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The application of quasispecies theory to viral populations has boosted our understanding of how endogenous and exogenous features condition their adaptation. Mounting empirical evidence demonstrates that internal interactions within mutant spectra may cause unexpected responses to antiviral treatments. In this scenario, increased mutagenesis could be efficient at low mutagen doses due to the lethal action of defective genomes, whereas sequential administration of antiviral drugs might be superior to combination therapies. Our ability to predict the outcome of a particular therapy takes advantage of the complementary use of in vivo observations, in vitro experiments, and mathematical models., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

Viral populations are extremely plastic. They maintain and steadily generate high levels of genotypic and phenotypic diversity that may result in different adaptive strategies. A major unknown factor in constructing realistic models of viral evolution is how mutations affect fitness, which amounts to unveiling the nature of viral fitness landscapes. Our understanding of viral complexity is improving thanks to new techniques as deep sequencing or massive computation, and to systematic laboratory assays. In this way, we are clearing up the role played by neutral networks of genotypes, by defective and cooperative interactions among viral mutants, or by co-evolution with immune systems. Models of viral evolution are thus improving their accuracy and becoming more competent from a conceptual and a predictive viewpoint., (Copyright © 2012 Elsevier B.V. All rights reserved.)

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.

Many patterns displayed by the distribution of human linguistic groups are similar to the ecological organization described for biological species. It remains a challenge to identify simple and meaningful processes that describe these patterns. The population size distribution of human linguistic groups, for example, is well fitted by a log-normal distribution that may arise from stochastic demographic processes. As we show in this contribution, the distribution of the area size of home ranges of those groups also agrees with a log-normal function. Further, size and area are significantly correlated: the number of speakers p and the area a spanned by linguistic groups follow the allometric relation a proportional to p2, with an exponent z varying accross different world regions. The empirical evidence presented leads to the hypothesis that the distributions of p and a, and their mutual dependence, rely on demographic dynamics and on the result of conflicts over territory due to group growth. To substantiate this point, we introduce a two-variable stochastic multiplicative model whose analytical solution recovers the empirical observations. Applied to different world regions, the model reveals that the retreat in home range is sublinear with respect to the decrease in population size, and that the population-area exponent z grows with the typical strength of conflicts. While the shape of the population size and area distributions, and their allometric relation, seem unavoidable outcomes of demography and inter-group contact, the precise value of z could give insight on the cultural organization of those human groups in the last thousand years.

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.

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., (Copyright © 2011 Elsevier Ltd. All rights reserved.)

Lethal mutagenesis is an antiviral strategy that aims to extinguish viruses as a consequence of enhanced mutation rates during virus replication. The molecular mechanisms that underlie virus extinction by mutagenic nucleoside analogues are not well understood. When mutagenic agents and antiviral inhibitors are administered sequentially or in combination, interconnected and often conflicting selective constraints can influence the fate of the virus either towards survival through selection of mutagen-escape or inhibitor-escape mutants or towards extinction. Here we report a study involving the mutagenesis of foot-and-mouth disease virus (FMDV) by the nucleoside analogue ribavirin (R) and the effect of R-mediated mutagenesis on the selection of FMDV mutants resistant to the inhibitor of RNA replication, guanidine hydrochloride (GU). The results show that under comparable (and low) viral load, an inhibitory activity by GU could not substitute for an equivalent inhibitory activity by R in driving FMDV to extinction. Both the prior history of R mutagenesis and the viral population size influenced the selection of GU-escape mutants. A sufficiently low viral load allowed continued viral replication without selection of inhibitor-escape mutants, irrespective of the history of mutagenesis. These observations imply that reductions of viral load as a result of a mutagenic treatment may provide an opportunity either for immune-mediated clearing of a virus or for an alternative antiviral intervention, even if extinction is not initially achieved., (Copyright © 2011. Published by Elsevier Ltd.)

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., Competing Interests: The authors have declared that no competing interests exist.

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.

