We study hyperedge-removal strategies for suppressing contagion on synthetic hypergraphs. Hypergraphs are generated from Erdős–Rényi, Barabási–Albert, and Watts–Strogatz seed graphs by promoting maximal cliques to hyperedges. For each hypergraph, we construct s-line graphs whose vertices correspond to hyperedges and whose edges encode hyperedge overlap of size at least s. Spectral k-way clustering of these s-line graphs yields a multiscale cut-persistence score used to rank hyperedges for removal. Simulations show that the effect of this intervention is strongly topology-dependent. In the reported Erdős–Rényi case, cut-persistence targeting reduces final infection size more than random hyperedge removal. In the Watts–Strogatz and Barabási–Albert cases, however, random removal is comparable to or better than cut-persistence targeting. These results suggest that spectral overlap structure can identify structurally salient hyperedges, but structural salience alone does not guarantee optimal contagion suppression. The study motivates further comparison with ensemble-level experiments and explicitly higher-order contagion models.

Social learning is important to humans and other animals as they gather information about their environment. Information and behaviours can therefore spread rapidly through social networks as contagions. However, the way individuals acquire and use social information is highly variable and frequently complex, often shaped by higher-order or multibody interactions that are not straightforwardly described by conventional dyadic networks. There has been considerable recent progress in modeling social contagions across higher-order networks that explicitly quantify these multibody interactions. A challenge for studying social contagion across multibody or higher-order interactions is the diversity of ways in which knowledge can be exchanged within or among groups. Here we provide a typology of knowledge exchange rules in higher-order networks, focusing on both learning and discovery. We also provide a non-exhaustive list of many basic knowledge exchange rules, to demonstrate our typology and its value in distinguishing between different mechanisms of social learning. Our aim is to provide a framework that helps researchers interested in modeling knowledge exchange in higher-order networks to develop new models and adapt existing models to questions of interest. By doing so we hope to promote interdisciplinarity in the study of how multibody interactions shape social contagions, especially at this critically incipient stage - avoiding the inevitable challenges from the eventual need to integrate parallel, independent, complementary advances among different disciplines.

The fast-slow continuum is a key axis of variation in life history strategies capturing the evolutionary trade-off between allocation in lifespan versus reproduction. It has been suggested that social behaviour, and therefore network structure, may vary across this continuum, but formal theory remains scarce. We develop a mathematical model to examine how the rate of demographic replacement may influence emergent social network structures under a range of social preferences and modes of social inheritance. Our key finding is that rapid demographic replacement can constrain emergent social network structure. We predict that generation time determines the drivers of variation in network structures; for longer generation times, emergent network properties are primarily influenced by social preferences, whereas for shorter generation times it is social inheritance. Variation in generation time alone can lead to substantial shifts in network properties; therefore, diversity in life history strategies can help explain diversity in social network structures.

We study a dynamical system modeling the Theory of Planned Behavior (TPB) in which each individual's behavioral intention evolves continuously under an ODE driven by internal attitudes, perceived social norms, and perceived behavioral control. Actions occur as discrete threshold events: when intention reaches a fixed threshold it is reset to 0 and produces a transient "nudge" that jumps to 1 and then decays exponentially. This yields a hybrid ODE-threshold system with psychologically interpretable parameters. We derive a partial classification in the general case of n individuals. Focusing on the two-individual case (n=2), we obtain explicit formulas for trajectories between action events and derive bounds for first-action times. In the mixed setting where one individual is intrinsically increasing and the other is not, we identify a scalar invariant, M, measuring the net effect of one period of excitation. We prove that non-positive M is equivalent to a partial-action state (only the intrinsically active individual acts countable infinitely often), while positive M is equivalent to full action (both individuals act countably infinitely often). Finally, we demonstrate numerically that these analytic boundaries partition the parameter space with near-perfect agreement, and we provide exploratory simulations suggesting analogous structures for three individuals.

