The turning point and end of an expanding epidemic cannot be precisely forecast.

Epidemic spread is characterized by exponentially growing dynamics, which are intrinsically unpredictable. The time at which the growth in the number of infected individuals halts and starts decreasing cannot be calculated with certainty before the turning point is actually attained; neither can the end of the epidemic after the turning point. A susceptible-infected-removed (SIR) model with confinement (SCIR) illustrates how lockdown measures inhibit infection spread only above a threshold that we calculate. The existence of that threshold has major effects in predictability: A Bayesian fit to the COVID-19 pandemic in Spain shows that a slowdown in the number of newly infected individuals during the expansion phase allows one to infer neither the precise position of the maximum nor whether the measures taken will bring the propagation to the inhibition regime. There is a short horizon for reliable prediction, followed by a dispersion of the possible trajectories that grows extremely fast. The impossibility to predict in the midterm is not due to wrong or incomplete data, since it persists in error-free, synthetically produced datasets and does not necessarily improve by using larger datasets. Our study warns against precise forecasts of the evolution of epidemics based on mean-field, effective, or phenomenological models and supports that only probabilities of different outcomes can be confidently given.

The simple emergence of complex molecular function.

At odds with a traditional view of molecular evolution that seeks a descent-with-modification relationship between functional sequences, new functions can emerge de novo with relative ease. At early times of molecular evolution, random polymers could have sufficed for the appearance of incipient chemical activity, while the cellular environment harbours a myriad of proto-functional molecules. The emergence of function is facilitated by several mechanisms intrinsic to molecular organization, such as redundant mapping of sequences into structures, phenotypic plasticity, modularity or cooperative associations between genomic sequences. It is the availability of niches in the molecular ecology that filters new potentially functional proposals. New phenotypes and subsequent levels of molecular complexity could be attained through combinatorial explorations of currently available molecular variants. Natural selection does the rest. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.

Standing Genetic Diversity and Transmission Bottleneck Size Drive Adaptation in Bacteriophage Qß.

A critical issue to understanding how populations adapt to new selective pressures is the relative contribution of the initial standing genetic diversity versus that generated de novo. RNA viruses are an excellent model to study this question, as they form highly heterogeneous populations whose genetic diversity can be modulated by factors such as the number of generations, the size of population bottlenecks, or exposure to new environment conditions. In this work, we propagated at nonoptimal temperature (43 °C) two bacteriophage Qß populations differing in their degree of heterogeneity. Deep sequencing analysis showed that, prior to the temperature change, the most heterogeneous population contained some low-frequency mutations that had previously been detected in the consensus sequences of other Qß populations adapted to 43 °C. Evolved populations with origin in this ancestor reached similar growth rates, but the adaptive pathways depended on the frequency of these standing mutations and the transmission bottleneck size. In contrast, the growth rate achieved by populations with origin in the less heterogeneous ancestor did depend on the transmission bottleneck size. The conclusion is that viral diversification in a particular environment may lead to the emergence of mutants capable of accelerating adaptation when the environment changes.

Endemicity and prevalence of multipartite viruses under heterogeneous between-host transmission.

Multipartite viruses replicate through a puzzling evolutionary strategy. Their genome is segmented into two or more parts, and encapsidated in separate particles that appear to propagate independently. Completing the replication cycle, however, requires the full genome, so that a systemic infection of a host requires the concurrent presence of several particles. This represents an apparent evolutionary drawback of multipartitism, while its advantages remain unclear. A transition from monopartite to multipartite viral forms has been described in vitro under conditions of high multiplicity of infection, suggesting that cooperation between defective mutants is a plausible evolutionary pathway towards multipartitism. However, it is unknown how the putative advantages that multipartitism might enjoy at the microscopic level affect its epidemiology, or if an explicit advantange is needed to explain its ecological persistence. In order to disentangle which mechanisms might contribute to the rise and fixation of multipartitism, we here investigate the interaction between viral spreading dynamics and host population structure. We set up a compartmental model of the spread of a virus in its different forms and explore its epidemiology using both analytical and numerical techniques. We uncover that the impact of host contact structure on spreading dynamics entails a rich phenomenology of ecological relationships that includes cooperation, competition, and commensality. Furthermore, we find out that multipartitism might rise to fixation even in the absence of explicit microscopic advantages. Multipartitism allows the virus to colonize environments that could not be invaded by the monopartite form, while homogeneous contacts between hosts facilitate its spread. We conjecture that these features might have led to an increase in the diversity and prevalence of multipartite viral forms concomitantly with the expansion of agricultural practices.

