Spatial metrics as indicators of biodegradation benefits from bacterial dispersal networks

Ecological dynamics often show intricate variations in response to different spatial configurations of environmental conditions. For instance, efficient turnover of natural or anthropogenic compounds in soils strongly depends on the bioavailability of these compounds to metabolically active bacteria. Experimental and modelling studies have highlighted that fungal networks may considerably enhance bioavailability by facilitating bacterial dispersal. Therefore, such dispersal networks may play a key role in many soil processes, for example, in contaminant degradation. Particularly, simulation studies revealed that the spatial configurations of networks may be a crucial factor determining the bacterial access to contaminants. Since these spatial configurations are typically complex and not precisely known, suitable metrics describing them in an aggregated manner are required for assessing expected biodegradation benefits from different bacterial dispersal networks. Using a spatially explicit microbial model we randomly created various dispersal network configurations and simulated the resulting bacterial degradation of organic compounds. We investigated numerous spatial metrics for characterizing the manifold network configurations, and identified appropriate metrics based on nonparametric correlation measures. Our results show that single metrics can approximately indicate biodegradation performance, and that well-chosen combinations of two metrics offer very good assessments. Thus, our analysis provides characteristics to focus on when dealing with real fungal networks in future practical applications in environmental management. Moreover, the protocol we employed for deriving the appropriate metrics is suited to be adapted to other ecological studies of functional responses to spatial environmental characteristics, for instance, changes in ecosystem services or biodiversity aspects due to habitat loss and fragmentation.     

Metrics for evaluating representation target achievement in protected area networks

Global conservation targets (e.g. Aichi Target 11) have helped drive a dramatic expansion of the global protected area (PA) network. Credible metrics have an important role to play in evaluating and expanding PAs to achieve conservation outcomes and objectives. For metrics to be useful and adopted, they need to be transparent, easy to understand, and easy to implement. We present two complementary metrics, “mean protection gap” and “mean target achievement”, for evaluating representation target achievement in PA networks along with the R package “ConsTarget” that calculates and plots both metrics. We use Australia's proposed Commonwealth Marine Reserve network as a case study to demonstrate the application of these metrics. We recommend the metrics be used to evaluate the progress towards building representative PA networks in line with Aichi target 11's goals.     

Graph theoretical analysis of functional brain networks: test-retest evaluation on short- and long-term resting-state functional MRI data

Graph-based computational network analysis has proven a powerful tool to quantitatively characterize functional architectures of the brain. However, the test-retest (TRT) reliability of graph metrics of functional networks has not been systematically examined. Here, we investigated TRT reliability of topological metrics of functional brain networks derived from resting-state functional magnetic resonance imaging data. Specifically, we evaluated both short-term (<1 hour apart) and long-term (>5 months apart) TRT reliability for 12 global and 6 local nodal network metrics. We found that reliability of global network metrics was overall low, threshold-sensitive and dependent on several factors of scanning time interval (TI, long-term>short-term), network membership (NM, networks excluding negative correlations>networks including negative correlations) and network type (NT, binarized networks>weighted networks). The dependence was modulated by another factor of node definition (ND) strategy. The local nodal reliability exhibited large variability across nodal metrics and a spatially heterogeneous distribution. Nodal degree was the most reliable metric and varied the least across the factors above. Hub regions in association and limbic/paralimbic cortices showed moderate TRT reliability. Importantly, nodal reliability was robust to above-mentioned four factors. Simulation analysis revealed that global network metrics were extremely sensitive (but varying degrees) to noise in functional connectivity and weighted networks generated numerically more reliable results in compared with binarized networks. For nodal network metrics, they showed high resistance to noise in functional connectivity and no NT related differences were found in the resistance. These findings provide important implications on how to choose reliable analytical schemes and network metrics of interest.     

