Estimation of the rate and effect of new beneficial mutations in asexual populations

The rate and effect of available beneficial mutations are key parameters in determining how a population adapts to a new environment. However, these parameters are poorly known, in large part because of the difficulty of designing and interpreting experiments to examine the rare and intrinsically stochastic process of mutation occurrence. We present a new approach to estimate the rate and selective advantage of beneficial mutations that underlie the adaptation of asexual populations. We base our approach on the analysis of experiments that track the effect of newly arising beneficial mutations on the dynamics of a neutral marker in evolving bacterial populations and develop efficient estimators of mutation rate and selective advantage. Using extensive simulations, we evaluate the accuracy of our estimators and conclude that they are quite robust to the use of relatively low experimental replication. To validate the predictions of our model, we compare theoretical and experimentally determined estimates of the selective advantage of the first beneficial mutation to fix in a series of ten replicate populations. We find that our theoretical predictions are not significantly different from experimentally determined selection coefficients. Application of our method to suitably designed experiments will allow estimation of how population evolvability depends on demographic and initial fitness parameters.     

Modelling the fracture-healing process as a moving-interface problem using an interface-capturing approach

We present a novel numerical model of the fracture-healing process using interface-capturing techniques, a well-known approach from fields like fluid dynamics, to describe tissue growth. One advantage of this method is its direct connection to experimentally observable parameters, including tissue-growth velocities. In our model, osteogenesis, chondrogenesis and revascularisation are triggered by mechanical stimuli via mechano-transduction based on previously established hypothesis of Claes and Heigele. After experimentally verifying the convergence of the numerical method, we compare the predictions of our model with those of the already established Ulm bone-healing model, which serves as a benchmark, and corroborate our results with existing animal experiments. We demonstrate that the new model can predict the history of the interfragmentary movement and forecast a tissue evolution that appears similar to the experimental results. Furthermore, we compare the relative tissue concentration in the healing domain with outcomes of animal experiments. Finally, we discuss the possible application of the model to new fields, where numerical simulations could also prove beneficial.     

Quasispecies Theory and the Behavior of RNA Viruses

A large number of medically important viruses, including HIV, hepatitis C virus, and influenza, have RNA genomes. These viruses replicate with extremely high mutation rates and exhibit significant genetic diversity. This diversity allows a viral population to rapidly adapt to dynamic environments and evolve resistance to vaccines and antiviral drugs. For the last 30 years, quasispecies theory has provided a population-based framework for understanding RNA viral evolution. A quasispecies is a cloud of diverse variants that are genetically linked through mutation, interact cooperatively on a functional level, and collectively contribute to the characteristics of the population. Many predictions of quasispecies theory run counter to traditional views of microbial behavior and evolution and have profound implications for our understanding of viral disease. Here, we discuss basic principles of quasispecies theory and describe its relevance for our understanding of viral fitness, virulence, and antiviral therapeutic strategy.     

A general theory for the evolutionary dynamics of virulence

Most theory on the evolution of virulence is based on a game-theoretic approach. One potential shortcoming of this approach is that it does not allow the prediction of the evolutionary dynamics of virulence. Such dynamics are of interest for several reasons: for experimental tests of theory, for the development of useful virulence management protocols, and for understanding virulence evolution in situations where the epidemiological dynamics never reach equilibrium and/or when evolutionary change occurs on a timescale comparable to that of the epidemiological dynamics. Here we present a general theory similar to that of quantitative genetics in evolutionary biology that allows for the easy construction of models that include both within-host mutation as well as superinfection and that is capable of predicting both the short- and long-term evolution of virulence. We illustrate the generality and intuitive appeal of the theory through a series of examples showing how it can lead to transparent interpretations of the selective forces governing virulence evolution. It also leads to novel predictions that are not possible using the game-theoretic approach. The general theory can be used to model the evolution of other pathogen traits as well.     

