Journal of The Royal Society Interface

Understanding how animals respond to their physical environment requires environmental observations at the scale at which behavioural decisions are made. For soaring birds, the coarse resolution of weather products has long hindered the analysis of their behavioural response to fine-scale atmospheric dynamics, forcing uplift sources to be inferred largely from behaviour itself. Here, we combined high-resolution movement data from 24 golden eagles with the kilometre-scale COSMO weather model. We first classified thermal, orographic, and gravity-wave uplifts using independent atmospheric predictors and then quantified the birds' use of each uplift type and their fine-scale behavioural responses. Eagles relied predominantly on thermals, but opportunistically adjusted their use of uplift sources seasonally. The birds' flight behaviour could not reliably indicate which uplift type was primarily used, and thus suggests that both atmospheric processes and behavioural responses are better described as continua than discrete categories. Finally, we compared vertical wind velocities derived from eagles soaring behaviour with those modelled by the COSMO weather model, showing that most of the thermals exploited by eagles remain unresolved at kilometre-scale model resolution. Our results demonstrate how high-resolution weather models provide new insights into bird movement decisions, while also highlighting the potential of soaring birds as biologically embedded atmospheric sensors that could help closing the resolution gap in atmospheric models.

Tissue shape and function are defined by the mechanical interactions of cellular and extracellular components. Lymph nodes cyclically remodel in response to immune challenges whilst preserving essential stromal structures. However, the relative contributions of the fibroblastic reticular stromal cell network and the ensheathed extracellular matrix, remain undefined. We quantified the contribution of ECM to the viscoelastic properties of lymph nodes to parameterise an in silico model exploring the FRC network's adaptation to pressure-driven tissue expansion. The balance between tissue pressure, FRC contractility and ECM stiffness permit robust remodelling and growth, while maintaining physiological geometries and balancing force distribution. Local perturbation of ECM stiffness or FRC contractility disrupts force distribution globally and impacts FRC proliferation and tissue expansion. Spatially dispersed perturbations exert higher impact on tissue architecture than equivalent localised perturbations, with effects propagating across the network. The integration of cellular and extracellular mechanics thereby enables robust lymph node remodelling.

Structural network representations of metastatic dissemination typically focus on static topology without resolving transport dynamics, relaxation timescales, or steady-state behaviour. Here, we formulate a discrete Markovian transport model on a directed higher-order network with transition rates derived from qualitative clinical affinity classes. By constructing a non-Hermitian row-stochastic transfer operator, we characterise the relaxation dynamics through its spectral decomposition. The system exhibits a fast-mixing regime characterised by a spectral gap of {gamma} {approx} 0.67, corresponding to a characteristic relaxation timescale of {tau} {approx} 1.49 discrete steps, with the influence of the primary tumour origin progressively attenuated during dissemination. Convergence towards a non-equilibrium steady state (NESS) is accompanied by a reduction in Shannon entropy, concentrating probability mass within specific topological sinks. This spectral relaxation delineates two distinct dynamical regimes: early transient dissemination (n < {tau}), dominated by local organ-specific transition probabilities (organotropism), and the asymptotic regime (n > {tau}), determined increasingly by the global transport architecture of the network. Comparison with independent clinical and autopsy observations across 21 primary tumours and 23 target organs indicates that the predicted stationary distribution is consistent with the observed hierarchy of metastatic organ involvement.

