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New network models of complex systems use layers, state nodes, or hyperedges to capture higher-order interactions and dynamics. Simplifying how the higher-order networks change over time or depending on the network model would be easy with alluvial diagrams, which visualize community splits and merges between networks. However, alluvial diagrams were developed for networks with regular nodes assigned to non-overlapping flat communities. How should they be defined for nodes in layers, state nodes, or hyperedges? How can they depict multilevel, overlapping communities? Here we generalize alluvial diagrams to map change in higher-order networks and provide an interactive tool for anyone to generate alluvial diagrams. We use the alluvial diagram generator in three case studies to illustrate significant changes in the organization of science, the effect of modeling network flows with memory in a citation network and distinguishing multidisciplinary from field-specific journals, and the effects of multilayer representation of a collaboration hypergraph.

Premise: Cacti are characteristic elements of the Neotropical flora and of major interest for biogeographic, evolutionary, and ecological studies. We tested global biogeographic boundaries for Neotropical Cactaceae using specimen-based occurrences, coupled with data from visual observations, as a means to tackle the known collection biases in the family.

Methods: Species richness and record density were assessed for preserved specimens and human observations, and a bioregional scheme tailored to Cactaceae was produced using the interactive web application Infomap Bioregions, based on data from 261,272 point records cleaned through automated and manual steps.

Results: We found that areas in Mexico and southwestern USA, in eastern Brazil, and along the Andean region have the greatest density of records and the highest species richness. Human observations complement information from preserved specimens substantially, especially along the Andes. We propose 24 cactus bioregions, among which the most species-rich are northern Mexico/southwestern USA, central Mexico, southern central Mexico, Central America, Mexican Pacific coast, central and southern Andes, northwestern Mexico/extreme southwestern USA, southwestern Bolivia, northeastern Brazil, and Mexico/Baja California.

Conclusions: The bioregionalization proposed shows biogeographic boundaries specific to cacti and can thereby aid further evolutionary, biogeographic, and ecological studies by providing a validated framework for further analyses. This classification builds upon, and is distinctive from, other expert-derived regionalization schemes for other taxa. Our results showcase how observation data, including citizen-science records, can complement traditional specimen-based data for biogeographic research, particularly for taxa with specific specimen collection and preservation challenges and those that are threatened or internationally protected.

Madagascar's biota is hyperdiverse and includes exceptional levels of endemicity. We review the current state of knowledge on Madagascar's past and current terrestrial and freshwater biodiversity by compiling and presenting comprehensive data on species diversity, endemism, and rates of species description and human uses, in addition to presenting an updated and simplified map of vegetation types. We report a substantial increase of records and species new to science in recent years; however, the diversity and evolution of many groups remain practically unknown (e.g., fungi and most invertebrates). Digitization efforts are increasing the resolution of species richness patterns and we highlight the crucial role of field- and collections-based research for advancing biodiversity knowledge and identifying gaps in our understanding, particularly as species richness corresponds closely to collection effort. Phylogenetic diversity patterns mirror that of species richness and endemism in most of the analyzed groups. We highlight humid forests as centers of diversity and endemism because of their role as refugia and centers of recent and rapid radiations. However, the distinct endemism of other areas, such as the grassland-woodland mosaic of the Central Highlands and the spiny forest of the southwest, is also biologically important despite lower species richness. The documented uses of Malagasy biodiversity are manifold, with much potential for the uncovering of new useful traits for food, medicine, and climate mitigation. The data presented here showcase Madagascar as a unique "living laboratory" for our understanding of evolution and the complex interactions between people and nature. The gathering and analysis of biodiversity data must continue and accelerate if we are to fully understand and safeguard this unique subset of Earth's biodiversity.

Madagascar's unique biota is heavily affected by human activity and is under intense threat. Here, we review the current state of knowledge on the conservation status of Madagascar's terrestrial and freshwater biodiversity by presenting data and analyses on documented and predicted species-level conservation statuses, the most prevalent and relevant threats, ex situ collections and programs, and the coverage and comprehensiveness of protected areas. The existing terrestrial protected area network in Madagascar covers 10.4% of its land area and includes at least part of the range of the majority of described native species of vertebrates with known distributions (97.1% of freshwater fishes, amphibians, reptiles, birds, and mammals combined) and plants (67.7%). The overall figures are higher for threatened species (97.7% of threatened vertebrates and 79.6% of threatened plants occurring within at least one protected area). International Union for Conservation of Nature (IUCN) Red List assessments and Bayesian neural network analyses for plants identify overexploitation of biological resources and unsustainable agriculture as the most prominent threats to biodiversity. We highlight five opportunities for action at multiple levels to ensure that conservation and ecological restoration objectives, programs, and activities take account of complex underlying and interacting factors and produce tangible benefits for the biodiversity and people of Madagascar.

We live in an interconnected world full of complex systems that cannot be understood simply by analyzing their components. From how genes regulate biological functions to the distribution of life on Earth, we need methods that can analyze systems as a whole.

Networks are abstractions of complex systems, helping capture properties that emerge from patterns of interactions rather than from the individual parts. To understand the patterns of interactions in large networks, we need to simplify them by discovering their modular structure that often characterizes complex systems. A hierarchical modular structure functions as a map that lets us navigate relational data efficiently and helps us see the general patterns. But how reliable is the map if it is based on incomplete data?