Eco‐evolutionary dynamics in a coevolving host–virus system

Eco‐evolutionary dynamics have been shown to be important for understanding population and community stability and their adaptive potential. However, coevolution in the framework of eco‐evolutionary theory has not been addressed directly. Combining experiments with an algal host and its viral parasite, and mathematical model analyses we show eco‐evolutionary dynamics in antagonistic coevolving populations. The interaction between antagonists initially resulted in arms race dynamics (ARD) with selective sweeps, causing oscillating host–virus population dynamics. However, ARD ended and populations stabilised after the evolution of a general resistant host, whereas a trade‐off between host resistance and growth then maintained host diversity over time (trade‐off driven dynamics). Most importantly, our study shows that the interaction between ecology and evolution had important consequences for the predictability of the mode and tempo of adaptive change and for the stability and adaptive potential of populations.     

Fitness recovery and compensatory evolution in natural mutant lines of C. elegans

Deleterious mutation accumulation plays a central role in evolutionary genetics, conservation biology, human health, and evolutionary medicine (e.g., methods of viral attenuation for live vaccines). It is therefore important to understand whether and how quickly populations with accumulated deleterious mutational loads can recover fitness through adaptive evolution. We used laboratory experimental evolution with four long-term mutation-accumulation (MA) lines of Caenorhabditis elegans nematodes to study the dynamics of such fitness evolution. We previously showed that when homozygous mutant populations are evolved in large population sizes, they can rapidly achieve wild-type fitness through the accumulation of new beneficial or compensatory epistatic mutations. Here, we expand this approach to demonstrate that when replicate lineages are initiated from the same mutant genotype, phenotypic evolution is only sometimes repeatable. MA genotypes that recovered ancestral fitness in the previous experiment did not always do so here. Further, the pattern of adaptive evolution in independently evolved replicates was contingent upon the MA genotype and varied among fitness-related traits. Our findings suggest that new beneficial mutations can drive rapid fitness evolution, but that the adaptive process is rendered somewhat unpredictable by its susceptibility to chance events and sensitivity to the evolutionary history of the starting population.     

Evolution and population dynamics in stochastic environments

Inter-generational temporal variability of the environment is important in the evolution and adaptation of phenotypic traits. We discuss a population-dynamic approach which plays a central role in the analysis of evolutionary processes. The basic principle is that the phenotypes with the greatest long-term average growth rate will dominate the entire population. The calculation of longterm average growth rates for populations under temporal stochasticity can be highly cumbersome. However, for a discrete non-overlapping population, it is identical to the geometric mean of the growth rates (geometric mean fitness), which is usually different from the simple arithmetic mean of growth rates. Evolutionary outcomes based on geometric mean fitness are often very different from the predictions based on the usual arithmetic mean fitness. In this paper we illustrate the concept of geometric mean fitness in a few simple models. We discuss its implications for the adaptive evolution of phenotypes, e.g. foraging under predation risks and clutch size. Next, we present an application: the risk-spreading egg-laying behaviour of the cabbage white butterfly, and develop a two-patch population dynamic model to show how the optimal solution diverges from the ssual arithmetic mean approach. The dynamics of these stochastic models cannot be predicted from the dynamics of simple deterministic models. Thus the inclusion of stochastic factors in the analyses of populations is essential to the understanding of not only population dynamics, but also their evolutionary dynamics.     

Non-Selective Evolution of Growing Populations

Non-selective effects, like genetic drift, are an important factor in modern conceptions of evolution, and have been extensively studied for constant population sizes (Kimura, 1955; Otto and Whitlock, 1997). Here, we consider non-selective evolution in the case of growing populations that are of small size and have varying trait compositions (e.g. after a population bottleneck). We find that, in these conditions, populations never fixate to a trait, but tend to a random limit composition, and that the distribution of compositions “freezes” to a steady state. This final state is crucially influenced by the initial conditions. We obtain these findings from a combined theoretical and experimental approach, using multiple mixed subpopulations of two Pseudomonas putida strains in non-selective growth conditions (Matthijs et al, 2009) as model system. The experimental results for the population dynamics match the theoretical predictions based on the Pólya urn model (Eggenberger and Pólya, 1923) for all analyzed parameter regimes. In summary, we show that exponential growth stops genetic drift. This result contrasts with previous theoretical analyses of non-selective evolution (e.g. genetic drift), which investigated how traits spread and eventually take over populations (fixate) (Kimura, 1955; Otto and Whitlock, 1997). Moreover, our work highlights how deeply growth influences non-selective evolution, and how it plays a key role in maintaining genetic variability. Consequently, it is of particular importance in life-cycles models (Melbinger et al, 2010; Cremer et al, 2011; Cremer et al, 2012) of periodically shrinking and expanding populations.     