Disentangling the effects of selection and loss bias on gene dynamics.

We combine mathematical modeling of genome evolution with comparative analysis of prokaryotic genomes to estimate the relative contributions of selection and intrinsic loss bias to the evolution of different functional classes of genes and mobile genetic elements (MGE). An exact solution for the dynamics of gene family size was obtained under a linear duplication-transfer-loss model with selection. With the exception of genes involved in information processing, particularly translation, which are maintained by strong selection, the average selection coefficient for most nonparasitic genes is low albeit positive, compatible with observed positive correlation between genome size and effective population size. Free-living microbes evolve under stronger selection for gene retention than parasites. Different classes of MGE show a broad range of fitness effects, from the nearly neutral transposons to prophages, which are actively eliminated by selection. Genes involved in antiparasite defense, on average, incur a fitness cost to the host that is at least as high as the cost of plasmids. This cost is probably due to the adverse effects of autoimmunity and curtailment of horizontal gene transfer caused by the defense systems and selfish behavior of some of these systems, such as toxin-antitoxin and restriction modification modules. Transposons follow a biphasic dynamics, with bursts of gene proliferation followed by decay in the copy number that is quantitatively captured by the model. The horizontal gene transfer to loss ratio, but not duplication to loss ratio, correlates with genome size, potentially explaining increased abundance of neutral and costly elements in larger genomes.

Internal Disequilibria and Phenotypic Diversification during Replication of Hepatitis C Virus in a Noncoevolving Cellular Environment.

Viral quasispecies evolution upon long-term virus replication in a noncoevolving cellular environment raises relevant general issues, such as the attainment of population equilibrium, compliance with the molecular-clock hypothesis, or stability of the phenotypic profile. Here, we evaluate the adaptation, mutant spectrum dynamics, and phenotypic diversification of hepatitis C virus (HCV) in the course of 200 passages in human hepatoma cells in an experimental design that precluded coevolution of the cells with the virus. Adaptation to the cells was evidenced by increase in progeny production. The rate of accumulation of mutations in the genomic consensus sequence deviated slightly from linearity, and mutant spectrum analyses revealed a complex dynamic of mutational waves, which was sustained beyond passage 100. The virus underwent several phenotypic changes, some of which impacted the virus-host relationship, such as enhanced cell killing, a shift toward higher virion density, and increased shutoff of host cell protein synthesis. Fluctuations in progeny production and failure to reach population equilibrium at the genomic level suggest internal instabilities that anticipate an unpredictable HCV evolution in the complex liver environment.IMPORTANCE Long-term virus evolution in an unperturbed cellular environment can reveal features of virus evolution that cannot be explained by comparing natural viral isolates. In the present study, we investigate genetic and phenotypic changes that occur upon prolonged passage of hepatitis C virus (HCV) in human hepatoma cells in an experimental design in which host cell evolutionary change is prevented. Despite replication in a noncoevolving cellular environment, the virus exhibited internal population disequilibria that did not decline with increased adaptation to the host cells. The diversification of phenotypic traits suggests that disequilibria inherent to viral populations may provide a selective advantage to viruses that can be fully exploited in changing environments.

Getting to Know Viral Evolutionary Strategies: Towards the Next Generation of Quasispecies Models.

