Systematic mapping of organism-scale gene-regulatory networks in aging using population asynchrony.

In aging, physiologic networks decline in function at rates that differ between individuals, producing a wide distribution of lifespan. Though 70% of human lifespan variance remains unexplained by heritable factors, little is known about the intrinsic sources of physiologic heterogeneity in aging. To understand how complex physiologic networks generate lifespan variation, new methods are needed. Here, we present Asynch-seq, an approach that uses gene-expression heterogeneity within isogenic populations to study the processes generating lifespan variation. By collecting thousands of single-individual transcriptomes, we capture the Caenorhabditis elegans "pan-transcriptome"-a highly resolved atlas of non-genetic variation. We use our atlas to guide a large-scale perturbation screen that identifies the decoupling of total mRNA content between germline and soma as the largest source of physiologic heterogeneity in aging, driven by pleiotropic genes whose knockdown dramatically reduces lifespan variance. Our work demonstrates how systematic mapping of physiologic heterogeneity can be applied to reduce inter-individual disparities in aging.

A network frame offers a promising transdisciplinary tool for understanding complex health and health care system problems like suicide.

As health and health care systems continue to face massive challenges from local to global well-being, understanding the processes that lead to improvement or deterioration in human health has embraced a broad range of forces from genes to national cultures. Despite the many efforts to deploy a common framework that captures diverse drivers at scale, the common missing element is the absence of a flexible mechanism that can guide research within and across levels. This hinders both the cumulation of knowledge and the development of a scientific foundation for multiplex interventions. However, studies across disciplines using a wide variety of methods and measures have converged on "connectedness" as crucial to understanding how factors operate in the health space. More formally, a focus on the critical role of the network structure and content of key elements and how they interact, rather than just on the elements themselves, offers both a generalized theory of active factors within levels and the potential to theorize interactions across levels. One critical contemporary health crisis, suicide, is deployed to illustrate the Network Embedded Symbiome Framework. The wide range of health and health care research where networks have been implicated supports its potential but also cautions against inevitable limits that will require creative theorizing and data harmonization to move forward.

Collective neural network behavior in a dynamically driven disordered system of superconducting loops.

Collective properties of complex systems composed of many interacting components such as neurons in our brain can be modeled by artificial networks based on disordered systems. We show that a disordered neural network of superconducting loops with Josephson junctions can exhibit computational properties like categorization and associative memory in the time evolution of its state in response to information from external excitations. Superconducting loops can trap multiples of fluxons in many discrete memory configurations defined by the local free energy minima in the configuration space of all possible states. A memory state can be updated by exciting the Josephson junctions to fire or allow the movement of fluxons through the network as the current through them surpasses their critical current thresholds. Simulations performed with a lumped element circuit model of a 4-loop network show that information written through excitations is translated into stable states of trapped flux and their time evolution. Experimental implementation on a high-Tc superconductor YBCO-based 4-loop network shows dynamically stable flux flow in each pathway characterized by the correlations between junction firing statistics. Neural network behavior is observed as energy barriers separating state categories in simulations in response to multiple excitations, and experimentally as junction responses characterizing different flux flow patterns in the network. The state categories that produce these patterns have different temporal stabilities relative to each other and the excitations. This provides strong evidence for time-dependent (short-to-long-term) memories, that are dependent on the geometrical and junction parameters of the loops, as described with a network model.

Information decomposition in complex systems via machine learning.

One of the fundamental steps toward understanding a complex system is identifying variation at the scale of the system's components that is most relevant to behavior on a macroscopic scale. Mutual information provides a natural means of linking variation across scales of a system due to its independence of functional relationship between observables. However, characterizing the manner in which information is distributed across a set of observables is computationally challenging and generally infeasible beyond a handful of measurements. Here, we propose a practical and general methodology that uses machine learning to decompose the information contained in a set of measurements by jointly optimizing a lossy compression of each measurement. Guided by the distributed information bottleneck as a learning objective, the information decomposition identifies the variation in the measurements of the system state most relevant to specified macroscale behavior. We focus our analysis on two paradigmatic complex systems: a Boolean circuit and an amorphous material undergoing plastic deformation. In both examples, the large amount of entropy of the system state is decomposed, bit by bit, in terms of what is most related to macroscale behavior. The identification of meaningful variation in data, with the full generality brought by information theory, is made practical for studying the connection between micro- and macroscale structure in complex systems.