Evolution of RNA virus in spatially structured heterogeneous environments

A hallmark of the infectious cycle for many RNA viruses parasitizing multicellular hosts is the need to invade and successfully replicate in tissues that comprise a variety of cell types. Thus, multicellular hosts represent a heterogeneous environment to evolving viral populations. To understand viral adaptation to multicellular hosts, we took a double approach. First, we developed a mathematical model that served to make predictions concerning the dynamics of viral populations evolving in heterogeneous environments. Second, the predictions were tested by evolving vesicular stomatitis virus in vitro on a spatially structured environment formed by three different cell types. In the absence of gene flow, adaptation was tissue-specific, but fitness in all tissues decreased with migration rate. The performance in a given tissue was negatively correlated with its distance to the tissue hosting the population. This correlation decreased with migration rate.     

Identifying Selection in the Within-Host Evolution of Influenza Using Viral Sequence Data

The within-host evolution of influenza is a vital component of its epidemiology. A question of particular interest is the role that selection plays in shaping the viral population over the course of a single infection. We here describe a method to measure selection acting upon the influenza virus within an individual host, based upon time-resolved genome sequence data from an infection. Analysing sequence data from a transmission study conducted in pigs, describing part of the haemagglutinin gene (HA1) of an influenza virus, we find signatures of non-neutrality in six of a total of sixteen infections. We find evidence for both positive and negative selection acting upon specific alleles, while in three cases, the data suggest the presence of time-dependent selection. In one infection we observe what is potentially a specific immune response against the virus; a non-synonymous mutation in an epitope region of the virus is found to be under initially positive, then strongly negative selection. Crucially, given the lack of homologous recombination in influenza, our method accounts for linkage disequilibrium between nucleotides at different positions in the haemagglutinin gene, allowing for the analysis of populations in which multiple mutations are present at any given time. Our approach offers a new insight into the dynamics of influenza infection, providing a detailed characterisation of the forces that underlie viral evolution.     

Lethal mutagenesis and evolutionary epidemiology

The lethal mutagenesis hypothesis states that within-host populations of pathogens can be driven to extinction when the load of deleterious mutations is artificially increased with a mutagen, and becomes too high for the population to be maintained. Although chemical mutagens have been shown to lead to important reductions in viral titres for a wide variety of RNA viruses, the theoretical underpinnings of this process are still not clearly established. A few recent models sought to describe lethal mutagenesis but they often relied on restrictive assumptions. We extend this earlier work in two novel directions. First, we derive the dynamics of the genetic load in a multivariate Gaussian fitness landscape akin to classical quantitative genetics models. This fitness landscape yields a continuous distribution of mutation effects on fitness, ranging from deleterious to beneficial (i.e. compensatory) mutations. We also include an additional class of lethal mutations. Second, we couple this evolutionary model with an epidemiological model accounting for the within-host dynamics of the pathogen. We derive the epidemiological and evolutionary equilibrium of the system. At this equilibrium, the density of the pathogen is expected to decrease linearly with the genomic mutation rate U. We also provide a simple expression for the critical mutation rate leading to extinction. Stochastic simulations show that these predictions are accurate for a broad range of parameter values. As they depend on a small set of measurable epidemiological and evolutionary parameters, we used available information on several viruses to make quantitative and testable predictions on critical mutation rates. In the light of this model, we discuss the feasibility of lethal mutagenesis as an efficient therapeutic strategy.     

