Papers

For many infectious diseases, behavior change is not a population-level reaction to rising case counts, but a personal one, triggered by how sick an individual feels. Yet most models fail to capture how illness severity drives this response. Multi-scale models that link the immunological scale to the epidemiological scale seem well-suited for capturing this behavior. Most multi-scale models link within-host viral load to population-level transmission rates through linking functions that are a function of viral load. However, viral load is often misaligned with symptom severity and thus possibly ill-suited for the purpose of informing behavior at a population level. We present a novel multi-scale model in which symptomatic individuals dynamically modify their transmission based on systemic symptom scores (a composite measure of muscle ache, fatigue, headache, and feverishness informed by within-host immune dynamics) while asymptomatic individuals do not change behavior. We find that stronger illness-driven behavior change delays and lowers the epidemic peak. Moreover, the resulting epidemic trajectory remains qualitatively similar to that of a standard SEIR model without behavior change, across several distinct choices of linking functions connecting the two scales. This stands in contrast to models where behavior change is driven by population-level feedback (e.g., reported cases or deaths), which can produce qualitatively distinct signatures such as plateaus, shoulders, or an elongated epidemic decline. In the case when an exponential function of symptom score is used as a linking function, we show that the standard SEIR model can closely reproduce the total number of infectious individuals at a given point in time generated through the multi-scale level.

Ecological theory predicts that herbivores adopt behaviors that balance energetic costs and benefits, shaping both foraging and reproductive organization. In some wild ungulates, such as camelids, males defend resource-rich areas to attract females and secure their offspring, leading to the emergence of territorial systems. However, existing territorial models rarely incorporate the well-established allometric relationships between body mass and metabolic costs. In this study, we develop a spatially explicit, individual-based model of territorial organization in camelids, in which male behavior is governed by an energy balance equation that includes allometric locomotion costs, resource acquisition, and the energetic risks of aggressive encounters. We show that (i) a body-mass-dependent threshold determines which individuals can establish and maintain territories, (ii) spatial resource connectivity strongly modulates competition intensity and territorial inequality, and (iii) confrontation costs play a key stabilizing role by limiting territorial expansion and promoting coexistence. Our results provide a mechanistic link between metabolic scaling, spatial structure, and social organization, offering new insights into the ecological and evolutionary drivers of territoriality in ungulates.

We introduce a simple reaction-network model of a quorum-sensing population that couples the cell density $x$ to the signal density $w$. In the four-channel cell-signal network studied here, scaling signal production and removal by the same factor $r$ leaves all deterministic equilibria, and their stability types, unchanged. Nevertheless, we show that $r$ shifts the quasipotential barrier $\Delta V(r)$ for rare transitions towards extinction, and thus, under metastable exit assumptions, the mean time to reach a fixed neighbourhood of the extinction state on the exponential scale $e^{N\Delta V(r)}$. We compute the barrier by minimization of the path action with the signal retained as a fluctuating coordinate, and we compare it with exact stochastic simulation of population-threshold crossing times regressed in $N$. Over a range of $r$, the minimum-action barriers satisfy $\Delta V(r)=\Delta V_\infty+O(1/r)$, where $\Delta V_\infty$ is obtained by eliminating the signal first. At $r=1$, the barrier is 55% larger than $\Delta V_\infty$. The saddle barrier $\Delta V(r)$ is also the least action needed to enter the basin of extinction, but the density threshold can be crossed more cheaply: at $r=0.5$ the cheapest crossing costs 7.7% less action, keeps the signal high, and is usually followed by recovery. Simulated arrival times in this neighbourhood, which include failed attempts, grow with slopes within two fitted standard errors of the saddle barrier at every tested rate, and within $0.004$ of it if the logarithmic prefactor term is omitted. Under either regression model they exclude $\Delta V_\infty$ at $r\le2$ by at least $4.4$ fitted standard errors, without using the action solver.

