Iacopo Iacopini

Plant–pollinator communities are typically represented as bipartite networks, whose edges are taken directly from field records of visits. These visits, however, are only a proxy for the object of ecological interest: the latent mutualistic preference between two species. While counts are shaped by preference, they also carry confounding factors such as species abundances, sampling effort, and site- or time-specific conditions. We introduce a hierarchical Bayesian framework that treats visit counts as a realisation of a Poisson process and, on the log scale, decomposes the corresponding pairwise rate into a baseline (community-wide activity together with sampling effort), individual species effects representing abundance, and pairwise mutualistic preferences. The model extends to data replicated across sites and time points, and to the inclusion of environmental or experimental covariates. Because the whole system is fitted jointly, we obtain posterior not only for the preferences but for every latent quantity, each carrying ecological signal of its own, with uncertainty propagated through every level of the model, down to any derived network metric. On synthetic data, we show that common practices, such as reading preferences off raw counts or aggregating replicated observations into a single network, confound abundance with preference. In contrast, our framework recovers the underlying preference structure. On empirical datasets, including a seasonal multi-site pollination study where urbanisation level enters as a covariate, the inferred preference network departs markedly from the observed visits, revealing structure hidden in the raw counts: how species vary across sites and time, and which parts of the community respond most to the covariate. When communities are compared along the urbanisation gradient, standard network metrics on the preference layer revise the conclusions drawn from visits alone. The framework offers a principled way to move from networks of observed visits to networks of underlying mutualistic preferences, carrying uncertainty from the data through to the ecological conclusions and accommodating the spatial, temporal, and covariate structure of modern plant-pollinator datasets. Because it acts on the foundational step of network construction, its implications are broad, placing network-based approaches on firmer ground.

Investigating how different ingredients are combined in popular dishes is crucial to uncover the principles behind food preferences. Here, we use data from public food repositories and network analysis to characterize and compare worldwide cuisines. Ingredients are first grouped into broader types, and each cuisine is then represented as a network in which nodes correspond to ingredient types and weighted links describe how frequently pairs of types co-occur in recipes. Cuisines differ not only in the popularity of ingredient types and range of recipe sizes, but also in the structural organization of ingredient-type combinations. By analyzing these networks, we uncover distinctive patterns of type associations that serve as culinary fingerprints. For example, European cuisines typically distribute ingredients across different types, whereas certain Asian and South American traditions emphasize one dominant type, such as vegetables or spices. The essence of these patterns is well captured by the networks' maximum spanning trees, which offer a simplified yet representative backbone for each cuisine. We demonstrate that both these full and simplified network representations enable machine learning models to identify cuisines from subsets of recipes with very high accuracy. Networks of ingredient combinations also cluster global cuisines into meaningful geo-cultural groups, reflecting shared patterns in culinary traditions. More broadly, our study offers novel insights into the structure of world cuisines, enabling data-driven approaches to their characterization, cross-cultural comparison, and potential adaptation.

We introduce group-based compartmental modeling (GBCM), a mean-field framework for irreversible contagion in higher-order networks that captures structural heterogeneity and correlations across group sizes. Validated through numerical simulations, GBCM analytically disentangles the role of each interaction order to the global epidemic dynamics, revealing how heterogeneity and inter-order correlations jointly shape the onset of outbreaks and the emergence of explosive dynamics. Crucially, we show that inter-order correlations drive the system along distinct pathways to explosive contagion—emerging universally across both irreversible and reversible spreading processes.

In this study we investigate how hierarchical structures within the Roman Catholic Church shape the ideological orientation of its leadership. The full episcopal genealogy dataset comprises over 35,000 bishops, each typically consecrated by one principal consecrator and two co-consecrators, forming a dense and historically continuous directed network of episcopal lineage. Within this broader structure, we focus on a dataset of 245 living cardinals to examine whether genealogical proximity correlates with doctrinal alignment on a broad set of theological and sociopolitical issues. We identify motifs that capture recurring patterns of lineage, such as shared consecrators or co-consecrators. In parallel, we apply natural language processing techniques to extract each cardinal's publicly stated positions on ten salient topics, including LGBTQIA+ rights, women's roles in the Church, liturgy, bioethics, priestly celibacy, and migration. Our results show that cardinals linked by specific genealogical motifs, particularly those who share the same principal consecrator, are significantly more likely to exhibit ideological similarity. We find that the influence of pope John Paul II persists through the bishops he consecrated, who demonstrate systematically more conservative views than their peers. These findings underscore the role of hierarchical mentorship in shaping ideological coherence within large-scale religious institutions. Our contribution offers quantitative evidence that institutional lineages, beyond individual background factors, may have an impact on the transmission and consolidation of doctrinal positions over time.

