arXiv subjects

Susanna Manrubia

Publications and source records attributed to Susanna Manrubia.

At least 19 recordsLinked to original sources

arXiv2026

Shared quasispecies architecture in experimental and natural RNA virus populations

RNA viruses form genetically diverse populations structured as mutant spectra, or quasispecies, whose internal organization influences their evolutionary and adaptive dynamics. While genetic diversity has been extensively characterized, the structural organization of viral populations in sequence space remains less explored. Here, we compare genotype network architectures in two RNA viruses with markedly different evolutionary contexts: bacteriophage $Qβ$ evolving in controlled laboratory conditions and SARS-CoV-2 evolving within infected human hosts. Using deep sequencing data, we reconstruct the genotype network of mutationally coupled variants within viral populations and analyze their topological properties. Despite large differences in genome size, mutation rate, and ecological setting, both viruses exhibit a common organization: a highly abundant central haplotype surrounded by layers of variants of diminishing abundance as Hamming distance to the central haplotype increases. All reconstructed networks share qualitative and quantitative topological features, displaying a hierarchical structure. The robust organization of both populations under multiple conditions suggests that RNA viruses may share a common genotype network architecture governed by fundamental properties of sequence space and the generic mechanisms of replication and mutation. Genotype networks provide a unifying framework to describe viral population structure beyond conventional diversity measures and, by revealing how local constraints shape mutational search, offers insights into the predictability of viral evolution.

q-bio.PE↗

arXiv2026

A generative model for bipartite gene-sharing networks

Gene-sharing networks provide a powerful framework to study the evolution of viruses and mobile genetic elements. These bipartite networks, which link genes to the genomes that contain them, exhibit characteristic degree distributions: a scale-free distribution for genes and an exponential-like decay for genomes. Here, we propose a mechanistic model that explains these patterns through fundamental evolutionary processes including horizontal gene transfer, capture of new genes, emergence of new genomes, and gene loss. Using a mean-field approximation, we derive analytical expressions for the asymptotic gene and genome degree distributions, recapitulating a power-law distribution for genes and an exponential distribution for genomes. Numerical simulations validate these predictions and yield parameter values that closely fit empirical data from dsDNA viruses, RNA viruses, and prokaryotic pangenomes. This simple model with only two parameters provides a generative framework for bipartite gene-sharing networks, offering qualitative and quantitative insights into the main evolutionary forces driving genome plasticity. Setting the gene loss rate to zero, the gene and genome degree distributions of the model closely fit the empirically observed distributions. Thus, evolution of viruses appears to be dominated by gene gain, in agreement with the results of independent reconstructions of viral evolution.

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arXiv2026

The challenge of scale in molecular adaptation: Local searches in astronomical genotype networks

The exploration of vast genotype spaces poses fundamental challenges for evolving populations. As the number of genotypes encoding viable phenotypes grows exponentially with genome length, populations can only explore a tiny fraction of these immense spaces, a fact consistently supported by empirical and theoretical evidence. Paradoxically, local, mutation-driven searches near abundant sequences allow populations to generate phenotypic improvements and functional innovations despite this immense search space. In this contribution, we integrate insights from viral evolution with theoretical expectations derived from genotype-phenotype maps to re-examine how high-dimensional sequence spaces shape evolutionary dynamics. In resolving the paradox, abundant phenotypes play a crucial role because their combinatorial weight biases evolutionary trajectories. We discuss how this bias, together with limited accessibility of fitness peaks, modifies traditional metaphors -- such as fitness landscapes -- and challenges standard notions of evolutionary optimality. Our results underscore that adaptation is predominantly local yet remarkably efficient, providing a unifying perspective on the coexistence of robustness, innovation, and constrained exploration in molecular evolution.

q-bio.PE↗

arXiv2025

Optimal COVID-19 vaccine prioritization by age depends critically on inter-group contacts and vaccination rates

