Journal of The Royal Society Interface

Human walking is often considered an inverted pendulum during single support, suggesting conservative dynamics. Gait consists of discrete steps connected by mechanically costly transitions. We examine how step length, walking speed, and work capacity jointly constrain walking mechanics. Using a powered simple walking model, minimum speed required to complete a step of given length is derived based on gravitational work; below this threshold, forward progression becomes mechanically infeasible, and the next heel-strike occurs early, producing shorter steps. Comparisons with empirical step length-speed relationships show that humans walk at higher speeds and require greater push-off work, indicating energy dissipation. We extend pendular dynamics by incorporating hip torque, a linearized axial force model, and muscle intervention. This framework reproduces key GRF features, including the M-shaped profile, without prescribing force trajectories a priori. Fitted parameters suggest reduced average loading (CBaseline < 1), active mid-stance unloading (Am < 0), and narrowly timed muscle action (small{sigma} m). Parameter studies show that increasing step length or speed increases transition work and peak forces, while hip torque timing indicates mechanical cost is minimized when energy modulation occurs after mid-stance. These findings indicate that preferred walking speed emerges from feasibility and work-capacity constraints, not energetic optimality alone.

The environments inhabited by flying insects demand a balance between flight efficiency and flight manoeuvrability. In structural oscillators such as the insect indirect flight motor, efficiency (arising from resonance) and manoeuvrability (arising from kinematic modulation) are typically quid pro quo, with modulation incurring penalties to efficiency. Band-type resonance is a phenomenon that offers, in theory, a strategy to lessen these penalties via careful navigation through a band of efficient kinematic states. However, identifying this band is challenging: no methods exist to identify the complete band in realistic motor models, involving elasticity distributed across thorax and wing. Nor are the effects of elasticity distribution on the band known. In this work, we address both open topics. We present a suite of numerical methods for identifying the complete resonance band in general systems. Applying them to models of the insect flight motor with distributed elasticity--thoracic and wing flexion--reveals that distributed elasticity is moderate-risk but high-reward morphological feature. Well-tuned distributions expand the resonance band over fourfold whereas poorly-tuned distributions completely extinguish the resonance band. These results indicate that distributing elasticity across the insect flight motor can have adaptive value, and motivate broader work identifying distributions across species.

Understanding structural similarities across dynamical systems at different scales remains a central problem in nonlinear science [1, 3]. Here we propose a modeling framework for cross-scale morphogenetic dynamics, termed Generalized Morphogenesis Theory (GMT), based on a flow-inertia formulation: O_FD O_INLINEFIG[Formula 1]C_INLINEFIGM_FD(1)C_FD where S denotes system state, E environmental input, F (E, S) a driving function, and {micro}(S) an inertia function representing resistance to change. This formulation provides a structural representation that encompasses several classical dynamical models--including Newtonian relaxation, logistic growth, and reaction-diffusion systems [13]--under appropriate parameterizations. Non-dimensionalization reveals a small set of control parameters governing regime transitions. Empirical validation is performed across two independent scales. At the organism scale, crop growth time-series datasets from multiple species exhibit consistent multiplicative dynamics F (E, S) = f (E) {middle dot} S, statistically preferred over additive alternatives in 5 of 6 independently tested systems ({Delta}AIC ranging from +2 to +891; R2 up to 0.98). Independently estimated inertia time constants agree in two plant systems (cucumber:{tau} = 3.7 days, CV=3.3%; maize:{tau} = 36.8 days, CV=17.3%), with the 10-fold ratio consistent with structural complexity differences. At the molecular scale, publicly available perturbation transcriptomics datasets (Perturb-seq) show directional response structures consistent with the proposed flow-inertia decomposition (93% causal direction agreement across three independent datasets; p < 10-25). Across domains, recurrent dynamical motifs are organized into 12 canonical design patterns, derived from a 2 x 2 x 3 orthogonal structure (4 elementary operations x 3 temporal scales), associated with stability classes and bifurcation conditions. These results suggest that the flow-inertia formulation functions as a domain-independent structural modeling principle for dissipative morphogenesis.

