Dynamic mutation-selection balance as an evolutionary attractor

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, ε, that maintains the balanced state. We find that a surprisingly low ε 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.     

Asexuals, polyploids, evolutionary opportunists...: the population genetics of positive but deteriorating mutations

Some genetic phenomena originate as mutations that are initially advantageous but decline in fitness until they become distinctly deleterious. Here I give the condition for a mutation-selection balance to form and describe some of the properties of the resulting equilibrium population. A characterization is also given of the fixation probabilities for such mutations.     

On the evolutionary advantage of fitness-associated recombination

The adaptive value of recombination remains something of a puzzle. One of the basic problems is that recombination not only creates new and advantageous genetic combinations, but also breaks down existing good ones. A negative correlation between the fitness of an individual and its recombination rate would result in prolonged integrity of fitter genetic combinations while enabling less fit ones to produce new combinations. Such a correlation could be mediated by various factors, including stress responses, age, or direct DNA damage. For haploid population models, we show that an allele for such fitness-associated recombination (FAR) can spread both in asexual populations and in populations reproducing sexually at any uniform recombination rate. FAR also carries an advantage for the population as a whole, resulting in a higher average fitness at mutation-selection balance. These results are demonstrated in populations adapting to new environments as well as in well-adapted populations coping with deleterious mutations. Current experimental results providing evidence for the existence of FAR in nature are discussed.     

Evolution by small steps and rugged landscapes in the RNA virus phi6

Fisher's geometric model of adaptive evolution argues that adaptive evolution should generally result from the substitution of many mutations of small effect because advantageous mutations of small effect should be more common than those of large effect. However, evidence for both evolution by small steps and for Fisher's model has been mixed. Here we report supporting results from a new experimental test of the model. We subjected the bacteriophage phi6 to intensified genetic drift in small populations and caused viral fitness to decline through the accumulation of a deleterious mutation. We then propagated the mutated virus at a range of larger population sizes and allowed fitness to recover by natural selection. Although fitness declined in one large step, it was usually recovered in smaller steps. More importantly, step size during recovery was smaller with decreasing size of the recovery population. These results confirm Fisher's main prediction that advantageous mutations of small effect should be more common. We also show that the advantageous mutations of small effect are compensatory mutations whose advantage is conditional (epistatic) on the presence of the deleterious mutation, in which case the adaptive landscape of phi6 is likely to be very rugged.     

Evolution of sex in RNA viruses

The distribution of deleterious mutations in a population of organisms is determined by the opposing effects of two forces, mutation pressure and selection. If mutation rates are high, the resulting mutation-selection balance can generate a substantial mutational load in the population. Sex can be advantageous to organisms experiencing high mutation rates because it can either buffer the mutation-selection balance from genetic drift, thus preventing any increases in the mutational load (Muller, 1964: Mut. Res. 1, 2), or decrease the mutational load by increasing the efficiency of selection (Crow, 1970: Biomathematics 1, 128). Muller's hypothesis assumes that deleterious mutations act independently, whereas Crow's hypothesis assumes that deleterious mutations interact synergistically, i.e., the acquisition of a deleterious mutation is proportionately more harmful to a genome with many mutations than it is to a genome with a few mutations. RNA viruses provide a test for these two hypotheses because they have extremely high mutation rates and appear to have evolved specific adaptations to reproduce sexually. Population genetic models for RNA viruses show that Muller's and Crow's hypotheses are also possible explanations for why sex is advantageous to these viruses. A re-analysis of published data on RNA viruses that are cultured by undiluted passage suggests that deleterious mutations in such viruses interact synergistically and that sex evolved there as a mechanism to reduce the mutational load.     