In social species, social context plays a key role in shaping transmission dynamics for the adoption of novel behaviours. For social learning to occur, an individual that knows how to produce a behaviour must first decide to produce that behaviour, and this decision can also be shaped by social context. For instance, the presence of socially dominant individuals can often suppress the production of behaviours by knowledgeable subordinate individuals seeking to avoid confrontation over resources. This highlights an important potential gap in the standard methods for evaluating the social spread of behaviours and innovations: the difference between knowing and acting. We develop a multinetwork model to investigate the interplay between social learning and socially informed decisions regarding whether to produce a novel behaviour. In particular, we explore how diffusion outcomes may be impacted when the latter process is modulated by social dynamics that extend beyond dyadic relationships to explicitly consider group structure and composition (i.e. higher-order effects). We demonstrate that when socially informed decisions to produce a novel behaviour are highly sensitive to differences in group composition, diffusion outcomes can vary dramatically, depending on whether models are restricted to dyadic information or allow for multiway interactions or group level social influences. Incorporating these latter elements into studies of transmission dynamics requires higher-order network tools that can capture the heterogeneity of social context and therefore also provide a compelling example of, and argument for, the necessity to develop more suitable approaches for studying higher-order social dynamics in animal populations. (c) 2026 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Computational simulation provides a powerful toolkit for in silico experimentation. However, while the field has developed best practices for the design and implementation of such models, there remains ambiguity in discussions about how to understand and/or interpret their results due to their inherent ability to overwhelm traditional frequentist statistics by simply increasing the number of trials simulated. This fails the discipline in two ways: first, it leaves the community unsure of what constitutes a best practice for uniform understanding, and second, it potentially overburdens computational studies that burn clock cycles solely to ensure "enough runs to satisfy peers" without any theoretical underpinning for a definition of "enough". We propose a simple and straightforward standard for when to stop simulating additional trials, the Ω test, designed to be analogous to the function of traditional frequentist P-tests. Community adoption of a reasonable and uniform standard will permit more efficient computational experimentation and clearly communication/interpretation of the findings discovered in this way.

Animals interact socially in diverse ways, with each interaction type contributing to ecological and evolutionary processes differently. When this is the case, using multilayer network representations to retain information on the multifaceted nature of a group's social network can help draw accurate conclusions. One context in which this has been well explored theoretically is in the study of contagions. Here we examine how models of multilayer contagions can contribute to animal behaviour research. We provide an overview of key phenomena that can be modelled as a contagion, discuss when multilayer models provide added value and introduce key concepts with links to key theory from outside the animal behaviour literature. We use two illustrative case studies to demonstrate how these models can generate predictions for empirical research, identify their potential applied value and examine key challenges in better integrating modelling theory with empirical data. We aim to both (1) encourage animal behaviour researchers to consider the ecological and evolutionary implications of inherently multilayer contagion processes in animal groups and (2) highlight the value of existing network science theory in providing hypotheses to be tested with the types of social data already being collected in nonhuman animals. (c) 2026 The Authors. Published by Elsevier Ltd on behalf of The Association for the Study of Animal Behaviour. This is an open access article under the CC BY license (http://creativecommons.org/licenses/ by/4.0/).

Investigations of infectious disease outbreaks often focus on identifying place- and context-dependent factors responsible for emergence and spread, resulting in phenomenological narratives ill-suited to developing generalizable predictive and preventive measures. We contend that case-control hypothesis testing is a more powerful framework for epidemiological investigation. The approach, widely used in medical research, involves identifying counterfactuals, with case-control comparisons drawn to test hypotheses about the conditions that manifest outbreaks. Here we outline the merits of applying a case-control framework as epidemiological study design. We first describe a framework for iterative multidisciplinary interrogation to discover minimally sufficient sets of factors that can lead to disease outbreaks. We then lay out how case-control comparisons can respectively center on pathogen(s), factor(s), or landscape(s) with vignettes focusing on pathogen transmission. Finally, we consider how adopting case-control approaches can promote evidence-based decision making for responding to and preventing outbreaks.