Patient-derived tumour spheroids are increasingly used as engineered three-dimensional tissue models for studying tumour growth, nutrient limitation, and therapeutic response. However, extracting quantitative, mechanistically interpretable information from longitudinal imaging data remains challenging. Here, we present a three-dimensional phase-field framework for modelling patient-derived tumour spheroids as continuum, self-organising tissues. The model captures the coupled evolution of viable and necrotic cell fractions through nutrient-limited growth, death, and mechanically and thermodynamically mediated motion, using seven biologically interpretable effective parameters. Key experimental observables emerge naturally from nutrient-growth coupling, without imposing explicit species interfaces or quiescent layers. The framework was quantitatively calibrated against longitudinal imaging data from melanoma spheroids across two cell lines and three initial seeding densities. Across all conditions, simulations reproduced the temporal evolution of all measured observables with low relative error ({approx} 3{sigma} of experimental data), and direct comparison with an established Greenspan-type ODE model demonstrated comparable or improved predictive accuracy. Parameter identifiability analysis revealed weak individual parameter constraints, yet model predictions remained robust, a profile consistent with biological models. We demonstrate that a general PDE-based growth framework can match or outperform a dedicated spheroid model while remaining fully biologically interpretable. Beyond predictive accuracy, the phase-field formulation naturally resolves internal mechanical structure, providing access to quantities that are not directly experimentally observable. These results establish that mechanistically grounded continuum models can be quantitatively calibrated to routine spheroid imaging data, offering a foundation for integrating spatial and mechanical information into the interpretation of organoid-based assays. Graphical Abstract O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=77 SRC="FIGDIR/small/717345v1_ufig1.gif" ALT="Figure 1"> View larger version (21K): org.highwire.dtl.DTLVardef@1cb3b45org.highwire.dtl.DTLVardef@1a053d5org.highwire.dtl.DTLVardef@dffe34org.highwire.dtl.DTLVardef@1aa0b72_HPS_FORMAT_FIGEXP M_FIG C_FIG

Atherosclerotic plaques are fatty deposits in arterial walls and a major cause of heart attacks and strokes. Macrophage proliferation triggers plaque growth and instability, but the exact conditions that cause stable plaques to become unstable remain unclear. To provide an insight into the conditions for this transition, we apply bifurcation analysis to the lipid-structured atherosclerosis model proposed by Chambers et al. (Bull Math Biol 86(8):104, 2024). Our main contribution is that the reduced dynamics of the system remain meaningful even beyond previously identified limits of validity. Furthermore, along with numerical bifurcation methods, the use of fast-slow analysis, combined with Fenichels theory, identifies a saddle-node bifurcation at infinity. A sharp threshold exists where macrophage proliferation balances emigration. Below this balance, the system stabilises in a biologically reasonable state; contrary to above it, macrophage numbers and lipid load grow unboundedly, triggering instability and runaway inflammation. Trends in determinant and eigenvalues also support this threshold. Parameter scans and heatmaps demonstrate that increased proliferation or reduced emigration enhances the number of macrophages and the lipid content of the necrotic core. Efferocytosis rate modulates downstream severity but does not shift the primary threshold. These findings reconcile conflicting results on macrophage proliferation, demonstrating that it is protective when emigration sufficiently balances this process. In other words, co-targeting reduced macrophage proliferation and enhanced emigration could help maintain plaque stability and reduce the risk of acute cardiovascular events. While this remains a theoretical recommendation, it offers a potential therapeutic strategy that authorises further investigation in experimental and clinical settings.

