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Populations threatened by an abrupt environmental change—due to rapid climate change, pathogens or invasive competitors—may survive if they possess or generate genetic combinations adapted to the novel, challenging condition. If these genotypes are initially rare or non-existent, the emergence of lineages that allow a declining population to survive is known as 'evolutionary rescue'. By contrast, the genotypes required for survival could, by chance, be common before the environmental change. Here, considering both of these possibilities, we find that the risk of extinction can be lower in very small or very large populations, but peaks at intermediate population sizes. This pattern occurs when the survival genotype has a small deleterious effect before the environmental change. Since mildly deleterious mutations constitute a large fraction of empirically measured fitness effects, we suggest that this unexpected result—an intermediate size that puts a population at a greater risk of extinction—may not be unusual in the face of environmental change. [ABSTRACT FROM AUTHOR]

With the twofold cost of sex, derived asexual organisms have an immediate reproductive advantage over their sexual sisters. Yet the "twiggy" phylogenetic distribution of asexual lineages implies that they become extinct relatively quickly over evolutionary time. Meanwhile, bacteria and archaea have persisted for billions of years without requiring sexual reproduction. A simple explanation for this difference is that prokaryotes have very large population sizes that are not subject to the accumulation of deleterious mutations, but this implies that drift and mutational meltdown dominate derived asexual populations. Here, we explore a different hazard, quantifying the degree to which genetic variation is lost in asexual populations experiencing selective sweeps. Even though large populations generate diversity by mutation during sweeps, we find that populations that are safe from mutational meltdown may still be reduced to dangerous effective population sizes by sweeps. Thus, ironically, adaptation itself reduces further adaptive potential and may predispose asexual populations to extinction. We derive a simple approximation for the effective population size after a hard sweep and explore the impact of recent sweeps on evolutionary rescue. These factors may help to explain the phylogenetic twigginess of asexuals, the maintenance of sex and recombination, and the evolutionary persistence of prokaryotes. [ABSTRACT FROM AUTHOR]

Mutation accumulation (MA) experiments, in which de novo mutations are sampled and subsequently characterized, are an essential tool in understanding the processes underlying evolution. In microbial populations, MA protocols typically involve a period of population growth between severe bottlenecks, such that a single individual can form a visible colony. While it has long been appreciated that the action of positive selection during this growth phase cannot be eliminated, it is typically assumed to be negligible. Here, we quantify the effect of both positive and negative selection in MA studies, demonstrating that selective effects can substantially bias the distribution of fitness effects (DFE) and mutation rates estimated from typical MA protocols in microbes. We then present a simple correction for this bias that applies to both beneficial and deleterious mutations, and can be used to correct the observed DFE in multiple environments. We use simulated MA experiments to illustrate the extent to which the MA‐inferred DFE differs from the underlying true DFE, and demonstrate that the proposed correction accurately reconstructs the true DFE over a wide range of scenarios; we also provide an example of these corrections applied to experimental data. These results highlight that positive selection during microbial MA experiments is in fact not negligible, but can be corrected to gain a more accurate understanding of fundamental evolutionary parameters. [ABSTRACT FROM AUTHOR]

Although vaccination has been remarkably effective against some pathogens, for others, rapid antigenic evolution results in vaccination conferring only weak and/or short‐lived protection. Consequently, considerable effort has been invested in developing more evolutionarily robust vaccines, either by targeting highly conserved components of the pathogen (universal vaccines) or by including multiple immunological targets within a single vaccine (multi‐epitope vaccines). An unexplored third possibility is to vaccinate individuals with one of a number of qualitatively different vaccines, creating a "mosaic" of individual immunity in the population. Here we explore whether a mosaic vaccination strategy can deliver superior epidemiological outcomes to "conventional" vaccination, in which all individuals receive the same vaccine. We suppose vaccine doses can be distributed between distinct vaccine "targets" (e.g., different surface proteins against which an immune response can be generated) and/or immunologically distinct variants at these targets (e.g., strains); the pathogen can undergo antigenic evolution at both targets. Using simple mathematical models, here we provide a proof‐of‐concept that mosaic vaccination often outperforms conventional vaccination, leading to fewer infected individuals, improved vaccine efficacy, and lower individual risks over the course of the epidemic. [ABSTRACT FROM AUTHOR]

Genome sequencing has revealed that prophages, viral sequences integrated in a bacterial chromosome, are abundant, accounting for as much as 20% of the bacterial genome. These sequences can confer fitness benefits to the bacterial host, but may also instigate cell death through induction. Several recent investigations have revealed that the distribution of prophage lengths is bimodal, with a clear distinction between small and large prophages. Here we develop a mathematical model of the evolutionary forces affecting the prophage size distribution, and fit this model to three recent data sets. This approach offers quantitative estimates for the relative rates of lysogeny, induction, mutational degradation and selection acting on a wide class of prophage sequences. The model predicts that large prophages are predominantly maintained by the introduction of new prophage sequences through lysogeny, whereas shorter prophages can be enriched when they no longer encode the genes necessary for induction, but still offer selective benefits to their hosts. [ABSTRACT FROM AUTHOR]