Background: Immigrant patients with limited dominant-language proficiency may face intersecting challenges when navigating cancer care and long-term oral anticancer treatment. Although studies have reported lower medication adherence among migrant and ethnic minority populations, less is known about how migration-related, linguistic, experiential and contextual factors shape treatment engagement from patients own perspectives. This study explored how immigrant patients experience illness, navigate treatment and engage with oral anticancer medication within the broader context of cancer care. Methods: Thirteen immigrant patients with limited dominant-language proficiency receiving oral anticancer medication for haematological malignancies were recruited from the haematology outpatient clinic of a Belgian university hospital. Semi-structured interviews were conducted in participants native languages using an adapted version of the McGill Illness Narrative Interview, with professional interpreters or intercultural mediators. Interviews were analysed using inductive reflexive thematic analysis within an interpretivist framework. Results: Analysis of patients illness narratives generated five experiential dimensions: 1) bodily, biographical and identity rupture; 2) temporal disruption and uncertainty; 3) linguistic vulnerability shaping the illness experience; 4) meaning-making and explanatory frameworks; and 5) resources sustaining treatment engagement. Linguistic vulnerability shaped access to biomedical knowledge, participation in healthcare encounters and patient autonomy, while patients mobilised personal, relational, existential, linguistic and institutional resources to sustain treatment continuity. Treatment engagement emerged as a dynamic and relational process embedded within broader migration-related, linguistic and healthcare contexts. Rather than representing fixed determinants or sequential stages, the five dimensions formed an evolving configuration whose relative salience varied throughout the illness trajectory. Conclusion: This study proposes a multidimensional interpretive model of engagement with oral anticancer medication among immigrant patients with limited dominant-language proficiency. Rather than conceptualising adherence as an isolated individual behaviour, the findings show how migration-related contexts shape the conditions under which treatment engagement becomes possible, difficult or fragile. By foregrounding immigrant patients lived experiences, the study identifies experiential, linguistic, relational and structural dimensions of cancer care that are difficult to capture through behavioural adherence measures alone and offers insights for more equitable, context-sensitive and patient-centred oncology care.

Motile microorganisms explore complex environments in search of nutrients, hosts and favourable ecological niches. Plant-pathogenic oomycetes, for instance, undergo such an exploratory phase through biflagellate zoospores that actively swim through water-filled soil pores before infecting host tissues. Linking individual zoospore swimming behaviour to emergent dispersal remains challenging. Here, we present an end-to-end, data-driven framework that transforms time-lapse microscopy image sequences into generative agent-based simulations of zoospore dispersal by inferring local behavioural rules directly from experimental trajectories. Using Phytophthora nicotianae as a model system, we isolated nearly 60,000 zoospore trajectories and quantified both local behavioural descriptors and emergent trajectory properties. Local behavioural measurements were first used to infer an empirical two-state model distinguishing SLOW and FAST swimming regimes while capturing temporal memory and the coupling between speed and turning. Implemented within an agent-based cellular automaton, this model reproduced the principal emergent properties of experimental dispersal. We then independently inferred the behavioural organisation of zoospore swimming using hidden Markov models. The most parsimonious two-state HMM recovered a closely related behavioural organisation, while revealing that the inferred states jointly reflected swimming speed, turning dynamics and directional persistence rather than speed alone. Finally, we challenged the inferred behavioural rules in an independent obstacle-filled environment. Combined with simple collision hypotheses, the model reproduced emergent dispersal without recalibrating the swimming rules and identified transient post-collision slowdown as a key response required to account for the experimental trajectories. Together, these results demonstrate that experimentally inferred local behavioural rules possess predictive power beyond the conditions used for their calibration. More broadly, this work establishes a predictive framework linking quantitative microscopy, behavioural-rule inference and generative modelling of microbial dispersal.

A variety of connected systems, ranging from the cytoskeleton to human organizations, dynamically rearrange themselves in order to move through physical or abstract space. However, our understanding of how systems-level behaviors arise from local restructuring actions remains limited, necessitating comparison of real-world data to models that predict network structure and dynamics. To understand these systems, we study an accessible example, the branching slime mold Physarum polycephalum, by imaging the organism as it travels and extracting key fundamental quantities from its continuously remodeling tubular network. By using these quantities as input parameters to a traveling network model, we find that with no further fitting, the model quantitatively matches key emergent properties from P. polycephalum dynamics including path length, relocation time, and search efficiency at different spatial resolutions. These findings demonstrate how a traveling network model can capture P. polycephalum behaviors, highlighting the potential to use traveling networks more broadly for understanding and predicting connected dynamic systems by linking local measurements to emergent, system-wide behaviors.

