Link Clustering with Extended Link Similarity and EQ Evaluation Division

Link Clustering (LC) is a relatively new method for detecting overlapping communities in networks. The basic principle of LC is to derive a transform matrix whose elements are composed of the link similarity of neighbor links based on the Jaccard distance calculation; then it applies hierarchical clustering to the transform matrix and uses a measure of partition density on the resulting dendrogram to determine the cut level for best community detection. However, the original link clustering method does not consider the link similarity of non-neighbor links, and the partition density tends to divide the communities into many small communities. In this paper, an Extended Link Clustering method (ELC) for overlapping community detection is proposed. The improved method employs a new link similarity, Extended Link Similarity (ELS), to produce a denser transform matrix, and uses the maximum value of EQ (an extended measure of quality of modularity) as a means to optimally cut the dendrogram for better partitioning of the original network space. Since ELS uses more link information, the resulting transform matrix provides a superior basis for clustering and analysis. Further, using the EQ value to find the best level for the hierarchical clustering dendrogram division, we obtain communities that are more sensible and reasonable than the ones obtained by the partition density evaluation. Experimentation on five real-world networks and artificially-generated networks shows that the ELC method achieves higher EQ and In-group Proportion (IGP) values. Additionally, communities are more realistic than those generated by either of the original LC method or the classical CPM method.     

Towards online multiresolution community detection in large-scale networks

The investigation of community structure in networks has aroused great interest in multiple disciplines. One of the challenges is to find local communities from a starting vertex in a network without global information about the entire network. Many existing methods tend to be accurate depending on a priori assumptions of network properties and predefined parameters. In this paper, we introduce a new quality function of local community and present a fast local expansion algorithm for uncovering communities in large-scale networks. The proposed algorithm can detect multiresolution community from a source vertex or communities covering the whole network. Experimental results show that the proposed algorithm is efficient and well-behaved in both real-world and synthetic networks.     

Discovering Link Communities in Complex Networks by an Integer Programming Model and a Genetic Algorithm

Identification of communities in complex networks is an important topic and issue in many fields such as sociology, biology, and computer science. Communities are often defined as groups of related nodes or links that correspond to functional subunits in the corresponding complex systems. While most conventional approaches have focused on discovering communities of nodes, some recent studies start partitioning links to find overlapping communities straightforwardly. In this paper, we propose a new quantity function for link community identification in complex networks. Based on this quantity function we formulate the link community partition problem into an integer programming model which allows us to partition a complex network into overlapping communities. We further propose a genetic algorithm for link community detection which can partition a network into overlapping communities without knowing the number of communities. We test our model and algorithm on both artificial networks and real-world networks. The results demonstrate that the model and algorithm are efficient in detecting overlapping community structure in complex networks.     

Community Landscapes: An Integrative Approach to Determine Overlapping Network Module Hierarchy,Identify Key Nodes and Predict Network Dynamics

Background

Network communities help the functional organization and evolution of complex networks. However, the development of a method, which is both fast and accurate, provides modular overlaps and partitions of a heterogeneous network, has proven to be rather difficult.

Methodology/Principal Findings

Here we introduce the novel concept of ModuLand, an integrative method family determining overlapping network modules as hills of an influence function-based, centrality-type community landscape, and including several widely used modularization methods as special cases. As various adaptations of the method family, we developed several algorithms, which provide an efficient analysis of weighted and directed networks, and (1) determine pervasively overlapping modules with high resolution; (2) uncover a detailed hierarchical network structure allowing an efficient, zoom-in analysis of large networks; (3) allow the determination of key network nodes and (4) help to predict network dynamics.

Conclusions/Significance

The concept opens a wide range of possibilities to develop new approaches and applications including network routing, classification, comparison and prediction.     