The evolution and adaptation of molecular populations is constrained by the diversity accessible through mutational processes. RNA is a paradigmatic example of biopolymer where genotype (sequence) and phenotype (approximated by the secondary structure fold) are identified in a single molecule. The extreme redundancy of the genotype-phenotype map leads to large ensembles of RNA sequences that fold into the same secondary structure and can be connected through single-point mutations. These ensembles define neutral networks of phenotypes in sequence space. Here we analyze the topological properties of neutral networks formed by 12-nucleotides RNA sequences, obtained through the exhaustive folding of sequence space. A total of 4(12) sequences fragments into 645 subnetworks that correspond to 57 different secondary structures. The topological analysis reveals that each subnetwork is far from being random: it has a degree distribution with a well-defined average and a small dispersion, a high clustering coefficient, and an average shortest path between nodes close to its minimum possible value, i.e. the Hamming distance between sequences. RNA neutral networks are assortative due to the correlation in the composition of neighboring sequences, a feature that together with the symmetries inherent to the folding process explains the existence of communities. Several topological relationships can be analytically derived attending to structural restrictions and generic properties of the folding process. The average degree of these phenotypic networks grows logarithmically with their size, such that abundant phenotypes have the additional advantage of being more robust to mutations. This property prevents fragmentation of neutral networks and thus enhances the navigability of sequence space. In summary, RNA neutral networks show unique topological properties, unknown to other networks previously described.

The production of large progeny numbers affected by high mutation rates is a ubiquitous strategy of viruses, as it promotes quick adaptation and survival to changing environments. However, this situation often ushers in an arms race between the virus and the host cells. In this paper we investigate in depth a model for the dynamics of a phenotypically heterogeneous population of viruses whose propagation is limited to two-dimensional geometries, and where host cells are able to develop defenses against infection. Our analytical and numerical analyses are developed in close connection to directed percolation models. In fact, we show that making the space explicit in the model, which in turn amounts to reducing viral mobility and hindering the infective ability of the virus, connects our work with similar dynamical models that lie in the universality class of directed percolation. In addition, we use the fact that our model is a multicomponent generalization of the Domany-Kinzel probabilistic cellular automaton to employ several techniques developed in the past in that context, such as the two-site approximation to the extinction transition line. Our aim is to better understand propagation of viral infections with mobility restrictions, e.g., in crops or in plant leaves, in order to inspire new strategies for effective viral control.

Since the introduction of the quasispecies and the error catastrophe concepts for molecular evolution by Eigen and their subsequent application to viral populations, increased mutagenesis has become a common strategy to cause the extinction of viral infectivity. Nevertheless, the high complexity of virus populations has shown that viral extinction can occur through several other pathways apart from crossing an error threshold. Increases in the mutation rate enhance the appearance of defective forms and promote the selection of mechanisms that are able to counteract the accelerated appearance of mutations. Current models of viral evolution take into account more realistic scenarios that consider compensatory and lethal mutations, a highly redundant genotype-to-phenotype map, rough fitness landscapes relating phenotype and fitness, and where phenotype is described as a set of interdependent traits. Further, viral populations cannot be understood without specifying the characteristics of the environment where they evolve and adapt. Altogether, it turns out that the pathways through which viral quasispecies go extinct are multiple and diverse.

For evolving populations of replicators, there is much evidence that the effect of mutations on fitness depends on the degree of adaptation to the selective pressures at play. In optimized populations, most mutations have deleterious effects, such that low mutation rates are favoured. In contrast to this, in populations thriving in changing environments a larger fraction of mutations have beneficial effects, providing the diversity necessary to adapt to new conditions. What is more, non-adapted populations occasionally benefit from an increase in the mutation rate. Therefore, there is no optimal universal value of the mutation rate and species attempt to adjust it to their momentary adaptive needs. In this work we have used stationary populations of RNA molecules evolving in silico to investigate the relationship between the degree of adaptation of an optimized population and the value of the mutation rate promoting maximal adaptation in a short time to a new selective pressure. Our results show that this value can significantly differ from the optimal value at mutation-selection equilibrium, being strongly influenced by the structure of the population when the adaptive process begins. In the short-term, highly optimized populations containing little variability respond better to environmental changes upon an increase of the mutation rate, whereas populations with a lower degree of optimization but higher variability benefit from reducing the mutation rate to adapt rapidly. These findings show a good agreement with the behaviour exhibited by actual organisms that replicate their genomes under broadly different mutation rates.

