In this report we re-examine some recent experiments with digital organisms to test some predictions of quasispecies theory. These experiments revealed that under high mutation rates populations of less fit organisms previously adapted to such high mutation rates were able to outcompete organisms with higher average fitness but adapted to low mutation rates.We have verified that these results do hold in the original conditions and, by extending the set of initial parameters, we have also detected that the critical mutation rate was independent of population size, a result that we have found to be dependent on a different, contingent factor, the initial fitness vector. Furthermore, in all but one case, the critical mutation rate is higher than the error threshold, a key parameter in quasispecies theory, which prevents its extrapolation to natural viral populations.From these results we conclude that digital organisms are useful tools for investigating evolutionary patterns and processes including some predictions from the quasispecies theory. RNA viruses are among the most infective pathogens affecting plants, animals and humans. Several of their features such as their reduced genomes, high genetic heterogeneity, large population sizes, short generation times and fast evolutionary rates place them among the best models for evolutionary and population genetic studies ,2. TheseAs a consequence, selection, that translates in competition with the host and among viral variants, usually results in the persistence of the most infective, pathogenic or more persistent variants. The molecular bases for this genetic variability are three mechanisms differentially used by each kind of virus: mutation, homologous and non-homologous recombination and genome rearrangement .10individuals in short times), high mutation rates  derived from lack of proof-read correction in the polymerase), and small genome sizes (ranging from 3 to 30 kilobases).Attempts to model the evolutionary dynamics of RNA viruses incorporate their most relevant features, such as large population sizes .- Genetic drift has no relevant effects: their tiny genomes, large population sizes and high mutation rates allow the exploration of all the neutral space around the master sequence.- The average consensus sequence remains stable along quasispecies evolution.This model contrasts sharply with conventional population genetic models in which the existence of a large number of neutral mutations would lead to genetic drift of the population and the individual is the unit of selection rather than a cloud of related variants . This laThe difficulty in experimentally testing some predictions of quasispecies theory has led to the search of alternative systems. In this work we have used digital organisms as an approximation to the population dynamics of RNA viruses. Digital organisms are self-replicating entities and compete for access to resources, in this case CPU cycles, as implemented in the AVIDA platform ,15.Avidians are programs (genomes) composed by arrays of logical instructions (genes) that allow them obtaining CPU cycles. There are 28 possible instructions. The number of instructions in a digital organism is equivalent to the genome size in a biological organism ,17.Many studies have been done using the AVIDA platform. The possibility that genome sizes change during the course of evolution and the rewards that they can obtain by the combination of functions have allowed investigations about the evolution of genomic complexity . Furthersurvival of the flattest and not survival of the fittest.In this work we have focused in a recent study by Wilke et al.  with digHere we have extended the original experimental conditions in order to study the effect and interaction between three of the key factors in the quasispecies model: population and genome sizes and mutation rates. Our results indicate that chance events in the form of historical contingency play an important role in the evolution of these populations. Moreover we have established a new, corrected mutation rate necessary for quasispecies formation with a higher value than the original one. The implications of this correction are discussed.We considered three factors affecting the critical mutation rate in our digital organisms: genome size, population size and the influence of the initial fitness vector. This is a vector of randomly assigned priorities for the first time evaluation of each organism fitness, incorporated to prevent the system from collapsing if all organisms simultaneously try to enter the CPU, and can be interpreted as a historical, contingent factor in evolution. The range of genome sizes studied varied from 54 to 272 instructions Table . Our expTable As expected from our preliminary results, the use of an initial random vector for each experiment and not for each organism resulted in clear differences with the results encountered by Wilke et al. . These dNevertheless, despite these differences between organisms we cannot conclude that there is a globally significant effect of population size on critical mutation rate. Using Bonferroni's correction for multiple comparisons we obtained a new significance level α' = 0.0045. Therefore only organism C148 has a significant, positive correlation . But the differences in the use of a random or fixed initial fitness vector are clear and can be observed by comparing Figures Table The quasispecies model requires a series of conditions to be fulfilled. These requirements are related to four key factors: population size, mutation rate, genome size and neutrality ,23. In o1) The use of different initial fitness vectors for otherwise identical experiments results in unpredictable effects on critical mutation rates for different population sizes. These effects were not detected in the original experiments by Wilke et al.  and can 2) There is no significant correlation between genome size and critical mutation rate.3) The originally calculated critical mutation rates underestimate their real values.Despite the lack of a general correlation between critical mutation rate and population size, the comparison of Figures Another key factor in the quasispecies model is genome size. The establishment of the quasispecies is easier in populations with small genomes, as in these the number of neutral sites is reduced and therefore the neutral space is also smaller. However the relationship between critical mutation rate and genomic size to be expected is somewhat contradictory. On the one hand, larger genomes need higher mutation rates because the neutral and adaptive landscapes are larger. On the other hand, it is well known that large genomes require a stability not supplied by high mutation rates, hence the existence of an error threshold that will be discussed later. In fact Eigen  proposedOur correction to the critical mutation rates estimated in the original paper relates directly to the limits imposed by the mutation rate. In most cases Wilke et al.  obtainedgag region in isolates from different patients, an indication of the limited adaptive solutions able to produce escape mutants to the immune response of cytotoxic T lymphocytes [In conclusion, although some predictions from quasispecies theory are not fulfilled in our experiments, we do have observed the principal prediction that lower fitness competitors can win the competition to high fitness ones, but only under very high mutation rates. Recently, several papers ,23,30 haphocytes . Furtherphocytes .Analogies are very useful in science, but they have to be used cautiously. Similar features and dynamics between digital organisms and RNA viruses are tempting and usually lead to conclude that both kinds of entities are governed by the same laws. This is not necessarily the case, as practitioners of the comparative method know. In any case, digital organisms are an extraordinary system to experiment with controlled, repeatable evolution conditions and further work with them is necessary to ascertain which evolution features are of their own and which are of common application to other evolving entities.The project was started with the twelve pairs of organisms generated in a previous experiment  that hadWith these twelve pairs we followed the same experimental procedure designed by Wilke et al. . BasicalIn AVIDA organisms occupy the limiting environmental resource, the computer CPU, depending on their "fitness". In order to prevent the collapse of the system when all the competing organisms simultaneously try to use the CPU, there exists one feature designed to prevent the simultaneous replication of all organisms at the start of the competition, when all the organisms might be equally fit since they have not been tested yet in the environment. This is achieved by asynchronously introducing organisms in the competition system by assigning an initial fitness to each organism that introduces a small time lag in the accession to the CPU. For this, Wilke et al.  generateDuring exploratory experiments we noticed that this vector could play a decisive influence in the result of the competition. In consequence, we divided the study into two parts. In the first one we kept the vector assigned by Wilke et al.  to each The critical mutation rate is "the midpoint between the highest rate at where A prevailed and the lowest rate where B prevailed" . It reprIt is necessary to clarify the conceptual difference between the critical mutation rate and the error threshold. The first one is the rate at which the prediction of quasispecies theory that organisms with lower fitness can win the competition is fulfilled. However the error threshold is the genomic mutation rate beyond which the information in the molecules that compose the quasispecies loses sense due to mutational degeneracy . In pracWe used versions 1.4 and 1.6 of the AVIDA program. Basically, digital organisms are chains of instructions that act over the CPU with the objective of reproducing as fast as possible. In this manner the CPU time becomes the limiting resource in their evolution. During replication their genomes can mutate and, as a result, a system with variation and therefore with selection and evolution is obtained. Genome sizes of the twelve pairs of digital organisms varied between 54 and 272 instructions . Generally 50 generations were enough for the fixation of the A or B organism in the population. Configuration files used in these experiments are available from the authors web site .Each mutation rate-population size combination was replicated six times. For the verification of the relation between the population size and the critical mutation rate we used Pearson's correlation coefficient and a significance level of 5% using Bonferroni's correction . The samIC performed all the simulations, made the statistical analyses and wrote the first draft of the manuscript. AM contributed to the design of the experiments and the discussion of the results. FGC designed and supervised the experiments, discussed the results and their analyses and wrote the final version of the manuscript. All the authors read and approved the final manuscript.