HiNO: an approach for inferring hierarchical organization from regulatory networks

Background

Gene expression as governed by the interplay of the components of regulatory networks is indeed one of the most complex fundamental processes in biological systems. Although several methods have been published to unravel the hierarchical structure of regulatory networks, weaknesses such as the incorrect or inconsistent assignment of elements to their hierarchical levels, the incapability to cope with cyclic dependencies within the networks or the need for a manual curation to retrieve non-overlapping levels remain unsolved.

Methodology/Results

We developed HiNO as a significant improvement of the so-called breadth-first-search (BFS) method. While BFS is capable of determining the overall hierarchical structures from gene regulatory networks, it especially has problems solving feed-forward type of loops leading to conflicts within the level assignments. We resolved these problems by adding a recursive correction approach consisting of two steps. First each vertex is placed on the lowest level that this vertex and its regulating vertices are assigned to (downgrade procedure). Second, vertices are assigned to the next higher level (upgrade procedure) if they have successors with the same level assignment and have themselves no regulators. We evaluated HiNO by comparing it with the BFS method by applying them to the regulatory networks from Saccharomyces cerevisiae and Escherichia coli, respectively. The comparison shows clearly how conflicts in level assignment are resolved in HiNO in order to produce correct hierarchical structures even on the local levels in an automated fashion.

Conclusions

We showed that the resolution of conflicting assignments clearly improves the BFS-method. While we restricted our analysis to gene regulatory networks, our approach is suitable to deal with any directed hierarchical networks structure such as the interaction of microRNAs or the action of non-coding RNAs in general. Furthermore we provide a user-friendly web-interface for HiNO that enables the extraction of the hierarchical structure of any directed regulatory network.

Availability

HiNO is freely accessible at http://mips.helmholtz-muenchen.de/hino/.     

Discovering Communities through Friendship

We introduce a new method for detecting communities of arbitrary size in an undirected weighted network. Our approach is based on tracing the path of closest-friendship between nodes in the network using the recently proposed Generalized Erds Numbers. This method does not require the choice of any arbitrary parameters or null models, and does not suffer from a system-size resolution limit. Our closest-friend community detection is able to accurately reconstruct the true network structure for a large number of real world and artificial benchmarks, and can be adapted to study the multi-level structure of hierarchical communities as well. We also use the closeness between nodes to develop a degree of robustness for each node, which can assess how robustly that node is assigned to its community. To test the efficacy of these methods, we deploy them on a variety of well known benchmarks, a hierarchal structured artificial benchmark with a known community and robustness structure, as well as real-world networks of coauthorships between the faculty at a major university and the network of citations of articles published in Physical Review. In all cases, microcommunities, hierarchy of the communities, and variable node robustness are all observed, providing insights into the structure of the network.     

Response of Methanogens in Arctic Sediments to Temperature and Methanogenic Substrate Availability

Although cold environments are major contributors to global biogeochemical cycles, comparatively little is known about their microbial community function, structure, and limits of activity. In this study a microcosm based approach was used to investigate the effects of temperature, and methanogenic substrate amendment, (acetate, methanol and H₂/CO₂) on methanogen activity and methanogen community structure in high Arctic wetlands (Solvatnet and Stuphallet, Svalbard). Methane production was not detected in Stuphallet sediment microcosms (over a 150 day period) and occurred within Solvatnet sediments microcosms (within 24 hours) at temperatures from 5 to 40°C, the maximum temperature being at far higher than in situ maximum temperatures (which range from air temperatures of -1.4 to 14.1°C during summer months). Distinct responses were observed in the Solvatnet methanogen community under different short term incubation conditions. Specifically, different communities were selected at higher and lower temperatures. At lower temperatures (5°C) addition of exogenous substrates (acetate, methanol or H₂/CO₂) had no stimulatory effect on the rate of methanogenesis or on methanogen community structure. The community in these incubations was dominated by members of the Methanoregulaceae/WCHA2-08 family-level group, which were most similar to the psychrotolerant hydrogenotrophic methanogen Methanosphaerula palustris strain E1-9c. In contrast, at higher temperatures, substrate amendment enhanced methane production in H₂/CO₂ amended microcosms, and played a clear role in structuring methanogen communities. Specifically, at 30°C members of the Methanoregulaceae/WCHA2-08 predominated following incubation with H₂/CO₂, and Methanosarcinaceaeand Methanosaetaceae were enriched in response to acetate addition. These results may indicate that in transiently cold environments, methanogen communities can rapidly respond to moderate short term increases in temperature, but not necessarily to the seasonal release of previously frozen organic carbon from thawing permafrost soils. However, as temperatures increase such inputs of carbon will likely have a greater influence on methane production and methanogen community structure. Understanding the action and limitations of anaerobic microorganisms within cold environments may provide information which can be used in defining region-specific differences in the microbial processes; which ultimately control methane flux to the atmosphere.     