Regulation of glutamate dehydrogenase activity by manipulation of nucleotide supply in Daucus carota suspension cultures

The enzyme glutamate dehydrogenase (GDH, EC 1.4.1.2) is ubiquitous in plant species. It is now generally accepted that the primary role of this enzyme is not assimilation of ammonium and it has been suggested that GDH may be important in provision of carbon skeletons under conditions of carbon limitation. In carrot ( Daucus carota L. Chantenay) cell suspension cultures carbon starvation results in de-repression of GDH activity. The regulation of this de-repression has not been investigated. This paper examines the possibility that the availability of adenosine nucleotides is instrumental in the regulation of GDH activity. In repressed cultures the adenosine nucleotides cAMP (0.2 m M ), AMP (0.2 m M ) and ADP (0.4 m M ) caused an increase in GDH activity of 61, 33 and 7%, respectively. ATP (0.2 m M ) had the opposite effect in maintaining repression of GDH. Under de-repressed conditions only cAMP (0.2 m M ) enhanced GDH activity (14%). Inhibition of oxidative phosphorylation using a range of inhibitors resulted in de-repression of GDH and stimulation of respiration. The results from this work indicate that exogenously applied adenosine nucleotides and electron transport inhibitors alter the GDH repression/de-repression status. Addition of these compounds alters or disrupts ATP levels, mimicking carbon depletion. This causes an increase in GDH activity, supporting the idea that GDH may provide carbon skeletons for carbon metabolism and suggesting that ATP status is important in regulation of the enzyme activity.     

The Interaction between Selection,Demography and Selfing and How It Affects Population Viability

Population extinction due to the accumulation of deleterious mutations has only been considered to occur at small population sizes, large sexual populations being expected to efficiently purge these mutations. However, little is known about how the mutation load generated by segregating mutations affects population size and, eventually, population extinction. We propose a simple analytical model that takes into account both the demographic and genetic evolution of populations, linking population size, density dependence, the mutation load, and self-fertilisation. Analytical predictions were found to be relatively good predictors of population size and probability of population viability when verified using an explicit individual based stochastic model. We show that initially large populations do not always reach mutation-selection balance and can go extinct due to the accumulation of segregating deleterious mutations. Population survival depends not only on the relative fitness and demographic stochasticity, but also on the interaction between the two. When deleterious mutations are recessive, self-fertilisation affects viability non-monotonically and genomic cold-spots could favour the viability of outcrossing populations.     

Optimal bacteriophage mutation rates for phage therapy

The mutability of bacteriophages offers a particular advantage in the treatment of bacterial infections not afforded by other antimicrobial therapies. When phage-resistant bacteria emerge, mutation may generate phage capable of exploiting and thus limiting population expansion among these emergent types. However, while mutation potentially generates beneficial variants, it also contributes to a genetic load of deleterious mutations. Here, we model the influence of varying phage mutation rate on the efficacy of phage therapy. All else being equal, phage types with historical mutation rates of approximately 0.1 deleterious mutations per genome per generation offer a reasonable balance between beneficial mutational diversity and deleterious mutational load. We determine that increasing phage inoculum density can undesirably increase the peak density of a mutant bacterial class by limiting the in situ production of mutant phage variants. For phage populations with minimal genetic load, engineering mutation rate increases beyond the mutation-selection balance optimum may provide even greater protection against emergent bacterial types, but only with very weak selective coefficients for de novo deleterious mutations (below approximately 0.01). Increases to the mutation rate beyond the optimal value at mutation-selection balance may therefore prove generally undesirable.     

A trade-off between neutrality and adaptability limits the optimization of viral quasispecies

Theoretical studies of quasispecies usually focus on two properties of those populations at the mutation-selection equilibrium, namely asymptotic growth rate and population diversity. It has been postulated that, as a consequence of the high error rate of quasispecies replication, an increase of neutrality facilitates population optimization by reducing the amount of mutations with a deleterious effect on fitness. In this study we analyse how the optimization of equilibrium properties is affected when a quasispecies evolves in an environment perturbed through frequent bottleneck events. By means of a simple model we demonstrate that high neutrality may be detrimental when the population has to overcome repeated reductions in the population size, and that the property to be optimized in this situation is the time required to regenerate the quasispecies, i.e. its adaptability. In the scenario described, neutrality and adaptability cannot be simultaneously optimized. When fitness is equated with long-term survivability, high neutrality is the appropriate strategy in constant environments, while populations evolving in fluctuating environments are fitter when their neutrality is low, such that they can respond faster to perturbations. Our results might be relevant to better comprehend how a minority virus could displace the circulating quasispecies, a fact observed in natural infections and essential in viral evolution.     