The limited availability of COVID-19 vaccines has prompted extensive research on optimal vaccination strategies. Previous studies have considered various non-pharmaceutical interventions, vaccine efficacy, and distribution strategies. In this work, we address the combined effects of inter-group contacts and vaccination rates under contact reduction, analyzing the Spanish population's demographic and age group contact patterns and incorporating reinfection dynamics. We conduct an exhaustive analysis, evaluating 362,880 permutations of 9 age groups across 6 vaccination rates and two distinct, empirically quantified scenarios for social contacts. Our results show that at intermediate-to-high vaccination rates with unrestricted social contacts, optimal age-based vaccination strategies only slightly deviate from older-to-younger prioritization, yielding marginal reductions in deaths and infections. However, when significant reductions in social contacts are enforced -similar to the lockdowns in 2020-, there are substantial improvements, particularly at moderate vaccination rates. These restrictions lead to a transition where infection propagation is halted, a scenario that became achievable during the pandemic with the observed vaccination rates. Our findings emphasize the importance of combining appropriate social contact reductions with vaccination to optimize age-based vaccination strategies, underscoring the complex, nonlinear dynamics involved in pandemic dynamics and the necessity for tailored, context-specific interventions.

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arXiv2024

Hierarchical genotype networks and incipient ecological speciation in Q$β$ phage quasispecies

Understanding how viral mutant spectra organize and explore genotype space is essential for unraveling the mechanisms driving evolution at the finest scale. Here we use deep-sequencing data of an amplicon in the A2 protein of the RNA bacteriophage Q$β$ to reconstruct genotype networks with tens of thousands of different haplotypes. The study of populations evolved under different temperature regimes uncovers generic topological features conditioned by fundamental structural motifs of genotype networks -- tetrahedrons, triangles, and squares -- that govern their local architecture. Mutant swarms display a hierarchical structure where sequences cluster around a highly connected and abundant sequence core that sustains population diversity. The immediate neighborhood of this core is comprehensively sampled, with no signs of selection, while a few mutations away sampling becomes dynamical and sparse, showing signs of purifying selection. By aggregating genotype networks from populations adapted to different temperatures, we capture the early stages of evolutionary divergence, with overlapping populations that remain connected through short mutational paths. Even at the time scale of these experiments, evolutionary pathways might be multiple, preventing the backward reconstruction of unique trajectories once mutations have been fixed. This analysis provides a detailed view of the local, fine-scale processes shaping viral quasispecies evolution and underscores the usefulness of genotype networks as an enlightening visualization of the organization of mutant swarms.

q-bio.PE↗

arXiv2023

Entropic contribution to phenotype fitness

All possible phenotypes are not equally accessible to evolving populations. In fact, only phenotypes of large size, i.e. those resulting from many different genotypes, are found in populations of sequences, presumably because they are easier to discover and maintain. Genotypes that map to these phenotypes usually form mostly connected genotype networks that percolate the space of sequences, thus guaranteeing access to a large set of alternative phenotypes. Within a given environment, where specific phenotypic traits become relevant for adaptation, the replicative ability of a phenotype and its overall fitness (in competition experiments with alternative phenotypes) can be estimated. Two primary questions arise: how do phenotype size, reproductive capability and topology of the genotype network affect the fitness of a phenotype? And, assuming that evolution is only able to access large phenotypes, what is the range of unattainable fitness values? In order to address these questions, we quantify the adaptive advantage of phenotypes of varying size and spectral radius in a two-peak landscape. We derive analytical relationships between the three variables (size, topology, and replicative ability) which are then tested through analysis of genotype-phenotype maps and simulations of population dynamics on such maps. Finally, we analytically show that the fraction of attainable phenotypes decreases with the length of the genotype, though its absolute number increases. The fact that most phenotypes are not visible to evolution very likely forbids the attainment of the highest peak in the landscape. Nevertheless, our results indicate that the relative fitness loss due to this limited accessibility is largely inconsequential for adaptation.

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arXiv2021

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 {\it 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 harbors 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.

q-bio.PE↗

arXiv2021

Fat Tails and Black Swans: Exact Results for Multiplicative Processes with Resets

We consider a class of multiplicative processes which, added with stochastic reset events, give origin to stationary distributions with power-law tails -- ubiquitous in the statistics of social, economic, and ecological systems. Our main goal is to provide a series of exact results on the dynamics and asymptotic behaviour of increasingly complex versions of a basic multiplicative process with resets, including discrete and continuous-time variants and several degrees of randomness in the parameters that control the process. In particular, we show how the power-law distributions are built up as time elapses, how their moments behave with time, and how their stationary profiles become quantitatively determined by those parameters. Our discussion emphasizes the connection with financial systems, but these stochastic processes are also expected to be fruitful in modeling a wide variety of social and biological phenomena.

q-fin.ST↗

arXiv2021

Individual risk-aversion responses tune epidemics to critical transmissibility ($R=1$)