Consistent estimation of the number of communities via regularized network embedding

The network analysis plays an important role in numerous application domains including biomedicine. Estimation of the number of communities is a fundamental and critical issue in network analysis. Most existing studies assume that the number of communities is known a priori, or lack of rigorous theoretical guarantee on the estimation consistency. In this paper, we propose a regularized network embedding model to simultaneously estimate the community structure and the number of communities in a unified formulation. The proposed model equips network embedding with a novel composite regularization term, which pushes the embedding vector toward its center and pushes similar community centers collapsed with each other. A rigorous theoretical analysis is conducted, establishing asymptotic consistency in terms of community detection and estimation of the number of communities. Extensive numerical experiments have also been conducted on both synthetic networks and brain functional connectivity network, which demonstrate the superior performance of the proposed method compared with existing alternatives.     

Link Community Detection Using Generative Model and Nonnegative Matrix Factorization

Discovery of communities in complex networks is a fundamental data analysis problem with applications in various domains. While most of the existing approaches have focused on discovering communities of nodes, recent studies have shown the advantages and uses of link community discovery in networks. Generative models provide a promising class of techniques for the identification of modular structures in networks, but most generative models mainly focus on the detection of node communities rather than link communities. In this work, we propose a generative model, which is based on the importance of each node when forming links in each community, to describe the structure of link communities. We proceed to fit the model parameters by taking it as an optimization problem, and solve it using nonnegative matrix factorization. Thereafter, in order to automatically determine the number of communities, we extend the above method by introducing a strategy of iterative bipartition. This extended method not only finds the number of communities all by itself, but also obtains high efficiency, and thus it is more suitable to deal with large and unexplored real networks. We test this approach on both synthetic benchmarks and real-world networks including an application on a large biological network, and compare it with two highly related methods. Results demonstrate the superior performance of our approach over competing methods for the detection of link communities.     

Recovery of ciliate communities from an oligotrophic mountain stream after a catastrophic wind damage

We studied the recovery of ciliate taxoceonoses in a mountain stream after a catastrophic windstorm that strongly affected mountainous regions of Slovakia in 2004. To this end, we analyzed changes in the community structure of ciliate assemblages from the Zubrovica stream in the Low Tatra Mts during the time frame between 2003 and 2008 by various statistical methods, including diversity and similarity indices, hierarchical clustering, multidimensional scaling, and PCA. The climax ciliate communities were characteristic for oligotrophic running waters, i.e., they were equitable (E_H = 0.75–1.00) and harbored a comparatively low number of species (2–9) with typically low abundances (10–125 ind./ml). However, the community structure changed dramatically after the devastating windstorm. There was a significant increase of species number (10–30) and abundance (260–1480 ind./ml), concomitant with a decrease of the equitability (E_H = 0.43–0.83). These changed quantitative and qualitative community parameters wore off comparatively quickly, i.e., about six months after the catastrophic windstorm, the ciliate taxocoenoses had reached a community structure similar to that before the wind damage. The present observations and those from terrestrial habitats indicate that ciliate communities have a good capability to comparatively quickly reach a climax even after a strong disturbance.     