When Darwin proposed the interplay between variation and natural selection as the driving force of evolution, he had no idea what material produced that variation. Ninety-one years later, Hershey and Chase's famous blender experiment identified the source of variation as DNA. Today, biologists are still struggling to elucidate the details of that interplay.Natural selection works on genetic variations that produce physical changes in an organism. Think of an organism as a collection of genes (its genotype), and its physical characteristics (its phenotype) as its genotype interfacing with the environment, a natural laboratory that saves or discards a genotype based on the performance of its phenotype. Assuming that a population of genotypes is well adapted to its environment, most mutations are likely to reduce performance in that environment. Thus, populations at equilibrium should experience selection for mechanisms that protect the phenotype against mounting deleterious mutations—a phenomenon called mutational (or genetic) robustness. Most of the evidence that robustness arises from selection rather than chance comes from theoretical studies and from studies of “digital organisms”—computer programs that self-replicate, mutate, and evolve—and has proved difficult to establish in the lab. In a new study, Rebecca Montville, Paul Turner, and their colleagues provide experimental evidence for adaptive genetic robustness by working with a mutation-prone virus that infects bacteria, called RNA phage ψ6.  Though theoretical predictions for mutational robustness assume that phenotype expression results solely from the underlying genotype, many viruses can overcome their own mutational deficiencies by co-opting the proteins produced by more fit viruses co-infecting the same host, a feature called complementation.In a previous study, the authors demonstrated for RNA phage ψ6 that complementation buffers less fit viruses against the harmful effects of mutations. They then created six replicate populations of phages and allowed them to adapt to their bacterial host over hundreds of virus generations; three populations evolved at a low ratio of infecting viruses to bacteria  and three at a high MOI. Populations at high MOI experienced higher rates of co-infection. In this study, the authors investigated the evolutionary consequences of this phenomenon with the hypothesis that selection for mutational robustness should be relaxed for co-infecting phages, since phenotype constancy is bolstered by co-infection with their fitter viral companions.Using clones from their six replicate populations, Montville et al. generated 60 new lineages and subjected them to a mutation accumulation experiment under conditions that allowed mutations to accumulate at roughly the same probability in high and low MOI lineages. The authors then evaluated the fitness consequences of mutation accumulation on the lineages by comparing their growth rate in the bacteria before and after mutation accumulation. The authors found greater variance in fitness change for the high co-infection lineages compared to the low-infection lineages, supporting the hypothesis that selection for mutational robustness is stronger in the absence of co-infection.The authors go on to rule out the notion that different fitness effects were produced by different mutation rates in the lineages. Interestingly, the less robust viral genomes were copied more accurately than their more robust counterparts; why less accurate genome replication might accompany the evolution of robustness is a question for future study.Liza GrossWhile complementation appears to buffer the damage of mutational onslaughts in the short-term, this benefit of co-infection eventually disappears because the buffer slows the rate that harmful mutations are culled from the virus population. The authors highlight an additional cost of co-infection: by weakening selection for robustness, co-infection may favor the evolution of genomes that are more vulnerable to the harmful effects of mutation. Future work is needed to examine this seeming tug-of-war between short-term and long-term consequences of co-infection, and its impact on the evolution of virus traits. —


Mutational robustness is defined as the constancy of a phenotype in the face of deleterious mutations. Whether robustness can be directly favored by natural selection remains controversial. Theory and in silico experiments predict that, at high mutation rates, slow-replicating genotypes can potentially outcompete faster counterparts if they benefit from a higher robustness. Here, we experimentally validate this hypothesis, dubbed the “survival of the flattest,” using two populations of the vesicular stomatitis RNA virus. Characterization of fitness distributions and genetic variability indicated that one population showed a higher replication rate, whereas the other was more robust to mutation. The faster replicator outgrew its robust counterpart in standard competition assays, but the outcome was reversed in the presence of chemical mutagens. These results show that selection can directly favor mutational robustness and reveal a novel viral resistance mechanism against treatment by lethal mutagenesis. Understanding the conditions that favor the constancy of phenotypes in the face of deleterious mutation pressure—mutational robustness—is an outstanding question in evolutionary biology. Theoretical and in silico studies utilizing digital organisms predict that slow-replicating populations can outcompete those with higher individual fitness if the former show greater robustness. This “survival of the flattest” hypothesis sits in contrast to most models of natural selection based on individual fitness, and hence challenges the “survival of the fittest” paradigm. In this work, the authors use experimental populations of the rapidly evolving vesicular stomatitis RNA virus to provide the first evidence of natural selection for mutational robustness. Based on the analysis of fitness distributions, genetic variability, and the ability to tolerate mutation accumulation, two populations with different levels of robustness were characterized. At artificially enhanced mutation rates following the application of mutagens, the more robust viral population outcompeted the other population despite having a lower replication rate. This study has important implications for lethal mutagenesis—an antiviral strategy that consists of increasing viral mutation rates through the use of mutagenic drugs—since selectively favored mutational robustness may allow RNA viruses to evolve resistance to this form of treatment. Lethal mutagenesis consists of overwhelming viral populations with an excessive number of deleterious mutations and has been proposed as a candidate therapeutic strategy against RNA viruses –4. SeverRobustness to mutation determines the phenotypic expression of genetic variation and thus should be central to many evolutionary processes . InsofarThe conditions for the evolution of robustness have been experimentally explored in silico –17. SuchDue to their high spontaneous mutation rates , RNA virRhabdoviridae family. We characterized two populations adapted to a common environment but with different evolutionary histories. We studied the genetic variability and the individual fitness distribution of each population near the mutation-selection balance, and we estimated mutation rates and selection coefficients for deleterious mutations. This allowed us to conclude that one population was replicating near a high fitness peak, but was also less robust to mutation than the other. Whereas at spontaneous mutation rates, the fitter population was the best competitor, the addition of mutagens provided an advantage to the more robust, flatter, population.Herein, we provide evidence for the survival of the flattest using experimental populations of VSV, a lytic negative-stranded RNA virus of the 21) . The expected genetic variance for log-fitness among lineages is σG2(logtW) ≈ dtEU[(log(1 − s))2], and the total variance is σT2(logW) = σE2(logW) + σG2(logW) where sub-index E refers to environmental variance. Since genetic variance is null for the ancestor and all fitness assays were performed in the same environmental conditions, σE2(logtW) = σE2(logW0) = σT2(logW0), and therefore σG2(logtW) = σT2(logtW) − σT2(logW0) = ΔσT2(logW). It follows thatθ is the coefficient of variation (standard deviation to mean ratio) of log W associated to single deleterious mutations. (1 + θ2)E[log(1 − s)] and dU/(1 + θ2) were directly estimated from the data.The expected change in log-fitness after θ = 1. Nonetheless, the actual distribution of mutational effects might have a heavier tail and thus a θ > 1. A previous fitness dataset of 28 nonlethal random mutants of VSV  and then, of s. For A, θ = 1.598 should be an accurate estimation of the true θ-value, because it was obtained for the above-mentioned full-length infectious cDNA clone. It is possible, however, that, due to its higher mutational robustness, B showed a lower θ-value. This potential bias could account for the slightly higher dU estimate in B, but it could not account for the nearly one order of magnitude difference in s-values .For an exponential distribution (a simple and relatively accurate model for describing fitness effects associated to single mutations), s of VSV  gave thedU and s between A and B were statistically significant, we generated 1,000 bootstrap pseudo-replicates from both the 24 averaged fitness values of the derived clones and the six averaged fitness values of the ancestors. After obtaining the corresponding 1,000 pseudo-replicates of dU, we counted the number of times dU was larger for A versus B, and the same for s.To address whether differences between dU and s were also estimated using the maximum likelihood approach implemented in the program MLGENOMEU (http://homepages.ed.ac.uk/eang33/mlgenomeu/mlginstructions.html), in which a Gamma distribution of the form Ga(s) = αβsβ− 1e − sα/Γ(β) is used to describe the distribution of mutational effects (s =β/α) [dU and α at fixed β-values varying from 99 to 0.01. The log likelihood monotonically increased as β decreased, yielding increasingly higher α-values (s → ∞ and dU → 0).Parameters (s =β/α) . Followihttp://www.microsoft.com) and the SPSS 12.0 package (http://www.spss.com). Resamplings and simulations were done using a Perl script.Statistics were done with MS Excel (http://www.ebi.ac.uk/cgi-bin/emblfetch) database accession numbers for the A and B evolved populations are AM690336 and AM690337, respectively. For nonmutagenized populations, accession numbers are AM689332–AM689519 and for 5-FU mutagenized populations, accession numbers are AM689705–AM689876.The European Molecular Biology Laboratory (EMBL) (


