Daniel Edler’s research while affiliated with Umeå University and other places

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Publications (31)


A natural history of networks: Modeling higher-order interactions in geohistorical data
  • Preprint
  • File available

October 2024

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60 Reads

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Anton Holmgren

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Paleobiologists are increasingly employing network-based methods to analyze the complex data retrieved from geohistorical records, including stratigraphic sections, sediments, and fossil collections. However, the lack of a common framework for designing, performing, evaluating, and communicating these studies, leads to issues of reproducibility and communicability. The high-dimensional geohistorical data also raises questions about the limitations of standard network approaches, which assume independent interactions between pairs of components. Higher-order network models better suited for the complex relational structure of the geohistorical data provide an opportunity to overcome these challenges. These models can represent temporal and spatial constraints inherent to the biosedimentary record and describe higher-order interactions, capturing more accurate biogeographical, biostratigraphic, and macroevolutionary patterns. Here we describe how to use the Map Equation framework for designing higher-order network models of geohistorical data, address some practical decisions involved in modeling complex dependencies, and discuss critical methodological and conceptual issues that currently make it difficult to compare results across studies in the growing body of network-based paleobiology research. We illustrate different higher-order network representations and models, including multilayers, hypergraphs, and varying Markov times models, using case studies on gradient analysis, bioregionalization, and macroevolution, and delineate future research directions for current challenges in the emerging field of network paleobiology.

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Figure 1: A standard GAN for tabular data.
Six categories determined by the statistical tests.
Description of experimented datasets. "Cat." and "Cont." stand for categorical and continuous variables, respectively. "Classif." denotes classification, while "Reg." is regression.
Nemenyi post-hoc test comparing the best configuration incorporating both correlation and mean terms ("c 1 m 1 ") to the vanilla loss ("c 0 m 0 ") across various tasks and generative models on MNIST28 dataset.
A Correlation- and Mean-Aware Loss Function and Benchmarking Framework to Improve GAN-based Tabular Data Synthesis

May 2024

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30 Reads

Advancements in science rely on data sharing. In medicine, where personal data are often involved, synthetic tabular data generated by generative adversarial networks (GANs) offer a promising avenue. However, existing GANs struggle to capture the complexities of real-world tabular data, which often contain a mix of continuous and categorical variables with potential imbalances and dependencies. We propose a novel correlation- and mean-aware loss function designed to address these challenges as a regularizer for GANs. To ensure a rigorous evaluation, we establish a comprehensive benchmarking framework using ten real-world datasets and eight established tabular GAN baselines. The proposed loss function demonstrates statistically significant improvements over existing methods in capturing the true data distribution, significantly enhancing the quality of synthetic data generated with GANs. The benchmarking framework shows that the enhanced synthetic data quality leads to improved performance in downstream machine learning (ML) tasks, ultimately paving the way for easier data sharing.


Spiny but photogenic: Amateur sightings complement herbarium specimens to reveal the bioregions of cacti

September 2023

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149 Reads

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6 Citations

American Journal of Botany

Premise: Cacti are characteristic elements of the Neotropical flora and of major interest for biogeographic, evolutionary, and ecological studies. Here we test 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. Key results: We find that areas in Mexico and southwestern USA, 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 cacti 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, Mexico/Baja California. Conclusions: The bioregionalization proposed shows biogeographical 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. This article is protected by copyright. All rights reserved.


Mapping change in higher-order networks with multilevel and overlapping communities

July 2023

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52 Reads

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2 Citations

Applied Network Science

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.


Figure 3: Mammal occurrences. It consists of 1.5M point occurrences of 4 972 species binned with an adaptive resolution to 5 219 grid cells with sides 1-4 degrees.
Figure 4: Three levels of nested mammalian bioregions detected with Infomap Bioregions 2. Map based on 1.5M point occurrences binned with an adaptive resolution to grid cells from 4 degrees to 1. Opacity shows the degree of species overlap, which highlights transition zones
Figure 6: Overlapping bioregions. By segregating the network between species and grid cells at time 110Ma, using higher-order networks, we can detect evolutionarily distinct bioregions and see where they overlap, such as in Australia, based on the opacity and mixed colors. Showing the bottom level of four from a hierarchical result of nested bioregions.
Infomap Bioregions 2 -- Exploring the interplay between biogeography and evolution

