The balance between mutators and nonmutators in asexual populations

Mutator alleles, which elevate an individual's mutation rate from 10 to 10,000-fold, have been found at high frequencies in many natural and experimental populations. Mutators are continually produced from nonmutators, often due to mutations in mismatch-repair genes. These mutators gradually accumulate deleterious mutations, limiting their spread. However, they can occasionally hitchhike to high frequencies with beneficial mutations. We study the interplay between these effects. We first analyze the dynamics of the balance between the production of mutator alleles and their elimination due to deleterious mutations. We find that when deleterious mutation rates are high in mutators, there will often be many "young," recently produced mutators in the population, and the fact that deleterious mutations only gradually eliminate individuals from a population is important. We then consider how this mutator-nonmutator balance can be disrupted by beneficial mutations and analyze the circumstances in which fixation of mutator alleles is likely. We find that dynamics is crucial: even in situations where selection on average acts against mutators, so they cannot stably invade, the mutators can still occasionally generate beneficial mutations and hence be important to the evolution of the population.     

Inbreeding depression in an asexual population of Mimulus guttatus

The reproductive mechanism, that is whether an organism outcrosses, selfs or asexually reproduces, has a substantial impact on the amount and pattern of genetic variation. In this study, we estimate genetic variation and genetic load for a predominately asexual population of Mimulus guttatus, and then compare our results to other studies of predominately sexually reproducing (outcrossing and selfing) populations of M. guttatus. The asexual population had low levels of heterozygosity (H_e = 0.03) and low (but significantly non‐zero) inbreeding load, especially when compared with other M. guttatus populations. This differs greatly from the sexual populations of Mimulus that display substantial inbreeding depression. We discuss a variety of reasons why we see such low load in this study and suggest future research projects to further explore the questions.     

The degeneration of asexual haploid populations and the speed of Muller's ratchet

The accumulation of deleterious mutations due to the process known as Muller's ratchet can lead to the degeneration of nonrecombining populations. We present an analytical approximation for the rate at which this process is expected to occur in a haploid population. The approximation is based on a diffusion equation and is valid when N exp(-u/s) > 1, where N is the population size, u is the rate at which deleterious mutations occur, and s is the effect of each mutation on fitness. Simulation results are presented to show that the approximation estimates the rate of the process better than previous approximations for values of mutation rates and selection coefficients that are compatible with the biological data. Under certain conditions, the ratchet can turn at a biologically significant rate when the deterministic equilibrium number of individuals free of mutations is substantially >100. The relevance of this process for the degeneration of Y or neo-Y chromosomes is discussed.     

The fate of transposable elements in asexual populations

Sexual reproduction and recombination are important for maintaining a stable copy number of transposable elements (TEs). In sexual populations, elements can be contained by purifying selection against host carriers with higher element copy numbers; however, in the absence of sex and recombination, asexual populations could be driven to extinction by an unchecked proliferation of TEs. Here we provide a theoretical framework for analyzing TE dynamics under asexual reproduction. Analytic results show that, in an infinite asexual population, an equilibrium in copy number is achieved if no element excision is possible, but that all TEs are eliminated if there is some excision. In a finite population, computer simulations demonstrate that small populations are driven to extinction by a Muller's ratchet-like process of element accumulation, but that large populations can be cured of vertically transmitted TEs, even with excision rates well below transposition rates. These results may have important consequences for newly arisen asexual lineages and may account for the lack of deleterious retrotransposons in the putatively ancient asexual bdelloid rotifers.     