Lytic viruses infect and kill host cells, producing a large number of viral copies. Temperate viruses, in contrast, are able to integrate viral genetic material into the host cell DNA, leaving a viable host cell. The evolutionary advantage of this strategy, lysogeny, has been demonstrated in complex environments that include spatial structure, oscillating population dynamics, or periodic environmental collapse. Here, we examine the evolutionary stability of the lysis–lysogeny decision, that is, we predict the long‐term outcome of the evolution of lysogeny rates. We demonstrate that viruses with high rates of lysogeny are stable against invasion by more virulent viral strains even in simple environments, as long as the pool of susceptible hosts is not unlimited. This mirrors well‐known results in both r‐K selection theory and virulence evolution: although virulent viruses have a faster potential growth rate, temperate strains are able to maintain positive growth on a lower density of the limiting resource, susceptible hosts. We then outline scenarios in which the rate of lysogeny is predicted to evolve either toward full lysogeny or full lysis. Finally, we demonstrate conditions under which intermediate rates of lysogeny, as observed in temperate viruses in nature, can be sustained long‐term. In general, intermediate lysogeny rates persist when the coupling between susceptible host density and virus density is relaxed. [ABSTRACT FROM AUTHOR]

Population bottlenecks—sudden, severe reductions in population size—are ubiquitous in nature. Because of their critical implications for conservation genetics, the effects of population bottlenecks on the loss of genetic diversity have been well studied. Bottlenecks also have important implications for adaptation, however, and these effects have been addressed more recently, typically in microbial populations. In this short review, we survey both experimental and theoretical work describing the impact of population bottlenecks on microbial adaptation. Focusing on theoretical contributions, we highlight emerging insights and conclude with several open questions of interest in the field. [ABSTRACT FROM AUTHOR]

Sequencing of bacterial genomes has revealed an abundance of prophage sequences in many bacterial species. Since these sequences are accessible, through recombination, to infecting phages, bacteria carry an arsenal of genetic material that can be used by these viruses. We develop a mathematical model to isolate the effects of this phenomenon on the coevolution of temperate phage and bacteria. The model predicts that prophage sequences may play a key role in maintaining the phage population in situations that would otherwise favor host cell resistance. In addition, prophage recombination facilitates the existence of multiple phage types, thus promoting diverse co-existence in the phage-host ecosystem. Finally, because the host carries an archive of previous phage strategies, prophage recombination can drive waves of innovation in the host cell population. [ABSTRACT FROM AUTHOR]

Clustered regularly interspaced short palindromic repeats (CRISPR), linked with CRISPR associated (Cas) genes, can confer adaptive immunity to bacteria, against bacteriophage infections. Thus from a therapeutic standpoint, CRISPR immunity increases biofilm resistance to phage therapy. Recently, however, CRISPR-Cas genes have been implicated in reducing biofilm formation in lysogenized cells. Thus CRISPR immunity can have complex effects on phage–host–lysogen interactions, particularly in a biofilm. In this contribution, we develop and analyse a series of dynamical systems to elucidate and disentangle these interactions. Two competition models are used to study the effects of lysogens (first model) and CRISPR-immune bacteria (second model) in the biofilm. In the third model, the effect of delivering lysogens to a CRISPR-immune biofilm is investigated. Using standard analyses of equilibria, stability and bifurcations, our models predict that lysogens may be able to displace CRISPR-immune bacteria in a biofilm, and thus suggest strategies to eliminate phage-resistant biofilms. [ABSTRACT FROM PUBLISHER]

Prophage sequences constitute a substantial fraction of the temperate virus gene pool. Although subject to mutational decay, prophage sequences can also be an important source of adaptive mutations for these viral populations. Here we develop a lifehistory model for temperate viruses, including both the virulent (lytic) and the temperate phases of the life cycle. We then examine the survival of mutations that increase fitness during the lytic phase (attachment rate, burst size), increase fitness in the temperate phase (increasing host survival), or affect transitions between the two phases (integration or induction probability). We find that beneficial mutations are much more likely to survive, ultimately, if they first occur in the prophage state. This conclusion applies even to traits that are only expressed during the lytic phase, and arises due to the substantially lower variance in the offspring distribution during the temperate cycle. This observation, however, is balanced by the fact that many more mutations can be generated during lytic replication. Overall we predict that the prophage state provides a refuge, relatively shielded from genetic drift, in which temperate viruses can explore possible adaptive steps. [ABSTRACT FROM AUTHOR]

Mobile promoters are emerging as a new class of mobile genetic elements, first identified by examining prokaryote genome sequences, and more recently confirmed by experimental observations in bacteria. Recent datasets have identified over 40,000 putative mobile promoters in sequenced prokaryote genomes, however only one-third of these are in regions of the genome directly upstream from coding sequences, that is, in promoter regions. The presence of many promoter sequences in non-promoter regions is unexplained. Here we develop a general mathematical model for the dynamics of mobile promoters, extending previous work to capture the dynamics both within and outside promoter regions. From this general model, we apply rigorous model selection techniques to identify which parameters are statistically justified in describing the available mobile promoter data, and find best-fit values of these parameters. Our results suggest that high rates of horizontal gene transfer maintain the population of mobile promoters in promoter regions, and that once established at these sites, mobile promoters are rarely lost, but are commonly copied to other genomic regions. In contrast, mobile promoter copies in non-promoter regions are more numerous and more volatile, experiencing substantially higher rates of duplication, loss and diversification. [ABSTRACT FROM AUTHOR]

Theoretical approaches are essential to our understanding of the complex dynamics of mobile genetic elements (MGEs) within genomes. Recently, the birth–death-diversification model was developed to describe the dynamics of mobile promoters (MPs), a particular class of MGEs in prokaryotes. A unique feature of this model is that genetic diversification of elements was included. To explore the implications of diversification on the longterm fate of MGE lineages, in this contribution we analyze the extinction probabilities, extinction times and equilibrium solutions of the birth–death-diversification model. We find that diversification increases both the survival and growth rate of MGE families, but the strength of this effect depends on the rate of horizontal gene transfer (HGT). We also find that the distribution of MGE families per genome is not necessarily monotonically decreasing, as observed for MPs, but may have a peak in the distribution that is related to the HGT rate. For MPs specifically, we find that new families have a high extinction probability, and predict that the number of MPs is increasing, albeit at a very slow rate. Additionally, we develop an extension of the birth–death-diversification model which allows MGEs in different regions of the genome, for example coding and non-coding, to be described by different rates. This extension may offer a potential explanation as to why the majority of MPs are located in non-promoter regions of the genome. [ABSTRACT FROM AUTHOR]