Elevated emotion network connectivity is associated with fluctuations in depression.

Elevated emotion network connectivity is thought to leave people vulnerable to become and stay depressed. The mechanism through which this arises is however unclear. Here, we test the idea that the connectivity of emotion networks is associated with more extreme fluctuations in depression over time, rather than necessarily more severe depression. We gathered data from two independent samples of N = 155 paid students and N = 194 citizen scientists who rated their positive and negative emotions on a smartphone app twice a day and completed a weekly depression questionnaire for 8 wk. We constructed thousands of personalized emotion networks for each participant and tested whether connectivity was associated with severity of depression or its variance over 8 wk. Network connectivity was positively associated with baseline depression severity in citizen scientists, but not paid students. In contrast, 8-wk variance of depression was correlated with network connectivity in both samples. When controlling for depression variance, the association between connectivity and baseline depression severity in citizen scientists was no longer significant. We replicated these findings in an independent community sample (N = 519). We conclude that elevated network connectivity is associated with greater variability in depression symptoms. This variability only translates into increased severity in samples where depression is on average low and positively skewed, causing mean and variance to be more strongly correlated. These findings, although correlational, suggest that while emotional network connectivity could predispose individuals to severe depression, it could also be leveraged to bring about therapeutic improvements.

Measuring response functions of active materials from data.

From flocks of birds to biomolecular assemblies, systems in which many individual components independently consume energy to perform mechanical work exhibit a wide array of striking behaviors. Methods to quantify the dynamics of these so-called active systems generally aim to extract important length or time scales from experimental fields. Because such methods focus on extracting scalar values, they do not wring maximal information from experimental data. We introduce a method to overcome these limitations. We extend the framework of correlation functions by taking into account the internal headings of displacement fields. The functions we construct represent the material response to specific types of active perturbation within the system. Utilizing these response functions we query the material response of disparate active systems composed of actin filaments and myosin motors, from model fluids to living cells. We show we can extract critical length scales from the turbulent flows of an active nematic, anticipate contractility in an active gel, distinguish viscous from viscoelastic dissipation, and even differentiate modes of contractility in living cells. These examples underscore the vast utility of this method which measures response functions from experimental observations of complex active systems.

A synergistic future for AI and ecology.

Research in both ecology and AI strives for predictive understanding of complex systems, where nonlinearities arise from multidimensional interactions and feedbacks across multiple scales. After a century of independent, asynchronous advances in computational and ecological research, we foresee a critical need for intentional synergy to meet current societal challenges against the backdrop of global change. These challenges include understanding the unpredictability of systems-level phenomena and resilience dynamics on a rapidly changing planet. Here, we spotlight both the promise and the urgency of a convergence research paradigm between ecology and AI. Ecological systems are a challenge to fully and holistically model, even using the most prominent AI technique today: deep neural networks. Moreover, ecological systems have emergent and resilient behaviors that may inspire new, robust AI architectures and methodologies. We share examples of how challenges in ecological systems modeling would benefit from advances in AI techniques that are themselves inspired by the systems they seek to model. Both fields have inspired each other, albeit indirectly, in an evolution toward this convergence. We emphasize the need for more purposeful synergy to accelerate the understanding of ecological resilience whilst building the resilience currently lacking in modern AI systems, which have been shown to fail at times because of poor generalization in different contexts. Persistent epistemic barriers would benefit from attention in both disciplines. The implications of a successful convergence go beyond advancing ecological disciplines or achieving an artificial general intelligence-they are critical for both persisting and thriving in an uncertain future.

Intrinsic neural diversity quenches the dynamic volatility of neural networks.

Heterogeneity is the norm in biology. The brain is no different: Neuronal cell types are myriad, reflected through their cellular morphology, type, excitability, connectivity motifs, and ion channel distributions. While this biophysical diversity enriches neural systems' dynamical repertoire, it remains challenging to reconcile with the robustness and persistence of brain function over time (resilience). To better understand the relationship between excitability heterogeneity (variability in excitability within a population of neurons) and resilience, we analyzed both analytically and numerically a nonlinear sparse neural network with balanced excitatory and inhibitory connections evolving over long time scales. Homogeneous networks demonstrated increases in excitability, and strong firing rate correlations-signs of instability-in response to a slowly varying modulatory fluctuation. Excitability heterogeneity tuned network stability in a context-dependent way by restraining responses to modulatory challenges and limiting firing rate correlations, while enriching dynamics during states of low modulatory drive. Excitability heterogeneity was found to implement a homeostatic control mechanism enhancing network resilience to changes in population size, connection probability, strength and variability of synaptic weights, by quenching the volatility (i.e., its susceptibility to critical transitions) of its dynamics. Together, these results highlight the fundamental role played by cell-to-cell heterogeneity in the robustness of brain function in the face of change.

