Conventional and network analyses of song organization and complexity in northern House Wrens (Troglodytes aedon parkmanii)

Among songbirds with large song-type repertoires, there may be functional variation in how individuals organize and display song-type diversity over time. Past studies focusing on conventional measures of song production have been extremely productive. However, network analysis offers a novel set of tools to quantify additional, previously unstudied elements of song organization and display. We studied protracted bouts of singing by 10 male House Wrens (Troglodytes aedon) to (1) test functional hypotheses of variation in song diversity in this species, and (2) evaluate the utility of network metrics in such research. Our analysis included a variety of conventional measures of song production and several standard metrics from network theory to quantify how variably the many song types in a male’s repertoire could be connected to one another and the limitations or diversity of their song sequences. Analysis of conventional variables showed that males produced more and longer songs, at shorter intervals, containing more syllables and more different syllable types, and also more different song types, prior to than after pairing and early in the morning regardless of breeding stage. These results are consistent with the hypothesis that song diversity functions in mate attraction and possibly in territory signaling. In contrast, analyses of network metrics revealed variety in song sequencing by males, but comparatively few and weak effects associated with either breeding stage or time of day. Overall, most song types connected to only a few others and a relatively small proportion of all possible song-type transitions actually occurred. Hence, much of the variety in song sequencing that was possible with the large song repertoires of males was not realized. The latter outcomes, brought to light via network analyses, highlight an important paradox for future research on this and related species with large song repertoires.     

Diversity in riverine metacommunities: a network perspective

The influence of spatial processes on diversity and community dynamics is generally recognized in ecology and also applied to conservation projects involving forest and grassland ecosystems. Riverine ecosystems, however, have been for a long time viewed from a local or linear perspective, even though the treelike branching of river networks is universal. River networks (so-called dendritic networks) are not only structured in a hierarchic way, but the dendritic landscape structure and physical flows often dictate distance and directionality of dispersal. Theoretical models suggest that the specific riverine network structure directly affects diversity patterns. Recent experimental and comparative data are supporting this idea. Here, I provide an introduction on theoretical findings suggesting that genetic diversity, heterozygosity and species richness are higher in dendritic systems compared to linear or two-dimensional lattice landscapes. The characteristic diversity patterns can be explained in a network perspective, which also offers universal metrics to better understand and protect riverine diversity. I show how appropriate metrics describing network centrality and dispersal distances are superior to classic measures still applied in aquatic ecology, such as Strahler order or Euclidian distance. Finally, knowledge gaps and future directions of research are identified. The network perspective employed here may help to generalize findings on riverine biodiversity research and can be applied to conservation and river restoration projects.     

Causal measures of structure and plasticity in simulated and living neural networks

A major goal of neuroscience is to understand the relationship between neural structures and their function. Recording of neural activity with arrays of electrodes is a primary tool employed toward this goal. However, the relationships among the neural activity recorded by these arrays are often highly complex making it problematic to accurately quantify a network's structural information and then relate that structure to its function. Current statistical methods including cross correlation and coherence have achieved only modest success in characterizing the structural connectivity. Over the last decade an alternative technique known as Granger causality is emerging within neuroscience. This technique, borrowed from the field of economics, provides a strong mathematical foundation based on linear auto-regression to detect and quantify "causal" relationships among different time series. This paper presents a combination of three Granger based analytical methods that can quickly provide a relatively complete representation of the causal structure within a neural network. These are a simple pairwise Granger causality metric, a conditional metric, and a little known computationally inexpensive subtractive conditional method. Each causal metric is first described and evaluated in a series of biologically plausible neural simulations. We then demonstrate how Granger causality can detect and quantify changes in the strength of those relationships during plasticity using 60 channel spike train data from an in vitro cortical network measured on a microelectrode array. We show that these metrics can not only detect the presence of causal relationships, they also provide crucial information about the strength and direction of that relationship, particularly when that relationship maybe changing during plasticity. Although we focus on the analysis of multichannel spike train data the metrics we describe are applicable to any stationary time series in which causal relationships among multiple measures is desired. These techniques can be especially useful when the interactions among those measures are highly complex, difficult to untangle, and maybe changing over time.     

