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 Mutations and Sex


The effects of mutations on organisms are poorly understood; indeed the eminent population geneticist Brian Charlesworth said that his two questions to a fairy godmother of evolutionary genetics would be:
―First, what is the frequency distribution of selective effects among new mutations — how often do they have positive, negative or neutral selective effects, and how large are these effects? And second, what is the total rate per genome at which mutations that have a sizeable impact on fitness appear?‖ (Charlesworth, 1996)
Much work has been undertaken on these two problems, but as yet there is no consensus on the values due to a number of difficulties. The problem is further exacerbated by the differing predictions about the effects of neutral, beneficial and detrimental mutations on the evolution of sex.
As mentioned in the introduction, the theories about the advantages of sex can be widely grouped into those that are hypothesised to give a benefit to sexual reproduction by indirect or direct means (Kondrashov, 1993). The indirect hypotheses are more general and account for the evolution of sex by an advantage to removing an excess of non-adapted genotypes. As outlined in the introduction, they can be grouped into those in which the source of these genotypes is a changing environment, and those in which the source is detrimental mutations (Kondrashov, 1993). At present, little work has been undertaken to examine the relative effects of the two classes, and here I attempt to undertake an empirical examination of the effects of these two classes.
The goals above are to be achieved using Saccharomyces cerevisiae, modified as outlined in the introductory chapter so as to be isogenic except for the ability to undergo sex and an antibiotic marker. The system is further modified by the increase of mutation rate by knocking out MSH2, a gene involved in mismatch repair. The four resulting lines (sexual, asexual, sexual mutator and asexual mutator) were then evolved either in a benign media where no adaptation is expected and a harsh media, where copious adaptation is possible. By examining the differences in adaptation between the lines in the benign media, it is possible to see the differences between sex and asex in environments where the supply of maladapted individuals is due to detrimental mutations. By examining the differences in adaptation in the harsh environment it is possible to determine the differences when the supply is due to the ancestral lines being maladapted, as well as the impact of detrimental mutations

U, S and Adaptation

In order to understand the differences in adaptation and mutation clearance, it is first necessary to understand how they are commonly discussed in the literature. The two most useful parameters are U, the per genome mutation rate and s, the effect of a mutation

Per Genome Mutation Rate, U

Mutation rate per offspring per generation is a vital parameter for population geneticists, and is generally denoted by U. U can be subdivided into Ub and Us, the rate for beneficial and detrimental mutations respectively. Often simply U is used to denote only detrimental mutations, and Ub used for beneficial. This is the standard that will be used here. U is correlated to the per genome DNA mutation rate, but exact correspondence is not possible: not all mutations are visible to selection due to synonymous mutations, non-coding areas or simply causing too small of an effect. In addition U is obviously heavily environmentally dependent. If a mutation occurs in a gene only expressed under a certain stressful condition, there will be no selective effect until that condition is encountered, if it ever is. Despite its drawbacks, U is a vital population genetic parameter in a number of models of adaptation and evolution. The supply of either beneficial or detrimental mutations gives a strong limit on the rate of adaptive evolution and gives a good estimate for the genetic load that a population will carry.
U has a large effect on the genetic load carried by a population. In general, a population will show a mean fitness loss of U at equilibrium (Haldane, 1937). It is an interesting occurrence that this is independent of s, the average fitness effect of mutations. This is due to the ―one mutation one genetic death‖ effect elegantly shown by Muller (1950). Mutations arise at frequency U per generation, with mutational effect s. For a mutation with s of 0.05, the relative fitness of 0.95 is still high, and thus the individual is still likely to reproduce, with a reduction in offspring of 5%. Similarly, for anything but an s of 1 which is lost immediately, rather than immediate clearance on average the mutation will have its relative frequency decreased by a factor of s. Thus, the number of individuals carrying the mutation between the origin of a mutation and its subsequent clearance by selection is inversely proportional to s: 1/s. Each organism carrying the mutation pays the cost the mutation, so the mean loss of fitness over time is thus s×1/s which is equal to 1. The cost of 1 (one genetic death) per mutation irrespective of s leads to the population as a whole showing a reduction in fitness equal to U. As these values are averages and U depends on the environment, it can be seen that the exact genetic load may fluctuate by chance and can take some time to find its equilibrium after the population enters a new environment. For a large U (>1) the population will head towards extinction in the absence of mitigating factors. The presence or absence of sex is one of these.
Ub has a smaller effect on the beneficial adaptation than U on load. The supply of beneficial mutations allows adaptive evolution, if Ub is 0, then no adaptive mutations will occur and the population is in evolutionary stasis. In contrast, a Ub which is greater than 0 allows for adaptive evolution. If Ub is sufficiently high, multiple beneficial mutations will be segregating at once. This leads to clonal interference and the FM effect, as detailed below