Background: The secondary structure of folded RNA sequences is a good model to map phenotype onto genotype, as represented by the RNA sequence. Computational studies of the evolution of ensembles of RNA molecules towards target secondary structures yield valuable clues to the mechanisms behind adaptation of complex populations. The relationship between the space of sequences and structures, the organization of RNA ensembles at mutation-selection equilibrium, the time of adaptation as a function of the population parameters, the presence of collective effects in quasispecies, or the optimal mutation rates to promote adaptation all are issues that can be explored within this framework., Results: We investigate the effect of microscopic mutations on the phenotype of RNA molecules during their in silico evolution and adaptation. We calculate the distribution of the effects of mutations on fitness, the relative fractions of beneficial and deleterious mutations and the corresponding selection coefficients for populations evolving under different mutation rates. Three different situations are explored: the mutation-selection equilibrium (optimized population) in three different fitness landscapes, the dynamics during adaptation towards a goal structure (adapting population), and the behavior under periodic population bottlenecks (perturbed population)., Conclusions: The ratio between the number of beneficial and deleterious mutations experienced by a population of RNA sequences increases with the value of the mutation rate mu at which evolution proceeds. In contrast, the selective value of mutations remains almost constant, independent of mu, indicating that adaptation occurs through an increase in the amount of beneficial mutations, with little variations in the average effect they have on fitness. Statistical analyses of the distribution of fitness effects reveal that small effects, either beneficial or deleterious, are well described by a Pareto distribution. These results are robust under changes in the fitness landscape, remarkably when, in addition to selecting a target secondary structure, specific subsequences or low-energy folds are required. A population perturbed by bottlenecks behaves similarly to an adapting population, struggling to return to the optimized state. Whether it can survive in the long run or whether it goes extinct depends critically on the length of the time interval between bottlenecks.

Networks of selectively neutral genotypes underlie the evolution of populations of replicators in constant environments. Previous theoretical analysis predicted that such populations will evolve toward highly connected regions of the genome space. We first study the evolution of populations of replicators on simple networks and quantify how the transient time to equilibrium depends on the initial distribution of sequences on the neutral network, on the topological properties of the latter, and on the mutation rate. Second, network neutrality is broken through the introduction of an energy for each sequence. This allows to study the competition between two features (neutrality and energetic stability) relevant for survival and subjected to different selective pressures. In cases where the two features are negatively correlated, the population experiences sudden migrations in the genome space for values of the relevant parameters that we calculate. The numerical study of larger networks indicates that the qualitative behavior to be expected in more realistic cases is already seen in representative examples of small networks.

Theoretical studies of quasispecies usually focus on two properties of those populations at the mutation-selection equilibrium, namely asymptotic growth rate and population diversity. It has been postulated that, as a consequence of the high error rate of quasispecies replication, an increase of neutrality facilitates population optimization by reducing the amount of mutations with a deleterious effect on fitness. In this study we analyse how the optimization of equilibrium properties is affected when a quasispecies evolves in an environment perturbed through frequent bottleneck events. By means of a simple model we demonstrate that high neutrality may be detrimental when the population has to overcome repeated reductions in the population size, and that the property to be optimized in this situation is the time required to regenerate the quasispecies, i.e. its adaptability. In the scenario described, neutrality and adaptability cannot be simultaneously optimized. When fitness is equated with long-term survivability, high neutrality is the appropriate strategy in constant environments, while populations evolving in fluctuating environments are fitter when their neutrality is low, such that they can respond faster to perturbations. Our results might be relevant to better comprehend how a minority virus could displace the circulating quasispecies, a fact observed in natural infections and essential in viral evolution.

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.

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.