Characterization of reticulate networks based on the coalescent with recombination

Phylogenetic networks aim to represent the evolutionary history of taxa. Within these, reticulate networks are explicitly able to accommodate evolutionary events like recombination, hybridization, or lateral gene transfer. Although several metrics exist to compare phylogenetic networks, they make several assumptions regarding the nature of the networks that are not likely to be fulfilled by the evolutionary process. In order to characterize the potential disagreement between the algorithms and the biology, we have used the coalescent with recombination to build the type of networks produced by reticulate evolution and classified them as regular, tree sibling, tree child, or galled trees. We show that, as expected, the complexity of these reticulate networks is a function of the population recombination rate. At small recombination rates, most of the networks produced are already more complex than regular or tree sibling networks, whereas with moderate and large recombination rates, no network fit into any of the standard classes. We conclude that new metrics still need to be devised in order to properly compare two phylogenetic networks that have arisen from reticulating evolutionary process.     

Characterizing topology of ecological networks along gradients: The limits of metrics’ standardization

Species interact in nature to form complex ecological networks. There has been a rising interest in recent years to characterize the topology of such networks along various gradients (e.g. successional, climatic, elevational) to better understand how they assemble in space and time. However, to compare structure of networks that vary in size, shape and connectance, topological metrics need to be standardized (as most metrics covary with such network attributes). Traditionally, this has been done by transforming network metrics into z-scores prior comparisons. Here, I show that such standardized metrics are not independent of basic network properties such as connectance. Instead, I found that there was a consistent tendency for z-scores to approach 0 when connectance progressively decreased and approached its minimal value. This is probably due to the reduced null space available for null models to randomize interactions at such low connectance. I discuss ways to circumvent the problem in future studies.     

Effects of different correlation metrics and preprocessing factors on small-world brain functional networks: a resting-state functional MRI study

Graph theoretical analysis of brain networks based on resting-state functional MRI (R-fMRI) has attracted a great deal of attention in recent years. These analyses often involve the selection of correlation metrics and specific preprocessing steps. However, the influence of these factors on the topological properties of functional brain networks has not been systematically examined. Here, we investigated the influences of correlation metric choice (Pearson's correlation versus partial correlation), global signal presence (regressed or not) and frequency band selection [slow-5 (0.01-0.027 Hz) versus slow-4 (0.027-0.073 Hz)] on the topological properties of both binary and weighted brain networks derived from them, and we employed test-retest (TRT) analyses for further guidance on how to choose the "best" network modeling strategy from the reliability perspective. Our results show significant differences in global network metrics associated with both correlation metrics and global signals. Analysis of nodal degree revealed differing hub distributions for brain networks derived from Pearson's correlation versus partial correlation. TRT analysis revealed that the reliability of both global and local topological properties are modulated by correlation metrics and the global signal, with the highest reliability observed for Pearson's-correlation-based brain networks without global signal removal (WOGR-PEAR). The nodal reliability exhibited a spatially heterogeneous distribution wherein regions in association and limbic/paralimbic cortices showed moderate TRT reliability in Pearson's-correlation-based brain networks. Moreover, we found that there were significant frequency-related differences in topological properties of WOGR-PEAR networks, and brain networks derived in the 0.027-0.073 Hz band exhibited greater reliability than those in the 0.01-0.027 Hz band. Taken together, our results provide direct evidence regarding the influences of correlation metrics and specific preprocessing choices on both the global and nodal topological properties of functional brain networks. This study also has important implications for how to choose reliable analytical schemes in brain network studies.     

Global patterns in anuran–prey networks: structure mediated by latitude

Life on Earth is supported by an infinite number of interactions among organisms. Species interactions in these networks are influenced by latitude, evolutionary history and species traits. We performed a global‐scale literature analysis to build up a database of interactions between anuran communities and their preys, from a wide range of geographical areas, using a network approach. For this purpose, we compiled a total of 55 weighted anuran–prey interaction networks, 39 located in the tropics and 16 in temperate areas. We tested the influence of latitude, as well as anuran taxonomic, functional and phylogenetic richness on network metrics. We found that anuran–prey networks are not nested, exhibit low complementary specialization and modularity and high connectance when compared to other types of networks. The main effects on network metrics were related to latitude, followed by anuran taxonomic, functional and phylogenetic richness, a pattern similar to the emerging in mutualistic networks. Our study is the first integrated analysis of the structural patterns in anuran–prey antagonistic interaction networks in different parts of the world. We suggest that different processes, mediated mainly by latitude, are modeling the architecture of anuran–prey networks across the globe.     