Toward data-driven, dynamical complex systems approaches to disaster resilience.

With rapid urbanization and increasing climate risks, enhancing the resilience of urban systems has never been more important. Despite the availability of massive datasets of human behavior (e.g., mobile phone data, satellite imagery), studies on disaster resilience have been limited to using static measures as proxies for resilience. However, static metrics have significant drawbacks such as their inability to capture the effects of compounding and accumulating disaster shocks; dynamic interdependencies of social, economic, and infrastructure systems; and critical transitions and regime shifts, which are essential components of the complex disaster resilience process. In this article, we argue that the disaster resilience literature needs to take the opportunities of big data and move toward a different research direction, which is to develop data-driven, dynamical complex systems models of disaster resilience. Data-driven complex systems modeling approaches could overcome the drawbacks of static measures and allow us to quantitatively model the dynamic recovery trajectories and intrinsic resilience characteristics of communities in a generic manner by leveraging large-scale and granular observations. This approach brings a paradigm shift in modeling the disaster resilience process and its linkage with the recovery process, paving the way to answering important questions for policy applications via counterfactual analysis and simulations.

Dynamics of cardio-muscular networks in exercise and fatigue.

A fundamental question in cardiovascular and muscle physiology is how the heart operates in synchrony with distinct muscles to regulate homeostasis, enable movement and adapt to exercise demands and fatigue. Here we investigate how autonomic regulation of cardiac function synchronizes and integrates as a network with the activity of distinct muscles during exercise. Further, we establish how the network of cardio-muscular interactions reorganizes with fatigue. Thirty healthy young adults performed two body weight squat tests until exhaustion. Simultaneous recordings were taken of a 3-lead electrocardiogram (EKG) along with electromyography (EMG) signals from the left and right vastus lateralis, and left and right erector spinae. We first obtained instantaneous heart rate (HR) derived from the EKG signal and decomposed the EMG recordings in 10 frequency bands (F1-F10). We next quantified pair-wise coupling (cross-correlation) between the time series for HR and all EMG spectral power frequency bands in each leg and back muscle. We uncovered the first profiles of cardio-muscular network interactions, which depend on the role muscles play during exercise and muscle fibre histochemical characteristics. Additionally, we observed a significant decline in the degree of cardio-muscular coupling with fatigue, characterized by complex transitions from synchronous to asynchronous behaviour across a range of timescales. The network approach we utilized introduces new avenues for the development of novel network-based markers, with the potential to characterize multilevel cardio-muscular interactions to assess global health, levels of fatigue, fitness status or the effectiveness of cardiovascular and muscle injury rehabilitation programmes. KEY POINTS: The heart operates in synchrony with muscles to regulate homeostasis, enable movement, and adapt to exercise demands and fatigue. However, the precise mechanisms regulating cardio-muscular coupling remain unknown. This study introduces a pioneering approach to assess cardio-muscular network interactions by examining the synchronization of cardiac function with muscle activity during exercise and fatigue. We uncover the first profiles of cardio-muscular interactions characterized by specific hierarchical organization of link strength. We observe a significant decline in the degree of cardio-muscular coupling with fatigue, marked by complex transitions from synchronous to asynchronous behaviour. This network approach offers new network-based markers to characterize multilevel cardio-muscular interactions to assess global health, levels of fatigue, fitness status or the effectiveness of cardiovascular and muscle injury rehabilitation programmes.

A taxonomy of multiple stable states in complex ecological communities.

Natural systems are built from multiple interconnected units, making their dynamics, functioning and fragility notoriously hard to predict. A fragility scenario of particular relevance concerns so-called regime shifts: abrupt transitions from healthy to degraded ecosystem states. An explanation for these shifts is that they arise as transitions between alternative stable states, a process that is well-understood in few-species models. However, how multistability upscales with system complexity remains a debated question. Here, we identify that four different multistability regimes generically emerge in models of species-rich communities and other archetypical complex biological systems assuming random interactions. Across the studied models, each regime consistently emerges under a specific interaction scheme and leaves a distinct set of fingerprints in terms of the number of observed states, their species richness and their response to perturbations. Our results help clarify the conditions and types of multistability that can be expected to occur in complex ecological communities.