A detailed knowledge of the mapping between sequence and structure spaces in populations of RNA molecules is essential to better understand their present-day functional properties, to envisage a plausible early evolution of RNA in a prebiotic chemical environment and to improve the design of in vitro evolution experiments, among others. Analysis of natural RNAs, as well as in vitro and computational studies, show that certain RNA structural motifs are much more abundant than others, pointing out a complex relation between sequence and structure. Within this framework, we have investigated computationally the structural properties of a large pool (10(8) molecules) of single-stranded, 35 nt-long, random RNA sequences. The secondary structures obtained are ranked and classified into structure families. The number of structures in main families is analytically calculated and compared with the numerical results. This permits a quantification of the fraction of structure space covered by a large pool of sequences. We further show that the number of structural motifs and their frequency is highly unbalanced with respect to the nucleotide composition: simple structures such as stem-loops and hairpins arise from sequences depleted in G, while more complex structures require an enrichment of G. In general, we observe a strong correlation between subfamilies-characterized by a fixed number of paired nucleotides-and nucleotide composition. Our results are compared to the structural repertoire obtained in a second pool where isolated base pairs are prohibited.

The diversity harbored by populations of RNA viruses results from high mutation rates, as well as from the characteristics of the environment where they evolve. By means of a simple model for structured quasispecies, we quantify how competition for space among phenotypic types shapes their distribution at the mutation-selection equilibrium. We introduce a general framework to treat this problem and relate mutation rate and competition strength to the quasispecies composition. For diffusion limited competition, diversity typically increases and the asymptotic growth rate of the population diminishes as diffusion decreases. Limited mobility confers a relative advantage to worse competitors. The stationary state is characterized by an over-production of viral particles. Empirical data allow an estimation of mutation rates compatible with the diversity observed in viral populations infecting cellular monolayers.

Background: RNA molecules, through their dual appearance as sequence and structure, represent a suitable model to study evolutionary properties of quasispecies. The essential ingredient in this model is the differentiation between genotype (molecular sequences which are affected by mutation) and phenotype (molecular structure, affected by selection). This framework allows a quantitative analysis of organizational properties of quasispecies as they adapt to different environments, such as their robustness, the effect of the degeneration of the sequence space, or the adaptation under different mutation rates and the error threshold associated., Results: We describe and analyze the structural properties of molecular quasispecies adapting to different environments both during the transient time before adaptation takes place and in the asymptotic state, once optimization has occurred. We observe a minimum in the adaptation time at values of the mutation rate relatively far from the phenotypic error threshold. Through the definition of a consensus structure, it is shown that the quasispecies retains relevant structural information in a distributed fashion even above the error threshold. This structural robustness depends on the precise shape of the secondary structure used as target of selection. Experimental results available for natural RNA populations are in qualitative agreement with our observations., Conclusion: Adaptation time of molecular quasispecies to a given environment is optimized at values of the mutation rate well below the phenotypic error threshold. The optimal value results from a trade-off between diversity generation and fixation of advantageous mutants. The critical value of the mutation rate is a function not only of the sequence length, but also of the specific properties of the environment, in this case the selection pressure and the shape of the secondary structure used as target phenotype. Certain functional motifs of RNA secondary structure that withstand high mutation rates (as the ubiquitous hairpin motif) might appear early in evolution and be actually frozen evolutionary accidents.

At early stages of biochemical evolution, the complexity of replicating molecules was limited by unavoidably high mutation rates. In an RNA world, prior to the appearance of cellular life, an increase in molecular length, and thus in functional complexity, could have been mediated by modular evolution. We describe here a scenario in which short, replicating RNA sequences are selected to perform a simple function. Molecular function is represented through the secondary structure corresponding to each sequence, and a given target secondary structure yields the optimal function in the environment where the population evolves. The combination of independently evolved populations may have facilitated the emergence of larger molecules able to perform more complex functions (including RNA replication) that could arise as a combination of simpler ones. We quantitatively show that modular evolution has relevant advantages with respect to the direct evolution of large functional molecules, among them the allowance of higher mutation rates, the shortening of evolutionary times, and the very possibility of finding complex structures that could not be otherwise directly selected.