The most consistent result in more than two decades of experimental evolution is that the fitness of populations adapting to a constant environment does not increase indefinitely, but reaches a plateau. Using experimental evolution with bacteriophage, we show here that the converse is also true. In populations small enough such that drift overwhelms selection and causes fitness to decrease, fitness declines down to a plateau. We demonstrate theoretically that both of these phenomena must be due either to changes in the ratio of beneficial to deleterious mutations, the size of mutational effects, or both. We use mutation accumulation experiments and molecular data from experimental evolution to show that the most significant change in mutational effects is a drastic increase in the rate of beneficial mutation as fitness decreases. In contrast, the size of mutational effects changes little even as organismal fitness changes over several orders of magnitude. These findings have significant implications for the dynamics of adaptation. In any population, two factors determine whether the average fitness of individuals will increase (adaptation) or decrease: the size of the population and the distribution of mutational effects . Although it is relatively simple to get quantitative information on population size, it is much harder to gain insight into the distribution of mutational effects. Very little information exists on the relative rates of beneficial versus deleterious effects, on the shapes of mutational distributions, or on whether the distributions change over time. Thus, it remains difficult to even speculate whether a given population will adapt over time. Here, we use laboratory evolution of a bacterial virus to quantify the distribution of mutational effects. Our results reveal that the average impact of a mutation is approximately constant with respect to fitness, that most mutations have small effects, and that the rate of beneficial mutation depends on the fitness of the organism. Our study demonstrates the simple, but perhaps underappreciated fact that mutational effects are dynamic. It also proposes and tests an explicit model of adaptation in which organismal fitness specifies both the rate and distribution of deleterious and beneficial mutations, and it presents specific and testable predictions of the circumstances under which populations will adapt. Experimental evolution of bacteriophage reveals that mutational effects are dynamic and dependent on genetic background, thus providing fundamental and testable insights into the nature of adaptation. The process of adaptation in finite populations is determined by the distribution of mutational effects on fitness and the size of the population. In large populations, beneficial mutations are frequently fixed, whereas deleterious mutations will only be fixed if they are of vanishingly small effect size (approximately the inverse of the effective population size ). In smaAn accurate description of the distribution of mutational effects is thus fundamental to understanding how adaptive changes occur in biological populations. Experimental manipulation of organisms in the laboratory  –15 and gImportantly, the rate and effect size of beneficial and deleterious mutations are not constant. These quantities change if the fitness of the evolving organism changes. One manifestation of this effect is the fitness plateaus reached by populations adapting to constant environments ,32,33. TThere is an analogous process that occurs in populations that experience decreases in fitness. This process is equally important for evolutionary dynamics, but has received less attention. When populations are so small that drift overwhelms selection, deleterious mutations frequently fix ,22,23, cWe used experimental evolution of a bacteriophage to investigate how the distribution of beneficial and deleterious mutations changes  when fitness changes in the course of evolution, and how this impacts adaptation. We corroborate the finding that in large populations, fitness increases to a plateau. We also report the complementary effect that in small populations, fitness does not decrease indefinitely, but reaches a lower plateau. The equilibrium level of fitness is thus largely determined by the effective population size, and we show that this is a consequence of simple changes in mutational effects that cause qualitative changes in the processes of selection and drift.To study the impact of population size on adaptation, we used experimental evolution in the bacteriophage φX174, an organism in which population sizes can be controlled by adjusting the bottleneck size at transfer. We used phage populations to investigate two related questions: First, do populations evolve to a fitness equilibrium? Second, do populations that differ in effective population size reach different fitness equilibria? As a measure for fitness, we used competition with a reference strain . Because4). Two lower fitness ancestors were derived by serially bottlenecking this clone and selecting small plaques. This procedure resulted in two strains that had low fitness in competition with the ancestral strain.To identify fitness equilibria, we initiated experimental populations with either an ancestor of high fitness or an ancestor of low fitness. We then investigated whether the populations converged toward the same fitness value, irrespective of their starting condition. If populations that were initialized with high- or low-fitness ancestors converged in fitness during evolution, the evolved fitness levels of these populations were concluded to bracket a fitness equilibrium. The high-fitness ancestor was a clone derived from a phage line that had been passaged in our laboratory for 100 transfers at a large population size , two maintained almost constant fitness (Ne = 10), and one declined only slightly in fitness (Ne = 3) (Ne = 30 and Ne = 100), five of the six evolved to a mean fitness above that of the high-fitness ancestor. It was thus difficult to ascertain whether these populations were evolving towards an equilibrium fitness. To establish whether these larger populations were evolving toward an equilibrium, we took the Ne = 100 population that had evolved the highest fitness and propagated it at an expanded population size of Ne = 250 for an additional 55 transfers (275 generations). Three Ne = 250 population replicates were propagated, and none changed significantly in fitness  . In the  fitness . This laAlthough care was taken to minimize the opportunity for cross-contamination between populations, it was important to directly rule out that contamination was responsible for the fitness convergence. To ascertain this, we sequenced the complete genome of one clone from each evolved population. Convergence of substitutions at a large fraction of sites would imply contamination. However, the number of sites at which convergence occurred was not significantly greater than expected by chance see , so crosThe sequence data revealed that the fitness convergence was achieved despite little indication of genetic convergence. Hence our system reproduced one previously observed phenomenon in experimental evolution: fitness in a large, adapting population does reach a plateau with different starting genotypes. Interestingly, our results show that this effect can be extended to small population sizes: small populations converge to low-fitness equilibria without genetic convergence.compensatory) when organismal fitness decreases  change as fitness changes. For simplicity, we illustrate the case in which the effect on fitness of all beneficial mutations is identical, as is the effect on fitness of all deleterious mutations . The substitution rates of deleterious and beneficial mutations are thus:Ne is the population size, ud is the deleterious mutation rate, ub is the beneficial mutation rate, pd = (1 − es2)/(1 − eNs2) [sd, and pb = (1 − es−2)/(1 − eNs−2) is the probability of fixation of a beneficial mutation of effect size sb. If a population is reduced in size such that fitness begins to decline, by definition,We focus on testing these two models here, by using an explicit model to describe how epistatic changes affect fitness convergence and equilibria. In this model, the deleterious and beneficial substitution rates  =  − e2s/. This required determining the ratio of beneficial and deleterious mutations, and the distribution of the effects of these mutations. To estimate these quantities, we used MA. In an MA experiment, mutations are allowed to accumulate by randomly collecting the progeny of a parental phage with no bias against low-fitness progeny. By measuring the fitness of a number of parents and a number of randomly chosen progeny, it is possible to estimate the fitness effects of mutations that occur in a single generation. We determined the fitness of 50 parents and 50 progeny for three high-fitness populations and three low-fitness populations . If negas, and the proportion of beneficial mutations, which we refer to as B, and define as ub/(ub + ud). Importantly, this analysis assumes that the distribution of mutational effects can be modeled as a reflected gamma distribution. The gamma distribution is used because it has great flexibility in terms of the shapes it can assume, with shapes ranging from highly leptokurtic to exponential to log-normal to Gaussian (We used maximum-likelihood (ML) analysis  to estimGaussian . Howevers and B requires an estimate of the mutation rate (U). We derived this estimate from sequence data rather than the ML analysis to avoid conflating estimates of s and U [Ne = 3 and Ne = 10 to estimate the neutral mutation rate.  