Ion-channel degeneracy and heterogeneities in the emergence of signature physiological characteristics of dentate gyrus granule cells.

Complex systems are neither fully determined nor completely random. Biological complex systems, including single neurons, manifest intermediate regimes of randomness that recruit integration of specific combinations of functionally specialized subsystems. Such emergence of biological function provides the substrate for the expression of degeneracy, the ability of disparate combinations of subsystems to yield similar function. Here, we present evidence for the expression of degeneracy in morphologically realistic models of dentate gyrus granule cells (GCs) through functional integration of disparate ion-channel combinations. We performed a 45-parameter randomized search spanning 16 active and passive ion channels, each biophysically constrained by their gating kinetics and localization profiles, to search for valid GC models. Valid models were those that satisfied 17 sub- and suprathreshold cellular-scale electrophysiological measurements from rat GCs. A vast majority (>99%) of the 15,000 random models were not electrophysiologically valid, demonstrating that arbitrarily random ion-channel combinations would not yield GC functions. The 141 valid models (0.94% of 15,000) manifested heterogeneities in and cross-dependencies across local and propagating electrophysiological measurements, which matched with their respective biological counterparts. Importantly, these valid models were widespread throughout the parametric space and manifested weak cross-dependencies across different parameters. These observations together showed that GC physiology could neither be obtained by entirely random ion-channel combinations nor is there an entirely determined single parametric combination that satisfied all constraints. The complexity, the heterogeneities in measurement and parametric spaces, and degeneracy associated with GC physiology should be rigorously accounted for while assessing GCs and their robustness under physiological and pathological conditions.NEW & NOTEWORTHY A recent study from our laboratory had demonstrated pronounced heterogeneities in a set of 17 electrophysiological measurements obtained from a large population of rat hippocampal granule cells. Here, we demonstrate the manifestation of ion-channel degeneracy in a heterogeneous population of morphologically realistic conductance-based granule cell models that were validated against these measurements and their cross-dependencies. Our analyses show that single neurons are complex entities whose functions emerge through intricate interactions among several functionally specialized subsystems.

Bridges and Mechanisms: Integrating Systems Science Thinking into Implementation Research.

We present a detailed argument for how to integrate, or bridge, systems science thinking and methods with implementation science. We start by showing how fundamental systems science principles of structure, dynamics, information, and utility are relevant for implementation science. Then we examine the need for implementation science to develop and apply richer theories of complex systems. This can be accomplished by emphasizing a causal mechanisms approach. Identifying causal mechanisms focuses on the "cogs and gears" of public health, clinical, and organizational interventions. A mechanisms approach focuses on how a specific strategy will produce the implementation outcome. We show how connecting systems science to implementation science opens new opportunities for examining and addressing social determinants of health and conducting equitable and ethical implementation research. Finally, we present case studies illustrating successful applications of systems science within implementation science in community health policy, tobacco control, health care access, and breast cancer screening.

High-pressure X-ray photon correlation spectroscopy at fourth-generation synchrotron sources.

A new experimental setup combining X-ray photon correlation spectroscopy (XPCS) in the hard X-ray regime and a high-pressure sample environment has been developed to monitor the pressure dependence of the internal motion of complex systems down to the atomic scale in the multi-gigapascal range, from room temperature to 600 K. The high flux of coherent high-energy X-rays at fourth-generation synchrotron sources solves the problems caused by the absorption of diamond anvil cells used to generate high pressure, enabling the measurement of the intermediate scattering function over six orders of magnitude in time, from 10-3 s to 103 s. The constraints posed by the high-pressure generation such as the preservation of X-ray coherence, as well as the sample, pressure and temperature stability, are discussed, and the feasibility of high-pressure XPCS is demonstrated through results obtained on metallic glasses.

Flexible parametrization of graph-theoretical features from individual-specific networks for prediction.