Recent data from space missions reveal that there are ongoing climatic changes and erosive processes that continuously modify surface features of Mars. We have investigated the seasonal dynamics of a number of morphological features located at Inca City, a representative area at high southern latitude that has undergone seasonal processes. By integrating visual information from the Mars Orbiter Camera on board the Mars Global Surveyor and climatic cycles from a Mars' General Circulation Model, and considering the recently reported evidence for the presence of water-ice and aqueous precipitates on Mars, we propose that a number of the erosive features identified in Inca City, among them spiders, result from the seasonal melting of aqueous salty solutions.

The correlation between water physicochemical parameters and eukaryotic benthic composition was examined in Río Tinto. Principal component analysis showed a high inverse relationship between pH and most of the heavy metals analyzed as well as Dunaliella sp., while Chlamydomonas sp. abundance was positively related. Zn, Cu, and Ni clustered together and showed a strong inverse correlation with the diversity coefficient and most of the species analyzed. These eukaryotic communities seem to be more influenced by the presence of heavy metals than by the pH.

The characteristics of natural populations result from different stochastic and deterministic processes that include reproduction with error, selection, and genetic drift. In particular, population fluctuations constitute a stochastic process that may play a very relevant role in shaping the structure of populations. For example, it is expected that small asexual populations will accumulate mutations at a higher rate than larger ones. As a consequence, in any population the fixation of mutations is accelerated when environmental conditions cause population bottlenecks. Bottlenecks have been relatively frequent in the history of life and it is generally accepted that they are highly relevant for speciation. Although population bottlenecks can occur in any species, their effects are more noticeable in organisms that form large and heterogeneous populations, such as RNA viral quasispecies. Bottlenecks can also positively select and isolate particles that still keep the ability to infect cells from a disorganized population created by crossing the error threshold.

This is the second of two papers dedicated to the relationship between population models of competition and biodiversity. Here, we consider species assembly models where the population dynamics is kept far from fixed points through the continuous introduction of new species, and generalize to such models the coexistence condition derived for systems at the fixed point. The ecological overlap between species and shared preys, that we define here, provides a quantitative measure of the effective interspecies competition and of the trophic network topology. We obtain distributions of the overlap from simulations of a new model based both on immigration and speciation, and show that they are in good agreement with those measured for three large natural food webs. As discussed in the first paper, rapid environmental fluctuations, interacting with the condition for coexistence of competing species, limit the maximal biodiversity that a trophic level can host. This horizontal limitation to biodiversity is here combined with either dissipation of energy or growth of fluctuations, which in our model limit the length of food webs in the vertical direction. These ingredients yield an effective model of food webs that produce a biodiversity profile with a maximum at an intermediate trophic level, in agreement with field studies.

This is the first of two papers where we discuss the limits imposed by competition to the biodiversity of species communities. In this first paper, we study the coexistence of competing species at the fixed point of population dynamic equations. For many simple models, this imposes a limit on the width of the productivity distribution, which is more severe the more diverse the ecosystem is (1994, Theor. Popul. Biol. 45, 227-276). Here we review and generalize this analysis, beyond the "mean-field"-like approximation of the competition matrix used in previous works, and extend it to structured food webs. In all cases analysed, we obtain qualitatively similar relations between biodiversity and competition: the narrower the productivity distribution is, the more species can stably coexist. We discuss how this result, considered together with environmental fluctuations, limits the maximal biodiversity that a trophic level can host.

RNA viruses replicate with a very high error rate and give rise to heterogeneous, highly plastic populations able to adapt very rapidly to changing environments. Viral diseases are thus difficult to control because of the appearance of drug-resistant mutants, and it becomes essential to seek mechanisms able to force the extinction of the quasispecies before adaptation emerges. An alternative to the use of conventional drugs consists in increasing the replication error rate through the use of mutagens. Here, we report about persistent infections of lymphocytic choriomeningitis virus treated with fluorouracil, where a progressive debilitation of infectivity leading to eventual extinction occurs. The transition to extinction is accompanied by the production of large amounts of RNA, indicating that the replicative ability of the quasispecies is not strongly impaired by the mutagen. By means of experimental and theoretical approaches, we propose that a fraction of the RNA molecules synthesized can behave as a defective subpopulation able to drive the viable class extinct. Our results lead to the identification of two extinction pathways, one at high amounts of mutagen, where the quasispecies completely loses its ability to infect and replicate, and a second one, at lower amounts of mutagen, where replication continues while the infective class gets extinct because of the action of defectors. The results bear on a potential application of increased mutagenesis as an antiviral strategy in that low doses of a mutagenic agent may suffice to drive persistent virus to extinction.