On the Correlation between Reservoir Metrics and Performance for Time Series Classification under the Influence of Synaptic Plasticity

Reservoir computing provides a simpler paradigm of training recurrent networks by initialising and adapting the recurrent connections separately to a supervised linear readout. This creates a problem, though. As the recurrent weights and topology are now separated from adapting to the task, there is a burden on the reservoir designer to construct an effective network that happens to produce state vectors that can be mapped linearly into the desired outputs. Guidance in forming a reservoir can be through the use of some established metrics which link a number of theoretical properties of the reservoir computing paradigm to quantitative measures that can be used to evaluate the effectiveness of a given design. We provide a comprehensive empirical study of four metrics; class separation, kernel quality, Lyapunov''s exponent and spectral radius. These metrics are each compared over a number of repeated runs, for different reservoir computing set-ups that include three types of network topology and three mechanisms of weight adaptation through synaptic plasticity. Each combination of these methods is tested on two time-series classification problems. We find that the two metrics that correlate most strongly with the classification performance are Lyapunov''s exponent and kernel quality. It is also evident in the comparisons that these two metrics both measure a similar property of the reservoir dynamics. We also find that class separation and spectral radius are both less reliable and less effective in predicting performance.     

Validation of Network Communicability Metrics for the Analysis of Brain Structural Networks

Computational network analysis provides new methods to analyze the brain''s structural organization based on diffusion imaging tractography data. Networks are characterized by global and local metrics that have recently given promising insights into diagnosis and the further understanding of psychiatric and neurologic disorders. Most of these metrics are based on the idea that information in a network flows along the shortest paths. In contrast to this notion, communicability is a broader measure of connectivity which assumes that information could flow along all possible paths between two nodes. In our work, the features of network metrics related to communicability were explored for the first time in the healthy structural brain network. In addition, the sensitivity of such metrics was analysed using simulated lesions to specific nodes and network connections. Results showed advantages of communicability over conventional metrics in detecting densely connected nodes as well as subsets of nodes vulnerable to lesions. In addition, communicability centrality was shown to be widely affected by the lesions and the changes were negatively correlated with the distance from lesion site. In summary, our analysis suggests that communicability metrics that may provide an insight into the integrative properties of the structural brain network and that these metrics may be useful for the analysis of brain networks in the presence of lesions. Nevertheless, the interpretation of communicability is not straightforward; hence these metrics should be used as a supplement to the more standard connectivity network metrics.     

Raccoon Social Networks and the Potential for Disease Transmission

Raccoons are an important vector of rabies and other pathogens. The degree to which these pathogens can spread through a raccoon population should be closely linked to association rates between individual raccoons. Most studies of raccoon sociality have found patterns consistent with low levels of social connectivity within populations, thus the likelihood of direct pathogen transmission between raccoons is theoretically low. We used proximity detecting collars and social network metrics to calculate the degree of social connectivity in an urban raccoon population for purposes of estimating potential pathogen spread. In contrast to previous assumptions, raccoon social association networks were highly connected, and all individuals were connected to one large social network during 15 out of 18 months of study. However, these metrics may overestimate the potential for a pathogen to spread through a population, as many of the social connections were based on relatively short contact periods. To more closely reflect varying probabilities of pathogen spread, we censored the raccoon social networks based on the total amount of time spent in close proximity between two individuals per month. As this time criteria for censoring the social networks increased from one to thirty minutes, corresponding measures of network connectivity declined. These findings demonstrate that raccoon populations are much more tightly connected than would have been predicted based on previous studies, but also point out that additional research is needed to calculate more precise transmission probabilities by infected individuals, and determine how disease infection changes normal social behaviors.     

EEG-Based Functional Brain Networks: Does the Network Size Matter?

Functional connectivity in human brain can be represented as a network using electroencephalography (EEG) signals. These networks--whose nodes can vary from tens to hundreds--are characterized by neurobiologically meaningful graph theory metrics. This study investigates the degree to which various graph metrics depend upon the network size. To this end, EEGs from 32 normal subjects were recorded and functional networks of three different sizes were extracted. A state-space based method was used to calculate cross-correlation matrices between different brain regions. These correlation matrices were used to construct binary adjacency connectomes, which were assessed with regards to a number of graph metrics such as clustering coefficient, modularity, efficiency, economic efficiency, and assortativity. We showed that the estimates of these metrics significantly differ depending on the network size. Larger networks had higher efficiency, higher assortativity and lower modularity compared to those with smaller size and the same density. These findings indicate that the network size should be considered in any comparison of networks across studies.     

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.     

A social network analysis of primate groups

Primate social systems are difficult to characterize, and existing classification schemes have been criticized for being overly simplifying, formulated only on a verbal level or partly inconsistent. Social network analysis comprises a collection of analytical tools rooted in the framework of graph theory that were developed to study human social interaction patterns. More recently these techniques have been successfully applied to examine animal societies. Primate social systems differ from those of humans in both size and density, requiring an approach that puts more emphasis on the quality of relationships. Here, we discuss a set of network measures that are useful to describe primate social organization and we present the results of a network analysis of 70 groups from 30 different species. For this purpose we concentrated on structural measures on the group level, describing the distribution of interaction patterns, centrality, and group structuring. We found considerable variability in those measures, reflecting the high degree of diversity of primate social organizations. By characterizing primate groups in terms of their network metrics we can draw a much finer picture of their internal structure that might be useful for species comparisons as well as the interpretation of social behavior.     

