Hypergraphs offer an explicit formalism to describe multibody interactions in complex systems. To connect dynamics and function in systems with these higher-order interactions, network scientists have generalised random-walk models to hypergraphs and studied the multibody effects on flow-based centrality measures. Mapping the large-scale structure of those flows requires effective community detection methods applied to cogent network representations. For different hypergraph data and research questions, which combination of random-walk model and network representation is best? We define unipartite, bipartite, and multilayer network representations of hypergraph flows and explore how they and the underlying random-walk model change the number, size, depth, and overlap of identified multilevel communities. These results help researchers choose the appropriate modelling approach when mapping flows on hypergraphs.

To understand how a complex system is organized and functions, researchers often identify communities in the system's network of interactions. Because it is practically impossible to explore all solutions to guarantee the best one, many community-detection algorithms rely on multiple stochastic searches. But for a given combination of network and stochastic algorithms, how many searches are sufficient to find a solution that is good enough? The standard approach is to pick a reasonably large number of searches and select the network partition with the highest quality or derive a consensus solution based on all network partitions. However, if different partitions have similar qualities such that the solution landscape is degenerate, the single best partition may miss relevant information, and a consensus solution may blur complementary communities. Here we address this degeneracy problem with coarse-grained descriptions of the solution landscape. We cluster network partitions based on their similarity and suggest an approach to determine the minimum number of searches required to describe the solution landscape adequately. To make good use of all partitions, we also propose different ways to explore the solution landscape, including a significance clustering procedure. We test these approaches on synthetic networks and a real-world network using two contrasting community-detection algorithms: The algorithm that can identify more general structures requires more searches, and networks with clearer community structures require fewer searches. We also find that exploring the coarse-grained solution landscape can reveal complementary solutions and enable more reliable community detection.

The hypothesis of the Great Evolutionary Faunas is a foundational concept of macroevolutionary research postulating that three global mega-assemblages have dominated Phanerozoic oceans following abrupt biotic transitions. Empirical estimates of this large-scale pattern depend on several methodological decisions and are based on approaches unable to capture multiscale dynamics of the underlying Earth-Life System. Combining a multilayer network representation of fossil data with a multilevel clustering that eliminates the subjectivity inherent to distance-based approaches, we demonstrate that Phanerozoic oceans sequentially harbored four global benthic mega-assemblages. Shifts in dominance patterns among these global marine mega-assemblages were abrupt (end-Cambrian 494 Ma; end-Permian 252 Ma) or protracted (mid-Cretaceous 129 Ma), and represent the three major biotic transitions in Earth’s history. Our findings suggest that gradual ecological changes associated with the Mesozoic Marine Revolution triggered a protracted biotic transition comparable in magnitude to the end-Permian transition initiated by the most severe biotic crisis of the past 500 million years. Overall, our study supports the notion that both long-term ecological changes and major geological events have played crucial roles in shaping the mega-assemblages that dominated Phanerozoic oceans.

Preserving the adaptive capacities of coastal ecosystems in the Anthropocene requires an understanding of their natural variability prior to modern times. We quantified responses of nearshore molluscs assemblages to past environmental changes using 101 samples ( c. 57 300 specimens) retrieved from the subsurface Holocene succession and present-day seabed of the Po–Adriatic System (Italy). Present-day assemblages shifted in their faunal composition with respect to their mid-late Holocene counterparts. Major differences are observed in lower nearshore settings, where present-day samples show higher heterogeneity, reduced standardized richness, reduced relative abundance of Lentidium mediterraneum, and increased relative abundance of Varicorbula gibba , scavengers (genus Tritia ), and deposit feeders (nuculid bivalves). A dominance of infaunal opportunistic species and shifts towards detritus-feeding and scavenging are often associated with disturbed benthic habitats. Our results suggest that the ongoing anthropogenic stressors (mainly bottom trawling and non-native species) are currently shifting benthic communities into novel states outside the range of natural variability archived in the fossil record. Supplementary material: A document containing additional statistics, figures, and tables, also considering different filters applied to the molluscan dataset, is provided as a Word file. In addition, appendices concerning sample and taxa information and R-scripts are provided as .csv and .r files. These are available at https://doi.org/10.6084/m9.figshare.c.6351348