The survival of rare beneficial mutations can be extremely sensitive to the organism's life history and the trait affected by the mutation. Given the tremendous impact of bacteria in batch culture as a model system for the study of adaptation, it is important to understand the survival probability of beneficial mutations in these populations. Here we develop a life-history model for bacterial populations in batch culture and predict the survival of mutations that increase fitness through their effects on specific traits: lag time, fission time, viability, and the timing of stationary phase. We find that if beneficial mutations are present in the founding population at the beginning of culture growth, mutations that reduce the mortality of daughter cells are the most likely to survive drift. In contrast, of mutations that occur de novo during growth, those that delay the onset of stationary phase are the most likely to survive. Our model predicts that approximately fivefold population growth between bottlenecks will optimize the occurrence and survival of beneficial mutations of all four types. This prediction is relatively insensitive to other model parameters, such as the lag time, fission time, or mortality rate of the population. We further estimate that bottlenecks that are more severe than this optimal prediction substantially reduce the occurrence and survival of adaptive mutations. [ABSTRACT FROM AUTHOR]

Since wild birds are the major natural reservoir for all known influenza A viruses, understanding the ecology of avian influenza (AI) viruses circulating in wild birds is critical to predicting disease risk in wild and domestic birds and preventing transmission to humans. AI virus which is shed by infected birds into aquatic environments plays a pivotal role in the sustained transmission of AI. Recent laboratory experiments, however, show that viral persistence in water is highly sensitive to environmental conditions such as temperature, which varies seasonally and geographically. Here, we develop mathematical models to study the effects of time-varying environmental conditions on AI dynamics, deriving the effects of temperature on the basic reproductive number (R0) the final outbreak size, and the effective reproductive number (Re) For periodic environmental temperatures, we derive a mathematical formulation of an AI invasion threshold (Ri) and conclude that apart from the mean temperature, the amplitude of the periodic temperature profile plays a significant role in the invasion of wild bird populations by AI. In particular, both higher means and higher amplitudes (warmer and more variable temperatures) reduce the likelihood of AI invasion. We also analyze the global dynamics of the model proving that AI is uniformly persistent in the wild bird population if Ri > 1. In numerical work, we fit the model to recent experimental data and field survey data from Northern Europe. Two important and robust quantitative conclusions emerge: that direct transmission is negligible compared to indirect and that immunity wanes within about 4 weeks. The latter conclusion is of particular interest since many previous models assume lifetime immunity. We also demonstrate that time-varying temperature may be the underlying cause of several features of AI dynamics which are observed in real data. In particular, AI prevalence is observed to peak in spring and fall but to wane in summer; this behavior naturally emerges from our model under a wide range of conditions. [ABSTRACT FROM AUTHOR]

Many autoimmune diseases are characterized by a pattern of recurrence and remission, in which periods of apparent self-tolerance are punctuated by intervals of recurring autoimmunity. We introduce a newly discovered class of terminally differentiated regulatory T cells, HLA-DR+ TReg cells, into an existing autoimmune disease model. Our newly developed 4-dimensional model exhibits recurrent dynamics, which are preserved in a reduced and rescaled 3-dimensional model as well. Applying dynamical systems theory, we analyze the dynamics underlying this behavior in both the 4-dimensional and 3-dimensional models and further prove that the recurrent behavior (or oscillation) arises due to a Hopf bifurcation or a persistent oscillation rather than from homoclinic orbits. Numerical simulations are conducted to verify the analytical results and identify the recurrent parameter region. [ABSTRACT FROM AUTHOR]

We propose a model that combines the dynamics of the spread of disease within a bee colony with the underlying demographic dynamics of the colony to determine the ultimate fate of the colony under different scenarios. The model suggests that key factors in the survival or collapse of a honey bee colony in the face of an infection are the rate of transmission of the infection and the disease-induced death rate. An increase in the disease-induced death rate, which can be thought of as an increase in the severity of the disease, may actually help the colony overcome the disease and survive through winter. By contrast, an increase in the transmission rate, which means that bees are being infected at an earlier age, has a drastic deleterious effect. Another important finding relates to the timing of infection in relation to the onset of winter, indicating that in a time interval of approximately 20 days before the onset of winter the colony is most affected by the onset of infection. The results suggest further that the age of recruitment of hive bees to foraging duties is a good early marker for the survival or collapse of a honey bee colony in the face of infection, which is consistent with experimental evidence but the model provides insight into the underlying mechanisms. The most important result of the study is a clear distinction between an exposure of the honey bee colony to an environmental hazard such as pesticides or insecticides, or an exposure to an infectious disease. The results indicate unequivocally that in the scenarios that we have examined, and perhaps more generally, an infectious disease is far more hazardous to the survival of a bee colony than an environmental hazard that causes an equal death rate in foraging bees. [ABSTRACT FROM AUTHOR]