Microbial Community in High Arsenic Shallow Groundwater Aquifers in Hetao Basin of Inner Mongolia,China

A survey was carried out on the microbial community of 20 groundwater samples (4 low and 16 high arsenic groundwater) and 19 sediments from three boreholes (two high arsenic and one low arsenic boreholes) in a high arsenic groundwater system located in Hetao Basin, Inner Mongolia, using the 454 pyrosequencing approach. A total of 233,704 sequence reads were obtained and classified into 12–267 operational taxonomic units (OTUs). Groundwater and sediment samples were divided into low and high arsenic groups based on measured geochemical parameters and microbial communities, by hierarchical clustering and principal coordinates analysis. Richness and diversity of the microbial communities in high arsenic sediments are higher than those in high arsenic groundwater. Microbial community structure was significantly different either between low and high arsenic samples or between groundwater and sediments. Acinetobacter, Pseudomonas, Psychrobacter and Alishewanella were the top four genera in high arsenic groundwater, while Thiobacillus, Pseudomonas, Hydrogenophaga, Enterobacteriaceae, Sulfuricurvum and Arthrobacter dominated high arsenic sediments. Archaeal sequences in high arsenic groundwater were mostly related to methanogens. Biota-environment matching and co-inertia analyses showed that arsenic, total organic carbon, SO₄^2-, SO₄^2-/total sulfur ratio, and Fe²⁺ were important environmental factors shaping the observed microbial communities. The results of this study expand our current understanding of microbial ecology in high arsenic groundwater aquifers and emphasize the potential importance of microbes in arsenic transformation in the Hetao Basin, Inner Mongolia.     

A Novel Top-k Strategy for Influence Maximization in Complex Networks with Community Structure

In complex networks, it is of great theoretical and practical significance to identify a set of critical spreaders which help to control the spreading process. Some classic methods are proposed to identify multiple spreaders. However, they sometimes have limitations for the networks with community structure because many chosen spreaders may be clustered in a community. In this paper, we suggest a novel method to identify multiple spreaders from communities in a balanced way. The network is first divided into a great many super nodes and then k spreaders are selected from these super nodes. Experimental results on real and synthetic networks with community structure show that our method outperforms the classic methods for degree centrality, k-core and ClusterRank in most cases.     

Insect-Flower Interaction Network Structure Is Resilient to a Temporary Pulse of Floral Resources from Invasive Rhododendron ponticum

Invasive alien plants can compete with native plants for resources, and may ultimately decrease native plant diversity and/or abundance in invaded sites. This could have consequences for native mutualistic interactions, such as pollination. Although invasive plants often become highly connected in plant-pollinator interaction networks, in temperate climates they usually only flower for part of the season. Unless sufficient alternative plants flower outside this period, whole-season floral resources may be reduced by invasion. We hypothesized that the cessation of flowering of a dominant invasive plant would lead to dramatic, seasonal compositional changes in plant-pollinator communities, and subsequent changes in network structure. We investigated variation in floral resources, flower-visiting insect communities, and interaction networks during and after the flowering of invasive Rhododendron ponticum in four invaded Irish woodland sites. Floral resources decreased significantly after R. ponticum flowering, but the magnitude of the decrease varied among sites. Neither insect abundance nor richness varied between the two periods (during and after R. ponticum flowering), yet insect community composition was distinct, mostly due to a significant reduction in Bombus abundance after flowering. During flowering R. ponticum was frequently visited by Bombus; after flowering, these highly mobile pollinators presumably left to find alternative floral resources. Despite compositional changes, however, network structural properties remained stable after R. ponticum flowering ceased: generality increased, but quantitative connectance, interaction evenness, vulnerability, H’₂ and network size did not change. This is likely because after R. ponticum flowering, two to three alternative plant species became prominent in networks and insects increased their diet breadth, as indicated by the increase in network-level generality. We conclude that network structure is robust to seasonal changes in floral abundance at sites invaded by alien, mass-flowering plant species, as long as alternative floral resources remain throughout the season to support the flower-visiting community.     