Experimental evolution and the dynamics of genomic mutation rate modifiers

Because genes that affect mutation rates are themselves subject to mutation, mutation rates can be influenced by natural selection and other evolutionary forces. The population genetics of mutation rate modifier alleles has been a subject of theoretical interest for many decades. Here, we review experimental contributions to our understanding of mutation rate modifier dynamics. Numerous evolution experiments have shown that mutator alleles (modifiers that elevate the genomic mutation rate) can readily rise to high frequencies via genetic hitchhiking in non-recombining microbial populations. Whereas these results certainly provide an explanatory framework for observations of sporadically high mutation rates in pathogenic microbes and in cancer lineages, it is nonetheless true that most natural populations have very low mutation rates. This raises the interesting question of how mutator hitchhiking is suppressed or its phenotypic effect reversed in natural populations. Very little experimental work has addressed this question; with this in mind, we identify some promising areas for future experimental investigation.     

Detecting the molecular signature of social conflict: theory and a test with bacterial quorum sensing genes

Extending social evolution theory to the molecular level opens the door to an unparalleled abundance of data and statistical tools for testing alternative hypotheses about the long-term evolutionary dynamics of cooperation and conflict. To this end, we take a collection of known sociality genes (bacterial quorum sensing [QS] genes), model their evolution in terms of patterns that are detectable using gene sequence data, and then test model predictions using available genetic data sets. Specifically, we test two alternative hypotheses of social conflict: (1) the "adaptive" hypothesis that cheaters are maintained in natural populations by frequency-dependent balancing selection as an evolutionarily stable strategy and (2) the "evolutionary null" hypothesis that cheaters are opposed by purifying kin selection yet exist transiently because of their recurrent introduction into populations by mutation (i.e., kin selection-mutation balance). We find that QS genes have elevated within- and among-species sequence variation, nonsignificant signatures of natural selection, and putatively small effect sizes of mutant alleles, all patterns predicted by our evolutionary null model but not by the stable cheater hypothesis. These empirical findings support our theoretical prediction that QS genes experience relaxed selection due to nonclonality of social groups, conditional expression, and the individual-level advantage enjoyed by cheaters. Furthermore, cheaters are evolutionarily transient, persisting in populations because of their recurrent introduction by mutation and not because they enjoy a frequency-dependent fitness advantage.     

A stochastic model of autocatalytic reaction networks

Autocatalytic cycles are rather widespread in nature and in several theoretical models of catalytic reaction networks their emergence is hypothesized to be inevitable when the network is or becomes sufficiently complex. Nevertheless, the emergence of autocatalytic cycles has been never observed in wet laboratory experiments. Here, we present a novel model of catalytic reaction networks with the explicit goal of filling the gap between theoretical predictions and experimental findings. The model is based on previous study of Kauffman, with new features in the introduction of a stochastic algorithm to describe the dynamics and in the possibility to increase the number of elements and reactions according to the dynamical evolution of the system. Furthermore, the introduction of a temporal threshold allows the detection of cycles even in our context of a stochastic model with asynchronous update. In this study, we describe the model and present results concerning the effect on the overall dynamics of varying (a) the average residence time of the elements in the reactor, (b) both the composition of the firing disk and the concentration of the molecules belonging to it, (c) the composition of the incoming flux.     

The genomic rate of molecular adaptation of the human influenza A virus

Quantifying adaptive evolution at the genomic scale is an essential yet challenging aspect of evolutionary biology. Here, we develop a method that extends and generalizes previous approaches to estimate the rate of genomic adaptation in rapidly evolving populations and apply it to a large data set of complete human influenza A virus genome sequences. In accord with previous studies, we observe particularly high rates of adaptive evolution in domain 1 of the viral hemagglutinin (HA1). However, our novel approach also reveals previously unseen adaptation in other viral genes. Notably, we find that the rate of adaptation (per codon per year) is higher in surface residues of the viral neuraminidase than in HA1, indicating strong antibody-mediated selection on the former. We also observed high rates of adaptive evolution in several nonstructural proteins, which may relate to viral evasion of T-cell and innate immune responses. Furthermore, our analysis provides strong quantitative support for the hypothesis that human H1N1 influenza experiences weaker antigenic selection than H3N2. As well as shedding new light on the dynamics and determinants of positive Darwinian selection in influenza viruses, the approach introduced here is applicable to other pathogens for which densely sampled genome sequences are available, and hence is ideally suited to the interpretation of next-generation genome sequencing data.     