Recurrent infection is characterized by short episodes of high viral reproduction, separated by long periods of relative quiescence. This recurrent pattern is observed in many persistent infections, including the "viral blips" observed during chronic infection with the human immunodeficiency virus (HIV). Although in-host models which incorporate forcing functions or stochastic elements have been shown to display viral blips, simple deterministic models also exhibit this phenomenon. We describe an analytical study of a 4-dimensional HIV antioxidant-therapy model which exhibits viral blips, showing that an increasing, saturating infectivity function contributes to the recurrent behavior of the model. Using dynamical systems theory, we hypothesize four conditions for the existence of viral blips in a deterministic in-host infection model. In particular, we explain how the blips are generated, which is not due to homoclinic bifurcation since no homoclinic orbits exist. These conditions allow us to develop very simple (2- and 3-dimensional) infection models which produce viral blips, and we determine the complete parameter range for the 3-dimensional model in which blips are possible, using stability analysis. We also use these conditions to demonstrate that low-dimensional in-host models with linear or constant infectivity functions cannot generate viral blips. Finally, we demonstrate that a 5-dimensional immunological model satisfies the conditions and exhibits recurrent infection even with constant infectivity; thus, an increasing, saturating infectivity function is not necessary if the model is sufficiently complex. [ABSTRACT FROM AUTHOR]

The rate at which a population adapts to its environment is a cornerstone of evolutionary theory, and recent experimental advances in microbial populations have renewed interest in predicting and testing this rate. Efforts to understand the adaptation rate theoretically are complicated by high mutation rates, to both beneficial and deleterious mutations, and by the fact that beneficial mutations compete with each other in asexual populations (clonal interference). Testable predictions must also include the effects of population bottlenecks, repeated reductions in population size imposed by the experimental protocol. In this contribution, we integrate previous work that addresses each of these issues, developing an overall prediction for the adaptation rate that includes: beneficial mutations with probabilistically distributed effects, deleterious mutations of arbitrary effect, population bottlenecks, and clonal interference. [ABSTRACT FROM AUTHOR]

Background: There is currently no way to verify the quality of a multiple sequence alignment that is independent of the assumptions used to build it. Sequence alignments are typically evaluated by a number of established criteria: sequence conservation, the number of aligned residues, the frequency of gaps, and the probable correct gap placement. Covariation analysis is used to find putatively important residue pairs in a sequence alignment. Different alignments of the same protein family give different results demonstrating that covariation depends on the quality of the sequence alignment. We thus hypothesized that current criteria are insufficient to build alignments for use with covariation analyses. Methodology/Principal Findings: We show that current criteria are insufficient to build alignments for use with covariation analyses as systematic sequence alignment errors are present even in hand-curated structure-based alignment datasets like those from the Conserved Domain Database. We show that current non-parametric covariation statistics are sensitive to sequence misalignments and that this sensitivity can be used to identify systematic alignment errors. We demonstrate that removing alignment errors due to 1) improper structure alignment, 2) the presence of paralogous sequences, and 3) partial or otherwise erroneous sequences, improves contact prediction by covariation analysis. Finally we describe two nonparametric covariation statistics that are less sensitive to sequence alignment errors than those described previously in the literature. Conclusions/Significance: Protein alignments with errors lead to false positive and false negative conclusions (incorrect assignment of covariation and conservation, respectively). Covariation analysis can provide a verification step, independent of traditional criteria, to identify systematic misalignments in protein alignments. Two non-parametric statistics are shown to be somewhat insensitive to misalignment errors, providing increased confidence in contact prediction when analyzing alignments with erroneous regions because of an emphasis on they emphasize pairwise covariation over group covariation. [ABSTRACT FROM AUTHOR]

We use a branching process approach to estimate the substitution rate, the rate at which beneficial mutations occur and fix, in populations of lytic viruses whose growth is controlled by periodic population bottlenecks. Our model predicts that substitution rates, and by extension adaptation rates, are profoundly affected by the survival of infected host cells at the bottleneck. In particular, we find that direct transfer (or environmental) bottlenecks, in which some fraction of both free virus and host cells are preserved, are associated with relatively slow adaptation rates for the virus. In contrast, viruses can adapt much more quickly when only free virus is transferred to a new host population, as is typical in an epidemiological setting. Finally, when premature lysis of the host-cell population is induced at the bottleneck, we predict that adaptation rates for the virus will, in general, be faster still. These results hold irrespective of the life-history trait affected by the beneficial mutation. The substitution rates in the presence of environmental bottlenecks are predicted to be as much as an order of magnitude lower than in the other two cases. [ABSTRACT FROM AUTHOR]

Background: Small, highly reactive molecules called reactive oxygen species (ROS) play a crucial role in cell signalling and infection control. However, high levels of ROS can cause significant damage to cell structure and function. Studies have shown that infection with the human immunodeficiency virus (HIV) results in increased ROS concentrations, which can in turn lead to faster progression of HIV infection, and cause CD4+ T-cell apoptosis. To counteract these effects, clinical studies have explored the possibility of raising antioxidant levels, with mixed results. Methods: In this paper, a mathematical model is used to explore this potential therapy, both analytically and numerically. For the numerical work, we use clinical data from both HIV-negative and HIV-positive injection drug users (IDUs) to estimate model parameters; these groups have lower baseline concentrations of antioxidants than non-IDU controls. Results: Our model suggests that increases in CD4+ T cell concentrations can result from moderate levels of daily antioxidant supplementation, while excessive supplementation has the potential to cause periods of immunosuppression. Conclusion: We discuss implications for HIV therapy in IDUs and other populations which may have low baseline concentrations of antioxidants. [ABSTRACT FROM AUTHOR]