Genetic variation and the fate of beneficial mutations in asexual populations

The fate of a newly arising beneficial mutation depends on many factors, such as the population size and the availability and fitness effects of other mutations that accumulate in the population. It has proved difficult to understand how these factors influence the trajectories of particular mutations, since experiments have primarily focused on characterizing successful clones emerging from a small number of evolving populations. Here, we present the results of a massively parallel experiment designed to measure the full spectrum of possible fates of new beneficial mutations in hundreds of experimental yeast populations, whether these mutations are ultimately successful or not. Using strains in which a particular class of beneficial mutation is detectable by fluorescence, we followed the trajectories of these beneficial mutations across 592 independent populations for 1000 generations. We find that the fitness advantage provided by individual mutations plays a surprisingly small role. Rather, underlying "background" genetic variation is quickly generated in our initially clonal populations and plays a crucial role in determining the fate of each individual beneficial mutation in the evolving population.     

A method to infer positive selection from marker dynamics in an asexual population

MOTIVATION: The observation of positive selection acting on a mutant indicates that the corresponding mutation has some form of functional relevance. Determining the fitness effects of mutations thus has relevance to many interesting biological questions. One means of identifying beneficial mutations in an asexual population is to observe changes in the frequency of marked subsets of the population. We here describe a method to estimate the establishment times and fitnesses of beneficial mutations from neutral marker frequency data. RESULTS: The method accurately reproduces complex marker frequency trajectories. In simulations for which positive selection is close to 5% per generation, we obtain correlations upwards of 0.91 between correct and inferred haplotype establishment times. Where mutation selection coefficients are exponentially distributed, the inferred distribution of haplotype fitnesses is close to being correct. Applied to data from a bacterial evolution experiment, our method reproduces an observed correlation between evolvability and initial fitness defect.     

Adaptive evolution in a spatially structured asexual population

We study the process of adaptation in a spatially structured asexual haploid population. The model assumes a local competition for replication, where each organism interacts only with its nearest neighbors. We observe that the substitution rate of beneficial mutations is smaller for a spatially structured population than that seen for populations without structure. The difference between structured and unstructured populations increases as the adaptive mutation rate increases. Furthermore, the substitution rate decreases as the number of neighbors for local competition is reduced. We have also studied the impact of structure on the distribution of adaptive mutations that fix during adaptation.     

Mathematical analysis of a model describing evolution of an asexual population in a changing environment

We investigate a mathematical model for an asexual population with non-overlapping (discrete) generations, that exists in a changing environment. Sexual populations are also briefly discussed at the end of the paper. It is assumed that selection occurs on the value of a single polygenic trait, which is controlled by a finite number of loci with discrete-effect alleles. The environmental change results in a moving fitness optimum, causing the trait to be subject to a combination of stabilising and directional selection.This model is different from that investigated by Waxman and Peck [Genetics 153 (1999) 1041] where overlapping generations and continuous effect alleles were considered. In this paper, we consider non-overlapping generations and discrete effect alleles. However in [Genetics 153 (1999) 1041] and the present work, there is the same pattern of environmental change, namely a constant rate of change of the optimum.From [Genetics 153 (1999) 1041], no rigorous theoretical conclusion can be drawn about the form of the solutions as t grows large. Numerical work carried out in [Genetics 153 (1999) 1041] suggests that the solution is a lagged travelling wave solution, but no mathematical proof exists for the continuous model. Only partial results, regarding existence of travelling wave solutions and perturbed solutions, have been established (see [Nonlin. Anal. 53 (2003) 683; An integral equation describing an asexual population in a changing environment, Preprint]). For the discrete case of this paper, under the assumption that the ratio between the unit of genotypic value and the speed of environment change is a rational number, we are able to give rigorous proof of the following conclusion: the population follows the environmental change with a small lag behind, moreover, the lag is represented using a calculable quantity.     

The approach to mutation-selection balance in an infinite asexual population, and the evolution of mutation rates

A method is described for calculating the dynamics of the distribution of fitness in an infinite asexual population which is subject to unconditionally deleterious mutations with independent effects. This method is applied to the problem of calculating the frequency of a mutator subpopulation, at equilibrium between mutation and indirect selection due to association with deleterious mutations. Many mutator alleles are produced by loss-of-function mutations in polymerase or mismatch repair genes. Previous calculations have ignored the fact that this creates a flux of higher fitness individuals into the mutator subpopulation. This flux raises the mean fitness of the mutator subpopulation, and when this factor is taken into account, the frequency of the mutator may be more than an order of magnitude greater than recent theoretical work has suggested.     