June 2023

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1,183 Reads

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1 Citation

Identifying and understanding the large-scale biodiversity patterns in time and space is vital for conservation and addressing fundamental ecological and evolutionary questions. Network-based methods have proven useful for simplifying and highlighting important structures in species distribution data. However, current network-based biogeography approaches cannot exploit the evolutionary information available in phylogenetic data. We introduce a method for incorporating evolutionary relationships into species occurrence networks to produce more biologically informative and robust bioregions. To keep the bipartite network structure where bioregions are grid cells indirectly connected through shared species, we incorporate the phylogenetic tree by connecting ancestral nodes to the grid cells where their descendant species occur. To incorporate the whole tree without destroying the spatial signal of narrowly distributed species or ancestral nodes, we weigh tree nodes by the geographic information they provide. For a more detailed analysis, we enable integration of the evolutionary relationships at a specific time in the tree. By sweeping through the phylogenetic tree in time, our method interpolates between finding bioregions based only on distributional data and finding spatially segregated clades, uncovering evolutionarily distinct bioregions at different time slices. We also introduce a way to segregate the connections between evolutionary branches at a selected time to enable exploration of overlapping evolutionarily distinct regions. We have implemented these methods in Infomap Bioregions, an interactive web application that makes it easy to explore the possibly hierarchical and fuzzy patterns of biodiversity on different scales in time and space.


Results for raw and cleaned datasets obtained from each record source.
Number of records and species in the three main centers of diversity for Neotropical Cactaceae.
Summary data for 24 bioregions of Neotropical Cactaceae: total number of species and number of species exclusive to the bioregion, estimated size (number of 2ºx2º grid cells), geographical location and correspondence with biomes of Dinerstein et al. (2017) and biogeographic provinces and dominions of Morrone et al. (2022). The ten most species-rich bioregions are highlighted in bold. * Indicate bioregions including areas with higher phylogenetic diversity (0.06-0.241, according to Amaral et al., 2022)
Spiny but photogenic: amateur sightings complement herbarium specimens to reveal the bioregions of cacti

March 2023

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249 Reads

Premise: Cacti are characteristic elements of the Neotropical flora and of major interest for biogeographic, evolutionary, and ecological studies. Here we test global biogeographic boundaries for Neotropical Cactaceae using specimen-based occurrences coupled with data from visual observations, including citizen science records, as a means to tackle the known collection biases in the family. Methods: Species richness and record density were assessed separately 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. Key Results: We find that areas in Mexico and southwestern USA, 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 cacti bioregions, among which the most species-rich are, in decreasing order: 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, Mexico/Baja California. Conclusions: The bioregionalization proposed shows novel or modified biogeographical 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.


Mapping change in higher-order networks with multilevel and overlapping communities

March 2023

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35 Reads

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 generator to illustrate the effect of modeling network flows with memory in a citation network, distinguishing multidisciplinary from field-specific journals.


Madagascar's extraordinary biodiversity: Evolution, distribution, and use

December 2022

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2,035 Reads

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67 Citations

Science

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 extraordinary biodiversity: Threats and opportunities

December 2022

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1,748 Reads

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70 Citations

Science

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.