Epistasis and the mutation load: a measurement-theoretical approach

An approximate solution for the mean fitness in mutation-selection balance with arbitrary order of epistatic interaction is derived. The solution is based on the assumptions of coupling equilibrium and that the interaction effects are multilinear. We find that the effect of m-order epistatic interactions (i.e., interactions among groups of m loci) on the load is dependent on the total genomic mutation rate, U, to the mth power. Thus, higher-order gene interactions are potentially important if U is large and the interaction density among loci is not too low. The solution suggests that synergistic epistasis will decrease the mutation load and that variation in epistatic effects will elevate the load. Both of these results, however, are strictly true only if they refer to epistatic interaction strengths measured in the optimal genotype. If gene interactions are measured at mutation-selection equilibrium, only synergistic interactions among even numbers of genes will reduce the load. Odd-ordered synergistic interactions will then elevate the load. There is no systematic relationship between variation in epistasis and load at equilibrium. We argue that empirical estimates of gene interaction must pay attention to the genetic background in which the effects are measured and that it may be advantageous to refer to average interaction intensities as measured in mutation-selection equilibrium. We derive a simple criterion for the strength of epistasis that is necessary to overcome the twofold disadvantage of sex.     

Horizontal Gene Transfer,Fitness Costs and Mobility Shape the Spread of Antibiotic Resistance Genes into Experimental Populations of Acinetobacter Baylyi

Horizontal gene transfer (HGT) is important for microbial evolution, but how evolutionary forces shape the frequencies of horizontally transferred genetic variants in the absence of strong selection remains an open question. In this study, we evolve laboratory populations of Acinetobacter baylyi (ADP1) with HGT from two clinically relevant strains of multidrug-resistant Acinetobacter baumannii (AB5075 and A9844). We find that DNA can cross the species barrier, even without strong selection, and despite substantial DNA sequence divergence between the two species. Our results confirm previous findings that HGT can drive the spread of antibiotic resistance genes (ARGs) without selection for that antibiotic, but not for all of the resistance genes present in the donor genome. We quantify the costs and benefits of horizontally transferred variants and use whole population sequencing to track the spread of ARGs from HGT donors into antibiotic-sensitive recipients. We find that even though most ARGs are taken up by populations of A. baylyi, the long-term fate of an individual gene depends both on its fitness cost and on the type of genetic element that carries the gene. Interestingly, we also found that an integron, but not its host plasmid, is able to spread in A. baylyi populations despite its strong deleterious effect. Altogether, our results show how HGT provides an evolutionary advantage to evolving populations by facilitating the spread of non-selected genetic variation including costly ARGs.     

Adaptive evolution on neutral networks

We study the evolution of large but finite asexual populations evolving in fitness landscapes in which all mutations are either neutral or strongly deleterious. We demonstrate that despite the absence of higher fitness genotypes, adaptation takes place as regions with more advantageous distributions of neutral genotypes are discovered. Since these discoveries are typically rare events, the population dynamics can be subdivided into separate epochs, with rapid transitions between them. Within one epoch, the average fitness in the population is approximately constant. The transitions between epochs, however, are generally accompanied by a significant increase in the average fitness. We verify our theoretical considerations with two analytically tractable bitstring models.     