From animal societies to self-organizing multi-agent systems, collectives adapt their group structure to tasks and environments. However, how they determine appropriate group sizes and the number of subgroups to form remains unclear. We formulate the Group Size and Number Regulation Problem (GSNRP), which asks how individuals regulate group sizes and numbers using only local information. In a first step, we establish a graph-theoretic model demonstrating that simple following behavior suffices to form group structures that match theoretical expectations, but is insufficient for active regulation of group size and number. In a second step, we operationalize individual group-size preferences in a decentralized fission-fusion mechanism based on perceived group size. Through multi-agent simulations, we validate that this mechanism achieves stable convergence across three signaling regimes, from position-only sensing to continuous group-size communication. Using tracking data from wild white-nosed coatis (mammals in the raccoon family), we calibrate individual group-size preferences and show that the controller recovers selected group-size, subgroup-count, and transition statistics. This in-sample case study demonstrates descriptive consistency with natural fission-fusion dynamics without establishing the underlying behavioral mechanism. These results suggest that natural and engineered collectives may share local principles of perception, preference, and response for regulating group structure.

Microbial populations generally evolve in fluctuating environments under time-varying conditions. These are often described by binary switching models, sometimes seen as coarse-grained feast-famine cycles, in which resource availability switches abruptly between abundant and scarce conditions. However, experimental studies suggest that feast-famine environments actually exhibit more complex temporal dynamics. Here, we study how two strains, one growing slightly slower than the other, compete for the same resources in fluctuating environments comprising a finite number of intermediate states, each having its own carrying capacity. Environmental switching between these states and their carrying capacities represents gradual changes in nutrient availability. This class of multi-state stochastic switching models can be interpreted as a coarse-grained description of feast-famine cycles and allows us to investigate strain competition under the gradual recovery and depletion of resources. By computational and analytical means, we characterise the population dynamics in these multi-state fluctuating environments. In particular, we study how the switching rates and distribution of carrying capacities affect the population-size statistics, fixation probability, and mean fixation time. By comparing these results with their counterparts in binary environments, we clarify how the frequency and amplitude of environmental fluctuations influence population dynamics in coarse-grained feast-famine cycles.

Can observations distinguish a bloom supplied from within a study volume from one supplied across its boundary? We develop a theoretical framework for that question at plankton bloom onset, conditional on a predeclared, observed or calibrated onset event and a declared set of environmental paths, biological responses, and model forms. The estimand follows source-event labels through forcing-dependent survival and genotype-specific growth. Its central certificate asks whether the local onset fraction is invariant over every source history that produces the same time-expanded observation record. For polyhedral history fibers, a Charnes-Cooper transformation computes both sharp dynamic-data endpoints as linear programs. When each source instead has a fixed normalized onset signature, the certificate reduces to a row-space test; uncertain signatures require a joint lifted program. For a finite compatible scenario ensemble, admissible fractions are the union across scenarios, and a point is justified only when every nonempty scenario gives the same singleton. A synthetic two-genotype witness gives the same observed total but local fractions of 2/3 and 1/3 under reversed forcing-response gains. The observer, mixture, and optimization ingredients are established; the contribution is their target-specific synthesis around source at onset. The framework is diagnostic rather than predictive. It specifies what a study must measure--local sources, boundary inflow, forcing, response, timing, and carrier signatures on one declared window--and returns an interval when missing components have justified bounds, including [0, 1] when they remain unconstrained.

Rhizomorphs are specialised, root-like fungal structures whose hierarchical organisation may offer a route to reinforcing mycelium-based materials, yet the environmental regulation of their network formation remains poorly understood. Here, we develop an image-based framework to characterise the longitudinal growth and organisation of Armillaria gallica rhizomorphs under varying nutrient availability and light exposure. Time-lapse imaging was combined with image segmentation, skeleton-based network analysis, optical measurements and Gompertz growth modelling. Nutrient availability produced a distinctly non-monotonic response. Moderate nutrient limitation (0.5 x standard concentration) favoured rapid and coherent exploratory growth, whereas intermediate enrichment (1.5 x) produced the greatest eventual network extent, reaching approximately 975 mm total strand length; network extent and radial expansion differed significantly across nutrient levels (padj = 0.0012). Further enrichment maintained substantial fungal coverage without additional network elaboration, consistent with a shift from long-range exploration towards more locally consolidating growth. By contrast, exclusion of ambient light produced no significant differences after multiple-testing correction. These results reveal a resource-dependent trade-off between exploration and network elaboration, demonstrate that fungal coverage and organised network formation are distinct outcomes, and provide a quantitative basis for controlling self-organised biological architectures for bio-derived material design.