Evaluating the impact of population bottlenecks in experimental evolution

Experimental evolution involves severe, periodic reductions in population size when fresh media are inoculated during serial transfer. These bottlenecks affect the dynamics of evolution, reducing the probability that a beneficial mutation will reach fixation. We quantify the impact of these bottlenecks on the evolutionary dynamics, for populations that grow exponentially between transfers and for populations in which growth is curbed by a resource-limited environment. We find that in both cases, mutations that survive bottlenecks are equally likely to occur, per unit time, at all times during the growth phase. We estimate the total fraction of beneficial mutations that are lost due to bottlenecks during experimental evolution protocols and derive the "optimal" dilution ratio, the ratio that maximizes the number of surviving beneficial mutations. Although more severe dilution ratios are often used in the literature, we find that a ratio of 0.1-0.2 minimizes the chances that rare beneficial mutations are lost. Finally, we provide a number of useful approximate results and illustrate our approach with applications to experimental evolution protocols in the literature.     

Monte Carlo estimates of natural variation in HIV infection

We describe a Monte Carlo simulation of the within-host dynamics of human immunodeficiency virus 1 (HIV-1). The simulation proceeds at the level of individual T-cells and virions in a small volume of plasma, thus capturing the inherent stochasticity in viral replication, mutation and T-cell infection. When cell lifetimes are distributed exponentially in the Monte Carlo approach, our simulation results are in perfect agreement with the predictions of the corresponding systems of differential equations from the literature. The Monte Carlo model, however, uniquely allows us to estimate the natural variability in important parameters such as the T-cell count, viral load, and the basic reproductive ratio, in both the presence and absence of drug therapy. The simulation also yields the probability that an infection will not become established after exposure to a viral inoculum of a given size. Finally, we extend the Monte Carlo approach to include distributions of cell lifetimes that are less-dispersed than exponential.     

Setting the absolute tempo of biodiversity dynamics

Neutral biodiversity theory has the potential to contribute to our understanding of how macroevolutionary dynamics influence contemporary biodiversity, but there are issues regarding its dynamical predictions that must first be resolved. Here we address these issues by extending the theory in two ways using a novel analytical approach: (1) we set the absolute tempo of biodiversity dynamics by explicitly incorporating population-level stochasticity in abundance; (2) we allow new species to arise with more than one individual. Setting the absolute tempo yields quantitative predictions on biodiversity dynamics that can be tested using contemporary and fossil data. Allowing incipient-species abundances greater than one individual yields predictions on how these dynamics, and the form of the species-abundance distribution, are affected by multiple speciation modes. We apply this new model to contemporary and fossil data that encompass 30 Myr of macroevolution for planktonic foraminifera. By synthesizing the model with these empirical data, we present evidence that dynamical issues with neutral biodiversity theory may be resolved by incorporating the effects of environmental stochasticity and incipient-species abundance on biodiversity dynamics.     

Evolutionary rescue beyond the models

Laboratory model systems and mathematical models have shed considerable light on the fundamental properties and processes of evolutionary rescue. But it remains to determine the extent to which these model-based findings can help biologists predict when evolution will fail or succeed in rescuing natural populations that are facing novel conditions that threaten their persistence. In this article, we present a prospectus for transferring our basic understanding of evolutionary rescue to wild and other non-laboratory populations. Current experimental and theoretical results emphasize how the interplay between inheritance processes and absolute fitness in changed environments drive population dynamics and determine prospects of extinction. We discuss the challenge of inferring these elements of the evolutionary rescue process in field and natural settings. Addressing this challenge will contribute to a more comprehensive understanding of population persistence that combines processes of evolutionary rescue with developmental and ecological mechanisms.