Molecular aspects of gene transfer and foreign DNA acquisition in prokaryotes with regard to safety issues

Horizontal gene transfer (HGT) is part of prokaryotic life style and a major factor in evolution. In principle, any combinations of genetic information can be explored via HGT for effects on prokaryotic fitness. HGT mechanisms including transformation, conjugation, transduction, and variations of these plus the role of mobile genetic elements are summarized with emphasis on their potential to translocate foreign DNA. Complementarily, we discuss how foreign DNA can be integrated in recipient cells through homologous recombination (HR), illegitimate recombination (IR), and combinations of both, site-specific recombination, and the reconstitution of plasmids. Integration of foreign DNA by IR is very low, and combinations of IR with HR provide intermediate levels compared to the high frequency of homologous integration. A survey of studies on potential HGT from various transgenic plants indicates very rare transfer of foreign DNA. At the same time, in prokaryotic habitats, genes introduced into transgenic plants are abundant, and natural HGT frequencies are relatively high providing a greater chance for direct transfer instead of via transgenic plants. It is concluded that potential HGT from transgenic plants to prokaryotes is not expected to influence prokaryotic evolution and to have negative effects on human or animal health and the environment.     

The population genetics of X-autosome synthetic lethals and steriles

Epistatic interactions are widespread, and many of these interactions involve combinations of alleles at different loci that are deleterious when present in the same individual. The average genetic environment of sex-linked genes differs from that of autosomal genes, suggesting that the population genetics of interacting X-linked and autosomal alleles may be complex. Using both analytical theory and computer simulations, we analyzed the evolutionary trajectories and mutation-selection balance conditions for X-autosome synthetic lethals and steriles. Allele frequencies follow a set of fundamental trajectories, and incompatible alleles are able to segregate at much higher frequencies than single-locus expectations. Equilibria exist, and they can involve fixation of either autosomal or X-linked alleles. The exact equilibrium depends on whether synthetic alleles are dominant or recessive and whether fitness effects are seen in males, females, or both sexes. When single-locus fitness effects and synthetic incompatibilities are both present, population dynamics depend on the dominance of alleles and historical contingency (i.e., whether X-linked or autosomal mutations occur first). Recessive synthetic lethality can result in high-frequency X-linked alleles, and dominant synthetic lethality can result in high-frequency autosomal alleles. Many X-autosome incompatibilities in natural populations may be cryptic, appearing to be single-locus effects because one locus is fixed. We also discuss the implications of these findings with respect to standing genetic variation and the origins of Haldane's rule.     

Mutation-selection balance accounting for genetic variation for viability in Drosophila melanogaster as deduced from an inbreeding and artificial selection experiment

We carried out an experiment of inbreeding and upward artificial selection for egg-to-adult viability in a recently captured population of Drosophila melanogaster, as well as computer simulations of the experimental design, in order to obtain information on the nature of genetic variation for this important fitness component. The inbreeding depression was linear with a rate of 0.70 +/- 0.11% of the initial mean per 1% increase in inbreeding coefficient, and the realized heritability was 0.06 +/- 0.07. We compared the empirical observations of inbreeding depression and selection response with computer simulations assuming a balance between the occurrence of partially recessive deleterious mutations and their elimination by selection. Our results suggest that a model assuming mutation-selection balance with realistic mutational parameters can explain the genetic variation for viability in the natural population studied. Several mutational models are incompatible with some observations and can be discarded. Mutational models assuming a low rate of mutations of large average effect and highly recessive gene action, and others assuming a high rate of mutations of small average effect and close to additive gene action, are compatible with all the observations.     

LONG-TERM EXPERIMENTAL EVOLUTION IN ESCHERICHIA COLI. VII. MECHANISMS MAINTAINING GENETIC VARIABILITY WITHIN POPULATIONS

Six replicate populations of the bacterium Escherichia coli were propagated for more than 10,000 generations in a defined environment. We sought to quantify the variation among clones within these populations with respect to their relative fitness, and to evaluate the roles of three distinct population genetic processes in maintaining this variation. On average, a pair of clones from the same population differed from one another in their relative fitness by approximately 4%. This within-population variation was small compared with the average fitness gain relative to the common ancestor, but it was statistically significant. According to one hypothesis, the variation in fitness is transient and reflects the ongoing substitution of beneficial alleles. We used Fisher's fundamental theorem to compare the observed rate of each population's change in mean fitness with the extent of variation for fitness within that population, but we failed to discern any correspondence between these quantities. A second hypothesis supposes that the variation in fitness is maintained by recurrent deleterious mutations that give rise to a mutation-selection balance. To test this hypothesis, we made use of the fact that two of the six replicate populations had evolved mutator phenotypes, which gave them a genomic mutation rate approximately 100-fold higher than that of the other populations. There was a marginally significant correlation between a population's mutation rate and the extent of its within-population variance for fitness, but this correlation was driven by only one population (whereas two of the populations had elevated mutation rates). Under a third hypothesis, this variation is maintained by frequency-dependent selection, whereby genotypes have an advantage when they are rare relative to when they are common. In all six populations, clones were more fit, on average, when they were rare than when they were common, although the magnitude of the advantage when rare was usually small (~1% in five populations and ~5% in the other). These three hypotheses are not mutually exclusive, but frequency-dependent selection appears to be the primary force maintaining the fitness variation within these experimental populations.     