Population bottlenecks are stochastic events that strongly condition the structure and evolution of natural populations. Their effects are readily observable in highly heterogeneous populations, such as RNA viruses, since bottlenecks cause a fast accumulation of mutations. Considering that most mutations are deleterious, it was predicted that the frequent application of bottlenecks would yield a population unable to replicate. However, in vitro as well as in vivo systems evolving through bottlenecks present a remarkable resistance to extinction. This observation reveals the robustness of RNA viruses and points to the existence of internal mechanisms which must confer a high degree of adaptability to fast mutating populations. In this contribution, we review experimental observations regarding the survival of RNA viruses, both in laboratory experiments and in natural populations. By means of a simple theoretical model of evolution which incorporates strong reductions of the population size, we explore the relationship between the number of replication rounds that a single founder particle undergoes before the next bottleneck is applied, and the mutation rate in a particular environment. Our numerical results reveal that the mutation rate has evolved in a concerted way with the degree of optimization achieved by the population originated from the founder particle. We hypothesize that this mechanism generates a mutation-selection equilibrium in natural populations that maximizes adaptability while maintaining their structure.

The extinction of foot-and-mouth disease virus (FMDV) is strongly influenced by mutation rates, types of mutations, relative viral fitness and virus population regimens during infection. Here we review experimental results and theoretical models that describe a contrast between the effective extinction of FMDV subjected to increased mutagenesis, and the remarkable resistance to extinction of the same and related FMDV clones subjected to serial bottleneck events. The results suggest procedures to master key parameters to develop effective antiviral strategies based on virus entry into error catastrophe.

The last two decades have witnessed an unsurpassed effort aimed at reconstructing the history of life from the genetic information contained in extant organisms. The availability of many sequenced genomes has allowed the reconstruction of phylogenies from gene families and its comparison with traditional single-gene trees. However, the appearance of major discrepancies between both approaches questions whether horizontal gene transfer (HGT) has played a prominent role in shaping the topology of the Tree of Life. Recent attempts at solving this controversy and reaching a consensus tree combine molecular data with additional phylogenetic markers. Translation is a universal cellular function that involves a meaningful, highly conserved set of genes: both rRNA and r-protein operons have an undisputed phylogenetic value and rarely undergo HGT. Ribosomal function reflects the concerted expression of that genetic network and consequently yields information about the evolutionary paths followed by the organisms. Here we report on tree reconstruction using a measure of the performance of the ribosome: antibiotic sensitivity of protein synthesis. A large database has been used where 33 ribosomal systems belonging to the three major cellular lineages were probed against 38 protein synthesis inhibitors. Different definitions of distance between pairs of organisms have been explored, and the classical algorithm of bootstrap evaluation has been adapted to quantify the reliability of the reconstructions obtained. Our analysis returns a consistent phylogeny, where archaea are systematically affiliated to eukarya, in agreement with recent reconstructions which used information-processing systems. The integration of the information derived from relevant functional markers into current phylogenetic reconstructions might facilitate achieving a consensus Tree of Life.