Fall Armyworm (FAW) poses a serious threat to maize production in many regions due to its aggressive feeding habits and rapid development cycle. In this study, we developed and analyzed a stage-structured mathematical model to evaluate the impact of different FAW larval instars on maize dynamics during the vegetative and reproductive stages. Analytical results indicate that the two models have unique and positively bounded solutions for all time $t\geq 0$ and admit four equilibrium points: the trivial, non-trivial, maize extinction and coexistence equilibria. The behavior of the model was studied using stability analysis to find conditions under which FAW dies out or continues to spread. Furthermore, sensitivity analysis and numerical simulations were conducted to examine how key parameters affect FAW population dynamics and maize. Numerical simulations of the model in both stages indicate that there is high destruction of maize plants in both vegetative and reproductive stages of maize production due to increased egg production and larval population density. The extensive damage caused by large populations of eggs, larvae and adult moths motivated an extension of the two models to include intervention measures such as traditional methods like handpicking and chemical pesticides. Numerical results indicate that these control strategies significantly suppressed the FAW population with a resultant increase in the maize plant population towards its maximum capacity during the vegetative and reproductive stages, respectively.

We present B-GRASP (Bayesian GRAph inference with SPDE priors), a Bayesian framework for inferring uncertain edge weights in stochastic dynamical systems on graphs from noisy observations of nodal states. The unknown edge weights parameterize the graph differential operator and therefore directly govern the evolution of the graph process. Motivated by connections between differential operators in PDEs and SPDEs and their graph counterparts, we construct stochastic graph models incorporating diffusion, reaction dynamics, and stochastic forcing. The resulting hierarchical formulation jointly represents uncertainty in the graph structure and stochastic forcing. Latent graph variables determine positive edge weights and the corresponding graph Laplacian, while latent Brownian variables represent the stochastic forcing. Conditional on these variables, the graph dynamics define a deterministic forward map from which the likelihood and posterior distribution are constructed. We characterize the posterior using maximum a posteriori estimation and the No-U-Turn Sampler, enabling both point estimation and uncertainty quantification. We demonstrate the framework on a one-dimensional inverse heat-conduction problem, stationary and nonstationary graph reaction-diffusion systems with nonlinear dynamics, and state-level COVID-19 data in the United States. The numerical results show that posterior uncertainty provides information not captured by point estimates, particularly for weakly identifiable or highly conductive edges, and enables uncertainty in both graph connectivity and stochastic forcing to be quantified within a Bayesian framework.

Planktonic communities exhibit ubiquitous population distributions and patchy spatial structures, yet the fundamental mechanisms driving them remain debated. Here, we derive these regularities from a minimalistic theoretical description that incorporates stochastic fluctuations in growth rates and effective ocean dispersal. We combine global metabarcoding, microscopy, and high-resolution chlorophyll datasets and show that the decay of spatial correlations, the crossover regimes of Taylor's law, the patterns of local species diversity and biomass distributions agree with common underlying dynamics. These results suggest that the intertwined effect of diffusivity and fluctuating growth rate, captured by an emergent correlation length, shapes plankton spatial heterogeneity from local to long-range scales, reconciling local variability with macroecological patterns.

We investigate a stochastic individual-based population model with trait-dependent reproduction, death, competition, variation, and deleterious transfer. Nonlinearities appear in the competition term and the transfer form, which moreover is asymmetric. In the large-population limit, the process converges to a deterministic measure-valued equation. The latter helps us to uncover the past history of living individuals. We replace in the interactions the original stochastic process with the deterministic large population approximation obtaining a nonhomogeneous measure-valued branching process, for which we use a spinal decomposition, generalizing a method that existed only for the stationary case. Reversing time, we identify the law of typical ancestral lineages. This approach encompasses a variety of settings and requires delicate functional analysis. In contrast to earlier approaches in the literature, which relied either on stochastic calculus or on favourable jump structures under stationarity assumptions, our method provides a more direct and more general point of view.

