In fact, classical population genetics (accounting for deleterious mutations only), and work by Rouzine et al [69,70] and Goyal et al [49] (accounting for beneficial and deleterious mutations) all indicate that, for low to moderate mutation rates, the fitness variance should tend towards ÀU d x following a perturbation in fitness and/or mutation rate. This suggests that an adjustment in the mutation rate (perhaps through increasing the dose of a mutagen, for example) to satisfy the condition ÀU d x .…”