Figure 1: Constant and variable Markov time in a toy network. Colors show detected communities, which capture nodes where a random walker tends to spend a relatively long time before exiting. Markov time describes the number of steps before reporting the node. With a default one-step random walk, the chain is optimally partitioned into two communities. With Markov time 2, the random walker takes two steps per recording which double the flow between nodes, indicated by the wider links. This increases the field-of-view limit and enables the random walker to optimally explore the chain as a single community. However, this comes with the cost of an increased resolution limit, which makes it harder to detect modular patterns in denser areas. Variable Markov time relaxes the constraint of moving with a constant encoding rate and adapts the encoding rate to the level of sparsity. Variable Markov time increases the gap between the lower resolution limit and upper field-of-view limit and enables us to detect community structures with a broader range of scales than was previously possible.
Figure 2: Mean number of communities (top row) and adjusted mutual information (bottom row) in synthetic networks consisting of two equally-sized cliques connected by a chain that represent planted communities. Results are obtained by the map equation with variable Markov time and with Markov time 1, the Leiden method, and the degree-corrected stochastic block model (DC-SBM). Results are averaged over 100 algorithm searches.
Figure 3: Electronic circuits network with 122 nodes and 189 links. Node colors indicate community assignments and Markov time-dependent link flow indicates the link thicknesses. With Markov time 1, the map equation returns 17 communities. Variable Markov time induces higher link flows in sparse regions and prevents splitting chain-like structures into separate communities, resulting in 10 communities.
Figure S1: Field-of-view and resolution limits for constant and variable Markov time. A field-of-view limit is an upper scale on the size of a graph structure where the community detection method will over-partition larger structures. A resolution limit on the other hand is a lower scale on the size of a graph structure where the community detection method will under-partition smaller structures. The Markov time is a global resolution parameter that describes the step length of a random walker and can be increased from the default value of 1 to detect larger structures, but this also raises the resolution limit. The chain is kept together in one module in the space above the blue line, which marks the field-of-view limit in terms of a minimum Markov time needed to not break the chain (a). The cliques are detected below the orange line, which marks resolution limits (b). All three parts -the two cliques and the chainare detected Between these limits (c). With constant Markov time, the chain is only detected below length 7 (d,f,h). With Variable Markov time, the field-of-view limit is pushed further away with increasing clique size (e, g), and disappears when the clique size grows the same as the chain (i).
Comparison between partitions detected by the map equation with Markov time 1 (MT=1) and variable Markov time (VMT) for four real-world infrastructure networks. For each network, we run 500 Infomap optimization trials. The columns m denote the average number of communities detected by the map equation with Markov time 1 and variable Markov time, respectively. The columns R report the average AMI between pairs of modular partitions, while the columns CV(L) report the average coefficient of variance of the codelengths L.
Variable Markov dynamics as a multi-focal lens to map multi-scale complex networks

November 2022

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113 Reads

From traffic flows on road networks to electrical signals in brain networks, many real-world networks contain modular structures of different sizes and densities. In the networks where modular structures emerge due to coupling between nodes with similar dynamical functions, we can identify them using flow-based community detection methods. However, these methods implicitly assume that communities are dense or clique-like which can shatter sparse communities due to a field-of-view limit inherent in one-step dynamics. Taking multiple steps with shorter or longer Markov time enables us to effectively zoom in or out to capture small or long-range communities. However, zooming out to avoid the field-of-view limit comes at the expense of introducing or increasing a lower resolution limit. Here we relax the constant Markov time constraint and introduce variable Markov dynamics as a multi-focal lens to capture functional communities in networks with a higher range of scales. With variable Markov time, a random walker can keep one-step dynamics in dense areas to avoid the resolution limit and move faster in sparse areas to detect long-range modular structures and prevent the field-of-view limit. We analyze the performance of variable Markov time using the flow-based community detection method called the map equation. We have implemented the map equation with variable Markov time in the search algorithm Infomap without any complexity overhead and tested its performance on synthetic and real-world networks from different domains. Results show that it outperforms the standard map equation in networks with constrained structures and locally sparse regions. In addition, the method estimates the optimal Markov time and avoids parameter tuning.


Citations (20)


... We further explored the discrepancies between iNaturalist observations and herbarium specimen vouchers of species with spines, thorns, or prickles, otherwise known as the pokey plants. These species do not lend themselves well to collection for herbarium specimens due to their sharp, prickly nature and are often avoided by collectors [54]. Additionally, succulent plants such as cacti require additional processing time and equipment [55]. ...

Reference:

EcoFloras Elucidate Insights from Biodiversity Data: Evaluating the Strengths and Limitations of iNaturalist Observations and Herbarium Specimens
Spiny but photogenic: Amateur sightings complement herbarium specimens to reveal the bioregions of cacti
  • Citing Article
  • September 2023

American Journal of Botany

... Alluvial diagrams facilitate the visual comparison of the community structures across different networks. Infomap communities and alluvial diagrams were generated by using the online alluvial generator [60]. ...