Animals use long-range signals, such as hormones and neural signals, to coordinate the actions of distant organs. There is no precise, quantitative framework that explains the problems these control systems must solve and thus predicts their behavior under varied conditions. We consider this problem in the context of blood glucose regulation by the hormone insulin, the failure of which produces diabetes. We show that existing mathematical models of glucose regulation admit equivalent control strategies with no hormones at all, and thus cannot explain the need for hormonal regulation. We therefore introduce a minimal model of inter-organ variations in local glucose, and show that control strategies based on local glucose measurements face severe trade-offs between different control objectives. In contrast, we show that hormonal control signals from the pancreas can overcome these limitations. By exposing the benefits of hormonal control, our work paves the way to a detailed understanding of physiological design principles, with possible implications for the engineering of an artificial pancreas.

Predicting patterns of behavioural coordination that emerge in small interacting groups is challenging because goal-directed social action is shaped by complex reciprocal and compensatory dynamics. In this study, we examined whether formal symmetry principles derived from group theory could explain coordination patterns among children performing a triadic jumping task. We investigated how geometric symmetries of the task environment and dispositional (a)symmetries associated with leader-follower tendencies jointly constrain collective behaviour. Forty-seven children were classified into symmetric or asymmetric triads based on teacher evaluations of leadership dispositions. Each triad completed multiple trials of a synchronized jumping game requiring movement between adjacent hoops arranged in triangular or square configurations. Results showed that temporal asymmetries in inter-child movement (first, second, or last to jump) were consistent with group-theoretic predictions. In triangular configurations, observed asymmetries corresponded to the highest-order subgroup defined by task and dispositional symmetries. These findings demonstrate that environmental symmetry exerts a hierarchically dominant constraint on collective coordination, within which actor dispositional (a)symmetries further modulate emerging patterns.

The dominant paradigm for temperature robustness in biomolecular circuits is for the parameters to be tuned to have matching temperature dependencies so that their overall effect cancels out. This contrasts with the robustness due to circuit structure, typically operative in circuits where robustness to a single input parameter is desired. The importance of the circuit structure in temperature robustness is generally unclear. We addressed this issue in a benchmark negative feedback circuit using a combination of theoretical modelling and experimental measurements. We found that the response to a temperature perturbation in a model of negative feedback was qualitatively different from the response in a model without feedback. We experimentally measured the response of the negative feedback circuit to a temperature perturbation and found that it was smaller than that of the circuit without feedback, in line with the theoretical finding. We confirmed this theoretical prediction experimentally. The initial response of the negative feedback circuit, paradoxically, was larger than the circuit without feedback. The resolution of this paradox was in accounting for the faster dynamics in the negative feedback circuit. These results show a simple design principle of temperature robustness that can operate in a widespread circuit motif and may also apply to other perturbations which, like temperature, affect multiple parameters simultaneously.

Zero-dimensional chemical master equations, ordinary differential equations, and compartmental population models replace spatial stochastic biological systems by vectors of total counts or densities. This study asks when that projection is exact and whether information retained in spatial correlations can diagnose its practical failure. Exact Markov closure is characterized by an aggregate-rate lumpability condition: for every retained transition, the sum of microscopic transition rates must be constant over all spatial configurations with the same counts. Violations are connected to BBGKY-type correlation hierarchies and to mean-field, pair, and triplet closures. Conditional rate, finite-time predictive, memory, path-space, and correlation Kullback-Leibler risks quantify distinct losses. An exactly solvable two-compartment reaction separates structural non-closure from recovery of a well-mixed law under fast hidden mixing. Copy number and a spatial mixing-interaction ratio connect concentration, volume, diffusion, and reaction parameters to practical screening, including an Escherichia coli-scale example. The same projection logic is evaluated in controlled spatial susceptible-infectious-removed and predator-prey benchmarks. Across mixed and segregated initial conditions and four mobility regimes, pair-correlation risk was strongly associated with the error of the corresponding zero-dimensional ordinary differential equations (Spearman correlations 0.95 and 1.00; pooled 0.99). A nearest-neighbour exchange sensitivity analysis preserved the positive risk-error ranking. These benchmarks do not establish a universal threshold, but support correlation information as a transferable diagnostic for selecting among count, pair, higher-order, and explicit spatial descriptions.