Neurodegenerative diseases are characterized by complex proteins misfolded that propagate within the brain. For instance, current findings highlight the role of 2 specific misfolded proteins in Alzheimer which are believed to spread using brain fibers as highways. Previous studies investigated such spreading by simulation models or machine learning-based predictors which adopt the brain connectome as the underlying spreading network. However, the structural connectome by construction only describes pairwise connections between nodes in a graph. High-order interaction complex networks offer significant advantages over normal graphs because they can capture interactions that go beyond simple pairwise relationships. Protein misfolding and aggregation often involve cooperative behaviors or group dynamics that normal graphs, with their focus on individual edges, cannot adequately represent. The non-linear and multiscale nature of protein misfolding might be better suited to a richer representation of higher-order models. In this study we investigate whether higher-order networks can provide improved fits and explanatory power in this context. More specifically, we employ a simplicial complex contagion model for amyloid beta to predict protein misfolding spread. The simplicial contagion complex produced a mean reconstruction error of 0.030 for Alzheimer’s patients regarding the predicted protein deposition across all brain region in a 2-year horizon and other results, outperforming previous studies, especially for cases in which the misfolded protein were non-increasing steadily. Despite the limited time span, this study highlights the potential of combining advanced network analysis to capture the intricate dynamics of protein aggregation across neural networks. Clinical relevance This study highlights the potential of high-order networks to improve predictions of misfolded protein spread in Alzheimer’s, offering better insight into protein aggregation dynamics.

Studying how we explore the world in search of novelties is key to understand the mechanisms that can lead to new discoveries. Previous studies analyzed novelties in various exploration processes, defining them as the first appearance of an element. However, novelties can also be generated by combining what is already known. We hence define higher-order novelties as the first time two or more elements appear together, and we introduce higher-order Heaps’ exponents as a way to characterize their pace of discovery. Through extensive analysis of real-world data, we find that processes with the same pace of discovery, as measured by the standard Heaps’ exponent, can instead differ at higher orders. We then propose to model an exploration process as a random walk on a network in which the possible connections between elements evolve in time. The model reproduces the empirical properties of higher-order novelties, revealing how the network we explore changes over time along with the exploration process.

Representing social systems as networks, starting from the interactions between individuals, sheds light on the mechanisms governing their dynamics. However, networks encode only pairwise interactions, while most social interactions occur among groups of individuals, requiring higher-order network representations. Despite the recent interest in higher-order networks, little is known about the mechanisms that govern the formation and evolution of groups, and how people move between groups. Here, we leverage empirical data on social interactions among children and university students to study their temporal dynamics at both individual and group levels, characterising how individuals navigate groups and how groups form and disaggregate. We find robust patterns across contexts and propose a dynamical model that closely reproduces empirical observations. These results represent a further step in understanding social systems, and open up research directions to study the impact of group dynamics on dynamical processes that evolve on top of them.

Several studies have investigated human interaction using modern tracking techniques for face-to-face encounters across various settings and age groups. However, little attention has been given to understanding how individual characteristics relate to social behavior. This is particularly important in younger age groups due to its potential effects on early childhood development. In this study, conducted during the Complexity 72h Workshop, we analyze human social interactions in a French preschool, where children's face-to-face interactions were monitored using proximity sensors over an academic year. We use metadata from parent surveys and preschool linguistic tests, covering demographic information and home habits, to examine the interplay between individual characteristics and contact patterns. Using a mixture of approaches, from random forest classifiers to network-based metrics at both dyadic and higher-order (group) levels, we identify sex, age, language scores, and number of siblings as the variables displaying the most significant associations with interaction patterns. We explore these variables' relationships to interactions within and outside classrooms and across mixed and single-grade classes. At the group level, we investigate how group affinity affects group persistence. We also find that higher-order network centrality (hypercoreness) is higher among children with siblings, indicating different group embedding despite similar total contact duration. This study aligns with existing literature on early social development and highlights the importance of integrating individual traits into the study of human interactions. Focusing on 2-5-year-olds offers insights into emerging social preferences during critical phases of cognitive development. Future research could use these findings to enhance mechanistic models of complex social systems by incorporating individual traits.

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’.