Biological organisation is inherently multi-level: molecular processes, membrane dynamics, cellular geometry and tissue context reciprocally constrain one another, often through boundary-mediated feedback. A recurring theme in theoretical biology is that such organisation is not well captured by models that assume a fixed repertoire of variables and a pre-given state space: what counts as a relevant state description can depend on organisational context and history. The principle of biological relativity further sharpens the same challenge from a different angle, emphasising that no level is causally privileged and that cross-level feedback can close into circular causality. These lines of work motivates for a structural multi-level semantics for modeling the biological pathways. We introduce a constraint-based semantic framework that distinguishes an evolving organisational scaffold--the admissible multi-level patterns and interfaces--from the pathways that traverse and coordinate them. This separation yields mathematical, loop-level diagnostics for boundary-driven circular causality: it identifies when organisational trajectories induce persistent reparameterisations of local state descriptions, and it classifies cyclic regimes into reversible loops, stable history-dependent loops, and unique (rare) organisational reconfigurations. The framework is accompanied by a systematic crosswalk to mainstream causal, dynamical and computational approaches, clarifying what is gained when interfaces and local-global consistency are treated as semantic, rather than purely parametric, structure. We demonstrate the approach on a canonical excitable-cell exemplar by modelling a single Hodgkin spike as a cross-level interface loop coupling membrane, molecular and cellular constraints. Without re-deriving Hodgkin-Huxley kinetics, the resulting diagnostics provide an explicit semantics for boundary-mediated feedback and spike-induced history dependence, including when cyclic activity imprints persistent changes in effective excitability. Together, the case study and comparisons position constraint semantics as a practical mathematical layer for multi-level biological organisation: compatible with existing mechanistic models, yet designed to expose circular causal closure and organisation-dependent state descriptions that standard formalisms typically leave implicit. AMS subject classifications92C30, 92C46, 92B05, 55U10, 55R10

1The timeliness of infectious disease surveillance systems largely determines the speed at which mitigation interventions may be implemented. However, it is unclear how surveillance timeliness evolves during a pandemic with changing government policies, testing tools, and population-level infection and immunity landscapes. Here, we adapt an agent-based model for COVID-19 transmission to explore the timeliness of the surveillance signals obtained from polymerase chain reaction (PCR) and rapid antigen (RAT) tests relative to true infection incidence. Across different pandemic scenarios, we investigate how surveillance timeliness depends on the prevalence of co-circulating influenza-like-illnesses (ILI) and test quality. If only PCR tests are available with symptom-based eligibility, and if tests can detect post-recovery residual viral load, then a surveillance lag may emerge which is amplified by ILI prevalence. When limited RATs are introduced with symptom-based eligibility, and PCR eligibility requires a recent positive RAT, then RAT/PCR timeliness is sensitive to ILI prevalence but insensitive to RAT failure probability. With unrestricted RAT supply, PCR timeliness varies with both ILI prevalence and RAT failure probability. Our work highlights how the timeliness of test-based surveillance signals can evolve throughout a pandemic, with important implications for interpreting real-time surveillance data and designing more effective, data-driven surveillance systems.

Large commercial and military aircraft can operate in a wide range of turbulent conditions, except during extreme weather events such as cyclones. Smaller man-made vehicles, such as micro aerial vehicles (MAVs) and nano aerial vehicles (NAVs), are significantly more sensitive to routine environmental wind fluctuations, making them difficult to control. In contrast, insects exhibit remarkable stability in naturally gusty conditions. Despite this, few studies have systematically investigated the impact of gusts and turbulence on insect flight performance. To address this gap and to gain fundamental insights into insect flight stability under gusty conditions, we examined the flight of freely flying black soldier flies subjected to a discrete head-on aerodynamic gust in a controlled laboratory environment. Flight motions were recorded using two high-speed cameras, and body and wing kinematics were analyzed across 14 distinct cases. In response to the gust, we observed consistent features across the cases: (1) asymmetry in wing stroke amplitude, (2) large changes in body roll angle--up to 160{degrees}--occurring over approximately two wing beats ([~]20 ms) with recovery over [~]9 wing beats, (3) transient pitch-down attitude, and (4) deceleration in the flight direction. These rapid responses, combining passive and active control mechanisms, provide insight into the flight control strategies employed by insects. The findings offer valuable guidance for the design of MAVs and NAVs capable of robustly responding to gusts and unsteady airflow in natural environments.