Altered topological properties of functional network connectivity in schizophrenia during resting state: a small-world brain network study

Aberrant topological properties of small-world human brain networks in patients with schizophrenia (SZ) have been documented in previous neuroimaging studies. Aberrant functional network connectivity (FNC, temporal relationships among independent component time courses) has also been found in SZ by a previous resting state functional magnetic resonance imaging (fMRI) study. However, no study has yet determined if topological properties of FNC are also altered in SZ. In this study, small-world network metrics of FNC during the resting state were examined in both healthy controls (HCs) and SZ subjects. FMRI data were obtained from 19 HCs and 19 SZ. Brain images were decomposed into independent components (ICs) by group independent component analysis (ICA). FNC maps were constructed via a partial correlation analysis of ICA time courses. A set of undirected graphs were built by thresholding the FNC maps and the small-world network metrics of these maps were evaluated. Our results demonstrated significantly altered topological properties of FNC in SZ relative to controls. In addition, topological measures of many ICs involving frontal, parietal, occipital and cerebellar areas were altered in SZ relative to controls. Specifically, topological measures of whole network and specific components in SZ were correlated with scores on the negative symptom scale of the Positive and Negative Symptom Scale (PANSS). These findings suggest that aberrant architecture of small-world brain topology in SZ consists of ICA temporally coherent brain networks.     

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.     

Metrics for Phylogenetic Networks I: Generalizations of the Robinson-Foulds Metric

The assessment of phylogenetic network reconstruction methods requires the ability to compare phylogenetic networks. This is the first in a series of papers devoted to the analysis and comparison of metrics for tree-child time consistent phylogenetic networks on the same set of taxa. In this paper, we study three metrics that have already been introduced in the literature: the Robinson-Foulds distance, the tripartitions distance and the $mu$-distance. They generalize to networks the classical Robinson-Foulds or partition distance for phylogenetic trees. We analyze the behavior of these metrics by studying their least and largest values and when they achieve them. As a by-product of this study, we obtain tight bounds on the size of a tree-child time consistent phylogenetic network.     

Strength and uncertainty of phytoplankton metrics for assessing eutrophication impacts in lakes

Phytoplankton constitutes a diverse array of short-lived organisms which derive their nutrients from the water column of lakes. These features make this community the most direct and earliest indicator of the impacts of changing nutrient conditions on lake ecosystems. It also makes them particularly suitable for measuring the success of restoration measures following reductions in nutrient loads. This paper integrates a large volume of work on a number of measures, or metrics, developed for using phytoplankton to assess the ecological status of European lakes, as required for the Water Framework Directive. It assesses the indicator strength of these metrics, specifically in relation to representing the impacts of eutrophication. It also examines how these measures vary naturally at different locations within a lake, as well as between lakes, and how much variability is associated with different replicate samples, different months within a year and between years. On the basis of this analysis, three of the strongest metrics (chlorophyll-a, phytoplankton trophic index (PTI), and cyanobacterial biovolume) are recommended for use as robust measures for assessing the ecological quality of lakes in relation to nutrient-enrichment pressures and a minimum recommended sampling frequency is provided for these three metrics.     

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.     

Applying Ecological Input-Output Flow Analysis to Material Flows in Industrial Systems

This article, continuing with the themes of the companion article, expounds the capabilities of input-output techniques as applied to material flows in industrial systems. Material flows are the primary focus because of their role in directly linking natural and industrial systems and thereby being fundamental components of environmental issues in industrial economies. The specific topic in this article concerns several material flow metrics used to characterize system behavior that are derived from the ecological development of input-output techniques; most notable of these metrics are several measures of material cycling and a measure of the number of processes visited by material while in a system. These metrics are shown to be useful in analyzing the state of material flow systems. Further-more, the metrics are shown to be a central link in connecting input-output flow analysis to synthesis (i.e., the process of using measurements of system behavior to design changes to that system). By connecting the flow metrics to both environmental objectives and controllable aspects of flow models, changes to existing flow systems are synthesized to generate improved system behavior. To bring this pair of articles to a close, several limitations of input-output flow analysis are summarized with the goal of stimulating further interest and research.     