Conservation efforts are under constant threat of failure due to poaching. Efforts to combat poaching may take a number of forms, but access to each form depends on resources, and access to these resources may depend on the success of previous efforts (e.g., monetary donations from supporters could directly combat poaching, but may be more effective if partially spent on recruiting additional supporters who then also donate). We adopted a mathematical framework with inspiration from the famous colonel blotto game to model the ongoing battle between conservationists and poachers. Focusing on a marine setting as a case study, players have budgets consisting of three types of resources: monetary, non-monetary, and supporters. The heterogeneous battlefields (laws, marine reserves, and community) reflect commonly employed conservation tactics meant to limit poaching. conservationists allocate resources to limit the success of poachers, while poachers allocate resources to overcome barriers implemented by conservationists. We assumed that no action can succeed without supporters, and thus whichever player wins over all the supporters in the community (i.e., the community battlefield), wins the game. We analyzed battlefield payoffs and player budget distributions to determine overall player success. We demonstrated how initially disadvantaged players may have an opportunity to win the game, although, we found that success in the first round can be most critical under certain scenarios. By framing the question in this way, we hope to provide additional tools for decision support to guide resource allocation, improving the efficacy of conservation efforts.

Coordination games have been of interest to game theorists, economists, and ecologists for many years to study such problems as the emergence of local conventions and the evolution of cooperative behavior. Approaches for understanding the coordination game with discrete structure have been limited in scope, often relying on symmetric reduction of the state space, or other constraints which limit the power of the model to give insight into desired applications. In this paper, we introduce a new way of thinking about equilibria of the structured coordination game with neutral strategies by means of graph partitioning. We begin with a few elementary game theoretical results and then catalogue all the Nash equilibria of the coordination game with neutral options for graphs with seven or fewer vertices. We extend our observations through the use of simulation on larger Erdős-Rényi random graphs to form the basis for proposing some conjectures about the general relationships among edge density, cluster number, and consensus stability.

Coordination games with explicit spatial or relational structure are of interest to economists, ecologists, sociologists, and others studying emergent global properties in collective behavior. When assemblies of individuals seek to coordinate action with one another through myopic best response or other replicator dynamics, the resulting dynamical system can exhibit many rich behaviors. However, these behaviors have been studied only in the case where the number of players is countable and the relational structure is described discretely. By giving an extension of a general class of coordination-like games, including true coordination games themselves, into a continuous setting, we can begin to study coordination and cooperative behavior with a new host of tools from PDEs and nonlocal equations. In this study, we propose a rigorously supported extension of structured coordination-type games into a setting with continuous space and continuous strategies and show that, under certain hypotheses, the dynamics of these games are described through a nonlinear, nonlocal diffusion equation. We go on to prove existence and uniqueness for the initial value problem in the case where no boundary data are prescribed. For true coordination games, we go further and prove a maximum principle, weak regularity results, as well as some numerical results toward understanding how solutions to the coordination equation behave. We present several modeling results, characterizing stationary solutions both rigorously and through numerical experiments and conclude with a result towards the inhomogeneous problem.

Global trade of material goods involves the potential to create pathways for the spread of infectious pathogens. One trade sector in which this synergy is clearly critical is that of wildlife trade networks. This highly complex system involves important and understudied bidirectional coupling between the economic decision making of the stakeholders and the contagion dynamics on the emergent trade network. While each of these components are independently well studied, there is a meaningful gap in understanding the feedback dynamics that can arise between them. In the present study, we describe a general game theoretic model for trade networks of goods susceptible to contagion. The primary result relies on the acyclic nature of the trade network and shows that, through the course of trading with stochastic infections, the probability of infection converges to a directly computable fixed point. This allows us to compute best responses and thus identify equilibria in the game. We present ways to use this model to describe and evaluate trade networks in terms of global and individual risk of infection under a wide variety of structural or individual modifications to the trade network. In capturing the bidirectional coupling of the system, we provide critical insight into the global and individual drivers and consequences for risks of infection inherent in and arising from the global wildlife trade, and any economic trade network with associated contagion risks.