This thesis applies and builds upon the map equation, which is an information-theoretic method for detecting modular regularities in the flow patterns on networks. To robustly map incomplete data, we have developed three general approaches: (1) Adaptive resolution in both sampling of and dynamics on networks better fits the data. (2) Regularization avoids overfitting to random patterns. (3) Richer data can be included into the network for a more complete map. Methods that can include evolutionary relationships and handle incomplete data provide more powerful tools for mapping biodiversity in space and time.

Vi lever i en sammankopplad värld full av komplexa system som inte låter sig förstås enbart genom att analysera dess komponenter. Från hur gener reglerar biologiska funktioner till livets utbredning på jorden behöver vi metoder som kan analysera system som en helhet.

Nätverk är abstraktioner av komplexa system som hjälper till att fånga egenskaper som uppstår genom interaktionsmönster snarare än hos de enskilda delarna. För att förstå dessa mönster i stora nätverk måste vi förenkla dem genom att upptäcka dess modulära stuktur som präglar komplexa system. En hierarkisk modulär struktur fungerar som en karta som låter oss navigera effektivt i relationsdata och hjälper oss att se de allmänna mönstren. Men hur tillförlitlig är kartan om den baseras på inkompletta data?

Den här avhandlingen applicerar och bygger vidare på kartekvationen som är en informationsteoretisk metod för att upptäcka modulära regelbundenheter i flödesmönstren på nätverk.För att robust kartlägga inkompletta data har vi utvecklat tre övergripande tillvägagångssätt: (1) Adaptiv upplösning i båda sampling av och dynamik på nätverk ger bättre anpassning till data. (2) Regularisering undviker överanpassning till slumpmässiga mönster. (3) Rikare data kan inkluderas i nätverket för en mer komplett karta. Metoder som kan inkludera evolutionära relationer och hantera inkompletta data ger kraftfullare verktyg för att kartlägga den biologiska mångfalden i rum och tid.

Aim: Geo-referenced species occurrence records are a prime example of biodiversity data and a cornerstone of biodiversity research. Yet, their availability depends on non-biological factors, including the political framework in the region of collection. Here we present Bio-Dem (www.bio-dem.surge.sh), an open-source software to explore the relationship between the availability of species occurrence records and the political framework in countries worldwide and through time.

Location: Global.

Taxon: Any.

Methods: Bio-Dem accesses the number of occurrence records available from countries worldwide from the Global Biodiversity Information Facility (www.gbif.org) and socio-political information from these countries from the Varieties of Democracy database (www.v-dem.net) as well as information on colonial history from the Issue Correlates of War Project.

Results: Bio-Dem is available as a free graphical user interface web application at www.bio-dem.surge.sh. Through three interactive graphs, Bio-Dem enables users to explore the relationship between species occurrence records and countries’ regime type, freedom of movement, freedom of association, gross domestic product, education length, political corruption, armed conflict and colonial history. We describe possible links of these specific political indicators with the collection and mobilization of biodiversity data. Illustrative examples and video tutorials explaining the use of Bio-Dem are available at www.bio-dem.surge.sh.

Main conclusions: Bio-Dem provides a user-friendly way to explore the link between socio-political variables and the availability of species occurrence records in user-selected taxa and geographic regions, and to generate hypotheses on their connection. We envision Bio-Dem as a useful tool for teachers communicating the caveats of available biodiversity data, for biodiversity scientists exploring potential spatial and temporal bias in their data, and for social scientists exploring the impact of political systems on scientific data collection and biodiversity conservation.

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.

Analysing how species interact in modules is a fundamental problem in network ecology. Theory shows that a modular network structure can reveal underlying dynamic ecological and evolutionary processes, influence dynamics that operate on the network and affect the stability of the ecological system. Although many ecological networks describe flows, such as biomass flows in food webs or disease transmission, most modularity analyses have ignored network flows, which can hinder our understanding of the interplay between structure and dynamics. Here we present Infomap, an established method based on network flows to the field of ecological networks. Infomap is a flexible tool that can identify modules in virtually any type of ecological network and is particularly useful for directed, weighted and multilayer networks. We illustrate how Infomap works on all these network types. We also provide a fully documented repository with additional ecological examples. Finally, to help researchers to analyse their networks with Infomap, we introduce the open-source R package infomapecology. Analysing flow-based modularity is useful across ecology and transcends to other biological and non-biological disciplines. A dynamic approach for detecting modular structure has strong potential to provide new insights into the organisation of ecological networks.

Detecting significant community structure in networks with incomplete observations is challenging because the evidence for specific solutions fades away with missing data. For example, recent research shows that flow-based community detection methods can highlight spurious communities in sparse undirected and unweighted networks with missing links. Current Bayesian approaches developed to overcome this problem do not work for incomplete observations in weighted and directed networks that describe network flows. To overcome this gap, we extend the idea behind the Bayesian estimate of the map equation for unweighted and undirected networks to enable more robust community detection in weighted and directed networks. We derive an empirical Bayes estimate of the transitions rates that can incorporate metadata information and show how an efficient implementation in the community-detection method Infomap provides more reliable communities even with a significant fraction of data missing.