Solitary animals face a tradeoff when detecting threats: faster detection means accepting more false alarms. We show that groups can manage this tradeoff better by treating an undisturbed neighbor as evidence against a threat, becoming both faster and more accurate than lone individuals. Modeling each animal as a noisy evidence-accumulator that flees when its belief crosses a threshold, we find that a neighbor's flight signals danger while its stillness signals safety. A naive responder reacts only to flights and inflates false alarms as the group grows; a Bayesian responder weighs both, approximated by a single social discounting rate that interpolates between these limits. This yields closed-form expressions for group performance, including cascade branching ratios that stay strongly subcritical in safety and turn supercritical under threat, so the rate at which an animal discounts a threat while its neighbors stay still can be inferred from behavior alone, and it sets a ceiling on how many neighbors an animal can attend before discounting alone can no longer hold its false-alarm rate. Wild sulphur molly shoals under bird attack are best described by discounting rates well above what individually Bayesian updating supplies over any neighborhood they could plausibly attend, and the same model, at the inferred value, predicts a false-alarm rate that stays constant as shoals grow.

Spatial population structure and seasonality are both central to the spread of many infectious diseases of plants, animals and humans. While seasonal forcing in transmission often plays an important role in epidemiological models of a wide range of infectious disease, and we now have some theoretical understanding of the dynamical impacts of spatial structure, the combined effects of these two ubiquitous processes has not been examined in detail. Here, we develop a novel model to explore the combined influence of spatial structure and temporal variability on disease dynamics. Spatial structure is represented using a lattice-based approach with near-neighbour interactions, while temporal variability is included through regular, seasonal, variation of the transmission rate. We use bifurcation analysis of a pair approximation of the full spatial model to identify the parameter regimes associated with qualitatively distinct dynamical behaviours. The model exhibits a remarkably wide range of complex dynamics, including limit cycles, quasi-periodic cycles, multi-year cycles, chaotic dynamics and bistability between these different states. In particular, complex dynamics occur when reproduction is predominantly local, with the dynamics depending critically on the amplitude of the seasonal transmission rate. We show how high transmission rates, high birth rates and in particular low recovery rates are requirements for complex dynamics. We predict that SI-type disease interactions in plant pathogen systems will show complex dynamics even with relatively global transmission dynamics.

Violent conflicts increasingly involve multiple armed actors competing for influence over shared civilian populations, creating complex dynamics that challenge conventional security analysis and policy design. We present a framework that adapts epidemiological methods informed by the conflict landscape in Nigeria to model multi-actor violent conflict as an epidemic process. We derive a basic insecurity reproduction number ($R_0$), identify violence-free and persistent-violence equilibria, and introduce a novel Civilian Harm Index (CHI) to quantify humanitarian impact. Sensitivity analyses identify recruitment, ideological support from civilian populations, and abduction as the key drivers of conflict persistence and civilian harm. The framework reveals several counterintuitive findings. Interventions that most effectively suppress violence transmission are not necessarily those that minimise civilian harm, demonstrating that epidemic control and humanitarian protection may require distinct optimisation criteria. Likewise, interventions effective against one armed actor may be ineffective, or even counterproductive, when applied uniformly across groups. In addition, prisoner exchange and ransom payments increase violence persistence and civilian harm. Although developed as an illustrative rather than predictive framework, our results show that epidemiological methods provide quantitative metrics for evaluating intervention priorities and trade-offs in complex multi-actor conflicts.