IntroductionStereological estimates of villous membrane thickness and surface area are widely used to infer the diffusive exchange capacity of the human placenta. A key geometric determinant of exchange capacity can be expressed as an effective diffusive length scale. Here we combine virtual histological sections with computational modelling in realistic villous geometries to assess the accuracy of classical stereological estimates of this diffusive length scale. MethodsTwo terminal villi, reconstructed from three-dimensional imaging, were digitally sectioned to generate random two-dimensional geometries containing fetal capillaries and surrounding villous tissue. For each section, we simulated steady diffusive transport between the fetal capillary and intervillous space boundaries to obtain a physics-based diffusive length scale as a reference case. Using the same geometries, we applied standard line-intercept stereology to measure harmonic-mean barrier thickness and boundary-length densities, from which a stereological estimate of diffusive length scale was derived. ResultsAcross both villi, stereology systematically overestimated the diffusive length scale by approximately 15-25%, depending on villus and section. We identified sources of this discrepancy, including interface curvature and assumptions underpinning the stereological correction factors, using idealised models of villus structure. ConclusionThese findings highlight the need for stereological approaches that account for curvature when interpreting placental structure-function relationships.

Network-based epidemic models have been instrumental in understanding how contact structure shapes infectious disease dynamics, yet widely used frameworks such as Erd[o]s-Renyi, configuration-model, and stochastic block networks do not explicitly capture the combination of fully accessible (saturated) within-group interactions and constrained between-group connectivity characteristic of many real-world settings. Here, we introduce the Multi-Clique (MC) network model, a generative framework in which individuals are organised into fully connected cliques representing stable contact groups (e.g., households, classrooms, or workplaces), with a limited number of external connections governing inter-group transmission. Using stochastic susceptible-infectious-recovered (SIR) simulations on degree-matched networks, we compare epidemic dynamics on MC networks with those on classical random graph models. Despite having an identical mean degree, MC networks exhibit systematically distinct behaviour, including slower epidemic growth, reduced peak prevalence, increased fade-out probability, and delayed time to peak. These effects arise from rapid within but constrained between clique transmission, creating structural bottlenecks that standard models do not capture. The MC framework provides an interpretable, data-driven representation of recurrent contact structure, with parameters that map directly to observable quantities such as household and classroom sizes. By isolating the role of intergroup connectivity, the model offers a basis for evaluating targeted intervention strategies that reduce between-group mixing while preserving within-group interactions. Our results highlight the importance of explicitly representing the real-life clique-based network structure in epidemic models and suggest that classical degree-matched networks may systematically overestimate epidemic speed and intensity in structured populations.

Movement is costly, and animals are under strong selective pressure to move efficiently, yet, in patchy, dynamic landscapes, decision-making is inherently uncertain. We quantify the energetic savings achieved by using up-to-date information presented within social cues for reducing movement costs. We use an agent-based model, founded on realistic aeronautical rules and parametrised on the Andean condor (Vultur gryphus), to study movement in patchy landscapes. By explicitly considering altitude, flight results in a sequence of soaring and gliding in the 3D space. We investigate how the cost of movement to an overall goal varies when birds use social information from others that are either fixed in space or moving collectively to the common goal, and under different risk-taking speed strategies, from slow and cautious to fast and risky. The value of social information is operationalised as energetic savings in units of basal metabolic rate. Under low predictability, agents with intermediate risk and high social-information use exhibit lowest movement costs, with up to 41% energy savings over asocial movement. By extending classical aeronautical theory to social and variable environments we demonstrate the adaptive value of social information for efficient movement in patchy, unpredictable landscapes.

Despite much of the literature perceiving fish schooling as an organized system with a focus on fixed formations for theoretical analyses, experimental observations suggest that frequent positional rearrangement commonly occurs. Previous studies have also demonstrated that fish schools reduce locomotor costs relative to individuals swimming alone. This introduces an intriguing dichotomy. How can individual fish within schools exhibit dynamic interactions while also saving energy? We hypothesize that schooling dynamics are the result of positional and kinematic modulation of individuals responding to fluid dynamic stimuli from the movement of neighbouring individuals. We propose a two-tier approach to studying kinematic modulation within fish schools. First, quantification of the variation of individual movement in a school relative to that of a solitary individual uses an analytical pipeline combining artificial-intelligence-enabled tracking and video processing. Second, the study of kinematic modulation in response to hydrodynamic stimuli uses a mechanical flapping mechanism coupled with an enclosure to control fish position. We discovered that fish in schools exhibit higher levels of positional and kinematic modulation than individuals swimming alone. Fish swimming in enclosures can robustly respond to fluid stimuli from either a simple robotic fish or other fish located in proximity. This two-tier approach allows high-resolution analysis of positional and kinematic modulation within fish schools and their impacts on energy conservation resulting from collective movement.

