We develop a continuous mathematical model of population dynamics that describes the sequential emergence of new genotypes under limited resources. The framework models genotype density as a nonlinear flow in mutation space, combining transport driven by a time-dependent mutation rate with logistic growth and nonlocal competition. For the advection-reaction regime without reverse mutations, we derive analytical solutions using the method of characteristics and obtain explicit expressions for time-varying carrying capacities and mutation velocities. We analyze how decaying and accelerating mutation rates shape the saturation and propagation of population fronts through level-set geometry. When reverse mutations are included, the system becomes a quasilinear parabolic equation with diffusion in genotype space; numerical experiments show that backward mutation flows stabilize the dynamics and smooth the evolving fronts. The proposed model generalizes classical quasispecies and Crow-Kimura formulations by incorporating logistic regulation, variable mutation rates, and reversible transitions, offering a unified approach to evolutionary processes relevant to virology, bacterial adaptation, and tumor progression.

Bacteriophage-bacteria interactions are central to microbial ecology, influencing evolution, biogeochemical cycles, and pathogen behavior. Most theoretical models assume static environments and passive bacterial hosts, neglecting the joint effects of bacterial traits and environmental fluctuations on coexistence dynamics. This limitation hinders the prediction of microbial persistence in dynamic ecosystems such as soils and this http URL a minimal ordinary differential equation framework, we show that the bacterial growth rate and the phage adsorption rate collectively determine three possible ecological outcomes: phage extinction, stable coexistence, or oscillation-induced extinction. Specifically, we demonstrate that environmental fluctuations can suppress destructive oscillations through resonance, promoting coexistence where static models otherwise predict collapse. Counterintuitively, we find that lower bacterial growth rates are helpful in enhancing survival under high infection pressure, elucidating the observed post-infection growth this http URL studies reframe bacterial hosts as active builders of ecological dynamics and environmental variation as a potential stabilizing force. Our findings thus bridge a key theory-experiment gap and provide a foundational framework for predicting microbial responses to environmental stress, which might have potential implications for phage therapy, microbiome management, and climate-impacted community resilience.

Finite and infinite population models are frequently used in population dynamics. However, their interrelationship is rarely discussed. In this work, we examine the limits of large populations of the Moran process (a finite-population birth-death process) and the replicator equation (an ordinary differential equation) as paradigmatic examples of finite and infinite population models, respectively, both of which are extensively used in population genetics. Except for certain degenerate cases, we completely characterize when these models exhibit similar dynamics, i.e., when there is a one-to-one relation between the stable attractors of the replicator equations and the metastable states of the Moran process. To achieve this goal, we first show that the asymptotic expression for the fixation probability in the Moran process, when the population size is large and individual interaction is almost arbitrary (including cases modeled through $d$-player game theory), is a convex combination of the asymptotic approximations obtained in the constant fitness case or 2-player game theory. We discuss several examples and the inverse problem, i.e., how to derive a Moran process that is compatible with a given replicator dynamics. In particular, we prove that modeling a Moran process with an inner metastable state may require the use of $d$-player game theory with possibly large $d$ values, depending on the precise location of the inner equilibrium.

Background: Adolescence is a critical period of brain maturation and heightened vulnerability to cognitive and mental health disorders. Sleep plays a vital role in neurodevelopment, yet the mechanisms linking insufficient sleep to adverse brain and behavioral outcomes remain unclear. The glymphatic system (GS), a brain-wide clearance pathway, may provide a key mechanistic link. Methods: Participants from the Adolescent Brain Cognitive Development (ABCD) Study (n =6,800; age ~ 11 years) were categorized into sleep-sufficient (>=9 h/night) and sleep-insufficient (<9 h/night) groups. Linear models tested associations among sleep, PVS burden, brain volumes, and behavioral outcomes. Mediation analyses evaluated whether PVS burden explained sleep-related effects. Results: Adolescents with insufficient sleep exhibited significantly greater PVS burden, reduced cortical, subcortical, and white matter volumes, poorer cognitive performance across multiple domains (largest effect in crystallized intelligence), and elevated psychopathology (largest effect in general problems). Sleep duration and quality were strongly associated with PVS burden. Mediation analyses revealed that PVS burden partially mediated sleep effects on cognition and mental health, with indirect proportions up to 10.9%. Sequential models suggested a pathway from sleep -> PVS -> brain volume -> behavior as the most plausible route. Conclusions: Insufficient sleep during adolescence is linked to glymphatic dysfunction, reflected by increased PVS burden, which partially accounts for adverse effects on brain structure, cognition, and mental health. These findings highlight the GS as a potential mechanistic pathway and imaging biomarker, underscoring the importance of promoting adequate sleep to support neurodevelopment and mental health.