The built environment provides an excellent setting for interdisciplinary research on the dynamics of microbial communities. The system is simplified compared to many natural settings, and to some extent the entire environment can be manipulated, from architectural design, to materials use, air flow, human traffic, and capacity to disrupt microbial communities through cleaning. Here we provide an overview of the ecology of the microbiome in the built environment. We address niche space and refugia, population and community (metagenomic) dynamics, spatial ecology within a building, including the major microbial transmission mechanisms, as well as evolution. We also address the landscape ecology connecting microbiomes between physically separated buildings. At each stage we pay particular attention to the actual and potential interface between disciplines, such as ecology, epidemiology, materials science, and human social behavior. We end by identifying some opportunities for future interdisciplinary research on the microbiome of the built environment.

Pace of life history is a key axis of variation in life history strategies that captures the evolutionary trade-off between investing in lifespan versus reproduction. It has been suggested that social behaviour, and therefore network structure, may vary with pace of life, but formal theory remains scarce. We develop a novel mathematical model to examine how differences in demographic turnover may constrain emergent social network structures in natural populations. We additionally consider variation in social preferences and social inheritance mechanisms. Our key finding is that rapid demographic turnover, associated with faster pace of life, can substantially constrain the structure of dynamic social networks. For slow pace of life, network structures are primarily determined by social preferences, while for fast pace of life they are primarily determined by mechanisms of social inheritance. By considering how demographic turnover can constrain social network organisation, our work provides important insights into social evolutionary ecology. ### Competing Interest Statement The authors have declared no competing interest.

Classification tasks are some of the most widely known machine learning applications. Computers can classify images, sounds, and patterns with high accuracy, given enough training data, time, and computational resources. After training, computers can perform identification tasks faster than humans and often with less error. In contrast, humans are well equipped for anomaly identification and can adapt to new information quickly and effectively. Thus we introduce DialectDecoder, a tool that uses human intelligence and machine learning to classify different dialects of White-crowned Sparrow songs, relying on both the human and the computer for different parts of the classification process. DialectDecoder is an example of humans and computers working together to detect and classify anomalies. After preprocessing the data and training the classifiers with the builtin tools, each new song is fed to the network where the computer classifies the song as a specific dialect or gives the song conflicting labels which, with the song, are sent to the expert human for classification. The human expert can label all songs with conflicting labels and append them to the training set, which provides the computer with updated information to retrain on. We performed three different tests that illustrate the applicability of human-machine teaming and demonstrate the ability of DialectDecoder, paired with an expert human, to classify different dialects of White-crowned Sparrow songs. Then, we discuss extensions of DialectDecoder and its applicability to other human-machine teaming tasks that leverage the distinct strengths contributed by each half of the partnership to improve overall performance.

Animal communication is frequently studied with conventional network representations that link pairs of individuals who interact, for example, through vocalization. However, acoustic signals often have multiple simultaneous receivers, or receivers integrate information from multiple signallers, meaning these interactions are not dyadic. Additionally, non-dyadic social structures often shape an individual’s behavioural response to vocal communication. Recently, major advances have been made in the study of these non-dyadic, higher-order networks (e.g. hypergraphs and simplicial complexes). Here, we show how these approaches can provide new insights into vocal communication through three case studies that illustrate how higher-order network models can: (i) alter predictions made about the outcome of vocally coordinated group departures; (ii) generate different patterns of song synchronization from models that only include dyadic interactions; and (iii) inform models of cultural evolution of vocal communication. Together, our examples highlight the potential power of higher-order networks to study animal vocal communication. We then build on our case studies to identify key challenges in applying higher-order network approaches in this context and outline important research questions that these techniques could help answer. This article is part of the theme issue ‘The power of sound: unravelling how acoustic communication shapes group dynamics’.