Statistical techniques are needed to analyze data structures with complex dependencies such that clinically useful information can be extracted. Individual-specific networks, which capture dependencies in complex biological systems, are often summarized by graph-theoretical features. These features, which lend themselves to outcome modeling, can be subject to high variability due to arbitrary decisions in network inference and noise. Correlation-based adjacency matrices often need to be sparsified before meaningful graph-theoretical features can be extracted, requiring the data analysts to determine an optimal threshold. To address this issue, we propose to incorporate a flexible weighting function over the full range of possible thresholds to capture the variability of graph-theoretical features over the threshold domain. The potential of this approach, which extends concepts from functional data analysis to a graph-theoretical setting, is explored in a plasmode simulation study using real functional magnetic resonance imaging (fMRI) data from the Autism Brain Imaging Data Exchange (ABIDE) Preprocessed initiative. The simulations show that our modeling approach yields accurate estimates of the functional form of the weight function, improves inference efficiency, and achieves a comparable or reduced root mean square prediction error compared to competitor modeling approaches. This assertion holds true in settings where both complex functional forms underlie the outcome-generating process and a universal threshold value is employed. We demonstrate the practical utility of our approach by using resting-state fMRI data to predict biological age in children. Our study establishes the flexible modeling approach as a statistically principled, serious competitor to ad-hoc methods with superior performance.

Uncovering physical activity trade-offs in transportation policy: A spatial agent-based model of Bogotá, Colombia.

BACKGROUND: Transportation policies can impact health outcomes while simultaneously promoting social equity and environmental sustainability. We developed an agent-based model (ABM) to simulate the impacts of fare subsidies and congestion taxes on commuter decision-making and travel patterns. We report effects on mode share, travel time and transport-related physical activity (PA), including the variability of effects by socioeconomic strata (SES), and the trade-offs that may need to be considered in the implementation of these policies in a context with high levels of necessity-based physical activity. METHODS: The ABM design was informed by local stakeholder engagement. The demographic and spatial characteristics of the in-silico city, and its residents, were informed by local surveys and empirical studies. We used ridership and travel time data from the 2019 Bogotá Household Travel Survey to calibrate and validate the model by SES. We then explored the impacts of fare subsidy and congestion tax policy scenarios. RESULTS: Our model reproduced commuting patterns observed in Bogotá, including substantial necessity-based walking for transportation. At the city-level, congestion taxes fractionally reduced car use, including among mid-to-high SES groups but not among low SES commuters. Neither travel times nor physical activity levels were impacted at the city level or by SES. Comparatively, fare subsidies promoted city-level public transportation (PT) ridership, particularly under a 'free-fare' scenario, largely through reductions in walking trips. 'Free fare' policies also led to a large reduction in very long walking times and an overall reduction in the commuting-based attainment of physical activity guidelines. Differential effects were observed by SES, with free fares promoting PT ridership primarily among low-and-middle SES groups. These shifts to PT reduced median walking times among all SES groups, particularly low-SES groups. Moreover, the proportion of low-to-mid SES commuters meeting weekly physical activity recommendations decreased under the 'freefare' policy, with no change observed among high-SES groups. CONCLUSIONS: Transport policies can differentially impact SES-level disparities in necessity-based walking and travel times. Understanding these impacts is critical in shaping transportation policies that balance the dual aims of reducing SES-level disparities in travel time (and time poverty) and the promotion of choice-based physical activity.

The current state of complex systems research on socioeconomic inequalities in health and health behavior-a systematic scoping review.

BACKGROUND: Interest in applying a complex systems approach to understanding socioeconomic inequalities in health is growing, but an overview of existing research on this topic is lacking. In this systematic scoping review, we summarize the current state of the literature, identify shared drivers of multiple health and health behavior outcomes, and highlight areas ripe for future research. METHODS: SCOPUS, Web of Science, and PubMed databases were searched in April 2023 for peer-reviewed, English-language studies in high-income OECD countries containing a conceptual systems model or simulation model of socioeconomic inequalities in health or health behavior in the adult general population. Two independent reviewers screened abstracts and full texts. Data on study aim, type of model, all model elements, and all relationships were extracted. Model elements were categorized based on the Commission on Social Determinants of Health framework, and relationships between grouped elements were visualized in a summary conceptual systems map. RESULTS: A total of 42 publications were included; 18 only contained a simulation model, 20 only contained a conceptual model, and 4 contained both types of models. General health outcomes (e.g., health status, well-being) were modeled more often than specific outcomes like obesity. Dietary behavior and physical activity were by far the most commonly modeled health behaviors. Intermediary determinants of health (e.g., material circumstances, social cohesion) were included in nearly all models, whereas structural determinants (e.g., policies, societal values) were included in about a third of models. Using the summary conceptual systems map, we identified 15 shared drivers of socioeconomic inequalities in multiple health and health behavior outcomes. CONCLUSIONS: The interconnectedness of socioeconomic position, multiple health and health behavior outcomes, and determinants of socioeconomic inequalities in health is clear from this review. Factors central to the complex system as it is currently understood in the literature (e.g., financial strain) may be both efficient and effective policy levers, and factors less well represented in the literature (e.g., sleep, structural determinants) may warrant more research. Our systematic, comprehensive synthesis of the literature may serve as a basis for, among other things, a complex systems framework for socioeconomic inequalities in health.