In any ecosystem, the conditions of the environment and the characteristics of the species that inhabit it are entangled, co-evolving in space and time. We introduce a model that couples active agents with a dynamic environment, interpreted as a nutrient source. Agents are persistent random walkers that gather food from the environment and store it in an inner energy depot. This energy is used for self-propulsion, metabolic expenses, and reproduction. The environment is a two-dimensional surface divided into patches, each of them producing food. Thus, population size and resource distribution become emergent properties of the system. Combining simulations and analytical framework to analyze limiting cases, we show that the system exhibits distinct phases separating quasi-static and highly motile regimes. We observe that, in general, population sizes are inversely proportional to the average energy per agent. Furthermore, we find that, counter-intuitively, reduced access to resources or increased metabolic expenditure can lead to a larger population size. The proposed theoretical framework provides a link between active matter and movement ecology, allowing to investigate short vs long-term strategies to resource exploitation and rationing, as well as sedentary vs wandering strategy. The introduced approach may serve as a tool to describe real-world ecological systems and to test environmental strategies to prevent species extinction.

Recent mosquito-borne outbreaks have revealed vulnerabilities in our abatement programmes, raising concerns about how abatement-districts should choose optimal future control strategies. Spatial dissemination of vector-borne disease is strongly shaped by the movement of both hosts and mosquitoes, creating substantial overlap between vector activity and pathogen spread. We developed a mathematical model for Culex mosquito dynamics in a patchy landscape, integrating entomological observations, weather-driven factors, and the vector control practices of the Northwest Mosquito Abatement District (NWMAD) in Cook County, Illinois. By coupling a temperature-driven multi-patch ODE model with NWMAD's adulticide and larvicide interventions, we investigated how spatial heterogeneity and control timing influence mosquito abundance. We also evaluated how mosquito dispersal modifies intervention effectiveness by comparing single-patch and two-patch model outcomes. Our results showed that models ignoring spatial connectivity can substantially overestimate the impact of interventions or misidentify the thresholds of vector persistence. Through numerical simulations, we analysed continuous and pulsatile control approaches under varying spatial and temporal configurations. These findings provide insight into optimal strategies for managing Culex populations and mitigating mosquito-borne disease risk in weather-driven, spatially connected environments across Cook County, Illinois.

In an emerging pandemic, policymakers need to make important decisions with limited information, for example choosing between a mitigation, suppression or elimination strategy. These strategies may require trade-offs to be made between the health impact of the pandemic and the economic costs of the interventions introduced in response. Mathematical models are a useful tool that can help understand the consequences of alternative policy options on the future dynamics and impact of the epidemic. Most models have focused on direct health impacts, neglecting the economic costs of control measures. Here, we introduce a model framework that captures both health and economic costs. We use this framework to compare the expected aggregate costs of mitigation, suppression and elimination strategies, across a range of different epidemiological and economic parameters. We find that for diseases with low severity, mitigation tends to be the most cost-effective option. For more severe diseases, suppression tends to be most cost effective if the basic reproduction number $R_0$ is relatively low, while elimination tends to be more cost-effective if $R_0$ is high. We use the example of New Zealand's elimination response to the Covid-19 pandemic in 2020 to anchor our framework to a real-world case study. We find that parameter estimates for Covid-19 in New Zealand put it close to or above the threshold at which elimination becomes more cost-effective than mitigation. We conclude that our proposed framework holds promise as a decision-support tool for future pandemic threats, although further work is needed to account for population heterogeneity and other factors relevant to decision-making.

Community science observational datasets are useful in epidemiology and ecology for modeling species distributions, but the heterogeneous nature of the data presents significant challenges for standardization, data quality assurance and control, and workflow management. In this paper, we present a data workflow for cleaning and harmonizing multiple community science datasets, which we implement in a case study using eBird, iNaturalist, GBIF, and other datasets to model the impact of highly pathogenic avian influenza in populations of birds in the subantarctic. We predict population sizes for several species where the demographics are not known, and we present novel estimates for potential mortality rates from HPAI for those species, based on a novel aggregated dataset of mortality rates in the subantarctic.

In this paper, we introduce a novel framework using inhomogeneous Branching Random Walks (BRWs) to model growth processes, specifically introducing genealogy-dependence in branching rates and displacement distributions to model phenomena like bacterial colony growth. Current stochastic models often either assume independent and identical behavior of individual agents or incorporate only spatiotemporal inhomogeneity, ignoring the effect of genealogy-based inhomogeneity on the long-time behavior of these processes. Such long-time asymptotics are of independent mathematical interest and are crucial in understanding the effect of patterns. We propose several inhomogeneous BRW models in 2D space where displacement distributions and branching rates vary with time, space, and genealogy. A combined model then uses a weighted average of positions given by these separate models to study the shape of the growth patterns. Using computer simulations, we tune parameters from these models, which are based on genealogical and spatiotemporal factors, observe the resulting structures, and compare them with images of real bacterial colonies.