Transposon proliferation in an asexual parasitoid

The widespread occurrence of sex is one of the most elusive problems in evolutionary biology. Theory predicts that asexual lineages can be driven to extinction by uncontrolled proliferation of vertically transmitted transposable elements (TEs), which accumulate because of the inefficiency of purifying selection in the absence of sex and recombination. To test this prediction, we compared genome-wide TE load between a sexual lineage of the parasitoid wasp Leptopilina clavipes and a lineage of the same species that is rendered asexual by Wolbachia-induced parthenogenesis. We obtained draft genome sequences at 15-20× coverage of both the sexual and the asexual lineages using next-generation sequencing. We identified transposons of most major classes in both lineages. Quantification of TE abundance using coverage depth showed that copy numbers in the asexual lineage exceeded those in the sexual lineage for DNA transposons, but not LTR and LINE-like elements. However, one or a small number of gypsy-like LTR elements exhibited a fourfold higher coverage in the asexual lineage. Quantitative PCR showed that high loads of this gypsy-like TE were characteristic for 11 genetically distinct asexual wasp lineages when compared to sexual lineages. We found no evidence for an overall increase in copy number for all TE types in asexuals as predicted by theory. Instead, we suggest that the expansions of specific TEs are best explained as side effects of (epi)genetic manipulations of the host genome by Wolbachia. Asexuality is achieved in a myriad of ways in nature, many of which could similarly result in TE proliferation.     

A stochastic model for the mutation-selection balance in an infinite asexual population with a genome of fixed size

A stochastic model is presented which describes the evolution of a genome of a haploid species in an infinite population. The genome is a finite set of elements. The elements are divided into different classes according to their effect on the fitness of the organism. Repeated mutations of the genome elements are permitted, in particular positive mutations are introduced. The distribution of the deleterious elements in the genome with respect to the impact on the fitness is given after the replication step. The steady state is fully described including the distribution and the fitness.     

Mutagenesis and repair in Bacillus anthracis: the effect of mutators

We have generated mutator strains of Bacillus anthracis Sterne by using directed gene knockouts to investigate the effect of deleting genes involved in mismatch repair, oxidative repair, and maintaining triphosphate pools. The single-knockout strains are deleted for mutS, mutY, mutM, or ndk. We also made double-knockout strains that are mutS ndk or mutY mutM. We have measured the levels of mutations in the rpoB gene that lead to the Rif(r) phenotype and have examined the mutational specificity. In addition, we examined the mutational specificity of two mutagens, 5-azacytidine and N-methyl-N'-nitro-N-nitroso-guanidine. The mutY and mutM single knockouts are weak mutators by themselves, but the combination of mutY mutM results in very high mutation rates, all due to G:C --> T:A transversions. The situation parallels that seen in Escherichia coli. Also, mutS knockouts are strong mutators and even stronger in the presence of a deletion of ndk. The number of sites in rpoB that can result in the Rif(r) phenotype by single-base substitution is more limited than in certain other bacteria, such as E. coli and Deinococcus radiodurans, although the average mutation rate per mutational site is roughly comparable. Hotspots at sites with virtually identical surrounding sequences are organism specific.     