Abstract: Viral load and CD4 T-cell counts in patients infected with the human immunodeficiency virus (HIV) are commonly used to guide clinical decisions regarding drug therapy or to assess therapeutic outcomes in clinical trials. However, random fluctuations in these markers of infection can obscure clinically significant change. We employ a Monte Carlo simulation to investigate contributing factors in the expected variability in CD4 T-cell count and viral load due solely to the stochastic nature of HIV infection. The simulation includes processes that contribute to the variability in HIV infection including CD4 and CD8 T-cell population dynamics as well as T-cell activation and proliferation. The simulation results may reconcile the wide range of variabilities in viral load observed in clinical studies, by quantifying correlations between viral load measurements taken days or weeks apart. The sensitivity of variability in T-cell count and viral load to changes in the lifetimes of CD4 and CD8 T-cells is investigated, as well as the effects of drug therapy. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Sperm competition is a major force of sexual selection, but its implications for mating system and life-history evolution are just beginning to be understood. Of particular importance is understanding the mechanisms of sperm competition. Models have been developed to determine if sperm competition operates in a fair raffle process, whereby each sperm from competing males has an equal chance of fertilizing a female's ova, or if it operates in a loaded raffle process, whereby one male's sperm has a fertilization advantage. These models require data on relative sperm and offspring (paternity) numbers of competing males. Here we develop a model based on maximum-likelihood methods for differentiating between the fair and loaded raffle processes. The model calculates the relative competitiveness of two males' sperm (loadings) as well as the economy of scale (nonlinear returns to sperm number). Previous models implicitly assumed that there is no economy of scale, which may not be the case when there is cooperation or interference among sperm from a given male. We demonstrate that our model has superior power--in some instances more than double--than previous models. We apply our model to an example of sperm competition in the guppy (Poecilia reticulata) and show that the system may be characterized by a loaded raffle attributable to effects of second male precedence. [ABSTRACT FROM AUTHOR]

Experimental evolution is characterized by exponential or logistic growth and periodic population bottlenecks. The fate of a rare beneficial mutation in these systems is influenced both by the bottleneck effect and by genetic drift. This paper explores the effects of incorporating genetic drift into models of fixation probability in populations with periodic bottlenecks. To model the inherent stochasticity during the growth phase in these populations, we assume a Poisson distribution of offspring. An analytical solution is developed to calculate the fixation probability and a computer simulation is used to verify the results. We find that the fixation rate of a favourable mutant is significantly lower when genetic drift is considered; fixation probability is reduced by over 25% for realistic experimental protocols. Our method is valid for both weak and strong selection; since very large selection coefficients have been reported in the experimental literature, this is an important improvement over previous results. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]

Presents a study that derived the ultimate probability of extinction for a beneficial mutation in a periodically bottlenecked population, using both discrete and continuous approaches. Effects of population bottlenecks on the dynamics of evolution; Information on the approximate expression for an effective population size; Implications for the quantitative analysis of experimental evolution.

Examines the role of genetic chance and selective necessity in models of experimental evolution. Evolution of a simple genome; Effect of allowing rate mutations; Effect of stochastic sampling; Behavior of genetic systems evolving under strong selective pressure.

Abstract. For the investigation of intracerebral dopamine metabolism, 6-[[sup 18]F]fluoro-L-m-tyrosine (FmT) has been proposed as an alternative tracer that, unlike 6-[[sup 18]F]fluoro-l-dopa, is not subjected to O-methylation. We have studied the time course of FmT and its labelled metabolites in plasma after intravenous injection into humans, employing a method that we have developed and validated to analyze labelled metabolites of FmT in plasma. The study population comprised 38 subjects, 14 of whom were taking an aromatic amino acid decarboxylase inhibitor (carbidopa), and obtained arterialized venous blood samples at various times alter an intravenous injection of between 185 and 370 MBq of FmT. The major metabolite of FmT present in plasma was 6-[[sup 18]F]fluoro-3-hydroxyphenylacetic acid. The time course of the fraction of radioactivity in plasma attributable to FmT was fitted well by the decay of two exponential functions. The fast component of the decay accounted for 40%-50% of the radioactivity and had a half-life of about 5 min. The slow component of the decay had a half-life of about 6 h in the subjects not taking carbidopa and 20 h in the patients taking carbidopa. When the total available FmT was calculated for each individual subject and expressed as a proportion of total radioactivity, this quantity did not differ significantly from that determined from the corresponding population mean. There was significantly more (15% on average) FmT available over the course of the 2-h experiment in the group pretreated with carbidopa. Our results demonstrate that... [ABSTRACT FROM AUTHOR]

Bacterial strains with a short minimal doubling time--'fast-growing' hosts--are more likely to contain prophages than their slow-growing counterparts. Pathogenic bacterial species are likewise more likely to carry prophages. We develop a bioinformatics pipeline to examine the distribution of prophages in fast- and slow-growing lysogens, and pathogenic and non-pathogenic lysogens, analysing both prophage length and gene content for each class. By fitting these results to a mathematical model of the evolutionary forces acting on prophages, we predict whether the observed differences can be attributed to different rates of lysogeny among the host classes, or other evolutionary pressures. We also test for significant differences in gene content among prophages, identifying genes that are preferentially lost or maintained in each class. We find that fast-growing hosts and pathogens have a greater fraction of full-length prophages, and our analysis predicts that induction rates are significantly reduced in slow-growing hosts and non-pathogenic hosts. Consistentwith previous results, we find that several proteins involved in the packaging of new phage particles and lysis are preferentially lost in cryptic prophages. [ABSTRACT FROM AUTHOR]