How search strategies evolve in finite, depletable landscapes remains a question in foraging theory. We study this problem with an evolutionary simulation in which agents forage on a two-dimensional toroidal lattice containing non-renewable resources distributed uniformly or as Lévy dust. Each agent carries a heritable genome encoding step lengths, velocities, and turning angles, and selection acts on a fitness function combining energetic gain, movement cost, and coverage efficiency. By allowing movement traits to evolve without imposing a prescribed power-law step-length distribution, we test whether evolved trajectories are better described by intermittent-search or Lévy-walk dynamics. Our results indicate that evolved search is more consistent with intermittent dynamics than with strict scale-free Lévy motion in the finite depletion-driven landscapes considered here. We characterize the dynamics by fitting second- and fourth-order displacement moments to intermittent-search and Lévy-walk models. While a Lévy-like random walk fits the evolutionary trajectories well (mean adjusted $R^2$ > 0.9 in most tested conditions), intermittent search achieves a closer fit (mean adjusted $R^2$ > 0.99) for all tested resource distributions. This preference holds across the tested grid sizes and resource densities. Five independent evolutionary runs per environment on a 503 x 503 grid at nominal resource density $\rho$ = 0.15 reproduce this preference for the uniform environment and five Lévy-dust environments. Evolution rapidly reshapes the movement genome toward short displacements while retaining a sparse tail of longer relocations, consistent with local exploitation punctuated by occasional transfer. The framework provides a controlled setting for studying how search rules emerge under resource limitation and may inform resource-constrained exploration in autonomous systems.

Flocking and schooling are thought to have evolved partly as defences against predation, but how prey should balance social and escape tendencies may depend on the predator's hunting strategy. We extend the predator-prey boids model of Ojo et al. (2023), itself based on Reynolds' boids, by combining six prey movement tendencies (alignment, cohesion, separation, dodge, repel and wiggle) into a single weighted acceleration update, and by reformulating wiggle as a sinusoidal manoeuvre. We then use an evolutionary strategy to optimise the six behaviour coefficients for collective prey survival against four predator hunting strategies: attack-centroid, attack-nearest, attack-random and attack-peripheral. Across five independent trials per strategy, coefficients converged within trials and mean fitness remained stable or increased, although trials often settled in different local optima. Prey survival was highest under attack-centroid and lowest under attack-nearest, in line with our hypotheses. Against attack-centroid, prey evolved individualistic predator avoidance with high escape coefficients, whereas against the other three strategies they largely kept their flock formation. Across all strategies, evolution favoured a low repel coefficient and relatively high dodge and wiggle coefficients. Our results suggest that optimal anti-predator behaviour depends on the interplay between escape tendencies and the predator's hunting strategy.

Nitrogen limitation is a key mechanism regulating the mutualism between photosymbiotic cnidarians and their algal symbionts. Algal-derived photosynthate facilitates host assimilation of inorganic nitrogen, specifically ammonium. The resulting competition between symbiotic partners for inorganic nitrogen leads to a negative feedback loop wherein symbiont density is effectively controlled through facilitation of their competitor. However, it is unclear whether this feedback loop is sufficient to stabilize the interaction absent other forms of regulation. Using a generalized modeling approach, we identify the conditions under which cnidarian-algal competition for nitrogen yields dynamically stable symbioses. We show that nitrogen limitation is sufficient to stabilize the interaction through the interplay of intraspecific (symbiont-symbiont) and interspecific (host-symbiont) competition. As host assimilation of inorganic nitrogen increases, the system shifts from being stabilized by intraspecific competition between symbionts to interspecific competition between host and symbionts, necessitating a positive coupling of symbiont density to host nitrogen assimilation via photosynthate translocation for dynamic stability.

Phenotypic plasticity, the ability of cells to switch between states, is central to development, differentiation, and therapy resistance. Although it is modeled at several scales, from compartmental ODEs to phenotype-structured PDEs and single-cell stochastic equations, a framework connecting these descriptions is missing. We present such a framework. Starting from a general $n$-compartment ODE model encompassing nonlinear growth and linear transitions between phenotypes, we show, with a new, elementary and generalizable proof of a recent theorem, that under uniform competition, the long-term population distribution is solely governed by transition rates. All phenotypes become selectively neutral at saturation, and the imprint of fitness differences during growth fades at an explicit rate. Restricting transitions to neighboring states transforms the model into a discretization of a phenotype-structured reaction-diffusion-advection PDE. In this continuum model, diffusion and advection are identified from switching rates, and fitness remains asymptotically irrelevant. Interpreting the advection velocity as the negative gradient of an effective epigenetic potential transforms the PDE into a Fokker–Planck equation and converts single-cell trajectories into stochastic gradient descent (SGD) in the Langevin sense on the phenotypic landscape. Non-local transitions, such as mutations, are incorporated via an integro-differential term, yielding a unified model with reaction, gradient flow, diffusion, and jumps. State-dependent noise reshapes the effective landscape without altering the underlying potential. This gives cancer a route to elevated plasticity that static, single-cell snapshots cannot distinguish from a changed landscape. This framework provides a physical interpretation of Waddington's landscape, where cells perform SGD, and cancer corresponds to a corrupted landscape.