Mutational effects on the clonal interference phenomenon

We study the process of fixation of beneficial mutations in an asexual population by means of a theoretical model. Particularly, we wish to investigate how the supply of deleterious and beneficial mutations influences the dynamics of the adaptive process of an evolving population. It is well known that the deleterious mutations drastically affect the fate of beneficial mutations. In addition, an increasing supply of favorable mutations, to compensate the decay of the fitness due to the accumulation of deleterious mutations, produces the clonal interference phenomenon where advantageous mutations in distinct lineages compete to reach fixation. This competition imposes a limit to the speed of adaptation of the population. Intuitively, we would expect that the interplay of the two mechanisms would conspire to ensure fixation of only large-effect beneficial mutations. Our results, however, show that beneficial mutations of small effect have an increased probability of fixation when both beneficial and deleterious mutations rates are increased.     

Dependence of epistasis on environment and mutation severity as revealed by in silico mutagenesis of phage t7

Understanding how interactions among deleterious mutations affect fitness may shed light on a variety of fundamental biological phenomena, including the evolution of sex, the buffering of genetic variations, and the topography of fitness landscapes. It remains an open question under what conditions and to what extent such interactions may be synergistic or antagonistic. To address this question, we employed a computer model for the intracellular growth of bacteriophage T7. We created in silico 90,000 mutants of phage T7, each carrying from 1 to 30 mutations, and evaluated the fitness of each by simulating its growth cycle. The simulations sought to account for the severity of single deleterious mutations on T7 growth, as well as the effect of the resource environment on our fitness measures. We found that mildly deleterious mutations interacted synergistically in poor-resource environments but antagonistically in rich-resource environments. However, severely deleterious mutations always interacted antagonistically, irrespective of environment. These results suggest that synergistic epistasis may be difficult to experimentally distinguish from nonepistasis because its effects appear to be most pronounced when the effects of mutations on fitness are most challenging to measure. Our approach demonstrates how computer simulations of developmental processes can be used to quantitatively study genetic interactions at the population level.     

Dynamics of inbreeding depression due to deleterious mutations in small populations: mutation parameters and inbreeding rate

A multilocus stochastic model is developed to simulate the dynamics of mutational load in small populations of various sizes. Old mutations sampled from a large ancestral population at mutation-selection balance and new mutations arising each generation are considered jointly, using biologically plausible lethal and deleterious mutation parameters. The results show that inbreeding depression and the number of lethal equivalents due to partially recessive mutations can be partly purged from the population by inbreeding, and that this purging mainly involves lethals or detrimentals of large effect. However, fitness decreases continuously with inbreeding, due to increased fixation and homozygosity of mildly deleterious mutants, resulting in extinctions of very small populations with low reproductive rates. No optimum inbreeding rate or population size exists for purging with respect to fitness (viability) changes, but there is an optimum inbreeding rate at a given final level of inbreeding for reducing inbreeding depression or the number of lethal equivalents. The interaction between selection against partially recessive mutations and genetic drift in small populations also influences the rate of decay of neutral variation. Weak selection against mutants relative to genetic drift results in apparent overdominance and thus an increase in effective size (Ne) at neutral loci, and strong selection relative to drift leads to a decrease in Ne due to the increased variance in family size. The simulation results and their implications are discussed in the context of biological conservation and tests for purging.