Despite the impacts of within-host disease dynamics on disease outcomes in individual hosts and disease spread among-hosts, generic models of within-host population dynamics have received far less attention than their among-host counterparts. While a number of models have been proposed to explore theoretical eco-evolutionary dynamics, they have yet to be evaluated for estimability, raising questions about their ability to provide reliable inference when confronted with data. We evaluated the estimability of two generic within-host population dynamics models by assessing: (1) parameter estimation, our ability to recover correct values of model parameters from data, (2) the consequences of mis-assigning the underlying mechanistic model on parameter estimation, and (3) the reproduction of qualitative dynamics, or, our ability to use parameter estimates to reproduce observed dynamical behaviours. In some cases, fitting a mis-matched mechanistic model to time series data produced reasonable parameter estimates that were able to reproduce system dynamics, and that when provided the data-generating model, parameter uncertainty can produce substantial behavioural uncertainty. Our findings highlight the impacts of structural, parametric, and behavioural uncertainty on inference, and demonstrate the value of improving system-specific knowledge to prevent the use of incorrect functional forms and of measuring consequential parameters to improve estimability.

Neutrophil swarming is a critical immune response in mammals and fish, in which neutrophils are recruited to inflammatory sites where they coordinate into a swarm that neutralizes pathogens. While excessive swarming can drive prolonged inflammation, a quantitative understanding of swarming dynamics remains limited. We developed a one-dimensional radial reaction-diffusion model of neutrophil swarming with two kinetic parameters, in order to capture the self-limiting swarming dynamics in both murine and human neutrophils in response to different inflammatory stimulus sizes. To ensure that the inverse problem is well-posed, we first performed sensitivity and identifiability analyses. We then developed a physics-informed neural network (PINN) to infer the key parameters governing swarm expansion and self-limitation. To account for uncertainty in noisy experimental measurements, we further extended this framework to a Bayesian PINN (B-PINN), which provides credible intervals for the inferred parameters. Both models were validated against synthetic data generated by numerical simulation and subsequently applied to in vitro experimental data from human and murine neutrophils in response to three bioparticle cluster sizes. The PINN-inferred dynamics show that larger bioparticle clusters are associated with greater cumulative recruitment and larger swarms in both species. The models further reveal species-specific differences in both the amplitude of initial recruitment and the timescale on which it self-limits. Additionally, the B-PINN posterior distributions quantify uncertainty in these species- and cluster size-dependent trends and identify where additional measurements would be most informative. To our knowledge, this is the first application of physics-informed machine learning to model neutrophil swarming dynamics. This framework provides a starting point for systematically comparing recruitment dynamics between human and murine neutrophils and offers guidance for future experimental design.

Cells respond to their environment through protein networks often dysregulated in cancer, making dynamical modelling crucial. Limitations in experimental data and computational resources motivate coarse-graining methods to build low-dimensional descriptions. Yet classical approaches to coarse-grained modelling rely on strong assumptions, leaving it unclear when partial experimental observations support reduced descriptions of system dynamics. Here we show that symbolic regression (SR) provides a data-driven way to test whether, and how compactly, the dynamics of a signalling system coarse-grain over the measured variables, and, when they do, infers mechanistically interpretable models. In synthetic enzyme systems, SR recovers Michaelis-Menten kinetics for the two-step mechanism and under three-step extensions. As data quality is degraded, SR simplifies toward effective kinetic laws while preserving correct theoretical limits. Applied to published time-resolved ERK phosphorylation data, SR identifies compact phospho-ERK rate laws in selected cancer-relevant gene overexpression contexts, yielding interpretable kinetic effects. A sparse neural ODE baseline requires few inputs where SR succeeds, but on average more where it fails, indicating that, where a reduced model is learnable at all, SR failure is associated with more complex dynamics that a simple mathematical model cannot describe. Together, these findings establish symbolic regression as a way to test when a compact coarse-grained description is warranted, generating hypotheses where one holds and motivating potential new measurements where it does not.