The average rate of synonymous substitution in these lineages was 0.18 per transfer. We extrapolated this rate to a genomic rate by multiplying by the ratio of total sites to synonymous sites in the ancestral genome while accounting for a proportion of lethal mutations . Although the estimate was slightly lower in the high-fitness populations (0.29 as compared to 0.40), this difference was not significantly different between the two groups . The joint ML estimate of B for all low-fitness populations was 16%, and was not significantly different between these populations  A. The esB for all the evolved populations. For a certain Ne and a specified distribution of s, it is possible to use numerical simulations to find the value of B at which mean population fitness no longer increases or decreases. Using the above estimate for the shape of the distribution of mutational effects, we could thus obtain an estimate of B at which each of the evolved populations should not increase or decrease in fitness , suggested that B must increase to approximately 18% to maintain fitness equilibrium in the Ne = 3 populations. We used additional simulations to derive the value of B required for all other population sizes to maintain fitness equilibria. We then used the median values of the experimentally determined equilibrium fitness values at each Ne  allows low-fitness populations to reach a fitness equilibrium. There are two different ways in which this ratio can increase, either through an increase in ub, the rate of beneficial mutations, or through a decrease in ud, the rate of deleterious mutations. The two alternatives have different biological meanings. An increase in ub with decreasing fitness would correspond to the hypothesis of compensatory epistasis. A decrease in ud, the rate of deleterious mutations, could result if a large fraction of deleterious mutations become lethal in less fit genotypes. In our experimental regimes, the number of lethal mutations was not directly measured, and it was thus important to test for such an increase directly.The results of the MA experiment and the above analysis suggest that an increase in the ratio between the rates of beneficial and deleterious mutations U, which is the sum of ub and ud. We derived an independent measure of U based on the total number of nucleotide substitutions that occurred in all lines; we used a ML analysis to determine the U that best fit the observed number of substitutions in each population . There is thus no evidence that low-fitness populations have lower U, as would be expected if the proportion of lethal mutations had increased in these populations. The new joint ML estimate of U using the nucleotide substitution data was 0.64. This closely matched our first estimate of 0.56, which relied only upon the number of synonymous substitutions observed in the Ne = 3 and Ne = 10 lines. Again, this suggests that our results are robust and internally consistent, and that increases in ub, and not a change in the genomic mutation rate, accounted for the observed changes in B . Conversely, if a population is decreasing in fitness, to stop this decrease, one or more of the following must occur: the mean effect size of beneficial mutations must increase; the rate of beneficial mutations must increase (and consequently the rate of deleterious mutations must decrease); or the effect size of deleterious mutations must increase.This distribution of mutational effects has significant implications for adaptation, because the direction and rate of fitness change in any population is governed by four quantities intrinsic to the organism: the rate and mutational distribution of beneficial mutations and the rate and mutational distribution of deleterious mutations. As shown above, that populations at a specific effective population size converge toward a single level of fitness necessarily constrains the values and dynamics of these quantities. In a population in which mean individual fitness is increasing, the rate of fixation of beneficial mutations multiplied by the mean effect size must outweigh this analogous quantity for deleterious mutations. In order for the rate of adaptation to decrease as fitness increases, one or more of the following must occur: the mean effect size of beneficial mutations must decrease; the rate of beneficial mutations must decrease (and consequently the rate of deleterious mutations must increase); or the effect size of deleterious mutations must decrease . Although the distribution differs slightly from others that have been recently proposed, it concurs well with others [To untangle the different possibilities, we performed MA experiments on lines differing by approximately 300-fold in fitness to characterize the distribution of deleterious mutation effects on fitness . This dih others . We alsoThe deleterious mutation distributions found do not provide significant support for the hypothesis that the effect size of deleterious mutations changes with fitness  , despiteB, the proportion in beneficial mutations, is not driven by a decrease in the deleterious mutation rate . This is shown through an analysis of the molecular data and is also suggested by the magnitude of change: it is likely that the beneficial mutation rate changes by much greater than 10-fold between the high- and low-fitness lines. A comparable change in the overall mutation rate would be easily detected; indeed, it is very unlikely that the rate of lethal mutation in the low-fitness lines increased more than 2-fold  and log-fitness is noteworthy. Because the shape of the mutational distribution does not change with fitness, log-fitness should, on average, scale linearly with the number of deleterious mutations that an individual has. Under the simplest mutational model, deleterious mutations interact multiplicatively i), and each deleterious mutation would result in a single beneficial mutation becoming available—the back mutation. Because the expected value of log-fitness and the number of deleterious mutations scales linearly (log(W) = i*log(1 − s)), and the number of deleterious mutations scales linearly with the number of beneficial mutations (in a 1:1 manner), then log-fitness should also scale linearly with the beneficial mutation rate. This is true under any model in which each deleterious mutation results in a constant average number of newly available beneficial mutations. The nonlinearity of the relationship between B and fitness thus implies that the number of beneficial (compensatory) mutations that become available in the context of each additional deleterious mutation increases as fitness decreases. This suggests that there may be changes in the number of loci involved in compensatory mechanisms as fitness declines. One interpretation of this is that pleiotropic interactions between genetic loci (functions) increase as fitness decreases. Although a negative relationship between the rate of compensatory mutation and fitness has been predicted by modeling, little has been predicted concerning pleiotropy. We hope that our results will spur new interest in this topic.The nonlinear relationship that we observed between This study is the first to propose and test an explicit model of adaptation in which organismal fitness specifies both the rate and distribution of deleterious and beneficial mutations. Although the model necessarily relies upon an idealized form of the genotypic landscape, it presents specific and testable predictions of the circumstances under which populations will increase or decrease in fitness.Additionally, the model offers a simple mechanistic explanation for the diminishing rate of fitness increase observed within large populations adapting in a constant environment , as wellEscherichia coli (mutT), obtained from D. Bregon at INSERM.The original φX174 bacteriophage used in this study was derived from a clone kindly provided by B. Fane. This clone was passaged for 100 transfers at 32 °C to allow general adaptation to laboratory conditions. The deleterious mutants were obtained through serial bottlenecks with mutagenesis (see below), during which small plaques were purposefully chosen. The host was E. coli (mutT), and then grown overnight at 32 °C. From these plates, a number of plaques equal to the bottleneck size were randomly selected and diluted into culture tubes containing 3 ml of 1 mM EDTA. These tubes were vortexed and centrifuged, after which 0.5 ml was removed to a fresh Eppendorf tube. Chloroform was added, the tubes were vortexed and centrifuged, and 0.3 ml was removed. This was used for further mutagenesis, and the remainder of the stock was stored in 40% glycerol at −20 °C.During passaging, phage were mutagenized in 250 mM hydroxylamine (HA) , 1 mM EDCompetition experiments were designed and performed as described previously in Burch and Chao . BrieflyNe = 100 populations  as a reflected gamma distribution [U, the distribution of s, and B, we fixed U based on the estimate from the synonymous substitution rates in the small bottleneck lines (see below). This independent estimate of U allowed greater confidence in the estimates of the distribution of s and B. The likelihood analysis assumes a normally distributed measurement error; the estimate of this error was allowed to vary between experiments, because all six MA experiments were not conducted simultaneously . For the analysis, log-transformed values of fitness were used, because without this transformation, error was not normally distributed. Additionally, the means of the ancestral  generation were set to one  for the analysis. After the analysis, the parameters were used to calculate a gamma distribution, and this distribution was then re-transformed to obtain the standard mutational distribution (transformation: s = 1 − 10s−). The maximum likelihood shape and size parameters for the mutational distribution values were 5.3 and 1.0, respectively.The ML model used models the distribution of selective coefficients ribution ,45. AlthB, 0 in the high-fitness lines and 0.16 in the low-fitness lines).The likelihood surfaces were generated by calculating the likelihood values over a grid of parameter values while maintaining the other parameters at their ML-estimated values  and the amount of over-dispersion of substitutions to infer an S, of the synonymous cytosine → thymine transitions result in a nonviable phenotype, the over-dispersion is decreased. We fit the λS parameter by minimizing the χ2 goodness-of-fit statistic; the value of this statistic is approximately equal to the probability of observing the data. We estimate λS = 0.14, with 95% confidence limits ranging from λS = 0 to λS = 0.40. A similar analysis may be done with non-synonymous missense sites. During experimental evolution, a total of 141 missense cytosine → thymine substitutions at 120 different sites occurred. We removed one of these sites from the analysis, because the substitution occurred in more than four independent lines, and was thus likely subject to strong positive selection. The estimate of λM was 0.37, with 95% confidence limits ranging from λM = 0.01 to λM = 0.61. Finally, we examine nonsense mutations. Of the 560 substitutions observed over all lines during the period of evolution, only one was a nonsense mutation, although the expected frequency is 9%. We thus estimate that λN is essentially 1. All of these estimates are similar to previously estimates values in other viruses, with λS estimated at 0.11 and λM at 0.40 [We base the estimate of the mutation rate on the substitutions observed in the populations