The overlapping community structure of structural brain network in young healthy individuals

Community structure is a universal and significant feature of many complex networks in biology, society, and economics. Community structure has also been revealed in human brain structural and functional networks in previous studies. However, communities overlap and share many edges and nodes. Uncovering the overlapping community structure of complex networks remains largely unknown in human brain networks. Here, using regional gray matter volume, we investigated the structural brain network among 90 brain regions (according to a predefined anatomical atlas) in 462 young, healthy individuals. Overlapped nodes between communities were defined by assuming that nodes (brain regions) can belong to more than one community. We demonstrated that 90 brain regions were organized into 5 overlapping communities associated with several well-known brain systems, such as the auditory/language, visuospatial, emotion, decision-making, social, control of action, memory/learning, and visual systems. The overlapped nodes were mostly involved in an inferior-posterior pattern and were primarily related to auditory and visual perception. The overlapped nodes were mainly attributed to brain regions with higher node degrees and nodal efficiency and played a pivotal role in the flow of information through the structural brain network. Our results revealed fuzzy boundaries between communities by identifying overlapped nodes and provided new insights into the understanding of the relationship between the structure and function of the human brain. This study provides the first report of the overlapping community structure of the structural network of the human brain.     

SHORT‐ VERSUS LONG‐TERM RESPONSES TO CHANGING CO2 IN A COASTAL DINOFLAGELLATE BLOOM: IMPLICATIONS FOR INTERSPECIFIC COMPETITIVE INTERACTIONS AND COMMUNITY STRUCTURE

Increasing pCO₂ (partial pressure of CO₂) in an “acidified” ocean will affect phytoplankton community structure, but manipulation experiments with assemblages briefly acclimated to simulated future conditions may not accurately predict the long‐term evolutionary shifts that could affect inter‐specific competitive success. We assessed community structure changes in a natural mixed dinoflagellate bloom incubated at three pCO₂ levels (230, 433, and 765 ppm) in a short‐term experiment (2 weeks). The four dominant species were then isolated from each treatment into clonal cultures, and maintained at all three pCO₂ levels for approximately 1 year. Periodically (4, 8, and 12 months), these pCO₂‐conditioned clones were recombined into artificial communities, and allowed to compete at their conditioning pCO₂ level or at higher and lower levels. The dominant species in these artificial communities of CO₂‐conditioned clones differed from those in the original short‐term experiment, but individual species relative abundance trends across pCO₂ treatments were often similar. Specific growth rates showed no strong evidence for fitness increases attributable to conditioning pCO₂ level. Although pCO₂ significantly structured our experimental communities, conditioning time and biotic interactions like mixotrophy also had major roles in determining competitive outcomes. New methods of carrying out extended mixed species experiments are needed to accurately predict future long‐term phytoplankton community responses to changing pCO₂.     

Vertical distribution of bacterial community is associated with the degree of soil organic matter decomposition in the active layer of moist acidic tundra

The increasing temperature in Arctic tundra deepens the active layer, which is the upper layer of permafrost soil that experiences repeated thawing and freezing. The increasing of soil temperature and the deepening of active layer seem to affect soil microbial communities. Therefore, information on soil microbial communities at various soil depths is essential to understand their potential responses to climate change in the active layer soil. We investigated the community structure of soil bacteria in the active layer from moist acidic tundra in Council, Alaska. We also interpreted their relationship with some relevant soil physicochemical characteristics along soil depth with a fine scale (5 cm depth interval). The bacterial community structure was found to change along soil depth. The relative abundances of Acidobacteria, Gammaproteobacteria, Planctomycetes, and candidate phylum WPS-2 rapidly decreased with soil depth, while those of Bacteroidetes, Chloroflexi, Gemmatimonadetes, and candidate AD3 rapidly increased. A structural shift was also found in the soil bacterial communities around 20 cm depth, where two organic (upper Oi and lower Oa) horizons are subdivided. The quality and the decomposition degree of organic matter might have influenced the bacterial community structure. Besides the organic matter quality, the vertical distribution of bacterial communities was also found to be related to soil pH and total phosphorus content. This study showed the vertical change of bacterial community in the active layer with a fine scale resolution and the possible influence of the quality of soil organic matter on shaping bacterial community structure.     