A system dynamics approach to understand Dutch adolescents' sleep health using a causal loop diagram.

BACKGROUND: Healthy sleep is crucial for the physical and mental wellbeing of adolescents. However, many adolescents suffer from poor sleep health. Little is known about how to effectively improve adolescent sleep health as it is shaped by a complex adaptive system of many interacting factors. This study aims to provide insights into the system dynamics underlying adolescent sleep health and to identify impactful leverage points for sleep health promotion interventions. METHODS: Three rounds of single-actor workshops, applying Group Model Building techniques, were held with adolescents (n = 23, 12-15 years), parents (n = 14) and relevant professionals (n = 26). The workshops resulted in a multi-actor Causal Loop Diagram (CLD) visualizing the system dynamics underlying adolescent sleep health. This CLD was supplemented with evidence from the literature. Subsystems, feedback loops and underlying causal mechanisms were identified to understand overarching system dynamics. Potential leverage points for action were identified applying the Action Scales Model (ASM). RESULTS: The resulting CLD comprised six subsystems around the following themes: (1) School environment; (2) Mental wellbeing; (3) Digital environment; (4) Family & Home environment; (5) Health behaviors & Leisure activities; (6) Personal system. Within and between these subsystems, 16 reinforcing and 7 balancing feedback loops were identified. Approximately 60 potential leverage points on different levels of the system were identified as well. CONCLUSIONS: The multi-actor CLD and identified system dynamics illustrate the complexity of adolescent sleep health and supports the need for developing a coherent package of activities targeting different leverage points at all system levels to induce system change.

Coalitions in international litigation: a network perspective.

We apply network science principles to analyse the coalitions formed by European Union nations and institutions during litigation proceedings at the European Court of Justice. By constructing Friends and Foes networks, we explore their characteristics and dynamics through the application of cluster detection, motif analysis and duplex analysis. Our findings demonstrate that the Friends and Foes networks exhibit disassortative behaviour, highlighting the inclination of nodes to connect with dissimilar nodes. Furthermore, there is a correlation among centrality measures, indicating that member states and institutions with a larger number of connections play a prominent role in bridging the network. An examination of the modularity of the networks reveals that coalitions tend to align along regional and institutional lines, rather than national government divisions. Additionally, an analysis of triadic binary motifs uncovers a greater level of reciprocity within the Foes network compared to the Friends network. This article is part of the theme issue 'A complexity science approach to law and governance'.

Legal hypergraphs.

Complexity science provides a powerful framework for understanding physical, biological and social systems, and network analysis is one of its principal tools. Since many complex systems exhibit multilateral interactions that change over time, in recent years, network scientists have become increasingly interested in modelling and measuring dynamic networks featuring higher-order relations. At the same time, while network analysis has been more widely adopted to investigate the structure and evolution of law as a complex system, the utility of dynamic higher-order networks in the legal domain has remained largely unexplored. Setting out to change this, we introduce temporal hypergraphs as a powerful tool for studying legal network data. Temporal hypergraphs generalize static graphs by (i) allowing any number of nodes to participate in an edge and (ii) permitting nodes or edges to be added, modified or deleted. We describe models and methods to explore legal hypergraphs that evolve over time and elucidate their benefits through case studies on legal citation and collaboration networks that change over a period of more than 70 years. Our work demonstrates the potential of dynamic higher-order networks for studying complex legal systems, and it facilitates further advances in legal network analysis. This article is part of the theme issue 'A complexity science approach to law and governance'.