Mapping change in higher-order networks with multilevel and overlapping communities

Applied Network Science

... Madagascar is known globally for its unique biodiversity that is threatened by the need for land and resources of the growing human population coupled with demands from the international market, poor governance, and climate change [1][2][3][4]. While these threats affect all natural ecosystems of the island, conservation efforts have focused on forests as the majority of the endemic species seem to have evolved in ecosystems that suffer from very high deforestation rates [5,6]. ...

Madagascar's extraordinary biodiversity: Threats and opportunities

Science

... Madagascar is a biodiversity hotspot with nearly unmatched frog species endemism and richness (Antonelli et al. 2022). Despite the country's rich anuran diversity, its endemic frogs face high extinction risk, with 46.7% of assessed species categorized as threatened by the IUCN (2023). ...

Madagascar's extraordinary biodiversity: Evolution, distribution, and use

Science

... The total probability for the random walker on node i to be teleported to node j is thus α i s in j l s in l . Such an approach is inspired by [24,25], where Smiljanić and collaborators use a Bayesian approach to reconstruct the community structure of an incomplete network with a maximum likelihood estimation of the transition matrix of a random walk. In [25], the authors show how the obtained maximum likelihood estimator for the transition rates (matrix elements of the transition matrix) together with their prior distribution "resemble modeling network flows with teleportation". ...

Mapping flows on weighted and directed networks with incomplete observations

Journal of Complex Networks

... More recently, collecting efforts are focused on those regions in which highly active taxonomic work is being performed. Such and similar variation in collecting efforts in time, and causes thereof, are starting to be addressed across collections and databases (Haripersaud et al. 2010;Zizka et al. 2021). For tropical Africa, in Benin (Akoègninou et al. 2006), Gabon (Sosef et al. 2006Texier et al. 2022), and for Annonaceae specifically in Cameroun (Couvreur et al. 2022), the floras have been investigated thoroughly in recent years. ...

Bio‐Dem, a tool to explore the relationship between biodiversity data availability and socio‐political conditions in time and space

Journal of Biogeography

... By preserving groupbased interactions, they improve our ability to understand the structures and dynamics of systems with many-body interactions [12,13]. Recently, a variety of measures have been introduced or extended to capture the higher-order organization of complex systems, including centrality [14,15], community structure [16][17][18] and motifs [19][20][21]. Moreover, new models have allowed to describe systems' evolution [22][23][24], and highlight the importance of higher-order interactions in shaping emergent behaviors in diffusion [25,26], synchronization [27][28][29], spreading [30,31] and evolutionary dynamics [32]. ...

How choosing random-walk model and network representation matters for flow-based community detection in hypergraphs

... The following multilayer network descriptors were calculated: (1) dispersers' activity, that is number of vegetation belts in which each disperser is present (Costa et al., 2020); (2) multistrength, that is a measure of species importance obtained by summing the weight of the links incident on a node, accounting for the links connecting nodes in different layers (De Domenico et al., 2013) implemented by the R package MUXVIZ (De Domenico, 2021); and (3) multilayer modularity, that is the extent to which species are organised into welldefined modules along the altitudinal gradient (De Domenico et al., 2015). Modularity was calculated using the INFOMAPE-COLOGY package (Farage et al., 2021). ...

Identifying flow modules in ecological networks using Infomap
  • Citing Article
  • February 2021

... The best-fit models for each partition and statistics are provided in Supplementary Table S10. Maximum likelihood (ML) phylogenetic analyses were then conducted using the same online web server, with branch confidence levels estimated using 1 000 replicates for both bootstrap analyses (Edler et al. 2021) and the Shimodaira-Hasegawa-like approximate likelihood-ratio test (SH-aLRT, Guindon et al. 2010), together with the approximate Bayes analysis (aBayes, Anisimova et al. 2011 ...

raxmlGUI 2.0: A graphical interface and toolkit for phylogenetic analyses using RAxML

... The total probability for the random walker on node i to be teleported to node j is thus α i s in j l s in l . Such an approach is inspired by [24,25], where Smiljanić and collaborators use a Bayesian approach to reconstruct the community structure of an incomplete network with a maximum likelihood estimation of the transition matrix of a random walk. In [25], the authors show how the obtained maximum likelihood estimator for the transition rates (matrix elements of the transition matrix) together with their prior distribution "resemble modeling network flows with teleportation". ...

Mapping flows on sparse networks with missing links

PHYSICAL REVIEW E