Pertussis remains an endemic and periodically resurgent vaccine-preventable disease despite long-standing immunisation programmes, reflecting complex interactions between transmission, waning immunity, vaccination history, and heterogeneous clinical presentation. We present a comprehensive age-structured mathematical model of pertussis transmission that explicitly represents infection heterogeneity, immunity dynamics, and detailed vaccination schedules across the life course. The model stratifies the population into 56 age groups and 29 epidemiological states, capturing four distinct infection types that differ by severity, symptoms, and infectiousness, including asymptomatic infection. Both naturally acquired and vaccine-derived immunity are modelled as non-lifelong, incorporating waning, partial protection, reinfection, and immune boosting following exposure without transmissible infection. Vaccination is represented at high resolution, including dose-specific primary series vaccination, booster doses in early childhood, childhood, and adolescence, and maternal immunisation during pregnancy, with differentiation between whole-cell and acellular pertussis vaccine formulations and historical changes in vaccine use and coverage. Periodicity and stochasticity are incorporated to reproduce observed multi-year epidemic cycles. A global sensitivity analysis using Latin hypercube sampling and partial rank correlation coefficients identifies immunity waning rates, immune boosting, and recovery from severe infection as key drivers of modelled incidence, mortality, and population protection. By integrating detailed immune processes with realistic vaccination histories, this model provides a flexible framework for evaluating pertussis epidemiology and assessing the population-level impact of alternative vaccination strategies, including booster and maternal immunisation policies.

Change point detection is critical for identifying structural transitions in time series data. While most existing methods focus on changes in statistical properties of the data such as the mean or variance, many real-world systems are governed by dynamical models in which changes occur in model parameters. We introduce MICA, an algorithm that detects change points by minimizing the discrepancy between model simulations with a given dynamical model and observed data. The method integrates binary segmentation with a genetic algorithm to identify both the timing and nature of model parameter changes. MICA simultaneously estimates segment-specific and global parameters alongside change points, offering enhanced flexibility and interpretability. We demonstrate its utility on synthetic datasets and real-world scenarios, including COVID-19 epidemiological modeling, under policy interventions, and the analysis of generator cooling systems in wind turbines to monitor operational status. While illustrated using differential and difference equation models, MICA is model-agnostic and applicable to any simulatable system, making it broadly useful for applications requiring accurate tracking of structural dynamics.

BackgroundHIV transmission is characterised by a low per-act probability, a relatively high proportion of multiple variant transmission events, and a plateauing of transmission risk at high viral loads. No existing mechanistic model can simultaneously recapitulate all of these observations, thereby limiting our ability to predict unobserved transmission phenomena and evaluate prevention strategies. MethodsWe developed a suite of mathematical models that encode an empirically plausible set of transmission mechanisms and then fit these models within a Bayesian framework to available epidemiological data to identify which set of mechanisms are sufficient to recapitulate the data. Following formal model comparison, we embedded the best-fit model into a phylodynamic framework and calibrated it using Approximate Bayesian Computation, to assess whether phylogenetic trees from individual transmission pairs were both consistent with the model and informative. Finally, we further validated our most likely model against two large prospective studies (PARTNER1 and STEP). ResultsOur calibrated model predicts that for each systemic infection, approximately four to five transient infections occur--exposure events in which viral replication occurs but is stochastically extinguished--consistent with indirect empirical evidence from the STEP vaccine trial. The model predicts a transmission rate of fewer than 0.05 systemic infections per 100 couple-years follow up from individuals with undetectable viral load, providing a mechanistic basis for the negligible risk observed in the PART-NER1 study. The model also predicts a strong link between the number of viral particles transmitted and the number of variants establishing infection, modulated by the transmitters infection stage. Recalibrating for men who have sex with men indicated that higher transmission rates in this population are explained by a single parameter: a greater probability of permissive conditions for infection. These predictions emerge from a model in which three mechanisms were needed to explain the epidemiological data: highly infrequent permissive conditions within the exposed partner, stage-dependent differences in the probability that infected cells establish systemic infection, and target cell limitation at the site of infection. The model was further validated against phylogenetic data from 48 transmission pairs, where combining mechanistic and phylogenetic information sharpened posterior estimates of time since infection in the majority of cases. ConclusionThree biologically grounded mechanisms are sufficient to explain the key features of HIV transmission. The resulting model provides a principled and mechanistic basis for estimating transmission risk and for designing interventions to reduce it.