A mutator is a variant in a population of organisms whose mutation rate is higher than the average mutation rate in the population. For genetic and population dynamics reasons, mutators are produced and survive with much greater frequency than anti-mutators (variants with a lower-than-average mutation rate). This strong asymmetry is a consequence of both fundamental genetics and natural selection; it can lead to a ratchet-like increase in the mutation rate. The rate at which mutators appear is, therefore, a parameter that should be of great interest to evolutionary biologists generally; for example, it can influence: (1) the survival duration of a species, especially asexual species (which are known to be short-lived), (2) the evolution of recombination, a process that can ameliorate the deleterious effects of mutator abundance, (3) the rate at which cancer appears, (4) the ability of pathogens to escape immune surveillance in their hosts, (5) the long-term fate of mitochondria, etc. In spite of its great relevance to basic and applied science, the rate of mutation to a mutator phenotype continues to be essentially unknown. The reasons for this gap in our knowledge are largely methodological; in general, a mutator phenotype cannot be observed directly, but must instead be inferred from the numbers of some neutral "marker" mutation that can be observed directly: different mutation-rate variants will produce this marker mutation at different rates. Here, we derive the expected distribution of the numbers of the marker mutants observed, accounting for the fact that some of the mutants will have been produced by a mutator phenotype that itself arose by mutation during the growth of the culture. These developments, together with previous enhancements of the Luria–Delbrück assay (by one of us, dubbed the "Jones protocol"), make possible a novel experimental protocol for estimating the rate of mutation to a mutator phenotype. Simulated experiments using biologically reasonable parameters that employ this protocol show that such experiments in the lab can give us fairly accurate estimates of the rate of mutation to a mutator phenotype. Although our ability to estimate mutation-to-mutator rates from simulated experiments is promising, we view this study as a proof-of-concept study and an important first step towards practical empirical estimation. [ABSTRACT FROM AUTHOR]

Integrated into their bacterial hosts' genomes, prophage sequences exhibit a wide diversity of length and gene content, from highly degraded cryptic sequences to intact, functional prophages that retain a full complement of lytic-function genes. We apply three approaches—bioinformatics, analytical modelling and computational simulation—to understand the diverse gene content of prophages. In the bioinformatics work, we examine the distributions of over 50,000 annotated prophage genes identified in 1384 prophage sequences, comparing the gene repertoires of intact and incomplete prophages. These data indicate that genes involved in the replication, packaging, and release of phage particles have been preferentially lost in incomplete prophages, while tail fiber, transposase and integrase genes are significantly enriched. Consistent with these results, our mathematical and computational approaches predict that genes involved in phage lytic function are preferentially lost, resulting in shorter prophages that often retain genes that benefit the host. Informed by these models, we offer novel hypotheses for the enrichment of integrase and transposase genes in cryptic prophages. Overall, we demonstrate that functional and cryptic prophages represent a diversity of genetic sequences that evolve along a parasitism-mutualism continuum. Author summary: Prophages exhibit tremendous variation in both length and gene content, but little is understood about the gene repertoires of intact (functional) or degraded (cryptic) prophage sequences. By comparing large datasets of annotated prophage genes, we offer evidence for both the enrichment and loss of genes of specific function, resulting in various "signatures" of prophage gene content. We then use analytical and computational models to understand the evolutionary forces underlying those genomic signatures. In particular, our data analysis demonstrates that tail fiber, integrase and transposase genes are enriched in cryptic prophages. Informed by our simulation studies, we offer novel hypotheses to explain these unexpected results. [ABSTRACT FROM AUTHOR]

Recent experimental evidence demonstrates that shifts in mutational biases—for example, increases in transversion frequency—can change the distribution of fitness effects of mutations (DFE). In particular, reducing or reversing a prevailing bias can increase the probability that a de novo mutation is beneficial. It has also been shown that mutator bacteria are more likely to emerge if the beneficial mutations they generate have a larger effect size than observed in the wild type. Here, we connect these two results, demonstrating that mutator strains that reduce or reverse a prevailing bias have a positively shifted DFE, which in turn can dramatically increase their emergence probability. Since changes in mutation rate and bias are often coupled through the gain and loss of DNA repair enzymes, our results predict that the invasion of mutator strains will be facilitated by shifts in mutation bias that offer improved access to previously undersampled beneficial mutations. [ABSTRACT FROM AUTHOR]

We investigate the fate of de novo mutations that occur during the in-host replication of a pathogenic virus, predicting the probability that such mutations are passed on during disease transmission to a new host. Using influenza A virus as a model organism, we develop a life-history model of the within-host dynamics of the infection, deriving a multitype branching process with a coupled deterministic model to capture the population of available target cells. We quantify the fate of neutral mutations and mutations affecting five life-history traits: clearance, attachment, budding, cell death, and eclipse phase timing. Despite the severity of disease transmission bottlenecks, our results suggest that in a single transmission event, several mutations that appeared de novo in the donor are likely to be transmitted to the recipient. Even in the absence of a selective advantage for these mutations, the sustained growth phase inherent in each disease transmission cycle generates genetic diversity that is not eliminated during the transmission bottleneck. [ABSTRACT FROM AUTHOR]

Biased mutation spectra are pervasive, with wide variation in the magnitude of mutational biases that influence genome evolution and adaptation. How do such diverse biases evolve? Our experiments show that changing the mutation spectrum allows populations to sample previously undersampled mutational space, including beneficial mutations. The resulting shift in the distribution of fitness effects is advantageous: Beneficial mutation supply and beneficial pleiotropy both increase, while deleterious load reduces. More broadly, simulations indicate that reducing or reversing the direction of a long-term bias is always selectively favored. Such changes in mutation bias can occur easily via altered function of DNA repair genes. A phylogenetic analysis shows that these genes are repeatedly gained and lost in bacterial lineages, leading to frequent bias shifts in opposite directions. Thus, shifts in mutation spectra may evolve under selection and can directly alter the outcome of adaptive evolution by facilitating access to beneficial mutations. [ABSTRACT FROM AUTHOR]