Short- and long-term conditioning of a temperate marine diatom community to acidification and warming

Ocean acidification and greenhouse warming will interactively influence competitive success of key phytoplankton groups such as diatoms, but how long-term responses to global change will affect community structure is unknown. We incubated a mixed natural diatom community from coastal New Zealand waters in a short-term (two-week) incubation experiment using a factorial matrix of warming and/or elevated pCO₂ and measured effects on community structure. We then isolated the dominant diatoms in clonal cultures and conditioned them for 1 year under the same temperature and pCO₂ conditions from which they were isolated, in order to allow for extended selection or acclimation by these abiotic environmental change factors in the absence of interspecific interactions. These conditioned isolates were then recombined into ‘artificial’ communities modelled after the original natural assemblage and allowed to compete under conditions identical to those in the short-term natural community experiment. In general, the resulting structure of both the unconditioned natural community and conditioned ‘artificial’ community experiments was similar, despite differences such as the loss of two species in the latter. pCO₂ and temperature had both individual and interactive effects on community structure, but temperature was more influential, as warming significantly reduced species richness. In this case, our short-term manipulative experiment with a mixed natural assemblage spanning weeks served as a reasonable proxy to predict the effects of global change forcing on diatom community structure after the component species were conditioned in isolation over an extended timescale. Future studies will be required to assess whether or not this is also the case for other types of algal communities from other marine regimes.     

Module detection in complex networks using integer optimisation

Background  

The detection of modules or community structure is widely used to reveal the underlying properties of complex networks in biology, as well as physical and social sciences. Since the adoption of modularity as a measure of network topological properties, several methodologies for the discovery of community structure based on modularity maximisation have been developed. However, satisfactory partitions of large graphs with modest computational resources are particularly challenging due to the NP-hard nature of the related optimisation problem. Furthermore, it has been suggested that optimising the modularity metric can reach a resolution limit whereby the algorithm fails to detect smaller communities than a specific size in large networks.     

The Temporal Scaling of Bacterioplankton Composition: High Turnover and Predictability during Shrimp Cultivation

The spatial distribution of microbial communities has recently been reliably documented in the form of a distance–similarity decay relationship. In contrast, temporal scaling, the pattern defined by the microbial similarity–time relationships (STRs), has received far less attention. As a result, it is unclear whether the spatial and temporal variations of microbial communities share a similar power law. In this study, we applied the 454 pyrosequencing technique to investigate temporal scaling in patterns of bacterioplankton community dynamics during the process of shrimp culture. Our results showed that the similarities decreased significantly (P?=?0.002) with time during the period over which the bacterioplankton community was monitored, with a scaling exponent of w?=?0.400. However, the diversities did not change dramatically. The community dynamics followed a gradual process of succession relative to the parent communities, with greater similarities between samples from consecutive sampling points. In particular, the variations of the bacterial communities from different ponds shared similar successional trajectories, suggesting that bacterial temporal dynamics are predictable to a certain extent. Changes in bacterial community structure were significantly correlated with the combination of Chl a, TN, PO₄ ^3-, and the C/N ratio. In this study, we identified predictable patterns in the temporal dynamics of bacterioplankton community structure, demonstrating that the STR of the bacterial community mirrors the spatial distance–similarity decay model.