Foot-and-mouth disease virus (FMDV) is genetically and phenotypically variable. As a typical RNA virus, FMDV follows a quasispecies dynamics, with the many biological implications of such a dynamics. Mutant spectra provide a reservoir of FMDV variants, and minority subpopulations may become dominant in response to environmental demands or as a result of statistical fluctuations in population size. Accumulation of mutations in the FMDV genome occurs upon subjecting viral populations to repeated bottleneck events and upon viral replication in the presence of mutagenic base or nucleoside analogs. During serial bottleneck passages, FMDV survive during extended rounds of replication maintaining low average relative fitness, despite linear accumulation of mutations in the consensus genomic sequence. The critical event is the occurrence of a low frequency of compensatory mutations. In contrast, upon replication in the presence of mutagens, the complexity of mutant spectra increases, apparently no compensatory mutations can express their fitness-enhancing potential, and the virus can cross an error threshold for maintenance of genetic information, resulting in virus extinction. Low relative fitness and low viral load favor FMDV extinction in cell culture. The comparison of the molecular basis of resistance to extinction upon bottleneck passage and extinction by enhanced mutagenesis is providing new insights in the understanding of quasispecies dynamics. Such a comparison is contributing to the development of new antiviral strategies based on the transition of viral replication into error catastrophe.

Passage of foot-and-mouth disease virus (FMDV) in cell culture resulted in the generation of defective RNAs that were infectious by complementation. Deletions (of nucleotides 417, 999, and 1017) mapped in the L proteinase and capsid protein-coding regions. Cell killing followed two-hit kinetics, defective genomes were encapsidated into separate viral particles, and individual viral plaques contained defective genomes with no detectable standard FMDV RNA. Infection in the absence of standard FMDV RNA was achieved by cotransfection of susceptible cells with transcripts produced in vitro from plasmids encoding the defective genomes. These results document the first step of an evolutionary transition toward genome segmentation of an unsegmented RNA virus and provide an experimental system to compare rates of RNA progeny production and resistance to enhanced mutagenesis of a segmented genome versus its unsegmented counterpart.

We study some exact properties of supercritical branching processes. A proper rescaling of the relevant variable allows us to determine the distribution of population sizes after a number of generations have elapsed. Both time-continuous and discrete processes are analysed and compared. The obtained results are of relevance for the growth of populations that are not resource limited (a typical situation in some biological processes that can be modelled by laboratory experiments). Large fluctuations inherent to the process play a main role when bottlenecks occur.

RNA viruses display high mutation rates and their populations replicate as dynamic and complex mutant distributions, termed viral quasispecies. Repeated genetic bottlenecks, which experimentally are carried out through serial plaque-to-plaque transfers of the virus, lead to fitness decrease (measured here as diminished capacity to produce infectious progeny). Here we report an analysis of fitness evolution of several low fitness foot-and-mouth disease virus clones subjected to 50 plaque-to-plaque transfers. Unexpectedly, fitness decrease, rather than being continuous and monotonic, displayed a fluctuating pattern, which was influenced by both the virus and the state of the host cell as shown by effects of recent cell passage history. The amplitude of the fluctuations increased as fitness decreased, resulting in a remarkable resistance of virus to extinction. Whereas the frequency distribution of fitness in control (independent) experiments follows a log-normal distribution, the probability of fitness values in the evolving bottlenecked populations fitted a Weibull distribution. We suggest that multiple functions of viral genomic RNA and its encoded proteins, subjected to high mutational pressure, interact with cellular components to produce this nontrivial, fluctuating pattern.

We explore a mean-field model for the evolution of exponentially growing populations of mutating replicators. Motivated by recent in vitro experiments devised to analyze phenotypic properties of bacterial and viral populations subjected to serial population transfers, we allow our in silico individuals to undergo unrestricted growth before applying bottleneck events. Different dynamical regimes of our model can be mapped to different experimental situations. Numerical and analytical results for fitness distributions calculated at the statistically stationary states of the dynamics compare favorably with available experimental data. Our model and results provide a common framework to better understand populations evolving under different selection pressures.