Resilient networks of ant-plant mutualists in amazonian forest fragments

Background

The organization of networks of interacting species, such as plants and animals engaged in mutualisms, strongly influences the ecology and evolution of partner communities. Habitat fragmentation is a globally pervasive form of spatial heterogeneity that could profoundly impact the structure of mutualist networks. This is particularly true for biodiversity-rich tropical ecosystems, where the majority of plant species depend on mutualisms with animals and it is thought that changes in the structure of mutualist networks could lead to cascades of extinctions.

Methodology/Principal Findings

We evaluated effects of fragmentation on mutualistic networks by calculating metrics of network structure for ant-plant networks in continuous Amazonian forests with those in forest fragments. We hypothesized that networks in fragments would have fewer species and higher connectance, but equal nestedness and resilience compared to forest networks. Only one of the nine metrics we compared differed between continuous forest and forest fragments, indicating that networks were resistant to the biotic and abiotic changes that accompany fragmentation. This is partially the result of the loss of only specialist species with one connection that were lost in forest fragments.

Conclusions/Significance

We found that the networks of ant-plant mutualists in twenty-five year old fragments are similar to those in continuous forest, suggesting these interactions are resistant to the detrimental changes associated with habitat fragmentation, at least in landscapes that are a mosaic of fragments, regenerating forests, and pastures. However, ant-plant mutualistic networks may have several properties that may promote their persistence in fragmented landscapes. Proactive identification of key mutualist partners may be necessary to focus conservation efforts on the interactions that insure the integrity of network structure and the ecosystems services networks provide.     

Observing frugivores or collecting scats: a method comparison to construct quantitative seed dispersal networks

Mutualistic interactions form the basis for many ecological processes and are often analyzed within the framework of ecological networks. These interactions can be sampled with a range of methods and first analyses of pollination networks sampled with different methods showed differences in common network metrics. However, it is yet unknown if metrics of seed dispersal networks are similarly affected by the sampling method and if different methods detect a complementary set of frugivores. This is necessary to better understand the (dis-)advantages of each method and to identify the role of each frugivore for the seed dispersal process. Here, we compare seed removal networks based on the observation of 2189 frugivore visits on ten focal plant species with seed deposition networks constructed by DNA barcoding of plant seeds in 3094 frugivore scats. We were interested in whether both methods identify the same disperser species and if species-level network metrics of plant species were correlated between network types. Both methods identified the same avian super-generalist frugivores, which accounted for the highest number of dispersed seeds. However, only with DNA barcoding, we detected elusive but frequent mammalian seed dispersers. The overall networks created by both methods were congruent but the plant species' degree, their interaction frequency and their specialization index (d′) differed. Our study suggests that DNA barcoding of defecated and regurgitated seeds can be used to construct quantitative seed deposition networks similar to those constructed by focal observations. To improve the overall completeness of seed dispersal networks it might be useful to combine both methods to detect interactions by both birds and mammals. Most importantly, the DNA barcoding method provides information on the post-dispersal stage and thus on the qualitative contribution of each frugivore for the plant community thereby linking species interactions to regeneration dynamics of fleshy-fruited plant species.     

On encodings of phylogenetic networks of bounded level

Phylogenetic networks have now joined phylogenetic trees in the center of phylogenetics research. Like phylogenetic trees, such networks canonically induce collections of phylogenetic trees, clusters, and triplets, respectively. Thus it is not surprising that many network approaches aim to reconstruct a phylogenetic network from such collections. Related to the well-studied perfect phylogeny problem, the following question is of fundamental importance in this context: When does one of the above collections encode (i.e. uniquely describe) the network that induces it? For the large class of level-1 (phylogenetic) networks we characterize those level-1 networks for which an encoding in terms of one (or equivalently all) of the above collections exists. In addition, we show that three known distance measures for comparing phylogenetic networks are in fact metrics on the resulting subclass and give the diameter for two of them. Finally, we investigate the related concept of indistinguishability and also show that many properties enjoyed by level-1 networks are not satisfied by networks of higher level.     

