Loss and Recovery of Genetic Diversity in Adapting Populations of HIV

The evolution of drug resistance in HIV occurs by the fixation of specific, well-known, drug-resistance mutations, but the underlying population genetic processes are not well understood. By analyzing within-patient longitudinal sequence data, we make four observations that shed a light on the underlying processes and allow us to infer the short-term effective population size of the viral population in a patient. Our first observation is that the evolution of drug resistance usually occurs by the fixation of one drug-resistance mutation at a time, as opposed to several changes simultaneously. Second, we find that these fixation events are accompanied by a reduction in genetic diversity in the region surrounding the fixed drug-resistance mutation, due to the hitchhiking effect. Third, we observe that the fixation of drug-resistance mutations involves both hard and soft selective sweeps. In a hard sweep, a resistance mutation arises in a single viral particle and drives all linked mutations with it when it spreads in the viral population, which dramatically reduces genetic diversity. On the other hand, in a soft sweep, a resistance mutation occurs multiple times on different genetic backgrounds, and the reduction of diversity is weak. Using the frequency of occurrence of hard and soft sweeps we estimate the effective population size of HIV to be ( confidence interval ). This number is much lower than the actual number of infected cells, but much larger than previous population size estimates based on synonymous diversity. We propose several explanations for the observed discrepancies. Finally, our fourth observation is that genetic diversity at non-synonymous sites recovers to its pre-fixation value within 18 months, whereas diversity at synonymous sites remains depressed after this time period. These results improve our understanding of HIV evolution and have potential implications for treatment strategies

Searching Market Equilibria under Uncertain Utilities

Our basic model is a noncooperative multi-player game in which the governments of neighboring counties trade emission reductions. We prove the existence of a market equilibrium (combining properties of Pareto and Nash equilibria) and study algorithms of searching a market equilibrium. The algorithms are interpreted as repeated auctions in which the auctioneer has no information on countries' costs and benefits and every government has no information on the costs and benefits of other countries. In each round of the auction, the auctioneer offers individual prices for emission reductions and observes countries' best replies. We consider several auctioneer's policies and provide conditions that guarantee approaching a market equilibrium. From a game-theoretical point of view, the repeated auction describes a process of learning in a noncooperative repeated game with incomplete information

Epistasis not needed to explain low dN/dS

An important question in molecular evolution is whether an amino acid that occurs at a given position makes an independent contribution to fitness, or whether its effect depends on the state of other loci in the organism's genome, a phenomenon known as epistasis. In a recent letter to Nature, Breen et al. (2012) argued that epistasis must be "pervasive throughout protein evolution" because the observed ratio between the per-site rates of non-synonymous and synonymous substitutions (dN/dS) is much lower than would be expected in the absence of epistasis. However, when calculating the expected dN/dS ratio in the absence of epistasis, Breen et al. assumed that all amino acids observed in a protein alignment at any particular position have equal fitness. Here, we relax this unrealistic assumption and show that any dN/dS value can in principle be achieved at a site, without epistasis. Furthermore, for all nuclear and chloroplast genes in the Breen et al. dataset, we show that the observed dN/dS values and the observed patterns of amino acid diversity at each site are jointly consistent with a non-epistatic model of protein evolution.Comment: This manuscript is in response to "Epistasis as the primary factor in molecular evolution" by Breen et al. Nature 490, 535-538 (2012

Optimal Economic Growth under Stochastic Environmental Impact: Sensitivity Analysis

In this work we present an approach toward the sensitivity analysis of optimal economic growth to a negative environmental impact driven by random natural hazards that damage the production output . We use a simplified model of the GDP whose growth leads to the increase of GHG in the atmosphere provided investment in cleaning is insufficient. The hypothesis of the Poisson probability distribution of the natural hazards is used at the first stage of the research. We apply the standard utility function - the discounted integral consumption and construct an optimal investment policy in production and cleaning together with optimal GDP trajectories. We calibrate the model in the global scale and analyze the sensitivity of obtained optimal growth scenarios with respect to uncertain parameters of the Poisson distribution

Canalization of the evolutionary trajectory of the human influenza virus

Since its emergence in 1968, influenza A (H3N2) has evolved extensively in genotype and antigenic phenotype. Antigenic evolution occurs in the context of a two-dimensional 'antigenic map', while genetic evolution shows a characteristic ladder-like genealogical tree. Here, we use a large-scale individual-based model to show that evolution in a Euclidean antigenic space provides a remarkable correspondence between model behavior and the epidemiological, antigenic, genealogical and geographic patterns observed in influenza virus. We find that evolution away from existing human immunity results in rapid population turnover in the influenza virus and that this population turnover occurs primarily along a single antigenic axis. Thus, selective dynamics induce a canalized evolutionary trajectory, in which the evolutionary fate of the influenza population is surprisingly repeatable and hence, in theory, predictable.Comment: 29 pages, 5 figures, 10 supporting figure