Evolution of fitness values upon replication of viral populations is strongly influenced by the size of the virus population that participates in the infections. While large population passages often result in fitness gains, repeated plaque-to-plaque transfers result in average fitness losses. Here we develop a numerical model that describes fitness evolution of viral clones subjected to serial bottleneck events. The model predicts a biphasic evolution of fitness values in that a period of exponential decrease is followed by a stationary state in which fitness values display large fluctuations around an average constant value. This biphasic evolution is in agreement with experimental results of serial plaque-to-plaque transfers carried out with foot-and-mouth disease virus (FMDV) in cell culture. The existence of a stationary phase of fitness values has been further documented by serial plaque-to-plaque transfers of FMDV clones that had reached very low relative fitness values. The statistical properties of the stationary state depend on several parameters of the model, such as the probability of advantageous versus deleterious mutations, initial fitness, and the number of replication rounds. In particular, the size of the bottleneck is critical for determining the trend of fitness evolution.

Surnames and non-recombining alleles are inherited from a single parent in a highly similar way. A simple birth-death model with mutations can accurately describe this process. Exponentially growing and constant populations are investigated, and we study how different compositions of the founder populations can be observed in present-day diversity distributions. We analyse different quantities in the statistically stationary state, both through analytic and numerical methods. Our results compare favourably to field data for family sizes in several countries. We discuss the relationship between the distribution of surnames and the genetic diversity of a population.

We study a dynamic model of ecosystems where an immigration flux assembles the species community and maintains its biodiversity. This framework is particularly relevant for insular ecosystems. Population dynamics is represented either as an individual-based model or as a set of deterministic equations for population abundances. Local extinctions and immigrations balance at a statistically stationary state where biodiversity fluctuates around a constant mean value. We find a number of scaling laws characterizing this stationary state. In particular, the number of species increases as a power law of the immigration rate. With additional assumptions on the immigration flux, we obtain species-area relationships in agreement with observations for archipelagos. We also find power-law distributions for species abundances and lifetimes., (Copyright 2001 Academic Press.)

We study the statistics of ecosystems with a variable number of coevolving species. The species interact in two ways: by prey-predator relationships and by direct competition with similar kinds. The interaction coefficients change slowly through successful adaptations and speciations. They are treated as quenched random variables. These interactions determine long-term topological features of the species network, which are found to agree with those of biological systems.

If one goes backward in time, the number of ancestors of an individual doubles at each generation. This exponential growth very quickly exceeds the population size, when this size is finite. As a consequence, the ancestors of a given individual cannot be all different and most remote ancestors are repeated many times in any genealogical tree. The statistical properties of these repetitions in genealogical trees of individuals for a panmictic closed population of constant size N can be calculated. We show that the distribution of the repetitions of ancestors reaches a stationary shape after a small number G(c) approximately log N of generations in the past, that only about 80% of the ancestral population belongs to the tree (due to coalescence of branches), and that two trees for individuals in the same population become identical after G(c)generations have elapsed. Our analysis is easy to extend to the case of exponentially growing population., (Copyright 2000 Academic Press.)

We introduce and study systems of randomly coupled maps where the relevant parameter is the degree of connectivity in the system. Global (almost-) synchronized states are found (equivalent to the synchronization observed in globally coupled maps) until a certain critical threshold for the connectivity is reached. We further show that not only the average connectivity, but also the architecture of the couplings is responsible for the cluster structure observed. We analyze the different phases of the system and use various correlation measures in order to detect ordered nonsynchronized states. Finally, it is shown that the system displays a dynamical hierarchical clustering which allows the definition of emerging graphs.

We study a stochastic multiplicative process with reset events. It is shown that the model develops a stationary power-law probability distribution for the relevant variable, whose exponent depends on the model parameters. Two qualitatively different regimes are observed, corresponding to intermittent and regular behavior. In the boundary between them, the mean value of the relevant variable is time independent, and the exponent of the stationary distribution equals -2. The addition of diffusion to the system modifies in a nontrivial way the profile of the stationary distribution. Numerical and analytical results are presented.

Fluctuations in ecological systems are known to involve a wide range of spatial and temporal scales, often displaying self-similar (fractal) properties. Recent theoretical approaches are trying to shed light on the nature of these complex dynamics. The results suggest that complexity in ecology and evolution comes from the network-like structure of multispecies communities that are close to instability. If true, these ideas might change our understanding of how complexity emerges in the biosphere and how macroevolutionary events could be decoupled from microevolutionary ones.