Content disputes in Wikipedia reflect geopolitical instability

Indicators that rank countries according socioeconomic measurements are important tools for regional development and political reform. Those currently in widespread use are sometimes criticized for a lack of reproducibility or the inability to compare values over time, necessitating simple, fast and systematic measures. Here, we applied the 'guilt by association' principle often used in biological networks to the information network within the online encyclopedia Wikipedia to create an indicator quantifying the degree to which pages linked to a country are disputed by contributors. The indicator correlates with metrics of governance, political or economic stability about as well as they correlate with each other, and though faster and simpler, it is remarkably stable over time despite constant changes in the underlying disputes. For some countries, changes over a four year period appear to correlate with world events related to conflicts or economic problems.     

Relations between BOLD fMRI-Derived Resting Brain Activity and Cerebral Blood Flow

Consistent resting brain activity patterns have been repeatedly demonstrated using measures derived from resting BOLD fMRI data. While those metrics are presumed to reflect underlying spontaneous brain activity (SBA), it is challenging to prove that association because resting BOLD fMRI metrics are purely model-free and scale-free variables. Cerebral blood flow (CBF) is typically closely coupled to brain metabolism and is used as a surrogate marker for quantifying regional brain function, including resting function. Assessing the correlations between resting BOLD fMRI measures and CBF correlation should provide a means of linking of those measures to the underlying SBA, and a means to quantify those scale-free measures. The purpose of this paper was to examine the CBF correlations of 3 widely used neuroimaging-based SBA measures, including seed-region based functional connectivity (FC), regional homogeneity (ReHo), and amplitude of low frequency fluctuation (ALFF). Test-retest data were acquired to check the stability of potential correlations across time. Reproducible posterior cingulate cortex (PCC) FC vs regional CBF correlations were found in much of the default mode network and visual cortex. Dorsal anterior cingulate cortex (ACC) FC vs CBF correlations were consistently found in bilateral prefrontal cortex. Both ReHo and ALFF were found to be reliably correlated with CBF in most of brain cortex. None of the assessed SBA measures was correlated with whole brain mean CBF. These findings suggest that resting BOLD fMRI-derived measures are coupled with regional CBF and are therefore linked to regional SBA.     

Loss in life expectancy and gain in life years as measures of cancer impact

There are a broad range of survival-based metrics that are available to report from cancer survival studies, with varying advantages and disadvantages. A combination of metrics should be considered to improve comprehensibility and give a fuller understanding of the impact of cancer. In this article, we discuss the utility of loss in life expectancy and gain in life years as measures of cancer impact, and to quantify differences across population groups. These measures are simple to interpret, have a real-world meaning, and evaluate impact over a life-time horizon. We illustrate the use of the loss in life expectancy measures through a range of examples using data on women diagnosed with cancer in England. We use four different examples across a number of tumour types to illustrate different uses of the metrics, and highlight how they can be interpreted and used in practice in population-based oncology studies. Extensions of the measures conditional on survival to specific times after diagnosis can be used to give updated prognosis for cancer patients. Furthermore, we show how the measures can be used to understand the impact of population differences seen across patient groups. We believe that these under-used, and relatively easy to calculate, measures of overall impact can supplement reporting of cancer survival metrics and improve the comprehensibility compared to the metrics typically reported.     

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.     

Matrix models for quantifying competitive intransitivity from species abundance data

In a network of competing species, a competitive intransitivity occurs when the ranking of competitive abilities does not follow a linear hierarchy (A > B > C but C > A). A variety of mathematical models suggests that intransitive networks can prevent or slow down competitive exclusion and maintain biodiversity by enhancing species coexistence. However, it has been difficult to assess empirically the relative importance of intransitive competition because a large number of pairwise species competition experiments are needed to construct a competition matrix that is used to parameterize existing models. Here we introduce a statistical framework for evaluating the contribution of intransitivity to community structure using species abundance matrices that are commonly generated from replicated sampling of species assemblages. We provide metrics and analytical methods for using abundance matrices to estimate species competition and patch transition matrices by using reverse‐engineering and a colonization–competition model. These matrices provide complementary metrics to estimate the degree of intransitivity in the competition network of the sampled communities. Benchmark tests reveal that the proposed methods could successfully detect intransitive competition networks, even in the absence of direct measures of pairwise competitive strength. To illustrate the approach, we analyzed patterns of abundance and biomass of five species of necrophagous Diptera and eight species of their hymenopteran parasitoids that co‐occur in beech forests in Germany. We found evidence for a strong competitive hierarchy within communities of flies and parasitoids. However, for parasitoids, there was a tendency towards increasing intransitivity in higher weight classes, which represented larger resource patches. These tests provide novel methods for empirically estimating the degree of intransitivity in competitive networks from observational datasets. They can be applied to experimental measures of pairwise species interactions, as well as to spatio‐temporal samples of assemblages in homogenous environments or environmental gradients.