Increasing human mobility and population connectivity have intensified the risks of global pathogen spread, while concurrent shifts in human demographic patterns, ecological factors, and climatic conditions have altered the global landscape of this risk. Genomic surveillance can serve as a critical tool for early detection of emerging pathogen threats; however, challenges remain in deciding where to monitor, in understanding trade-offs among surveillance modalities, and in translating detections into actionable estimates of importation and local transmission for public health decision-making. Here we develop a computational framework to evaluate strategies for respiratory pathogen detection that integrates an established clinical surveillance modality, intensive care unit (ICU) sampling, with an emerging environmental modality, aircraft wastewater (AWW) sampling. Detections are translated into risk via a multi-scale, stochastic global transmission model that combines international flight data with a detailed agent-based local transmission model. The resulting model-based estimates contrast the time to pathogen detection via AWW at airports with that in the community via realistic healthcare testing pathways. Using real-world data from England and Wales (EW), we find that employing AWW in EW airports can improve first detection times by 12.5-37.7 days for a range of epidemiological parameters under realistic healthcare testing scenarios and random aircraft sampling between 25 and 50%. In particular, for a SARS-CoV-2-like pathogen, we expect AWW to outperform ICU in first detection timing by 22.0-25.6 days, with [~]21.9-42.6 times fewer cases at their respective time of detection. While false detection remains a risk, we show that follow-up confirmatory testing can improve detection confidence substantially. Together our results demonstrate the potential utility of AWW surveillance and how it can reduce detection times and improve global health security.

Spaceflight-Associated Neuro-ocular Syndrome (SANS) involves complex interactions between intracranial pressure (ICP), intraocular pressure (IOP), and cerebrospinal fluid (CSF) dynamics within the optic nerve subarachnoid space (ONSAS). While existing computational models address specific aspects of these interactions, they lack a comprehensive, system-level representation. To bridge this gap, we present the HEAD (Hemodynamic Eye-brain Associated Dynamics) model. By consistently integrating several previously proposed physiological sub-models, HEAD provides a unified lumped-parameter framework that fully couples cerebrovascular autoregulation, multi-territory ocular hemodynamics, and compartmentalized craniospinal-ONSAS CSF circulation under gravitational loading. This formulation enables the simultaneous analysis of eye-brain-CSF dynamics within a single computational tool. Model predictions were validated against experimental data from supine (0{degrees}) to head-down tilt (HDT, -30{degrees}) postures, accurately reproducing posture-dependent IOP increases and achieving an excellent ICP match against clinical benchmarks at the -6{degrees} HDT standard bed-rest angle. The coupled system predicts bed-specific ocular hemodynamic responses, with retinal blood flow exhibiting the largest relative increase under HDT compared to the ciliary and choroidal circulations. Crucially, explicitly modeling the ONSAS as a distinct compartment reveals a posture-dependent pressure drop of 1.89-3.69 mmHg between the intracranial and perioptic spaces. This compartmentalization yields a translaminar pressure profile that remains positive (8.05-11.83 mmHg) across all simulated conditions but is chronically reduced under sustained HDT. Ultimately, the HEAD model elucidates the physiological mechanisms linking gravitational stress to translaminar mechanics, providing a robust computational foundation to investigate SANS and supply boundary conditions for structural models of the optic nerve head.