A computational tool for quantitative analysis of vascular networks

Angiogenesis is the generation of mature vascular networks from pre-existing vessels. Angiogenesis is crucial during the organism' development, for wound healing and for the female reproductive cycle. Several murine experimental systems are well suited for studying developmental and pathological angiogenesis. They include the embryonic hindbrain, the post-natal retina and allantois explants. In these systems vascular networks are visualised by appropriate staining procedures followed by microscopical analysis. Nevertheless, quantitative assessment of angiogenesis is hampered by the lack of readily available, standardized metrics and software analysis tools. Non-automated protocols are being used widely and they are, in general, time--and labour intensive, prone to human error and do not permit computation of complex spatial metrics. We have developed a light-weight, user friendly software, AngioTool, which allows for quick, hands-off and reproducible quantification of vascular networks in microscopic images. AngioTool computes several morphological and spatial parameters including the area covered by a vascular network, the number of vessels, vessel length, vascular density and lacunarity. In addition, AngioTool calculates the so-called "branching index" (branch points/unit area), providing a measurement of the sprouting activity of a specimen of interest. We have validated AngioTool using images of embryonic murine hindbrains, post-natal retinas and allantois explants. AngioTool is open source and can be downloaded free of charge.     

How does the metric choice affect brain functional connectivity networks?

Brain functional connectivity has gained increasing interest over the last few years. The application of Graph Theory on functional connectivity networks (FCNs) has shed light into different topics related to physiology as well as pathology. To this end, different connectivity metrics may be used; however, some concerns are often raised related with inconsistency of results and their associated neurophysiological interpretations depending on the metric used. This paper examines how the use of different connectivity metrics affects the small-world-ness of the FCNs and eventually the neuroscientific evidences and their interpretation; to achieve this, electroencephalography (EEG) data recorded from healthy subjects during an emotional paradigm are utilized. Participants passively viewed emotional stimuli from the international affective picture system (IAPS), categorized in four groups ranging in pleasure (valence) and arousal. Four different pair-wise metrics were used to estimate the connectivity between each pair of EEG channels: the magnitude square coherence (MSC), cross-correlation (CCOR), normalized mutual information (NMI) and normalized joint entropy (NJE). The small-world-ness is found to be varying among the connectivity metrics, while it was also affected by the choice of the threshold level. The use of different connectivity metrics affected the significance of the neurophysiological results. However, the results from different metrics were to the same direction: pleasant images exhibited shorter characteristic path length than unpleasant ones, while high arousing images were related to lower local efficiency as compared to the low arousing ones. Our findings suggest that the choice of different metrics modulates the small-world-ness of the FCNs as well as the neurophysiological results and should be taken into account when studying brain functional connectivity using graph theory.     

Altered small-world brain networks in schizophrenia patients during working memory performance

Impairment of working memory (WM) performance in schizophrenia patients (SZ) is well-established. Compared to healthy controls (HC), SZ patients show aberrant blood oxygen level dependent (BOLD) activations and disrupted functional connectivity during WM performance. In this study, we examined the small-world network metrics computed from functional magnetic resonance imaging (fMRI) data collected as 35 HC and 35 SZ performed a Sternberg Item Recognition Paradigm (SIRP) at three WM load levels. Functional connectivity networks were built by calculating the partial correlation on preprocessed time courses of BOLD signal between task-related brain regions of interest (ROIs) defined by group independent component analysis (ICA). The networks were then thresholded within the small-world regime, resulting in undirected binarized small-world networks at different working memory loads. Our results showed: 1) at the medium WM load level, the networks in SZ showed a lower clustering coefficient and less local efficiency compared with HC; 2) in SZ, most network measures altered significantly as the WM load level increased from low to medium and from medium to high, while the network metrics were relatively stable in HC at different WM loads; and 3) the altered structure at medium WM load in SZ was related to their performance during the task, with longer reaction time related to lower clustering coefficient and lower local efficiency. These findings suggest brain connectivity in patients with SZ was more diffuse and less strongly linked locally in functional network at intermediate level of WM when compared to HC. SZ show distinctly inefficient and variable network structures in response to WM load increase, comparing to stable highly clustered network topologies in HC.     