Changes in human behavior are increasingly recognized as a major determinant of epidemic dynamics. Although collective activity can be modified through imposed measures to control epidemic progression, spontaneous changes can also arise as a result of uncoordinated individual responses to the perceived risk of contagion. Here we introduce a stochastic epidemic model that implements population responses driven by individual- and time-dependent risk-taking propensity. The model reveals an emergent mechanism for the generation of multiple infection waves of decreasing amplitude without the need to consider external modulation of parameters. Successive waves tune the effective reproduction number to its critical value $R=1$. This process is a consequence of the interplay of the fractions of susceptible and infected population and the average risk-taking propensity, as shown by a mean-field approach. The proposed mechanism also shows how, under the threat of contagion, the distribution of individual risk propensities evolves towards a well-defined profile. Successive waves trigger selective sweeps of risk-taking propensity at a pace determined by individual risk reaction rates. This kind of collective, self-generated pressure, may therefore shape risk-aversion profiles associated to epidemics in human groups. The final state is self-organized and generic, independent of the parameter values. We conclude that uncoordinated changes in human behavior can, by themselves, explain major qualitative and quantitative features of the epidemic process, as the emergence of multiple waves and the tendency to remain around $R=1$ observed worldwide after the first few waves of COVID-19.

q-bio.PE↗

arXiv2021

From genotypes to organisms: State-of-the-art and perspectives of a cornerstone in evolutionary dynamics

Understanding how genotypes map onto phenotypes, fitness, and eventually organisms is arguably the next major missing piece in a fully predictive theory of evolution. We refer to this generally as the problem of the genotype-phenotype map. Though we are still far from achieving a complete picture of these relationships, our current understanding of simpler questions, such as the structure induced in the space of genotypes by sequences mapped to molecular structures, has revealed important facts that deeply affect the dynamical description of evolutionary processes. Empirical evidence supporting the fundamental relevance of features such as phenotypic bias is mounting as well, while the synthesis of conceptual and experimental progress leads to questioning current assumptions on the nature of evolutionary dynamics-cancer progression models or synthetic biology approaches being notable examples. This work delves into a critical and constructive attitude in our current knowledge of how genotypes map onto molecular phenotypes and organismal functions, and discusses theoretical and empirical avenues to broaden and improve this comprehension. As a final goal, this community should aim at deriving an updated picture of evolutionary processes soundly relying on the structural properties of genotype spaces, as revealed by modern techniques of molecular and functional analysis.

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arXiv2020

Predictability: Can the turning point and end of an expanding epidemic be precisely forecast?

No, they can't. 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. An 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 slow-down in the number of newly infected individuals during the expansion phase allows 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 mid-term is not due to wrong or incomplete data, since it persists in error-free, synthetically produced data sets, and does not necessarily improve by using larger data sets. 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.

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arXiv2019

Epistasis between cultural traits drives paradigm shifts in cultural evolution

Every now and then the cultural paradigm of a society changes. Human history can be regarded as a sequence of long periods of cultural stasis punctuated by paradigm shifts that transform culture upside-down over the turn of a few generations. We propose here a population dynamics model devised to analyse paradigm shifts. In this model individuals are defined by a vector of cultural traits that can change mainly through imitation of other individuals' traits. The novelty of the model is that cultural traits may interact reinforcing or hindering each other. Imitation is then biased by the 'cultural fitness' landscape thus defined. Our main result is that abrupt paradigm shifts occur, as a response to weak changes in the landscape, only when cultural traits do interact---whereas adaptation is smooth if there is no interaction. Borrowing the genetic term, this interaction is called 'cultural epistasis'. The result is robust to the way that epistasis is implemented, to whether imitation is biased by homophily, or to changes in other model parameters. Finally, a relevant consequence of this dynamics is the irreversible nature of paradigm shifts: the old paradigm cannot be restored even if the external changes are undone. Our model puts the phenomenon of paradigm shifts in cultural evolution in the same category as catastrophic shifts in ecology or phase transitions in physics.

physics.soc-ph↗

arXiv2019

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. To disentangle which mechanisms might contribute to the rise and fixation of multipartitism, we 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. We find 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, facilitated by homogeneous contacts among hosts. 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.

physics.soc-ph↗

arXiv2018

Statistical theory of phenotype abundance distributions: a test through exact enumeration of genotype spaces