Viral populations are formed by complex ensembles of genomes with broad phenotypic diversity. The adaptive strategies deployed by these ensembles are multiple and often cannot be predicted a priori. Our understanding of viral dynamics is mostly based on two kinds of empirical approaches: one directed towards characterizing molecular changes underlying fitness changes and another focused on population-level responses. Simultaneously, theoretical efforts are directed towards developing a formal picture of viral evolution by means of more realistic fitness landscapes and reliable population dynamics models. New technologies, chiefly the use of next-generation sequencing and related tools, are opening avenues connecting the molecular and the population levels. In the near future, we hope to be witnesses of an integration of these still decoupled approaches, leading into more accurate and realistic quasispecies models able to capture robust generalities and endowed with a satisfactory predictive power.

Enumerating secondary structures and structural moieties for circular RNAs.

A quantitative characterization of the relationship between molecular sequence and structure is essential to improve our understanding of how function emerges. This particular genotype-phenotype map has been often studied in the context of RNA sequences, with the folded configurations standing as a proxy for the phenotype. Here, we count the secondary structures of circular RNAs of length n and calculate the asymptotic distributions of different structural moieties, such as stems or hairpin loops, by means of symbolic combinatorics. Circular RNAs differ in essential ways from their linear counterparts. From the mathematical viewpoint, the enumeration of the corresponding secondary structures demands the use of combinatorial techniques additional to those used for linear RNAs. The asymptotic number of secondary structures for circular RNAs grows as ann-5/2, with a depending on particular constraints applied to the secondary structure. As it occurs with linear RNA, the abundance of any structural moiety is normally distributed in the limit n→∞, with a mean and a variance that increase linearly with n.

New patterns in human biogeography revealed by networks of contacts between linguistic groups.

Human languages differ broadly in abundance and are distributed highly unevenly on the Earth. In many qualitative and quantitative aspects, they strongly resemble biodiversity distributions. An intriguing and previously unexplored issue is the architecture of the neighbouring relationships between human linguistic groups. Here we construct and characterize these networks of contacts and show that they represent a new kind of spatial network with uncommon structural properties. Remarkably, language networks share a meaningful property with food webs: both are quasi-interval graphs. In food webs, intervality is linked to the existence of a niche space of low dimensionality; in language networks, we show that the unique relevant variable is the area occupied by the speakers of a language. By means of a range model analogous to niche models in ecology, we show that a geometric restriction of perimeter covering by neighbouring linguistic domains explains the structural patterns observed. Our findings may be of interest in the development of models for language dynamics or regarding the propagation of cultural innovations. In relation to species distribution, they pose the question of whether the spatial features of species ranges share architecture, and eventually generating mechanism, with the distribution of human linguistic groups.

Large-scale genomic analysis suggests a neutral punctuated dynamics of transposable elements in bacterial genomes.

Insertion sequences (IS) are the simplest and most abundant form of transposable DNA found in bacterial genomes. When present in multiple copies, it is thought that they can promote genomic plasticity and genetic exchange, thus being a major force of evolutionary change. The main processes that determine IS content in genomes are, though, a matter of debate. In this work, we take advantage of the large amount of genomic data currently available and study the abundance distributions of 33 IS families in 1811 bacterial chromosomes. This allows us to test simple models of IS dynamics and estimate their key parameters by means of a maximum likelihood approach. We evaluate the roles played by duplication, lateral gene transfer, deletion and purifying selection. We find that the observed IS abundances are compatible with a neutral scenario where IS proliferation is controlled by deletions instead of purifying selection. Even if there may be some cases driven by selection, neutral behavior dominates over large evolutionary scales. According to this view, IS and hosts tend to coexist in a dynamic equilibrium state for most of the time. Our approach also allows for a detection of recent IS expansions, and supports the hypothesis that rapid expansions constitute transient events-punctuations-during which the state of coexistence of IS and host becomes perturbated.

River density and landscape roughness are universal determinants of linguistic diversity.