We present a model and associated simulation package (www.beeplusplus.ca) to capture the natural dynamics of a honey bee colony in a spatially-explicit landscape, with temporally-variable, weather-dependent parameters. The simulation tracks bees of different ages and castes, food stores within the colony, pollen and nectar sources and the spatial position of individual foragers outside the hive. We track explicitly the intake of pesticides in individual bees and their ability to metabolize these toxins, such that the impact of sub-lethal doses of pesticides can be explored. Moreover, pathogen populations (in particular, Nosema apis, Nosema cerenae and Varroa mites) have been included in the model and may be introduced at any time or location. The ability to study interactions among pesticides, climate, biodiversity and pathogens in this predictive framework should prove useful to a wide range of researchers studying honey bee populations. To this end, the simulation package is written in open source, object-oriented code (C++) and can be easily modified by the user. Here, we demonstrate the use of the model by exploring the effects of sub-lethal pesticide exposure on the flight behaviour of foragers. [ABSTRACT FROM AUTHOR]

A previous study of prokaryotic genomes identified large reservoirs of putative mobile promoters (PMPs), that is, homologous promoter sequences associated with nonhomologous coding sequences. Here we extend this data set to identify the full complement of mobile promoters in sequenced prokaryotic genomes. The expanded search identifies nearly 40,000 PMP sequences, 90% of which occur in noncoding regions of the genome. To gain further insight from this data set, we develop a birth-death-diversification model for mobile genetic elements subject to sequence diversification; applying the model to PMPs we are able to quantify the relative importance of duplication, loss, horizontal gene transfer (HGT), and diversification to the maintenance of the PMP reservoir. The model predicts low rates of HGT relative to the duplication and loss of PMP copies, rapid dynamics of PMP families, and a pool of PMPs that exist as a single copy in a genome at any given time, despite their mobility. We report evidence of these "singletons" at high frequencies in prokaryotic genomes. We also demonstrate that including selection, either for or against PMPs, was not necessary to describe the observed data. [ABSTRACT FROM AUTHOR]

Outbreaks of highly pathogenic strains of avian influenza (HPAI) cause high mortality in avian populations worldwide. When spread from avian reservoirs to humans, HPAI infections cause mortality in about 50% of human infections. Cases of human-to-human transmission of HPAI are relatively rare, and have, to date, only been reported in situations of close contact. These transmissions have resulted in isolated clusters of human HPAI infections, but have not yet caused a pandemic. Given the large number of human H5N1 HPAI infections to date, none of which has resulted in a pandemic, we estimate an upper bound on the probability of H5N1 pandemic emergence. We use this estimate to provide the likelihood of observing such a pandemic over the next decade. We then develop a more accurate parameter-based estimate of the emergence probability and predict the likelihood that, through rare mutations, an H5N1 influenza pandemic will emerge over the same time span. [ABSTRACT FROM AUTHOR]

Information theory was used to identify nonconserved coevolving positions in multiple sequence alignments from a variety of protein families. Coevolving positions in these alignments fall into two general categories. One set is composed of positions that coevolve with only one or two other positions. These positions often display direct amino acid side-chain interactions with their coevolving partner. The other set comprises positions that coevolve with many others and are frequently located in regions critical for protein function, such as active sites and surfaces involved in intermolecular interactions and recognition. We find that coevolving positions are more likely to change protein function when mutated than are positions showing little coevolution. These results imply that information theory may be applied generally to find coevolving, nonconserved positions that are part of functional sites in uncharacterized protein families. We propose that these coevolving positions compose an important subset of the positions in an alignment, and may be as important to the structure and function of the protein family as are highly conserved positions. [ABSTRACT FROM AUTHOR]

The emergence and re-emergence of pathogens remains a major public health concern. Unfortunately, when and where pathogens will (re-)emerge is notoriously difficult to predict, as the erratic nature of those events is reinforced by the stochastic nature of pathogen evolution during the early phase of an epidemic. For instance, mutations allowing pathogens to escape host resistance may boost pathogen spread and promote emergence. Yet, the ecological factors that govern such evolutionary emergence remain elusive because of the lack of ecological realism of current theoretical frameworks and the difficulty of experimentally testing their predictions. Here, we develop a theoretical model to explore the effects of the heterogeneity of the host population on the probability of pathogen emergence, with or without pathogen evolution. We show that evolutionary emergence and the spread of escape mutations in the pathogen population is more likely to occur when the host population contains an intermediate proportion of resistant hosts. We also show that the probability of pathogen emergence rapidly declines with the diversity of resistance in the host population. Experimental tests using lytic bacteriophages infecting their bacterial hosts containing Clustered Regularly Interspaced Short Palindromic Repeat and CRISPR-associated (CRISPR-Cas) immune defenses confirm these theoretical predictions. These results suggest effective strategies for cross-species spillover and for the management of emerging infectious diseases. [ABSTRACT FROM AUTHOR]

Within-host SARS-CoV-2 modelling studies have been published throughout the COVID-19 pandemic. These studies contain highly variable numbers of individuals and capture varying timescales of pathogen dynamics; some studies capture the time of disease onset, the peak viral load and subsequent heterogeneity in clearance dynamics across individuals, while others capture late-time post-peak dynamics. In this study, we curate multiple previously published SARS-CoV-2 viral load data sets, fit these data with a consistent modelling approach, and estimate the variability of in-host parameters including the basic reproduction number, R 0 , as well as the best-fit eclipse phase profile. We find that fitted dynamics can be highly variable across data sets, and highly variable within data sets, particularly when key components of the dynamic trajectories (e.g. peak viral load) are not represented in the data. Further, we investigated the role of the eclipse phase time distribution in fitting SARS-CoV-2 viral load data. By varying the shape parameter of an Erlang distribution, we demonstrate that models with either no eclipse phase, or with an exponentially-distributed eclipse phase, offer significantly worse fits to these data, whereas models with less dispersion around the mean eclipse time (shape parameter two or more) offered the best fits to the available data across all data sets used in this work. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics". [Display omitted] • SARS-CoV-2 early in-host infection data is necessary for proper parameter estimation. • Time of peak viral load and associated parameters for SARS-CoV-2 cannot be accurately estimated with late infection data. • Robust exploration of in-host parameter variability and practical identifiability. • SARS-CoV-2 dynamics are highly variable across and within data sets. • The eclipse dynamics are best described by an Erlang distribution. [ABSTRACT FROM AUTHOR]