The dynamics of adaptation in a population are informed by its mode of reproduction. Whether individuals reproduce sexually or asexually, then, can have large effects on population persistence and extinction in changing environments. Classical theory explains this dependence via genetic variance without further accounting for a fundamentally different mode of inheritance. Recent theoretical advances capture these mechanisms, highlighting how they dramatically change the nature of adaptation in gradually changing environments. Here we show that these recent predictions, which assume infinite-population sizes, are overly optimistic about the fate of finite asexual populations when environmental change is rapid. This is because every individual in an infinite asexual population descends from a once optimal ancestor and the likelihood of finding this optimal individual in the population declines rapidly with population size. To predict the fate of finite asexual populations we derive the equilibrium phenotypic distribution assuming there exist no individuals beyond some unknown trait. As expected, we find that when the phenotypic distribution contains the optimal trait, the population's fate is consistent with previous predictions. When the optimal trait is lost, however, an additional fitness load is incurred. We further derive a prediction for the typical trajectory of an ancestral lineage, which explains the additional load: all individuals descend from a common ancestor carrying the fittest trait, which may be suboptimal. Our work uncovers a finite-population effect that is specific to asexual adaptation and distinct from genetic drift, which significantly hinders the ability of small asexual populations to persist in changing environments.

Bacteriophage Q$\beta$, first isolated in 1961, has served for more than six decades as a model system for molecular and viral evolution. The development of cell-free replication systems based on the Q$\beta$ replicase enabled the first demonstrations of Darwinian evolution in RNA molecules. In parallel, the phage's compact RNA genome, high mutation rate, and ease of propagation established Q$\beta$ as an exceptionally tractable model for studying viral evolution. The discovery of extensive genetic heterogeneity made of Q$\beta$ the first biological system in which molecular quasispecies theory found direct experimental support. Building on this foundation, decades of evolution experiments under thermal, ecological, and mutagenic pressures established how mutation, selection, epistasis, and population structure jointly shape adaptive trajectories. Deep sequencing has recently allowed the mutant spectrum of Q$\beta$ populations to be resolved as large, structured genotype networks, revealing a hierarchical organization around dominant sequences that generalizes classical mutation-selection balance to a dynamic process, and uncovering topological features shared with RNA viruses evolving within natural hosts. In parallel, the catalytic core of the Q$\beta$ replication system has been repurposed in synthetic biology to revive cell-free Darwinian evolution within compartmentalized, cell-like systems, opening new avenues for studying the origin and early evolution of life. Further recent work has pushed the phage into new experimental territories, including extreme, astrobiologically relevant environments and biotechnological platforms for peptide display. Together, these developments illustrate how a single bacteriophage has repeatedly anticipated and continues to clarify general principles of molecular, population, and ecological evolution.

Mass gathering events like concerts, sports matches, and festivals bring many people into close contact within a short period, creating localized bursts of infection that can shape epidemic outcomes across an entire city. To evaluate how these transient transmission events translate into broader urban impacts, we developed a simulation model linking event-scale contact dynamics with citywide commuting networks. Using Madrid, Spain, as a case study, we compared several types of gatherings and examined how their effects changed under different levels of disease transmissibility. We found that mass gatherings consistently amplified outbreak magnitude, accelerated progression, advanced district-level arrival times, and synchronized spatial spread. Remarkably, while the initial seed size generated at the event accounted for much of this acceleration, post-event transmission conditions provided complementary predictive signal regarding invasion timing. These findings demonstrate that mitigating transmission during mass gatherings can yield downstream public health benefits by delaying broader spatial spread. More generally, this multiscale framework offers a tool to evaluate how temporary, localized contact shifts produce longer-lasting consequences for urban populations.

Ecological fitting describes a situation where species interact despite no shared evolutionary history. It is both a null model for adaptation and an important process in its own right, for example, the establishment of a non-native species is ecological fitting, and it is a major mechanism in the formation of Novel Ecosystems. In this paper we introduce and analyse a model of ecological fitting. We demonstrate both analytically and through simulation that the main factors determining invasion success are the invaded ecosystem's population and diversity, which set the size of the barrier for invaders. We also study the situation where many evolutionarily unrelated species simultaneously colonise an empty area. We show that a successful equilibrium is likely to be established, but the diversity tends to be very much less than the number of species in the starting pool and discuss the implications of this.