propagated at the smallest effective population sizes, because mutations appearing in these lineages should be least subject to selection. Within these lineages, a total of 162 synonymous or intergenic cytosine → thymine substitutions occurred at 117 different sites. These substitutions are slightly over-dispersed when compared to the random expectation, although not significantly. If we assume that some proportion, λS = 0.14, this suggests that substitutions can occur at 265 of these sites. Similarly, with 736 cytosines at which cytosine → thymine substitutions are non-synonymous, and an estimated λN = 0.37, this suggests that substitutions can occur at 466 of these sites. The ratio of total substitutable cytosine sites to substitutable synonymous sites is 2.76, implying a genomic cytosine → thymine mutation rate of 0.50 per transfer. Finally, because cytosine → thymine substitutions account for only 89% of all substitutions, we estimate the total effective genomic mutation rate as 0.56 per transfer.We calculated the effective mutation rate using these parameters. The genome of the ancestral φX174 clone contains 1,151 cytosines; at 309 (27%) of these residues, a transition from cytosine to thymine is synonymous or intergenic; at 736 (64%), a transition is non-synonymous; and at 106 (9%), a transition results in a change to or from a stop codon. The observed rate of synonymous cytosine → thymine substitution was 0.18 per transfer. With a total of 309 cytosines at which this transition is synonymous or intergenic, and an estimated λS includes zero.)If cross-contamination occurred, one would expect that two lines would share substitutions at a large number of sites (thus significantly increasing over-dispersion). This is clearly not the case for synonymous substitutions. . Thus the bottleneck population sizes are an accurate characterization of the effective population size of the phage populations. Secondly, even if individual phage were tracked, this would give rise to similar rates of fixation , and the following equation was numerically solved for each population size:B is the fraction of beneficial mutations, u(s) is the ML gamma distribution of mutational effects, and pfix is the probability of fixing a mutation of effect s in a haploid population of size N: (1 − es−2)/(1 − eNs−2) [We modified an individual-based model of adaptation  for the tion see . The two size N:  − e−2s/ Confidence limits for the ML parameter values of the gamma distribution in the low-fitness clones. The proportion of beneficial mutations, B, was left at its ML value of zero.(B) Confidence limits for the ML parameter values of the gamma distribution in the high-fitness lines. The proportion of beneficial mutations, B, was left at its ML value (0.16 or 0). The joint log-likelihood value is indicated to the right of each panel; the ellipses indicate the 50%, 80%, 90%, and 95% confidence limits. The y-axis shows the estimated mean of the distribution, while the x-axis is the coefficient of variation (1/√β). The estimated mean of the distribution is relatively constant for the two groups, providing little support for any hypothesis under which the mean value of the selection coefficient changes with fitness. However, there is less confidence in the shape of the distribution (beta).(C) Confidence limits for the ML parameter values of the gamma distribution in all MA lines. The proportion of beneficial mutations, (146 KB PDF)Click here for additional data file.Figure S2(A) Confidence limits for the ML parameter values of the gamma distribution in the low-fitness clones. The value of beta was kept constant, at one.y-axis shows the estimated mean of the distribution, while the x-axis indicates the estimated proportion of beneficial mutations (B).(B) Confidence limits for the maximum likelihood parameter values of the gamma distribution in the high-fitness lines. Again, the value of beta was kept constant, at one. The (100 KB PDF)Click here for additional data file.Text S1(26 KB DOC)Click here for additional data file.http://www.ncbi.nlm.nih.gov/Genbank) accession numbers for the genome sequences of the bacteriophage φX174 lineages discussed in this paper are EF380009—EF380032.The GenBank (


Escherichia coli and measured its effect on adaptation at high and low mutation rates. Recombination increased the rate of adaptation ∼3-fold more in the high mutation rate treatment, where beneficial mutations had to compete for fixation. Sequencing of candidate loci revealed the presence of a beneficial mutation in six high mutation rate lines. In the absence of recombination, this mutation took longer to fix and, over the course of its substitution, conferred a reduced competitive advantage, indicating interference between competing beneficial mutations. Together, these results provide experimental support for the Fisher–Muller model and demonstrate that plasmid-mediated gene transfer can accelerate bacterial adaptation.Identification of the selective forces contributing to the origin and maintenance of sex is a fundamental problem in biology. The Fisher–Muller model proposes that sex is advantageous because it allows beneficial mutations that arise in different lineages to recombine, thereby reducing clonal interference and speeding adaptation. I used the F plasmid to mediate recombination in the bacterium  Why have sex? One explanation is that sex is good because it allows beneficial mutations from different lineages to recombine. This reduces competition between mutations in a population and can increase the speed with which the population can adapt to environmental change. This explanation, known as the Fisher–Muller model, has extensive theoretical support; however, it is difficult to test experimentally. Using a simple microbial system I showed that recombination increased the rate of fitness improvement when beneficial mutations were common in the population and had to compete for fixation, but had little effect when mutations occurred rarely. Sequencing of candidate genes revealed the presence of the same beneficial mutation in a number of replicate populations. In the absence of recombination, this mutation took longer to spread and conferred a lower overall competitive advantage, indicating interference between competing beneficial mutations. Together, these results provide direct experimental support for the Fisher–Muller model. Why there is sexual reproduction is an important question. Here the authors show that making bacteria have sex allows faster accumulation and fixation of beneficial mutations. Understanding the factors that contribute to the origin and maintenance of sex is an important unanswered problem in evolutionary biology –4. A larThe Fisher–Muller (FM) model proposes that the advantage of sex results from recombining competing beneficial mutations into one lineage ,14. In tDespite extensive theoretical support for the FM model, the ability of the model to predict the effect of recombination in biological systems is subject to at least two caveats. First, an advantage of recombination depends on competition between beneficial mutations arising in different lineages being strong enough that the fixation of the higher fitness mutation is appreciably slowed. If that is not the case, competition will not effectively limit the rate of adaptation, and recombination will have little effect . ResultsAn ideal experimental test of the FM model would compare the effect of recombination on the rate of adaptation in treatments that differ solely in the extent of competition between beneficial mutations. In practice this ideal has been hard to achieve. A number of experimental studies have examined aspects of the relationship between recombination and environment –12. ThesmutS, was shown to control the rate of adaptation in evolving populations of the bacterium Escherichia coli by increasing the rate at which new mutations were produced by ∼30-fold. By using the same strains and environmental conditions, I define high and low mutation rate treatments that differ only in the supply of new mutations and thus the degree of competition between beneficial mutations. All other aspects of the environment, including population size, remain constant. To permit recombination I use recombination proficient (rec+) strains made by introducing the F plasmid into the ancestral strains used by de Visser et al.  × 34.9 × [4.64 × 106 bp])—well short of the genomic mutation rate of ∼1 required by the mutational deterministic model to explain an advantage to recombination. Also, there is no general tendency for deleterious mutations to interact synergistically in this strain, a second prerequisite of the mutational deterministic model [The results presented above are consistent with the FM model, whereby recombination provides an advantage when multiple beneficial mutations compete for fixation by combining them in the same lineage. However, a possible alternative explanation is that recombination was advantageous because it separated beneficial mutations from linked deleterious mutations ,33–37. Bckground ,35. Thisckground . Thus, tneration . Multiplic model .In the light of the alternative mutation load explanation for the observed benefit of recombination, I sought to directly examine the prediction made by the FM model that recombination reduces competition between beneficial mutations. To do this, I compared the dynamics of a focal beneficial mutation as it rose in frequency and ultimately fixed in rec+ and rec− populations. A decrease in the fitness conferred by a focal beneficial mutation, relative to contemporary clones that did not have this mutation, would be consistent with the spread of alternative beneficial mutations in competing lineages.spoT, that contributed to adaptation of E. coli to an environment nearly identical to the one used here [spoT in three randomly chosen clones isolated from each of the 16 populations in the high mutation rate treatment and found mutations in four rec+ and two rec− lines. The temporal dynamics of each mutation were examined by screening clones at regular intervals from stored samples of the evolved lines. spoT (spoTEv) alleles were very different in the rec+ and rec− lines. The time between detection and fixation averaged 300 generations in rec+ lines and 900 generations in rec− lines . Thus, a beneficial mutation in the same gene took longer to fix in the absence of recombination.A previous study found a mutation in a regulatory gene, sed here . This gespoTEv alleles to fix in rec+ and rec− lines was due to an increase in competition, the selective advantage conferred by each allele was measured at different time points during its substitution. I isolated