This review explores the integration of Artificial Intelligence into Horizon Scanning, focusing on identifying and responding to emerging threats and opportunities linked to Infectious Diseases. We examine how AI tools can enhance signal detection, data monitoring, scenario analysis, and decision support. We also address the risks associated with AI adoption and propose strategies for effective implementation and governance. The findings contribute to the growing body of Foresight literature by demonstrating the potential and limitations of AI in Public Health preparedness.

Antimicrobial resistance (AMR) poses a mounting global health crisis, requiring rapid and reliable prediction frameworks that capture its complex evolutionary dynamics. Traditional antimicrobial susceptibility testing (AST), while accurate, remains laborious and time-consuming, limiting its clinical scalability. Existing computational approaches, primarily reliant on single nucleotide polymorphism (SNP)-based analysis, fail to account for evolutionary drivers such as horizontal gene transfer (HGT) and genome-level interactions. This study introduces a novel Evolutionary Mixture of Experts (Evo-MoE) framework that integrates genomic sequence analysis, machine learning, and evolutionary algorithms to model and predict AMR evolution. A Mixture of Experts model, trained on labeled genomic data for multiple antibiotics, serves as the predictive core, estimating the likelihood of resistance for each genome. This model is embedded as a fitness function within a Genetic Algorithm designed to simulate AMR development across generations. Each genome, encoded as an individual in the population, undergoes mutation, crossover, and selection guided by predicted resistance probabilities. The resulting evolutionary trajectories reveal dynamic pathways of resistance acquisition, offering mechanistic insights into genomic evolution under selective antibiotic pressure. Sensitivity analysis of mutation rates and selection pressures demonstrates the model's robustness and biological plausibility. Validation against curated AMR databases and literature evidence further substantiates the framework's predictive fidelity. This integrative approach bridges genomic prediction and evolutionary simulation, offering a powerful tool for understanding and anticipating AMR dynamics, and potentially guiding rational antibiotic design and policy interventions.

The Eigen model is a prototypical toy model of evolution that is synonymous with the so-called error catastrophe: when mutation rates are sufficiently high, the genetic variant with the largest replication rate does not occupy the largest fraction of the total population because it acts as a source for the other variants. Here we show that, in the stochastic version of the Eigen model, there is also a fidelity catastrophe. This arises due to the state-dependence of fluctuations and occurs when rates of mutation fall beneath a certain threshold, which we calculate. The result is a type of noise-induced multistability whereupon the system stochastically switches between short-lived regimes of effectively clonal behavior by different genetic variants. Most notably, when the number of possible variants -- typically $\sim4^L$, with $L\gg 1$ the length of the genome -- is significantly larger than the population size, there is only a vanishingly small interval of mutation rates for which the Eigen model is neither in the fidelity- nor error-catastrophe regimes, seemingly subverting traditional expectations for evolutionary systems.

Coalescent models of bifurcating genealogies are used to infer evolutionary parameters from molecular data. However, there are many situations where bifurcating genealogies do not accurately reflect the true underlying ancestral history of samples, and a multifurcating genealogy is required. The space of multifurcating genealogical trees, where nodes can have more than two descendants, is largely underexplored in the setting of coalescent inference. In this paper, we examine the space of rooted, ranked, and unlabeled multifurcating trees. We recursively enumerate the space and then construct a partial ordering which induces a lattice on the space of multifurcating ranked tree shapes. The lattice structure lends itself naturally to defining Markov chains that permit exploration on the space of multifurcating ranked tree shapes. Finally, we prove theoretical bounds for the mixing time of two Markov chains defined on the lattice, and we present simulation results comparing the distribution of trees and tree statistics under various coalescent models to the uniform distribution on this tree space.

Modelling the evolution of a continuous trait in a biological population is one of the oldest problems in evolutionary biology, which led to the birth of quantitative genetics. With the recent development of GWAS methods, it has become essential to link the evolution of the trait distribution to the underlying evolution of allelic frequencies at many loci, co-contributing to the trait value. The way most articles go about this is to make assumptions on the trait distribution, and use Wright's formula to model how the evolution of the trait translates on each individual locus. Here, we take a gene's eye-view of the system, starting from an explicit finite-loci model with selection, drift, recombination and mutation, in which the trait value is a direct product of the genome. We let the number of loci go to infinity under the assumption of strong recombination, and characterize the limit behavior of a given locus with a McKean-Vlasov SDE and the corresponding Fokker-Planck IPDE. In words, the selection on a typical locus depends on the mean behaviour of the other loci which can be approximated with the law of the focal locus. Results include the independence of two loci and explicit stationary distribution for allelic frequencies at a given locus (under some assumptions on the fitness function).