When people of reproductive age move between regions, replacement-level fertility need not produce spatially balanced population replacement. Migration genealogies connect a woman's birth region, through survival and movement, to her daughters' birth regions across generations. We decompose existing genealogical series for stable births and reproductive value into first-return paths, on which a lineage again produces a descendant in its reference region without intermediate births there. Discounting at the intrinsic growth rate yields a first-return distribution with an Euler–Lotka-type normalization. Its mean recurrence generation, the expected generations until first return, equals the normalized product of stable births and reproductive value and, at replacement, reciprocal net reproduction sensitivity to within-region reproduction. Using Japan's 2010, 2015, and 2020 censuses, vital statistics, and life tables, we compare 47 prefectures under national replacement. Based on 2020 rates, mean recurrence is approximately 10 generations for Tokyo and 500 for Akita; Fukushima varies across observation years. Similar one-generation birth contributions conceal different descendant destinations and subsequent return pathways. These period-based results reveal how reproductive pathways generate regional differences in stationary populations. Population replacement must therefore be analyzed jointly through fertility, migration, and regional conditions, with mean recurrence identifying the strength of closed reproductive pathways.

Infectious disease models that allow for reinfection, such as the SIS or SIRS frameworks, typically treat all infections as exchangeable and independent, erasing the temporal structure of individual reinfection histories. Here, we introduce a minimal "chain SIR" model that resolves this limitation by indexing compartments by reinfection count and allowing transmission, recovery, and waning rates to depend on that count. The dynamics generate an advective flux along the reinfection ladder, producing traveling waves in reinfection space and a coherent structure in the population's lifetime infection histories. We derive an analytical expression for the wave speed and identify the general conditions under which such cohort waves exist and persist, offering a new lens to interpret long-term prevalence patterns and the emergence of age- or immunity-structured endemicity. Finally, comparing the speed formula with longitudinal cohort data, we quantify the reduction in reinfection rate attributable to immunological responses for several seasonal viruses, including influenza A/H3N2 and respiratory syncytial virus (RSV).

We prove that, in phenotype-structured populations under uniform competition, the long-term phenotypic distribution does not depend on the proliferation rates: it is the stationary distribution of the switching dynamics alone. The density u(x,t) of cells with phenotype x evolves by advection and diffusion in phenotype space (switching) and by proliferation at a phenotype-dependent rate r(x,t), modulated by a factor g(U) common to all phenotypes, where U is the total population. This extends to continuous phenotypes a recent result for compartmental models. On a bounded interval with no-flux boundary conditions, the total population converges monotonically to the carrying capacity U*, the density converges in L1 to U*psi, where psi is the stationary density of the switching dynamics, and the nonlinear model is asymptotically equivalent to the linear one; by an explicit estimate, the imprint of fitness decays at the spectral gap of the switching dynamics. On the whole real line we prove the same convergence under two natural conditions, confinement and no escape to infinity, covering Ornstein-Uhlenbeck dynamics, multi-well landscapes, and heavy-tailed densities. If g'(U*) < 0 and psi satisfies a Poincare inequality, convergence is exponential in a weighted L2 norm, while no uniform L1 rate holds for Ornstein-Uhlenbeck dynamics. The proof follows the compartmental one: under uniform competition the reaction term has one sign, so its size is the growth rate of the total population, integrable in time, and the switching dynamics contracts the zero-mass perturbations it produces. Since it uses only the Markov semigroup generated by switching, the proof extends to general mechanisms; we apply it to nonlocal switching by jumps and to diffusions with non-gradient drift in bounded domains of R^d, whose stationary density is not of Boltzmann form and carries a circulating flux.