two clones that had spoTEv alleles from three of the rec+ and two rec− lines that fixed a mutation in this gene , and estimated their fitness relative to five contemporary clones that were isolated from the same line and time point, but that did not have the focal mutation   , the average advantage conferred by focal = 0.878) . To testh slower . Here, the other ; Table 2= 0.322) . No signmutation . TherefospoTEv mutations became negative, such that additional beneficial mutations must have occurred on the same background in order for the focal mutation to fix. The possible existence of linked deleterious mutations cannot explain this result by itself, because the deleterious mutations would impose a constant cost to the focal mutation. By contrast, in the rec+ lines, the relative advantage conferred by the spoTEv mutations showed no overall change, indicating that recombination effectively reduced the effect of competition between beneficial mutations. This reduction in competition is consistent with recombination bringing competing beneficial mutations together into one lineage, the mechanism proposed by the FM model.The findings presented above indicate that multiple beneficial mutations were present in the evolving populations and that, as required by the FM model, in the absence of recombination, competition between these mutations was associated with slower fixation times. Indeed, this competition was so strong that in the rec− lines, the relative effect of the focal spoTEv beneficial mutation in one rec− line, consistent with at least one additional beneficial mutation having arisen and reached an appreciable frequency within this lineage  . Third, the advantage conferred by spoTEv alleles in the competitions carried out against contemporary clones is substantially lower than the advantage of ∼9.4% seen in competition with the ancestral strain (cf. [s = −0.014) [Three additional lines of evidence support the interpretation that competition between beneficial mutations was a significant factor in the adaptation of the high mutation rate lines. First, there was a significant difference in relative fitness between the two clones containing a fixation   .w(gen), prevailing in the rec+ lines at the time when the focal mutations arose. For deleterious mutations to play an influential role in limiting the spread of these mutations, the benefit they confer must be small relative to this variance (s ≪ 6σw(gen) [w(gen) in the rec+ lines, based on those clones that did not have the focal spoTEv mutation, when this mutation was at a low frequency. This measure is conservative because it combines differences between clones due to beneficial as well as deleterious mutations. I found that the genetic variance in fitness was clearly sufficient to influence the spread of the focal mutation in only one of the three rec+ populations  ). Removiulations . TherefoThe results reported in this study have important implications for bacterial adaptation. Competition between different lineages of the same species may be common in certain environments, for example, in clinical settings where adaptation to novel hosts can select for strains with high mutation rates ,43. In tIn summary, I found that recombination and mutation rate interact with each other in determining the speed of adaptive evolution. This finding supports the FM model for the evolution of sex, demonstrating that recombination increases the rate of adaptation only when competing beneficial mutations are present in the population. Also, I was able to identify a beneficial mutation that contributed to adaptation in a number of evolved populations. Comparing the dynamics of this mutation across recombination treatments allowed me to demonstrate directly that recombination reduced the amount of interference between a focal beneficial mutation and other competing beneficial mutations. This reduction in competition shortened the time needed for the focal mutation to fix in the population, providing an explanation for the observed benefit of recombination.E. coli genome encompassing the lac operon. This plasmid was chosen because this region of homology increases the rate at which the plasmid recombines into the host chromosome and therefore the frequency of chromosomal gene transfer. To make a rec− derivative of this plasmid, a non-polar traD deletion was introduced using a PCR-based approach [4-fold and reduced the frequency of chromosomal gene transfer to undetectable levels [traD deletion affected this cost, I performed a competition assay (see below) to measure the relative fitness of identical host cells carrying either the F plasmid or the F ΔtraD derivative. This assay found that the cost of carriage was reduced slightly, but not significantly, by the traD mutation .An F plasmid was obtained from the Coli Genetic Stock Center , as an isolate from strain K603 (CGSC#6451). This plasmid, designated F1–10, encodes resistance to tetracycline and contains a portion of the approach . This mue levels . This gee levels  and has e levels . The F pe levels . To testE. coli B, REL606, was used as the host bacterium in the low mutation rate lines [mutS, mutS::Tn5, into REL606 [mutS allele does not have any measurable effect on fitness [mutS::Tn5 were made by using standard methods to separately introduce F and FΔ traD plasmids into both backgrounds to create the four ancestral strains used to found the evolution experiment. REL607, a spontaneous mutant of REL606 that is able to utilise arabinose, and a spontaneous nalidixic acid (Nx) resistant mutant of REL606 were obtained and used to allow selection of different strains in control assays designed to measure recombination rates (see below). Control experiments found that the rate of recombination was not affected by the mutS::Tn5 allele.A previously described strain of te lines . This sto REL606 . Disrupt fitness . Rec+ anhttp://www.qiagen.com/) with shaking at 150 rpm. Each well was filled with 1 ml of medium. LB broth was used to grow cells from −80 °C freezer stocks. Davis minimal medium supplemented with glucose at 25 mg/l (DM25) was used at all other times.All incubations were carried out at 37 °C in 96 × 2-ml blocks . These strains were inoculated from frozen stocks into LB medium and incubated for 24 h. Strains were then diluted 100-fold and 5 μl inoculated separately into DM25. Following a further 24 h of incubation, the two strains were mixed 1:1 and diluted 1:100 into fresh DM25 medium. After 24 h of co-incubation, cells were plated on minimal arabinose plates supplemented with Nx. Only cells that had recombined the Nx resistant and Ara+ markers could grow on this plate. To estimate the total amount of horizontal gene transfer, the number of recombinant cells was first multiplied by the number of genes separating the two markers. Assuming that only half of these transmitted genes become incorporated into the recipient cell's chromosome  and thatmutation ,38. It itraD) , REL606 mutS::Tn5 (F) , and REL606 mutS::Tn5 (F ΔtraD) . All lines were propagated in 1 ml of DM25 medium in 96 × 2-ml blocks. Each day 5 μl of culture was transferred to 1 ml of fresh medium, allowing ∼7.64 generations per day (= log2 200). This environment and strain combination corresponds to a relative mutation supply  of ∼2.9 in the low mutation rate lines and ∼101.1 in the high mutation rate lines with respect to The evolution experiment consisted of eight replicate lines started with each of four ancestral strains: REL606 (F) , REL606 /NE(0))/ln(NA(1)/NA(0)), where NE(0) and NA(0) represent the initial densities of the evolved and ancestral strains, respectively, and NE(1) and NA(1) represent corresponding densities at the end of the competition. All competitions between ancestral and evolved clones were carried out with 10-fold replication.The fitness of evolved strains relative to the ancestor was assayed by competitions carried out in the same conditions prevailing during the evolution experiment. All evolved strains were Ara−, to allow these strains to be distinguished from their ancestors; derivatives of the ancestral strains were selected that were Ara+. These two marker types can be distinguished by plating on tetrazolium arabinose indicator medium. On this medium, cells that can utilise arabinose form white colonies, whereas cells that cannot use arabinose form red colonies. The arabinose marker is selectively neutral in the evolution environment . Before spoTEv allele were performed similarly. All clones were initially Ara−. To allow the two types to be distinguished from one another, spontaneous Ara+ revertants were selected from those clones that had the spoTEv allele and used in competitions. These competitions were carried out over two or four transfer cycles to increase the precision of fitness estimates. Competitions were carried out with 3-fold replication.Competitions involving evolved clones that did and did not have the spoT including upstream regulatory regions. Purified PCR products were sequenced on an Applied Biosystems (http://www.appliedbiosystems.com/) 3130XL capillary sequencer. Three clones were assayed at the final time point in each high mutation rate line. I sequenced spoT in three randomly chosen clones isolated from each of the 32 lines in the high and low mutation rate treatments and found mutations in four rec+ and two rec− lines in the high mutation rate treatment and one rec− line in the low mutation rate treatment. In one high mutation rate treatment rec− line, the spoTEv allele had not fixed by 1,000 generations. This line was continued for a further 300 generations, after which time the line was screened again and the allele was found to have fixed. The mutations found all caused amino acid substitutions in a region of SpoT involved in the synthesis of the “alarmone” molecule (p)ppGpp [Primers were designed to amplify overlapping fragments of the gene (p)ppGpp , but no spoTEv allele isolated from early time points and (ii) there was no effect of sample time (early versus late) on the relative fitness of clones having a spoTEv allele in the absence of recombination. In all cases denominator degrees of freedom was estimated using a Satterthwaite approximation.Mixed models were run to test the interaction between recombination and mutation rate, with replicate evolved line nested within recombination and mutation rate treatments. Mixed models were also used to test the null hypotheses that (i) there was no effect of recombination treatment on the relative fitness of clones having a Table S1(30 KB DOC)Click here for additional data file.Table S2(30 KB DOC)Click here for additional data file.Table S3(29 KB DOC)Click here for additional data file.