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The Effect of Mutations, s

A related parameter is s, the selection coefficient or net effect of a mutation. s can be used as a measure of the effects of an individual mutation, the average effect of all mutations that can occur, or a measure of the distribution of mutational effects. These are related to organismal fitness, where 1.00 is the average population fitness, and s is given as an addition or subtraction to that fitness to give a relative fitness of an individual carrying that mutation. For example, an individual carrying a detrimental mutation with s of 0.05 has a fitness of 1-s = 0.95 compared to the average individual. The distribution and mean effect of s for both positive and detrimental mutations has a large effect on the evolutionary dynamics of a population.
The effects of s on adaptation are less clear. A large s for detrimental mutations should lead to more rapid clearance of detrimental mutations, but as outlined above the total load should stay the same as it is dependent only on U. Of interest is the number of mutations in an average individual under equilibrium genetic load. A large U allows more mutations to coexist in individuals. The exact distribution of mutations in individuals at equilibrium is likely to be complex (Eyre-Walker & Keightley, 2007). This has been modelled by a number of authors using the extreme value theorem, for a review; see Orr (2005). The number of mutations present becomes vital once theories incorporating epistasis and truncation are introduced.
The effects of the distribution of beneficial mutations are clearer. A large positive s results in quicker fixation of a mutation. Formula 2.4 (more detail below) details the exact relationship. If s is sufficiently large, the new mutation can fix before another beneficial mutation occurs, thus avoiding clonal interference. In contrast smaller s can lead to a number of smaller beneficial mutations coexisting, with the population being a mixture of a number of varying lines, all consisting of a number of difference beneficial mutations in combination (Gerrish & Lenski, 1998). The polymorphism in an asexual population can be extreme, and sexual reproduction will often serve to reduce this diversity.

Sex, U and S

The interaction of sex with U and s is of interest in that it can provide a way to mitigate some of the costs of sex, dependent on the exact values of the parameters. Here I will outline in more detail some of the theories only given a brief overview in the introductory chapter

 Deterministic Mutation Hypothesis

The deterministic mutation hypothesis (DMH) provides an advantage for sex by reduction of genetic load. As it is one of the most predictive and potentially universal theories for the evolution of sex (Meirmans & Strand, 2010) it is one of the favoured possible explanations. The theory was first proposed by Kondrashov (1982) and subsequently much expanded upon. As the deterministic epithet in its name suggests, it is deterministic – independent of stochastic processes in the population. The basic mechanism is that detrimental mutations can be removed together rather than singly if epistasis is synergistic, thus reducing genetic load. The benefit relies only on the magnitude of U and the degree of epistasis, and if these conditions are met provides a benefit to sexual reproduction. The theory makes strong predictions about the benefits of sex giving sex a 2 fold advantage (enough to overcome the commonly invoked 2 fold cost of sex in anisogamous organisms) if U is greater than 1 and epistasis is on average weak and synergistic.
Epistasis is the interaction of mutations, and can take several forms. Under synergistic epistasis each detrimental mutation has an increased effect on fitness of the individual. Kondrashovs‘ original formulation (Kondrashov, 1982) gives the fitness of an individual with i mutations of equal effect as:
Where k is the number of mutations which cause a fitness cost of 1 (i.e. lethality) and is the epistasis coefficient (Figure 2.1). An α of <1 gives antagonistic epistasis, 1 gives linear selection, >1 gives synergistic epistasis, and ∞ gives threshold selection.
Synergistic epistasis can also be described as a ―buffering‖ of fitness as when the number of mutations is low, the total fitness cost is less

2.2 AIMS

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