Ovarian follicle development has been modeled either by compartmental models, where developmental stages are represented by discrete compartments, or by physiologically structured population models (PSPMs), formulated as transport PDEs describing follicles along a continuous maturation variable. Compartmental models reproduce full-cycle hormonal and follicular dynamics but cannot describe cellular features. PSPMs capture multiscale behavior, yet lack a direct link to compartmental descriptions, making hormonal feedback difficult to incorporate. Here, we introduce a class of ODE systems derived as finite-dimensional reductions of PSPMs via a perturbative moment closure. These systems provide backbone approximations of the structured dynamics, retaining key nonlinear mechanisms governing recruitment, selection for dominance, and atresia while projecting maturation onto macroscopic variables. Zero- and first-order moments, derived from phenomenological assumptions regarding follicular maturation, allow us to realistically model follicle sizes and blood estradiol concentrations over one follicular wave. This application is supported by bovine data and likely generalizable to other mammalian species.

Single-cell time-lapse microscopy now provides high-resolution size trajectories for thousands of individual cells, yet principled methods for simultaneously learning the functional form of growth laws and the distribution of cell-to-cell physiological variability remain limited. We present a data-driven framework based on the recent Weak-form Estimation of Nonlinear Dynamics (WENDy) algorithm to (i) select the best supported growth law from a set of candidate laws, and (ii) recover individual-level growth parameters via empirical Bayes shrinkage within a random-effects model. We demonstrate the approach on both synthetic individual size data incorporating commonly found growth laws and recorded real size trajectories, showing that the method accurately recovers both growth-law structure and parameter heterogeneity at reasonable noise levels. We finally end with a discussion on how the results obtained by the method here can be upscaled to the population level.

Epidemic spread and collective opinion formation are tightly coupled processes: individual beliefs about the severity of an outbreak and the value of protective measures shape behavior, while the evolving epidemic itself reshapes public sentiment through risk perception. We propose an agent-based framework that couples opinion dynamics with a compartmental epidemic model, in which each agent carries both a health status and a continuous opinion variable describing adherence to protective measures. Opinion evolution is driven by binary interactions among agents and by an exogenous background field that reflects the current state of the epidemic, while the disease transmission rate depends explicitly on the opinions of interacting agents. Using methods of statistical mechanics, we characterize the resulting macroscopic system for the compartmental mass fractions and mean opinions in both far-from-equilibrium and close-to-equilibrium regimes. The calibration shows that incorporating behavioral opinion dynamics substantially improves the interpretation of epidemic evolution. In particular, the inferred risk perception function evolves consistently with the observed epidemic burden, indicating that behavioral adaptation can explain part of the temporal variation that would otherwise be absorbed into time-dependent transmission parameters. Our results illustrate how integrating opinion heterogeneity in kinetic epidemic models offers quantitative insights into the feedback between behavior and disease spread.

Knowing where species occur is fundamental for biodiversity research and conservation. Species distribution models (SDMs) link species observations to environmental conditions to estimate their spatial distribution. However, accuracy varies with the underlying data and models, making it essential to know for which species models can be trusted. Deep-learning-based SDMs ("DeepSDMs") now jointly model thousands of species, drawing on hundreds of millions of community-science records. At this scale, averaging performance hides substantial species-level variability, particularly for rare species, often of greatest conservation concern. Records are also strongly biased, making occurrence counts misleading. Accounting for these factors is essential for a reliable and informative evaluation of multi-species SDMs. Here, we introduce a Sampling-Aware Global Evaluation (SAGE) benchmark, combining GBIF records for training with sPlotOpen vegetation plots for presence-absence evaluation across 5771 plant species. We propose an evaluation framework that groups species based on two properties, sampling effort and relative prevalence, which describe how densely a species' range is sampled and how frequently the species is recorded. Evaluating single-species SDMs and multi-species DeepSDMs, we find that Random Forests and DeepSDMs perform best overall, but neither dominates: DeepSDMs outperform single-species SDMs for infrequently recorded species while offering no consistent advantage for well-sampled ones. Crucially, this advantage emerges only when established bias-correction practices, such as spatial thinning and reweighting, are carried over to the deep-learning setting. SAGE helps identify the species and data conditions for which a given approach is beneficial, thereby supporting the development of more transparent and ecologically credible SDMs. Data and code: https://earens.github.io/sage/