In the 1930s, a flock was relocated to Hirta, an adjacent island in the St. Kilda archipelago, after villagers evacuated to the mainland. Since then, the sheep have been left mostly to their own devices, save for ongoing encounters with scientists keen to test a range of evolutionary hypotheses on this unique population.No one knows for sure when or how they got there, but Soay sheepMark-and-recapture studies have revealed important clues to the ecology of the population, which periodically crashes, typically when a severe winter follows a robust reproductive season. These studies have also generated a wealth of information on birth and death rates, reproduction, pedigree , and phenotype (such as birth weight).Alastair Wilson, Loeske Kruuk, and colleagues took advantage of a 20-year study of birth weight in Soay sheep—which covered nine generations and significant climatic fluctuations—to examine the impact of environmental quality on the strength of selection and the amount of genetic variation associated with a fitness-related trait. Evolution should occur when selection acts on a trait, such as birth weight, that has a genetic basis. Birth weight is closely linked to juvenile mortality, with larger lambs having higher survival and higher fitness. The first six months of life are critical; lamb deaths during this crucial window account for nearly a quarter of all deaths.Even though birth weight has all the raw materials for evolution—a positive correlation between birth weight and survival, and a heritable basis for variation, attributed to maternal genetic effects—previous studies found no evidence for evolution of the trait. Since annual birth weight had not increased over the 20 years, the researchers hypothesized that a variable environment could limit its micro-evolution by limiting heritability, selection, or both. Wilson et al. found evidence that that this is indeed the case.To study the micro-evolutionary dynamics of a wild population, they adapted a theoretical model long used by animal breeders. Quantitative genetic models measure the genetic contribution  to variation in a given trait, such as milk production in dairy cows. With these models, plant and animal breeders maintain or develop desired traits by predicting an evolutionary path based on the strength of selection and the amount of genetic variance underlying the trait. Some of these models assume a constant environment, which is fine for breeders, who can artificially control their subjects' environment, but proves problematic for evolutionary studies of wild populations.To overcome these limitations, the researchers incorporated a statistical tool called random regression analysis. With this approach, they could not only model the effects of environmental variation on selection and heritability but also maximize the statistical power of their dataset. This is a particularly effective technique for natural populations, for which the data are inevitably limited. It also allowed the researchers to model the genetic variance underlying lamb birth weight as a function of environmental quality , creating a more realistic evolutionary picture. The most powerful modeling result showed that the extent to which birth weight is heritable—that is, the variance caused by maternal genetic effects—increased along with environmental quality. But when Wilson et al. modeled the relationship between birth weight and fitness  across environments, they found that the strength of selection followed a different pattern. Fitness increased with birth weight, and with environmental quality, but the positive relationship between fitness and birth weight—indicating the strength of selection—became weaker in better environments.Environmental quality shapes the trajectories for both genetic variance and the strength of selection. Lambs are not growing bigger and bigger because there's a lack of heritable variation for selection to act on in harsh environments and there's a lack of selection to act on higher genetic variation during favorable conditions. These results emphasize the importance of using biologically realistic models to predict the evolution of traits in wild populations—an important component of genetic restoration for endangered species, for example. They also confirm the value of long-term studies on wild populations to better detect patterns of selection and genetic variation in the natural world.


Female only unisexual vertebrates that reproduce by hybridogenesis show an unusual genetic composition. They are of hybrid origin but show no recombination between the genomes of their parental species. Instead, the paternal genome is discarded from the germline prior to meiosis, and gametes (eggs only) contain solely unrecombined maternal genomes. Hence hybridogens only transmit maternally inherited mutations. Hybridity is restored each generation by backcrossing with males of the sexual parental species whose genome was eliminated. In contrast, recombining sexual species propagate an intermixed pool of mutations derived from the maternal and paternal parts of the genome. If mutation rates are lower in female gametes than males, it raises the possibility for lower mutation accumulation in a hybridogenetic population, and consequently, higher population fitness than its sexual counterpart.We show through Monte-Carlo simulations that at higher male to female mutation ratios, and sufficiently large population sizes, hybridogenetic populations can carry a lower mutation load than sexual species. This effect is more pronounced with synergistic forms of epistasis. Mutations accumulate faster on the sexual part of the genome, and with the purifying effects of epistasis, it makes it more difficult for mutations to be transmitted on the clonal part of the genome. In smaller populations, the same mechanism reduces the speed of Muller's Ratchet and the number of fixed mutations compared to similar asexual species.Since mutation accumulation can be less pronounced in hybridogenetic populations, the question arises why hybridogenetic organisms are so scarce compared to sexual species. In considering this, it is likely that comparison of population fitnesses is not sufficient. Despite competition with the sexual parental species, hybrid populations are dependent on the maintenance of – and contact with – their sexual counterpart. Other problems may involve too little genetic diversity to respond to changing environments and problems in becoming hybridogenetic (e.g. disruption of meiosis and subsequent infertility or sterility). Yet, lower mutation accumulation in hybridogenetic populations opens the possibility that hybridogenetic species can develop into new sexual species once recombination is re-established and reproductive isolation from sexual ancestors has occurred. Finding explanations for the evolution and maintenance of sexual reproduction is a long-running research problem in evolutionary biology. A large number of scenarios and models have been developed under which either sexual or asexual reproduction could have advantages or disadvantages . In the Whereas the theories of mutation accumulation and selection against deleterious mutations are well established for asexual and sexual species, they are not for unisexual vertebrates that reproduce by hybridogenesis, a reproductive mode that is intermediate between sexual and asexual reproduction. Figure Poeciliopsis with supposed hybridogenetic ancestry.The long time evolutionary perspectives of such hybridogenetic unisexuals have been questioned by several authors e.g. -12] base base12]]Such speciation events can only be successful if the newly arising species has not accumulated too many deleterious mutations during its hybridogenetic history. In evaluating the risk of mutation accumulation in hybridogens, as compared to other reproductive modes, one has to consider that parthenogenetic (including gynogenetic) and hybridogenetic vertebrates are all-female species (with the exception of hybridogenetic water frogs), whereas sexual species consist of males and females. This becomes important when mutation rates are sex-specific. Starting with Haldane ,15 a numet al.  but  but 22]]The fitness effects of deleterious mutation accumulation in hybridogens are not simply at an intermediate level between sexual and asexual populations. The latter comparison depends on the ratio of male to female mutation rates α. If α = 1 in a large population with synergistic epistasis, conventional expectations hold and the average fitness of a hybridogenetic population is indeed intermediate between sexuals and asexuals. This intermediate position is due to the property that mutation accumulation is slower within the chromosomes derived from the sexually reproducing parental species (where mutations are more effectively purified due to synergistic epistasis and recombination). However, the situation starts to change as α becomes larger than a value of one. In the latter case, sexually reproducing species not only face the often cited twofold costs of reproduction , but alsTo understand the simulation results presented here, it is necessary not only to consider the mechanistic differences in modes of genetic transmission, as represented by the three reproductive systems discussed here. It is also necessary to understand the interplay of population dynamics with these mechanisms. This becomes apparent when one considers mutation accumulation in the clonal part of the hybrid genome. As seen in the cases with quadratic and truncation selection Figure , as α beThis is not because mutations do not occur on the clonal part, but rather that they accumulate much faster on the sexual part of the genome, and hence the quadratic and truncation selection effects allow for no more mutations to accumulate on the whole genome. Selection is too effective in purging the "late arriving" mutants on the clonal part of the genome. In other words, if all mutations that a hybridogen carries affect fitness, regardless whether they reside on the sexually or clonally transmitted part of the genome, selection against all newly acquired mutations is strong if mutations interact synergistically, because of the "borrowed" high mutational load on the paternal genome. Since only the maternal genome can be transmitted (which has been under strong selection against new mutations), the clonally transmitted part of the genomes of hybridogenetic organisms stays remarkably  free ofA challenge for the persistence of asexually and hemiclonally reproducing organisms are drift effects in small or fragmented populations . The comAlthough population size had little influence on the mutational load and on the number of fixed alleles in the size-limited populations with epistatic mutation interaction, hybridogenetically reproducing populations were generally less prone to the accumulation of deleterious mutations than asexual populations. The selective forces against deleterious mutations seemed to be sufficiently effective to prevent a substantial drop in average population fitness , as the mutation rate on the clonally transmitted genome is reduced relative to that on the sexual genome.U are still debated , and, andU arRedfield . At highc models ,28.The simulation results in this work indicate that with male to female mutation rates higher than one (α > 1), hybridogenetic populations can be less prone to the accumulation of deleterious mutations, and hence have a higher population fitness than their sexual counterpart. As α becomes larger, mutation accumulation in the part of the genome derived form the sexual species is faster, and these mutations make it more difficult for new mutations to accumulate on the clonal part of the genome (which has a slower mutation rate). This effect becomes more pronounced with synergistic forms of epistasis (quadratic and truncation). Furthermore, in cases with epistasis and α = 1, although sexual populations have a higher fitness than the hybrids, the hybrids in turn do better than the asexuals, because mutations are purged more effectively in the sexually derived part of their genome.These results lead to the question why hybridogenetic organisms are so scarce compared to sexual species. At the genetic level, one reason could be that, in the real world, mutation interactions are far more complicated and diverse