Global linguistic diversity (LD) displays highly heterogeneous distribution patterns. Though the origin of the latter is not yet fully understood, remarkable parallelisms with biodiversity distribution suggest that environmental variables should play an essential role in their emergence. In an effort to construct a broad framework to explain world LD and to systematize the available data, we have investigated the significance of 14 variables: landscape roughness, altitude, river density, distance to lakes, seasonal maximum, average and minimum temperature, precipitation and vegetation, and population density. Landscape roughness and river density are the only two variables that universally affect LD. Overall, the considered set accounts for up to 80% of African LD, a figure that decreases for the joint Asia, Australia and the Pacific (69%), Europe (56%) and the Americas (53%). Differences among those regions can be traced down to a few variables that permit an interpretation of their current states of LD. Our processed datasets can be applied to the analysis of correlations in other similar heterogeneous patterns with a broad spatial distribution, the clearest example being biological diversity. The statistical method we have used can be understood as a tool for cross-comparison among geographical regions, including the prediction of spatial diversity in alternative scenarios or in changing environments.

Tempo and mode of inhibitor-mutagen antiviral therapies: a multidisciplinary approach.

The continuous emergence of drug-resistant viruses is a major obstacle for the successful treatment of viral infections, thus representing a persistent spur to the search for new therapeutic strategies. Among them, multidrug treatments are currently at the forefront of pharmaceutical, clinical, and computational investigation. Still, there are many unknowns in the way that different drugs interact among themselves and with the pathogen that they aim to control. Inspired by experimental studies with picornavirus, here, we discuss the performance of sequential vs. combination therapies involving two dissimilar drugs: the mutagen ribavirin and an inhibitor of viral replication, guanidine. Because a systematic analysis of viral response to drug doses demands a precious amount of time and resources, we present and analyze an in silico model describing the dynamics of the viral population under the action of the two drugs. The model predicts the response of the viral population to any dose combination, the optimal therapy to be used in each case, and the way to minimize the probability of appearance of resistant mutants. In agreement with the theoretical predictions, in vitro experiments with foot-and-mouth disease virus confirm that the suitability of simultaneous or sequential administration depends on the drug doses. In addition, intrinsic replicative characteristics of the virus (e.g., replication through RNA only or a DNA intermediate) play a key role to determine the appropriateness of a sequential or combination therapy. Knowledge of several model parameters can be derived by means of few, simple experiments, such that the model and its predictions can be extended to other viral systems.

Viral genome segmentation can result from a trade-off between genetic content and particle stability.

The evolutionary benefit of viral genome segmentation is a classical, yet unsolved question in evolutionary biology and RNA genetics. Theoretical studies anticipated that replication of shorter RNA segments could provide a replicative advantage over standard size genomes. However, this question has remained elusive to experimentalists because of the lack of a proper viral model system. Here we present a study with a stable segmented bipartite RNA virus and its ancestor non-segmented counterpart, in an identical genomic nucleotide sequence context. Results of RNA replication, protein expression, competition experiments, and inactivation of infectious particles point to a non-replicative trait, the particle stability, as the main driver of fitness gain of segmented genomes. Accordingly, measurements of the volume occupation of the genome inside viral capsids indicate that packaging shorter genomes involves a relaxation of the packaging density that is energetically favourable. The empirical observations are used to design a computational model that predicts the existence of a critical multiplicity of infection for domination of segmented over standard types. Our experiments suggest that viral segmented genomes may have arisen as a molecular solution for the trade-off between genome length and particle stability. Genome segmentation allows maximizing the genetic content without the detrimental effect in stability derived from incresing genome length.

Evolutionary dynamics of genome segmentation in multipartite viruses.

Multipartite viruses are formed by a variable number of genomic fragments packed in independent viral capsids. This fact poses stringent conditions on their transmission mode, demanding, in particular, a high multiplicity of infection (MOI) for successful propagation. The actual advantages of the multipartite viral strategy are as yet unclear. The origin of multipartite viruses represents an evolutionary puzzle. While classical theories suggested that a faster replication rate or higher replication fidelity would favour shorter segments, recent experimental results seem to point to an increased stability of virions with incomplete genomes as a factor able to compensate for the disadvantage of mandatory complementation. Using as main parameters differential stability as a function of genome length and MOI, we calculate the conditions under which a set of complementary segments of a viral genome would outcompete the non-segmented variant. Further, we examine the likeliness that multipartite viral forms could be the evolutionary outcome of the competition among the defective genomes of different lengths that spontaneously arise under replication of a complete, wild-type genome. We conclude that only multipartite viruses with a small number of segments could be produced in our scenario, and discuss alternative hypotheses for the origin of multipartite viruses with more than four segments.