Translation of the genetic code into proteins is universal across life, with ribosomes serving as the ancient molecular machines enabling this information transformation. We propose that early replication and protein biosynthesis were inseparable functions performed by a single ancient RNA molecule: the riboreplisome. This hypothesis addresses fundamental challenges facing RNA world, protein world, and RNA-protein co-evolution theories – particularly the problem of non-Darwinian starting points and the interdependence of replication and translation machineries. We present a 12-step evolutionary pathway from simple RNA replicase to proto-ribosome, supported by quantitative modelling demonstrating that only two steps require non-Darwinian transitions while the remaining ten proceed through standard selection. The single-molecule riboreplisome architecture provides an approximately 6-fold evolutionary advantage over multi-component "RNA soup" scenarios, principally by maintaining genetic linkage and retaining catalytic products close to the replicating genome (resisting diffusion loss); structural resistance to parasitic "cheater" molecules follows as a corollary. The riboreplisome framework explains the origins of ribosomal, transfer, and messenger RNA as derivatives of a single ancestral molecule, while providing a driving force for cellular compartmentalisation. Although the original riboreplisome is likely lost to deep time, molecular remnants may persist in extant biological RNA. Identification or reconstruction of riboreplisome-like molecules could advance both origin-of-life research and synthetic biology applications.

Influenza A persists by continually changing the antigens that its host population recognizes. How fast it evolves and how many hosts it infects are not independent, because the immunity that selects new variants is produced by the infections the pathogen has already caused. We analyze a model of Andreasen et.\ al.\ that captures this eco-evolutionary feedback, and we extend it to the case where infection may kill the host. In the model infected and recovered hosts are distributions over a one-dimensional antigenic space coupled by cross-immunity. The endemic state is a traveling pulse: the infected distribution keeps a fixed shape and advances through antigenic space at constant speed. In the limit of weak antigenic mutation we construct the pulse asymptotically and find that: (i) the speed of antigenic evolution decreases as prevalence rises, (ii) less standing antigenic variation accompanies either faster or slower antigenic evolution, depending on whether pathogens differ in immune evasion or host lifespan (iii) the total number of infected hosts is largest at an intermediate virulence when the host birth rate is sufficiently low.

The stability of an ecological community is conventionally defined through species interactions, which quantify how species affect one another. Interaction strengths are notoriously difficult to measure in species-rich assemblages. Long-term monitoring of species-rich communities, however, provides species abundance time series, increasingly available across habitats and taxa but not yet connected to the stability properties of the communities they describe. Here we develop a statistical framework that infers stability regimes in large ecological communities directly from abundance time series. We study stochastic Generalized Lotka–Volterra dynamics with random interactions and environmental fluctuations using dynamical mean-field theory, reducing the multispecies system to an effective stochastic process for a representative species. The theory predicts three stability regimes (stable coexistence, intermittent dynamics close to extinction, and unbounded growth) separated by analytical boundaries, and shows that environmental stochasticity systematically destabilizes coexistence by promoting intermittent low-abundance dynamics. The resulting steady-state species abundance distribution is a Gamma law that ties the dynamical phases to the variability-based stability metrics used in empirical studies. Recasting the effective dynamics as a multivariate regression model, we infer interaction statistics, environmental variability and the characteristic timescale of the dynamics from community data, without reconstructing the interaction network. Applied to natural communities spanning a broad range of habitats and taxa, the method resolves contrasting stability regimes and yields quantitative estimates of species extinction risk.

We develop and analyse a mechanistic ODE model of within-host HIV dynamics that includes uninfected CD4$^+$ T cells, latently and productively infected cells, free virions, and cytotoxic immune effectors. Antiretroviral therapy is described by two time-dependent efficacy functions that separately reduce new infections and virion production. We show that solutions remain non-negative and bounded, identify the infection-free and endemic equilibria, and derive the basic reproduction number together with the local stability condition for the infection-free state. We also obtain treatment-dependent suppression thresholds and an analytical estimate of when this threshold is crossed as treatment efficacy declines. Numerical simulations consider untreated infection, ART initiation, periodic variation in efficacy, and progressive loss of treatment effect. Without therapy, the model approaches a state of persistent infection. ART reduces viral load and promotes recovery of the CD4$^+$ T-cell population, while the latent reservoir persists under the parameter set considered. Periodic changes in treatment efficacy produce sustained forced oscillations. These results connect the analytical threshold conditions with the treatment-dependent dynamics of the model and provide a basis for future calibration, sensitivity analysis, uncertainty quantification, and extensions informed by clinical data.