Rapidly evolving pathogens can escape antibody-mediated immunity, leading to recurrent epidemics. Vaccination is a key intervention to reduce infections and severe disease, yet concerns remain that it may accelerate antigenic evolution, potentially undermining long-term vaccine effectiveness. We developed a multi-strain mathematical model, parameterized for a rapidly evolving pathogen, to systematically explore how vaccination influences both the speed of antigenic evolution and the incidence of infection across a range of biological vaccine characteristics (efficacy, neutralization breadth, and vaccine strain) and implementation strategies (vaccination coverage and frequency). In the model, pathogen evolution is driven by cross-immunity and stochastic mutations in a one-dimensional antigenic space, and vaccination reduces an individuals susceptibility to circulating strains according to the cross-immunity conferred by the vaccine strain. We find that vaccination generally reduces infection incidence, with higher coverage and efficacy leading to larger declines and, eventually, pathogen extinction. When transmission is substantially suppressed, antigenic evolution slows down. However, when vaccines match circulating strains but confer narrow cross-immunity, vaccination may accelerate antigenic evolution and potentially increase incidence. In a case study of seasonal influenza, vaccines with increased efficacy can speed up antigenic evolution but do not raise incidence. Overall, our results show that vaccination can effectively reduce both infection incidence and the speed of antigenic evolution in many scenarios. Nevertheless, the potential for vaccine-driven evolution warrants careful consideration, particularly when vaccine effectiveness in reducing incidence is limited.

Fuel availability and fuel dryness are consistently shown to be the primary drivers of wildfire intensity and burnt area. Here we hypothesise that differences in the timing of fuel build up and drying determine the optimal time for wildfire occurrence. We use gross primary production (GPP) as a measure of biomass production and hence fuel availability, and vapour pressure deficit (VPD) as a measure of fuel drying. We use the phase difference in the seasonal time course and magnitude of GPP and VPD to cluster regions that should therefore have distinct wildfire behaviour. We then show that each of the resultant clusters is distinctive in terms of one or more fire properties, specifically number of ignitions, burnt area, size, speed, duration, intensity, and length of the wildfire season. The emergence of distinct regimes as a function of two biophysical drivers reflects the fact that both vegetation and wildfire properties are a consequence of eco-evolutionary adaptions to environmental conditions. We then examine the degree to which human activities or vegetation properties modify these fire regimes within each of these clusters. Variability in GPP and VPD largely explains the within-cluster variation in fire properties. The type of vegetation cover has an influence on burnt area and carbon emissions in particular, while human activities are more important for fire properties such as size, rate of spread and duration largely through their influence of landscape fragmentation. Although both human activities and vegetation properties modify wildfire regimes, the ability to distinguish wildfire regimes using GPP and VPD alone emphasizes that land management, fire use and fire suppression are constrained by environmental conditions. This eco-evolutionary optimality approach to characterising wildfire regimes provides a basis for designing a simple fire model for Earth System modelling.

Identifying sudden transitions during phenotypic decision-making of complex biological systems can be crucial for our ability to control a cellular state. Yet, prior determination of these sudden transitions or tipping points remains challenging, as biological systems often exhibit only subtle early changes, which are often masked by inherent noise or rapid transition dynamics. Using Notch signaling as a model, we systematically analyze dynamical transitions in Notch-Delta (ND), Notch-Delta-Jagged (NDJ), and Fringe-mediated NDJ systems for both one and two-cell contexts. In the one-cell ND system, critical slowing down (CSD)-based early warning signals (EWSs) reliably capture transitions between sender (S) and receiver (R) states and remain robust to variation in forcing rate. We further find that flickering is a precursor to transitions in one-cell NDJ system. In contrast, flickering does not occur in the two-cell Notch model due to the presence of a supercritical bifurcation. Our analysis also offers insight into how NICD (Notch Intracellular Domain)-driven and Fringe-mediated asymmetries, along with the strength of external signals, control the emergence of flickering. Overall, this study identifies sudden transitions in Notch signaling under demographic noise and can be extended to other noisy biological systems, with potential applications in drug development and targeted therapeutic interventions.