Slow molecular evolution in an ancient asexual ostracod

Genetic variability of the non-marine ostracod species Darwinula stevensoni was estimated by sequencing part of the nuclear and the mitochondrial genome. As Darwinulidae are believed to be ancient asexuals, accumulation of mutations should have occurred, both between alleles within lineages and between lineages, during the millions of years of parthenogenetic reproduction. However, our sequence data show the opposite: no variability in the nuclear ITS1 region was observed within or among individuals of D. stevensoni, despite sampling a geographical range from Finland to South Africa. Lack of allelic divergence might be explained by concerted evolution of rDNA repeats. Homogeneity among individuals may be caused either by slow molecular evolution in ITS1 or by a recent selective sweep. Variability of mitochondrial cytochrome oxidase (COI) was similar to intraspecific levels in other invertebrates, thus weakening the latter hypothesis. Calibrating interspecific, genetic divergences among D. stevensoni and other Darwinulidae using their fossil record enabled us to estimate rates of molecular evolution. Both COI and ITS1 evolve half as fast, at most, in darwinulids as in other invertebrates, and molecular evolution has significantly slowed down in ITS1 of D. stevensoni relative to other darwinulids. A reduced ITS1 mutation rate might explain this inconsistency between nuclear and mitochondrial evolution in D. stevensoni.     

Walking motion of an overdamped active particle in a ratchet potential

An active particle can convert its internal energy into mechanical work. We study a generalized energy-depot model of an overdamped active particle in a ratchet potential. Using well-known biological parameters for kinesin-1 and modeling ATP influx as a pulsed energy supply, we apply our model to the molecular motor system. We find that our simple model can capture the essential properties of the kinesin motor such as forward stepping, stalling, backward stepping, dependence on ATP concentration, and stall force. Our model might be quite universal in the sense that it is able to describe dynamics of various types of motors as long as realistic parameters for each motor species are adopted.     

A general purpose genotype in an ancient asexual

Many parthenogenetic species are geographically more widely distributed than their sexual relatives. Their success has been partly attributed to the existence of general purpose genotypes (GPGs). Darwinula stevensoni is an ostracod species, which has persisted for >25 million years without sex, and is both ubiquitous and cosmopolitan. Here, we test the hypothesis that this ancient asexual species may possess a highly generalised (or general purpose) genotype. The ecological tolerance of D. stevensoni was compared with asexual populations of Heterocypris incongruens, a common cypridinid species with mixed reproduction, as well as with that of another ancient asexual darwinulid species with a limited geographic and ecological distribution, Vestalenula molopoensis. The unusually wide tolerance range for both salinity (0-30 g/l) and temperature (10°C, 20°C and 30°C) of the freshwater species D. stevensoni, supports the hypothesis that this ancient asexual has indeed developed a GPG. This coincides with its wide geographic and ecological distribution and might explain its persistence as an obligate asexual in its long-term evolution. The more restricted salinity tolerance of V. molopoensis (maximum at 12 g/l) shows that not all species of the ancient asexual family Darwinulidae have a GPG. D. stevensoni has a much broader tolerance than the asexuals of H. incongruens. We argue why a GPG is most likely to develop in long-term asexuals.     

A population of sexual Daphnia pulex resists invasion by asexual clones

Asexual reproduction avoids the costs associated with sex, predicting that invading asexual clones can quickly replace sexual populations. Daphnia pulex populations in the Great Lakes area are predominately asexual, but the elimination of sexual populations by invading clones is poorly understood. Asexual clones were detected at low frequency in one rare sexual population in 1995, with some increase in frequency during 2003 and 2004. However, these clones remained at low frequency during further yearly sampling (2005–2013) with no evidence that the resident sexual population was in danger of elimination. There was evidence for hybridization between rare males produced by asexual clones and sexual females with the potential to produce new asexual genotypes and spread the genetic factors for asexuality. In a short-term laboratory competition experiment, the two most common asexual clones did not increase in frequency relative to a genetically diverse sexual population due in part to a greater investment in diapausing eggs that trades-off current population growth for increased contribution to the egg bank. Our results suggest that a successful invasion can be prolonged, requiring a combination of clonal genotypes with high fitness, persistence of clones in the egg bank and negative factors affecting the sexual population such as inbreeding depression resulting from population bottlenecks.