Abstract Desert communities are threatened with species loss due to climate change, and their resistance to such losses is unknown. We constructed a food web of the Mojave Desert terrestrial community (300 nodes, 4080 edges) to empirically examine the potential cascading effects of bird extinctions on this desert network, compared to losses of mammals and lizards. We focused on birds because they are already disappearing from the Mojave, and their relative thermal vulnerabilities are known. We quantified bottom‐up secondary extinctions and evaluated the relative resistance of the community to losses of each vertebrate group. The impact of random bird species loss was relatively low compared to the consequences of mammal (causing the greatest number of cascading losses) or reptile loss, and birds were relatively less likely to be in trophic positions that could drive top‐down effects in apparent competition and tri‐tropic cascade motifs. An avian extinction cascade with year‐long resident birds caused more secondary extinctions than the cascade involving all bird species for randomized ordered extinctions. Notably, we also found that relatively high interconnectivity among avian species has formed a subweb, enhancing network resistance to bird losses.

When we think of model ensembling or ensemble modeling, there are many possibilities that come to mind in different disciplines. For example, one might think of a set of descriptions of a phenomenon in the world, perhaps a time series or a snapshot of multivariate space, and perhaps that set is comprised of data-independent descriptions, or perhaps it is quite intentionally fit *to* data, or even a suite of data sets with a common theme or intention. The very meaning of 'ensemble' - a collection together - conjures different ideas across and even within disciplines approaching phenomena. In this paper, we present a typology of the scope of these potential perspectives. It is not our goal to present a review of terms and concepts, nor is it to convince all disciplines to adopt a common suite of terms, which we view as futile. Rather, our goal is to disambiguate terms, concepts, and processes associated with 'ensembles' and 'ensembling' in order to facilitate communication, awareness, and possible adoption of tools across disciplines.

Network analysis is becoming a popular tool for the study of animal movement. Proliferation of software enables researchers to use network measures without reflecting on the underlying mathematics and biology. One common use characterizing movement networks, such as migration, with centrality measures. Predominantly developed to evaluate social systems, these measures now appear in applications across disciplines that vary greatly in system properties. Each network measure has a very specific mathematical definition, with implicit assumptions about system properties to which they are applied that often make them inappropriate for migration. We report mismatches between mathematical assumptions and applications of network measures to migration, primarily with bird examples. For example, of 11 trajectory-transmission network-flow processes observed in the real world, only two are applicable to bird migration, neither of which allows valid application of classical centrality measures. We also identify misinterpretations of network measures, such as nodes with the highest degree centrality as locations where individuals intermingle. Other misinterpretations include that a high betweenness score translates to a node that is frequently used or is an important site along a main migratory route. Finally, networks are used in different ways, ranging from descriptive visualization to quantitative prediction and we identify common cases, such as migratory connectivity, where this leads to miscommunication. Network-theoretic approaches to answer ecological research and conservation questions associated with migration are numerous, but new measures need to be developed for animal migration. We provide a guide for researchers of animal movement for measure selection, development, and documentation.

Social interactions are important for how societies function, conferring robustness and resilience to environmental changes. The structure of social interactions can shape the dynamics of information and goods transmission. In addition, the availability and type of resources that are transferred might impact the structure of interaction networks. For example, storable resources might reduce the required speed of distribution and altering interaction structure can facilitate such change. Here we use ants as a model system to examine how social interactions are impacted by group size, food availability, and food type. We compare global- and individual-level network measures across experiments in which groups of different sizes received limited or unlimited food that is either favorable and cannot be stored (carbohydrates), or unfavorable but with a potential of being stored (protein). We found that as group size increased, individuals interacted with more social partners and interaction networks became more compartmentalized. Furthermore, group compartmentalization increased when food was limited and when transferring storable goods. Our findings highlight how biological systems can adjust their interaction networks in ways that relate to their function. The study of such biological flexibility can inspire novel and important solutions to the design of robust and resilient supply chains.