Identification of fossil species is crucial to evolutionary studies. Recent advances from deep learning have shown promising prospects in fossil image identification. However, the quantity and quality of labeled fossil images are often limited due to fossil preservation, conditioned sampling, and expensive and inconsistent label annotation by domain experts, which pose great challenges to training deep learning based image classification models. To address these challenges, we follow the idea of the wisdom of crowds and propose a multiview ensemble framework, which collects Original (O), Gray (G), and Skeleton (S) views of each fossil image reflecting its different characteristics to train multiple base models, and then makes the final decision via soft voting. Experiments on the largest fusulinid dataset with 2400 images show that the proposed OGS consistently outperforms baselines (using a single model for each view), and obtains superior or comparable performance compared to OOO (using three base models for three the same Original views). Besides, as the training data decreases, the proposed framework achieves more gains. While considering the identification consistency estimation with respect to human experts, OGS receives the highest agreement with the original labels of dataset and with the re-identifications of two human experts. The validation performance provides a quantitative estimation of consistency across different experts and genera. We conclude that the proposed framework can present state-of-the-art performance in the fusulinid fossil identification case study. This framework is designed for general fossil identification and it is expected to see applications to other fossil datasets in future work. The source code is publicly available at this https URL to benefit future research in fossil image identification.

Co-evolutionary algorithms have a wide range of applications, such as in hardware design, evolution of strategies for board games, and patching software bugs. However, these algorithms are poorly understood and applications are often limited by pathological behaviour, such as loss of gradient, relative over-generalisation, and mediocre objective stasis. It is an open challenge to develop a theory that can predict when co-evolutionary algorithms find solutions efficiently and reliable. This paper provides a first step in developing runtime analysis for population-based competitive co-evolutionary algorithms. We provide a mathematical framework for describing and reasoning about the performance of co-evolutionary processes. To illustrate the framework, we introduce a population-based co-evolutionary algorithm called \pdcoea, and prove that it obtains a solution to a bilinear maximin optimisation problem in expected polynomial time. Finally, we describe settings where \pdcoea needs exponential time with overwhelmingly high probability to obtain a solution.

A fundamental problem associated with the task of network reconstruction from dynamical or behavioral data consists in determining the most appropriate model complexity in a manner that prevents overfitting, and produces an inferred network with a statistically justifiable number of edges. The status quo in this context is based on $L_{1}$ regularization combined with cross-validation. However, besides its high computational cost, this commonplace approach unnecessarily ties the promotion of sparsity with weight "shrinkage". This combination forces a trade-off between the bias introduced by shrinkage and the network sparsity, which often results in substantial overfitting even after cross-validation. In this work, we propose an alternative nonparametric regularization scheme based on hierarchical Bayesian inference and weight quantization, which does not rely on weight shrinkage to promote sparsity. Our approach follows the minimum description length (MDL) principle, and uncovers the weight distribution that allows for the most compression of the data, thus avoiding overfitting without requiring cross-validation. The latter property renders our approach substantially faster to employ, as it requires a single fit to the complete data. As a result, we have a principled and efficient inference scheme that can be used with a large variety of generative models, without requiring the number of edges to be known in advance. We also demonstrate that our scheme yields systematically increased accuracy in the reconstruction of both artificial and empirical networks. We highlight the use of our method with the reconstruction of interaction networks between microbial communities from large-scale abundance samples involving in the order of $10^{4}$ to $10^{5}$ species, and demonstrate how the inferred model can be used to predict the outcome of interventions in the system.

The seasonal human influenza virus undergoes rapid evolution, leading to significant changes in circulating viral strains from year to year. These changes are typically driven by adaptive mutations, particularly in the antigenic epitopes, the regions of the viral surface protein haemagglutinin targeted by human antibodies. Here we describe a consistent set of methods for data-driven predictive analysis of viral evolution. Our pipeline integrates four types of data: (1) sequence data of viral isolates collected on a worldwide scale, (2) epidemiological data on incidences, (3) antigenic characterization of circulating viruses, and (4) intrinsic viral phenotypes. From the combined analysis of these data, we obtain estimates of relative fitness for circulating strains and predictions of clade frequencies for periods of up to one year. Furthermore, we obtain comparative estimates of protection against future viral populations for candidate vaccine strains, providing a basis for pre-emptive vaccine strain selection. Continuously updated predictions obtained from the prediction pipeline for influenza and SARS-CoV-2 are available on the website this https URL

Jukes-Cantor model is one of the most meaningful statistical models from a biological perspective. We are interested in computing the algebraic degrees for phylogenetic varieties, which we call phylogenetic degrees, associated to the Jukes-Cantor model and any tree. As these varieties are toric, their geometry is hidden in the associated polytopes. For this reason, we provide two different combinatorial approaches to compute the volume for these polytopes.