Supplying a released predator with additional, non reproducing food is a standard lever in augmentative biological control, with a known drawback with nothing limiting the predators own numbers, the extra food lets its population grow without bound. Competition among the predators supplies the missing brake. Howthis self limitation reshapes the spatial arrangement of the two species has not been asked. We address it with a reaction diffusion model of a logistically growing prey and a predator feeding through a Holling type II response that also draws on additional food , the predators competing among themselves at strength. In the well mixed setting we locate the Hopf bifurcation of the coexistence state exactly and show the cycle born there is stable, so weak competition gives boom bust oscillations, not runaway growth. Allowing movement, we obtain the diffusion driven Turing threshold at which the uniform state breaks into stationary patches of high and low density, and find the uniform oscillation stable as it appears. With prey mobility and competition strength as control parameters, the pattern forming and oscillatory instabilities meet at a single point, where we compute the dynamics. Simulations confirm the sequence weak competition gives a wholefield oscillation, stronger competition with faster prey spread gives fixed patterns, and near the crossover the two combine into patterns that pulse in time. Predator self competition therefore sets the spatial structure of the community, which is what matters when additional food is used to steer a control agent in the field.

The coalescent is a central framework in population genetics for modelling the ancestral relationships among sampled individuals through a genealogy, represented as a rooted and ranked binary tree. In this model, lineages coalesce at a rate inversely proportional to the effective population size, a time-varying quantity of primary interest. The bounded coalescent conditions genealogies on the time to the most recent common ancestor being bounded above by a fixed time. This model is useful in various contexts, such as phylodynamics of infectious diseases with known introduction times and single-cell lineage tracing in synthetic barcoding experiments. To our knowledge, there is no existing tool that infers variable effective population size trajectories under the bounded coalescent. We view estimation under the bounded coalescent as equivalent to estimation of the intensity function of an inhomogeneous point process. We provide an efficient algorithm for coalescent simulation under the bounded coalescent using point process methods, retaining the exactness of naive rejection sampling while substantially reducing computational cost and avoiding repeated numerical inversion of the bounded cumulative hazard. We then develop a Markov chain Monte Carlo procedure for posterior inference of effective population size trajectories that avoids discretization of the likelihood integrals. In simulations, conditioning on the bound reduces the median sum of squared errors in two of three settings, with less favourable results in the most rapidly varying setting. We illustrate the method using severe acute respiratory syndrome coronavirus 2 sequence data from Washington State.

Rooted phylogenetic networks are widely used to represent the evolution of species that have undergone reticulate processes. However, these networks can be highly non-planar, making them more difficult to visualise and interpret than evolutionary trees. In this paper, we investigate planarity properties of galled networks, an important subclass of phylogenetic networks. We show that all planar galled networks are necessarily upward planar. Furthermore, by leveraging recent results on planar phylogenetic networks, we provide three characterisations for each of the outerplanar and terminal planar galled network classes in terms of forbidden vertex configurations, forbidden directed subgraphs, and forbidden structures in their associated underlying undirected graphs. These results contribute to a deeper understanding of the structural properties of galled networks and may inform future methods for their construction and visualisation.

Weekly scarlet fever (SF) mortality records for London, UK, from 1842 to 1939, together with notified case records from 1901 to 1939, reveal a strong annual epidemic pattern with peak prevalence in the autumn. In addition to the annual epidemic pattern, this long time series reveals a cyclical envelope with a period that lengthened over the decades. In particular, the period of the envelope increased from about four years to about eight years between 1880 and 1920, coinciding with a dramatic decline in pre-antibiotic-era SF deaths (from about 2300/yr to about 80/yr). We quantify the spectral features of the SF time series using a wavelet transform, and attempt to explain why the frequency structure changed over time, using a mechanistic mathematical model of SF transmission dynamics. We estimate the parameters of the model in part from the literature and in part by fitting mortality and incidence jointly. We use a mechanistic transition analysis (considering both attractors and transients in model solutions) to relate the observed changes in frequency structure to our estimated changes in model parameters. We find that almost all spectral evolution in the time series can be explained by changes in the effective reproduction number and the amplitude of seasonal forcing. These changes reflect observed variation in birth rates together with inferred changes in transmission, which may in part have arisen through pathogen evolution.