The dawn of the RNA World: toward functional complexity through ligation of random RNA oligomers.

A main unsolved problem in the RNA World scenario for the origin of life is how a template-dependent RNA polymerase ribozyme emerged from short RNA oligomers obtained by random polymerization on mineral surfaces. A number of computational studies have shown that the structural repertoire yielded by that process is dominated by topologically simple structures, notably hairpin-like ones. A fraction of these could display RNA ligase activity and catalyze the assembly of larger, eventually functional RNA molecules retaining their previous modular structure: molecular complexity increases but template replication is absent. This allows us to build up a stepwise model of ligation-based, modular evolution that could pave the way to the emergence of a ribozyme with RNA replicase activity, step at which information-driven Darwinian evolution would be triggered.

Potential benefits of sequential inhibitor-mutagen treatments of RNA virus infections.

Lethal mutagenesis is an antiviral strategy consisting of virus extinction associated with enhanced mutagenesis. The use of non-mutagenic antiviral inhibitors has faced the problem of selection of inhibitor-resistant virus mutants. Quasispecies dynamics predicts, and clinical results have confirmed, that combination therapy has an advantage over monotherapy to delay or prevent selection of inhibitor-escape mutants. Using ribavirin-mediated mutagenesis of foot-and-mouth disease virus (FMDV), here we show that, contrary to expectations, sequential administration of the antiviral inhibitor guanidine (GU) first, followed by ribavirin, is more effective than combination therapy with the two drugs, or than either drug used individually. Coelectroporation experiments suggest that limited inhibition of replication of interfering mutants by GU may contribute to the benefits of the sequential treatment. In lethal mutagenesis, a sequential inhibitor-mutagen treatment can be more effective than the corresponding combination treatment to drive a virus towards extinction. Such an advantage is also supported by a theoretical model for the evolution of a viral population under the action of increased mutagenesis in the presence of an inhibitor of viral replication. The model suggests that benefits of the sequential treatment are due to the involvement of a mutagenic agent, and to competition for susceptible cells exerted by the mutant spectrum. The results may impact lethal mutagenesis-based protocols, as well as current antiviral therapies involving ribavirin.

Struggle for space: viral extinction through competition for cells.

The design of protocols to suppress the propagation of viral infections is an enduring enterprise, especially hindered by limited knowledge of the mechanisms leading to viral extinction. Here we report on infection extinction due to intraspecific competition to infect susceptible hosts. Beneficial mutations increase the production of viral progeny, while the host cell may develop defenses against infection. For an unlimited number of host cells, a feedback runaway coevolution between host resistance and progeny production occurs. However, physical space limits the advantage that the virus obtains from increasing offspring numbers; thus, infection clearance may result from an increase in host defenses beyond a finite threshold. Our results might be relevant to devise improved control strategies in environments with mobility constraints or different geometrical properties.

Motif frequency and evolutionary search times in RNA populations.

RNA molecules, through their dual identity as sequence and structure, are an appropriate experimental and theoretical model to study the genotype-phenotype map and evolutionary processes taking place in simple replicator populations. In this computational study, we relate properties of the sequence-structure map, in particular the abundance of a given secondary structure in a random pool, with the number of replicative events that an initially random population of sequences needs to find that structure through mutation and selection. For common structures, this search process turns out to be much faster than for rare structures. Furthermore, search and fixation processes are more efficient in a wider range of mutation rates for common structures, thus indicating that evolvability of RNA populations is not simply determined by abundance. We also find significant differences in the search and fixation processes for structures of same abundance, and relate them with the number of base pairs forming the structure. Moreover, the influence of the nucleotide content of the RNA sequences on the search process is studied. Our results advance in the understanding of the distribution and attainability of RNA secondary structures. They hint at the fact that, beyond sequence length and sequence-to-function redundancy, the mutation rate that permits localization and fixation of a given phenotype strongly depends on its relative abundance and global, in general non-uniform, distribution in sequence space.