than the ones used in this model ,30. If wFurthermore, one cannot consider the evolution of hybridogenesis by only looking at genetic mechanisms but has to include ecology as well. The survival of the hybrid population totally depends on the continued contact with the sexual parental population which serves as an indispensable sperm donor. Their sperm-dependence prohibits the hybridogens to occupy niches which are markedly different from the niche of the sexual parent and does not allow out-competing the parental species and leading it to extinction. Hence, hybridogenesis can only evolve and persist under ecological conditions that allow stable populations of both, the sexual parasite (i.e. the hybridogens) and their sexual hosts . This ecological issue was not considered in the present work, but has been dealt with in previous publications -35Our result, that clonal or hemiclonal polymorphism can not be maintained with the used model framework, suggests that the often observed diversity in sympatric clones or hemiclones either originates from subsequent recruitments of new clones or hemiclones through repeated primary hybridization, or that diversity in clones is maintained through the occupancy of different microhabitats or "frozen niches" -39Although mutation accumulation is less of a threat to hybridogenetic populations  under several of the conditions used in this model, there are other factors inherent to asexual or hybridogenetic reproduction which affect the long time success of such populations: the response to rapidly changing environments or to parasites is still best ensured through sexual reproduction ,41. But Here, we describe the models for infinite und finite populations, and how the respective simulations were implemented. The features common to all model populations have been mentioned in the Background section.In our simulations, we used three different types of selection against mutations, each represented by a fitness function with a specific form of gene interaction : namely independent, quadratic, and truncation interaction Figure . The funi be the relative fitness (in terms of the number of gametes it is able to produce) of individuals with i mutations compared to an individual with no mutations. With independent fitness effects,Let Ws is the selection coefficient for each new mutation. For our simulations, we chose an s of 0.1, so the relative fitness of an individual with i mutations is Wi= (0.9)iwhere i be the relative fitness of individuals with i mutations compared to an individual with no mutations. Based on Kimura and Maruyama [Again, let WMaruyama , and RedMaruyama  the syneh1 and h2 are constants. The third term in this equation is the nonlinear term that produces the synergistic effects as i becomes larger. In our simulations, h1 = 0.014 and h2 = 0.0112 [Wi ≤ 0, we set the value of Wi to zero.where = 0.0112 . For valWi= 1 if i < = 7, else Wi= 0.Under truncation interaction, accumulated mutations do not have a negative effect on fitness until the number of mutations reaches a threshold. Beyond this threshold, fitness drops to zero, thus U, the genomic mutation rate per individual and generation. Hence the probability P(j) that an individual acquires j mutations is given by (j) = UjeU-(j!)-1. Let us assume that all individuals reproduce at the same time and that generations do not overlap and that there are no back mutations. The class of individuals with i mutations at the beginning of their lifespan originates from a set of parents who could be sequentially ordered into classes , composed of parents with 0 to i mutations. Individuals in each parental class ci-j, would have to produce j mutations to produce progeny in the class ci. Hence, the number of individuals in class ci is the sum of the progeny from each class ci-j with j mutations, where 0 ≤ j ≤ i. If Wi is the relative fitness of individuals in the class with i mutations compared to the class with no mutations and fitness is expressed in the number of gametes an individual can produce, the frequency ci of the class with i mutations in the generation t+1 then calculates asAccording to Kimura & Maruyama  the mutaWi-j is the fitness of individuals with i-j mutations. If ci(t+1) = ci(t) for all i, the population has reached a stable state between mutation pressure and selection against deleterious mutations. The fitness of such a population in mutation-selection balance, relative to a mutation free population, is then where ci(t+1) by c'i(t) in equation 1. The term c'i(t) now describes the frequencies of mutation classes after the new mutations in the same generation have occurred, and ci(t) the distribution before the acquisition of new mutations. If we apply the modified equation 1 separately for both sexes with different values for U, we will get two distributions, c'Ξi(t) and c'Xi(t), for all i. For convenience, we assume here that genomes recombine freely and that none of the mutations occur in homozygous state (i.e. mutations do not coincide at the same locus). An individual bearing a total of i mutations on its entire genome can produce gametes containing 0 to i mutations. We model gamete production as a Bernoulli trials process with i chance experiments, with the probability of passing on a mutant allele for each of the i heterozygous loci being 1/2. Hence the relative frequencies pi(k) of gametes containing k mutations produced by an individual with i mutations follows a binomial distribution withFor the sexual populations we add an additional stage to the asexual model. The individuals in the population are first subject to mutation and selection, following equation (1), and then, subsequent to recombination, are used as a source to form the male and female gamete pool for the next generation. Individuals of the next generation are formed by randomly combining gametes from the latter pool. Infinite sexual populations can be modeled if we replace t for the male gametes mt(g), and for the female gametes ft(g), calculate as:If we pool all male gametes and all female gametes produced by the entire population, the mutation class distribution functions at time g indicates the number of mutations in the specific gamete class.where i mutations in the new generation before mutation accumulation then calculate asBy randomly combining gametes from the two distributions in equation 2, we can build the new generation of individuals. The frequencies of the male and female classes with cΞi(t+1) and cXi(t+1) again in equation 1 the values for c'Ξi(t+1) and c'Xi(t+1) can be calculated with the respective mutation rates.Using z new mutations in the time span between birth and reproduction, 0 to z of these mutations may end up on the clonally transmitted part of the genome. The probability qz(x) that x of these z mutations end up on the clonally transmitted part of the genome follows again a binomial distribution with If a hybrid acquires fn(t+1) of eggs containing n mutations at time t+1 produced by the hybridogens can be calculated asUsing again equation 1, the frequency U being the genomic mutation rate for the hybrid females. The first term in equation (4) comes from equation (1), delineating mutation and selection. The second term gives the frequency of individuals with i-j mutations, having y mutations on the egg and i-j-y mutations on the sperm. The third term gives the probability that of the j mutations occurring in an individual of class ci-j, n-y of those mutations (where n-y ≤ j) occur on an egg with y mutations to give an egg with n mutations. We assume that the distribution of mutation classes within sperms ml is constant over time since the sperms originate from males of the sexual population in mutation selection balance.with ci of hybrids with i mutations in the next generation before mutation accumulation is again The new generation of hybridogens is then again built by randomly combining eggs with sperms. Thus the frequency For the finite populations, we used a Monte Carlo approach to simulate the effect of stochasticity and to be able to model effects of genetic drift and Muller's ratchet. A total of 1000 loci susceptible to deleterious mutations is assumed for all individuals of the different reproductive types. We further assume that initially all genomes are free of deleterious mutations and that back-mutations do not occur. All simulations were programmed in Pascal or C++ using Metrowerks CodeWarrior 5 on an IBM-compatible PC.At the end of one generation all offspring produced by the individuals are pooled. The offspring inherits all mutations (the inherited and the newly acquired ones) from its parent. The relative contribution of an individual's offspring to this pool corresponds to its fitness compared to the fitness of the other individuals. The fitness is determined by the number of deleterious mutations on an individual's genome and the chosen mutation interaction for the simulation . From this pool of offspring, random individuals are drawn to build the new generation until a preset maximum population size is reached.In sexual populations, simulation starts with randomly choosing two parents. The likelihood of a parent to sire offspring is proportional to its fitness compared to the rest of the population of the same sex. Once a pair is determined, it produces a single offspring. For convenience, we assume that all mutations in the parent's genome reside on separate chromosomes. The offspring then inherits each of its parent's heterozygous mutations with a probability of 0.5. All homozygous mutations present in the parents are transferred to the offspring. After the process, the individuals are put back into the pool of parents. The whole process is repeated until the maximum population size is reached. After the new generation is established, each individual undergoes mutation accumulation. Note that males and females can have different average mutation rates and that the number of new mutations per individuals follows again a Poisson distribution with the sex specific genomic mutation rate as the mean.U. A newly acquired mutation occurs with the same probability on the hybrid parents' part of the genome as on the sexual parent's part. The fitness of a hybrid is determined by the total number of mutations in its soma . All mutations affect the hybrid's fitness equally, regardless where they reside. At reproduction, the number of gametes produced by the hybrids corresponds to their relative fitness compared to the other hybrids but the gametes contain only the mutations that resided on the clonally transmitted part of the parents' genome. For the next generation random gametes from this pool are drawn and combined with sperms from the infinite sexual population. The frequencies of mutation classes in the sexual parent population remain constant.The simulation starts with a hybridogenetic subpopulation where no mutations are present on the clonally transmitted part of the hybrid's genome . The sympatric sexual population on the other hand shows the stable distribution of mutation classes, determined with the model for infinite sexual populations. The reproductive cycle starts by randomly combining sperms from males from the sexual population and eggs from the all female hybrid population. As in the previous models, the all-female hybrids acquire a random number of mutations with a probability that follows a Poisson distribution with the mean of the female specific Wherever applicable, the same parameter sets were used as in the model of Redfield . Genomicfi is the fitness of the class with i mutations and nj the frequency of the clonally transmitted haploid set with j mutations in the hybrid population.We furthermore tested the average health of the clonally transmitted part of the genomes of hybridogenetically reproducing populations. This was achieved by calculating the mutation load of a hypothetical diploid population built by combining the clonally transmitted haploid sets of the hybrids with the formula CS came up with idea for this study, developed the model and wrote the initial version of the manuscript as part of his PhD thesis. H-UR wrote the research proposal that lead to this study, obtained the funding and drafted the present version of the paper. HB helped in rewriting the present version of the manuscript. All authors read and approved of the final manuscript.