Gene regulatory networks from multifactorial perturbations using Graphical Lasso: application to the DREAM4 challenge

A major challenge in the field of systems biology consists of predicting gene regulatory networks based on different training data. Within the DREAM4 initiative, we took part in the multifactorial sub-challenge that aimed to predict gene regulatory networks of size 100 from training data consisting of steady-state levels obtained after applying multifactorial perturbations to the original in silico network. Due to the static character of the challenge data, we tackled the problem via a sparse Gaussian Markov Random Field, which relates network topology with the covariance inverse generated by the gene measurements. As for the computations, we used the Graphical Lasso algorithm which provided a large range of candidate network topologies. The main task was to select the optimal network topology and for that, different model selection criteria were explored. The selected networks were compared with the golden standards and the results ranked using the scoring metrics applied in the challenge, giving a better insight in our submission and the way to improve it.Our approach provides an easy statistical and computational framework to infer gene regulatory networks that is suitable for large networks, even if the number of the observations (perturbations) is greater than the number of variables (genes).     

Analysing ecological networks of species interactions

Network approaches to ecological questions have been increasingly used, particularly in recent decades. The abstraction of ecological systems – such as communities – through networks of interactions between their components indeed provides a way to summarize this information with single objects. The methodological framework derived from graph theory also provides numerous approaches and measures to analyze these objects and can offer new perspectives on established ecological theories as well as tools to address new challenges. However, prior to using these methods to test ecological hypotheses, it is necessary that we understand, adapt, and use them in ways that both allow us to deliver their full potential and account for their limitations. Here, we attempt to increase the accessibility of network approaches by providing a review of the tools that have been developed so far, with – what we believe to be – their appropriate uses and potential limitations. This is not an exhaustive review of all methods and metrics, but rather, an overview of tools that are robust, informative, and ecologically sound. After providing a brief presentation of species interaction networks and how to build them in order to summarize ecological information of different types, we then classify methods and metrics by the types of ecological questions that they can be used to answer from global to local scales, including methods for hypothesis testing and future perspectives. Specifically, we show how the organization of species interactions in a community yields different network structures (e.g., more or less dense, modular or nested), how different measures can be used to describe and quantify these emerging structures, and how to compare communities based on these differences in structures. Within networks, we illustrate metrics that can be used to describe and compare the functional and dynamic roles of species based on their position in the network and the organization of their interactions as well as associated new methods to test the significance of these results. Lastly, we describe potential fruitful avenues for new methodological developments to address novel ecological questions.     

Duality between time series and networks

Studying the interaction between a system's components and the temporal evolution of the system are two common ways to uncover and characterize its internal workings. Recently, several maps from a time series to a network have been proposed with the intent of using network metrics to characterize time series. Although these maps demonstrate that different time series result in networks with distinct topological properties, it remains unclear how these topological properties relate to the original time series. Here, we propose a map from a time series to a network with an approximate inverse operation, making it possible to use network statistics to characterize time series and time series statistics to characterize networks. As a proof of concept, we generate an ensemble of time series ranging from periodic to random and confirm that application of the proposed map retains much of the information encoded in the original time series (or networks) after application of the map (or its inverse). Our results suggest that network analysis can be used to distinguish different dynamic regimes in time series and, perhaps more importantly, time series analysis can provide a powerful set of tools that augment the traditional network analysis toolkit to quantify networks in new and useful ways.     

An ensemble framework for clustering protein-protein interaction networks

MOTIVATION: Protein-Protein Interaction (PPI) networks are believed to be important sources of information related to biological processes and complex metabolic functions of the cell. The presence of biologically relevant functional modules in these networks has been theorized by many researchers. However, the application of traditional clustering algorithms for extracting these modules has not been successful, largely due to the presence of noisy false positive interactions as well as specific topological challenges in the network. RESULTS: In this article, we propose an ensemble clustering framework to address this problem. For base clustering, we introduce two topology-based distance metrics to counteract the effects of noise. We develop a PCA-based consensus clustering technique, designed to reduce the dimensionality of the consensus problem and yield informative clusters. We also develop a soft consensus clustering variant to assign multifaceted proteins to multiple functional groups. We conduct an empirical evaluation of different consensus techniques using topology-based, information theoretic and domain-specific validation metrics and show that our approaches can provide significant benefits over other state-of-the-art approaches. Our analysis of the consensus clusters obtained demonstrates that ensemble clustering can (a) produce improved biologically significant functional groupings; and (b) facilitate soft clustering by discovering multiple functional associations for proteins. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Vocal networks remain stable after a disturbance in Emei music frogs