Baiyangdian (BYD) virus is a recently-identified mosquito-borne flavivirus that causes severe disease in ducks, with extremely rapid transmission, up to 15% mortality within 10 days and 90% reduction in egg production on duck farms within 5 days of infection. Because of the zoonotic nature of flaviviruses, the characterization of BYD virus and its epidemiology are important public health concerns. Here, we develop a mathematical model for the transmission dynamics of this novel virus. We validate the model against BYD outbreak data collected from duck farms in Southeast China, as well as experimental data obtained from an animal facility. Based on our model, the basic reproductive number of BYD virus is high (R0 = 21) indicating that this virus is highly transmissible, consistent with the dramatic epidemiology observed in BYDV-affected duck farms. Our results indicate that younger ducks are more vulnerable to BYD disease and that ducks infected with BYD virus reduce egg production (to about 33% on average) for about 3 days post-infection; after 3 days infected ducks are no longer able to produce eggs. Using our model, we predict that control measures which reduce contact between mosquitoes and ducks such as mosquito nets are more effective than insecticides. [ABSTRACT FROM AUTHOR]

Background: Unigenic evolution is a large-scale mutagenesis experiment used to identify residues that are potentially important for protein function. Both currently-used methods for the analysis of unigenic evolution data analyze 'windows' of contiguous sites, a strategy that increases statistical power but incorrectly assumes that functionally-critical sites are contiguous. In addition, both methods require the questionable assumption of asymptotically-large sample size due to the presumption of approximate normality. Results: We develop a novel approach, termed the Evidence of Selection (EoS), removing the assumption that functionally important sites are adjacent in sequence and and explicitly modelling the effects of limited samplesize. Precise statistical derivations show that the EoS score can be easily interpreted as an expected log-odds-ratio between two competing hypotheses, namely, the hypothetical presence or absence of functional selection for a given site. Using the EoS score, we then develop selection criteria by which functionally-important yet nonadjacent sites can be identified. An approximate power analysis is also developed to estimate the reliability of inference given the data. We validate and demonstrate the the practical utility of our method by analysis of the homing endonuclease I-Bmol, comparing our predictions with the results of existing methods. Conclusions: Our method is able to assess both the evidence of selection at individual amino acid sites and estimate the reliability of those inferences. Experimental validation with I-Bmol proves its utility to identify functionally-important residues of poorly characterized proteins, demonstrating increased sensitivity over previous methods without loss of specificity. With the ability to guide the selection of precise experimental mutagenesis conditions, our method helps make unigenic analysis a more broadly applicable technique with which to probe protein function. Availability: Software to compute, plot, and summarize EoS data is available as an open-source package called 'unigenic' for the 'R' programming language at http://www.fernandes.org/txp/article/13/an-analytical-framework-forunigenic- evolution. [ABSTRACT FROM AUTHOR]

Bone remodeling occurs asynchronously at multiple sites in the adult skeleton and involves resorption by osteoclasts, followed by formation of new bone by osteoblasts. Disruptions in bone remodeling contribute to the pathogenesis of disorders such as osteoporosis, osteoarthritis, and Paget’s disease. Interactions among cells of osteoblast and osteoclast lineages are critical in the regulation of bone remodeling. We constructed a mathematical model of autocrine and paracrine interactions among osteoblasts and osteoclasts that allowed us to calculate cell population dynamics and changes in bone mass at a discrete site of bone remodeling. The model predicted different modes of dynamic behavior: a single remodeling cycle in response to an external stimulus, a series of internally regulated cycles of bone remodeling, or unstable behavior similar to pathological bone remodeling in Paget’s disease. Parametric analysis demonstrated that the mode of dynamic behavior in the system depends strongly on the regulation of osteoclasts by autocrine factors, such as transforming growth factor β. Moreover, simulations demonstrated that nonlinear dynamics of the system may explain the differing effects of immunosuppressants on bone remodeling in vitro and in vivo. In conclusion, the mathematical model revealed that interactions among osteoblasts and osteoclasts result in complex, nonlinear system behavior, which cannot be deduced from studies of each cell type alone. The model will be useful in future studies assessing the impact of cytokines, growth factors, and potential therapies on the overall process of remodeling in normal bone and in pathological conditions such as osteoporosis and Paget’s disease. [Copyright &y& Elsevier]

Background: Small, highly reactive molecules called reactive oxygen species (ROS) play a crucial role in cell signalling and infection control. However, high levels of ROS can cause significant damage to cell structure and function. Studies have shown that infection with the human immunodeficiency virus (HIV) results in increased ROS concentrations, which can in turn lead to faster progression of HIV infection, and cause CD4+ T-cell apoptosis. To counteract these effects, clinical studies have explored the possibility of raising antioxidant levels, with mixed results.Methods: In this paper, a mathematical model is used to explore this potential therapy, both analytically and numerically. For the numerical work, we use clinical data from both HIV-negative and HIV-positive injection drug users (IDUs) to estimate model parameters; these groups have lower baseline concentrations of antioxidants than non-IDU controls.Results: Our model suggests that increases in CD4+ T cell concentrations can result from moderate levels of daily antioxidant supplementation, while excessive supplementation has the potential to cause periods of immunosuppression.Conclusion: We discuss implications for HIV therapy in IDUs and other populations which may have low baseline concentrations of antioxidants. [ABSTRACT FROM AUTHOR]