The evolutionary dynamics of molecular populations are strongly dependent on the structure of genotype spaces. The map between genotype and phenotype determines how easily genotype spaces can be navigated and the accessibility of evolutionary innovations. In particular, the size of neutral networks corresponding to specific phenotypes and its statistical counterpart, the distribution of phenotype abundance, have been studied through multiple computationally tractable genotype-phenotype maps. In this work, we test a theory that predicts the abundance of a phenotype and the corresponding asymptotic distribution (given the compositional variability of its genotypes) through the exact enumeration of several GP maps. Our theory predicts with high accuracy phenotype abundance, and our results show that, in navigable genotype spaces ---characterised by the presence of large neutral networks---, phenotype abundance converges to a log-normal distribution.

q-bio.PE↗

arXiv2018

Limited role of spatial self-structuring in emergent trade-offs during pathogen evolution

Pathogen transmission and virulence are main evolutionary variables broadly assumed to be linked through trade-offs. In well-mixed populations, these trade-offs are often ascribed to physiological restrictions, while populations with spatial self-structuring might evolve emergent trade-offs. Here, we reexamine a model of the latter kind proposed by Ballegooijen and Boerlijst with the aim of characterising the mechanisms causing the emergence of the trade-off and its structural robustness. Using invadability criteria, we establish the conditions under which an evolutionary feedback between transmission and virulence mediated by pattern formation can poise the system to a critical boundary separating a disordered state (without emergent trade-off) from a self-structured phase (where the trade-off emerges), and analytically calculate the functional shape of the boundary in a certain approximation. Beyond evolutionary parameters, the success of an invasion depends on the size and spatial structure of the invading and invaded populations. Spatial self-structuring is often destroyed when hosts are mobile, changing the evolutionary dynamics to those of a well-mixed population. In a metapopulation scenario, the systematic extinction of the pathogen in the disordered phase may counteract the disruptive effect of host mobility, favour pattern formation and therefore recover the emergent trade-off.

q-bio.PE↗

arXiv2018

On the networked architecture of genotype spaces and its critical effects on molecular evolution

Evolutionary dynamics is often viewed as a subtle process of change accumulation that causes a divergence among organisms and their genomes. However, this interpretation is an inheritance of a gradualistic view that has been challenged at the macroevolutionary, ecological, and molecular level. Actually, when the complex architecture of genotype spaces is taken into account, the evolutionary dynamics of molecular populations becomes intrinsically non-uniform, sharing deep qualitative and quantitative similarities with slowly driven physical systems: non-linear responses analogous to critical transitions, sudden state changes, or hysteresis, among others. Furthermore, the phenotypic plasticity inherent to genotypes transforms classical fitness landscapes into multiscapes where adaptation in response to an environmental change may be very fast. The quantitative nature of adaptive molecular processes is deeply dependent on a networks-of-networks multilayered structure of the map from genotype to function that we begin to unveil.

q-bio.PE↗

arXiv2017

Distribution of phenotype sizes in sequence-to-structure genotype-phenotype maps

An essential quantity to ensure evolvability of populations is the navigability of the genotype space. Navigability relies on the existence of sufficiently large genotype networks, that is ensembles of sequences with the same phenotype that guarantee an efficient random drift through sequence space. The number of sequences compatible with a given structure (e.g. the number of RNA sequences folding into a particular secondary structure, or the number of DNA sequences coding for the same protein structure) is astronomically large in all functional molecules investigated. However, an exhaustive experimental or computational study of all RNA folds or all protein structures becomes impossible even for moderately long sequences. Here, we analytically derive the distribution of phenotype sizes for a hierarchy of models which successively incorporate features of increasingly realistic sequence-to-structure genotype-phenotype maps. The main feature of these models relies on the characterization of each phenotype through a prototypical sequence whose sites admit a variable fraction of letters of the alphabet. Our models interpolate between two limit distributions: a powerlaw distribution, when the ordering of sites in the prototypical sequence is strongly constrained, and a lognormal distribution, as suggested for RNA, when different orderings of the same set of sites yield different phenotypes. Our main result is the qualitative and quantitative identification of those features of the sequence-to-structure map that lead to different distributions of phenotype sizes.

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arXiv2017

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 $a^nn^{-5/2}$, with a depending on particular constraints applied to the secondary structure. The abundance of any structural moiety is normally distributed in the limit $n\to\infty$, with a mean and a variance that increase linearly with $n$.

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