Social network analysis has been widely used to investigate the dynamics of social interactions and the evolution of social complexity across a range of taxa. Anuran species are highly dependent on vocal communication in mate choice; however, these species have rarely been the subject of social network analysis. The present study used social network analysis to investigate whether vocal network structures are consistent in Emei music frog (Babina daunchina) after the introduction of a simulated exotic rival of varying competitiveness into the social group. We broadcasted six categories of artificial calls (either highly sexually attractive calls produced from inside male nests or calls of low sexual attractiveness produced outside nests with three, five or seven notes, respectively) to simulate an intruder with different levels of competitiveness. We then constructed vocal networks for two time periods (before and after the disturbance) and quantified three network metrics (strength, closeness, and betweenness) that measure different aspects of individual‐level position. We used the mean values of these network metrics to evaluate group‐level changes in network structure. We found that the mean strength, mean closeness and mean betweenness were consistent between two time periods in all ponds, despite the fact that the positions of some individuals had changed markedly after disturbance. In addition, there was no significant interaction effect between period and numbers of notes on the three network metrics. These finding suggest that the structure of vocal networks in Emei music frogs remain stable at the group level after a conspecific disturbance, regardless of the intruder's competitiveness.     

Functional structure and specialization in three tropical plant–hummingbird interaction networks across an elevational gradient in Costa Rica

Understanding causes of variation in multispecies assemblages along spatial environmental gradients is a long‐standing research topic in ecology and biogeography. Ecological networks comprising interacting species of plants and pollinators are particularly suitable for testing effects of environmental gradients on the functional structure and specialization in multispecies assemblages. In this study, we investigated patterns in functional assemblage structure and specialization of hummingbirds at the individual and species level along a tropical elevational gradient. We mist‐netted hummingbirds at three elevations in Costa Rica in seven temporally distinct sampling periods and used the pollen carried by hummingbird individuals to construct plant–hummingbird networks at each elevation. We measured four functional traits of hummingbird species and quantified different metrics of functional community structure. We tested the effect of elevation on functional metrics of hummingbird assemblages and specialization within the networks, employing the variability across sampling periods and hummingbird species to compare the respective metrics among elevations. Hummingbird species and individuals were more specialized at low and mid elevations than at the highest elevation. This pattern corresponded to a more even and over‐dispersed assemblage structure at the lower elevations throughout the year and suggests a high level of floral resource partitioning in functionally diversified communities. In contrast, an uneven and clustered functional structure of the highland assemblage across all sampling periods suggests that this assemblage was structured by environmental filtering and by niche expansion of hummingbird individuals and species at this elevation. We conclude that high degrees of specialization on specific floral resources might be crucial for the coexistence of hummingbird species in diversified lowland communities. Spatial variation in animal resource use may be an important crucial driver of spatial patterns in the functional structure of diversified species assemblages also in other types of ecological networks.     

垂叶榕榕小蜂群落及种间互作网络季节动态

群落中的物种相互作用构成了复杂的生态网络。有关物种的数量和组成的季节性动态变化已有较多的研究, 但是对于生态网络的动态变化知之甚少。揭示生态网络的动态变化对于理解群落的稳定性以及群落的动态变化过程和机理具有重要意义。本研究以垂叶榕(Ficus benjamina)榕小蜂群落为研究对象, 分别在西双版纳的干季和雨季采集了榕小蜂的种类和数量信息。比较了两个季节榕小蜂群落的动态变化以及共存网络的参数(例如网路直径、连接数、嵌套性和群落矩阵温度)变化。结果显示: 雨季榕果内传粉榕小蜂Eupristina koningsbergeri所占比例高于干季, 传粉榕小蜂的种群数量也高于干季, 而在干季非传粉榕小蜂的种类增加(干季15种小蜂, 雨季14种)。从榕树-传粉榕小蜂互利共生系统的适合度来看, 干季非传粉小蜂的增加对传粉榕小蜂和榕树的适合度是不利的。在干季, 共存网络物种间的连接数(干季0.95, 雨季0.47)多于雨季, 群落矩阵温度(干季23.24, 雨季2.64)也显著高于雨季。表明干季榕小蜂群落组成及种间关系较雨季更为复杂而多样, 高的矩阵温度暗示群落受到的干扰更大。