Detecting Past Positive Selection through Ongoing Negative Selection

Detecting positive selection is a challenging task. We propose a method for detecting past positive selection through ongoing negative selection, based on comparison of the parameters of intraspecies polymorphism at functionally important and selectively neutral sites where a nucleotide substitution of the same kind occurred recently. Reduced occurrence of recently replaced ancestral alleles at functionally important sites indicates that negative selection currently acts against these alleles and, therefore, that their replacements were driven by positive selection. Application of this method to the Drosophila melanogaster lineage shows that the fraction of adaptive amino acid replacements remained approximately 0.5 for a long time. In the Homo sapiens lineage, however, this fraction drops from approximately 0.5 before the Ponginae–Homininae divergence to approximately 0 after it. The proposed method is based on essentially the same data as the McDonald–Kreitman test but is free from some of its limitations, which may open new opportunities, especially when many genotypes within a species are known

Microevolution of Helicobacter pylori during prolonged infection of single hosts and within families

Our understanding of basic evolutionary processes in bacteria is still very limited. For example, multiple recent dating estimates are based on a universal inter-species molecular clock rate, but that rate was calibrated using estimates of geological dates that are no longer accepted. We therefore estimated the short-term rates of mutation and recombination in Helicobacter pylori by sequencing an average of 39,300 bp in 78 gene fragments from 97 isolates. These isolates included 34 pairs of sequential samples, which were sampled at intervals of 0.25 to 10.2 years. They also included single isolates from 29 individuals (average age: 45 years) from 10 families. The accumulation of sequence diversity increased with time of separation in a clock-like manner in the sequential isolates. We used Approximate Bayesian Computation to estimate the rates of mutation, recombination, mean length of recombination tracts, and average diversity in those tracts. The estimates indicate that the short-term mutation rate is 1.4×10−6 (serial isolates) to 4.5×10−6 (family isolates) per nucleotide per year and that three times as many substitutions are introduced by recombination as by mutation. The long-term mutation rate over millennia is 5–17-fold lower, partly due to the removal of non-synonymous mutations due to purifying selection. Comparisons with the recent literature show that short-term mutation rates vary dramatically in different bacterial species and can span a range of several orders of magnitude

The Role of GC-Biased Gene Conversion in Shaping the Fastest Evolving Regions of the Human Genome

GC-biased gene conversion (gBGC) is a recombination-associated evolutionary process that accelerates the fixation of guanine or cytosine alleles, regardless of their effects on fitness. gBGC can increase the overall rate of substitutions, a hallmark of positive selection. Many fast-evolving genes and noncoding sequences in the human genome have GC-biased substitution patterns, suggesting that gBGC—in contrast to adaptive processes—may have driven the human changes in these sequences. To investigate this hypothesis, we developed a substitution model for DNA sequence evolution that quantifies the nonlinear interacting effects of selection and gBGC on substitution rates and patterns. Based on this model, we used a series of lineage-specific likelihood ratio tests to evaluate sequence alignments for evidence of changes in mode of selection, action of gBGC, or both. With a false positive rate of less than 5% for individual tests, we found that the majority (76%) of previously identified human accelerated regions are best explained without gBGC, whereas a substantial minority (19%) are best explained by the action of gBGC alone. Further, more than half (55%) have substitution rates that significantly exceed local estimates of the neutral rate, suggesting that these regions may have been shaped by positive selection rather than by relaxation of constraint. By distinguishing the effects of gBGC, relaxation of constraint, and positive selection we provide an integrated analysis of the evolutionary forces that shaped the fastest evolving regions of the human genome, which facilitates the design of targeted functional studies of adaptation in humans

Intraseasonal Dynamics and Dominant Sequences in H3N2 Influenza

Long-term influenza evolution has been well studied, but the patterns of sequence diversity within seasons are less clear. H3N2 influenza genomes sampled from New York State over ten years indicated intraseasonal changes in evolutionary dynamics. Using the mean Hamming distance of a set of amino acid or nucleotide sequences as an indicator of its diversity, we found that influenza sequence diversity was significantly higher during the early epidemic period than later in the influenza season. Diversity was lowest during the peak of the epidemic, most likely due to the high prevalence of a single dominant amino acid sequence or very few dominant sequences during the peak epidemic period, corresponding with rapid expansion of the viral population. The frequency and duration of dominant sequences varied by influenza protein, but all proteins had an abundance of one distinct sequence during the peak epidemic period. In New York State from 1995 to 2005, high sequence diversity during the early epidemic suggested that seasonal antigenic drift could have occurred primarily in this period, followed by a clonal expansion of typically one clade during the peak of the epidemic, possibly indicating a shift to neutral drift or purifying selection

Security in the Age of Systemic Risk: Strategies, Tactics and Options for Dealing with Femtorisks and Beyond

The world today is increasingly confronted with systemic threats and challenges, in which femtorisks - small-scale dangers that are inherent to system structures and function and which pose asymmetrically catastrophic risks - can build in consequence, spreading uncontrollably like epidemics in both natural and social systems in such diverse areas as ecology, epidemiology, finance, the Internet, terrorism, and international relations. They have been successfully modeled in ecology in the context of complex adaptive systems: systems made up of individual agents, whose interactions have macroscopic consequences that feed back to influence individual behavior. While acknowledging challenges, this paper argues for the value of applying to societal systems the approaches that natural scientists have developed in quantifying and modeling biological interactions and ecosystems