A highly resolved network reveals the role of terrestrial herbivory in structuring aboveground food webs

Comparative studies suggest remarkable similarities among food webs across habitats, including systematic changes in their structure with diversity and complexity (scale-dependence). However, historic aboveground terrestrial food webs (ATFWs) have coarsely grouped plants and insects such that these webs are generally small, and herbivory is disproportionately under-represented compared to vertebrate predator-prey interactions. Furthermore, terrestrial herbivory is thought to be structured by unique processes compared to size-structured feeding in other systems. Here, we present the richest ATFW to date, including approximately 580 000 feeding links among approximately 3800 taxonomic species, sourced from approximately 27 000 expert-vetted interaction records annotated as feeding upon one of six different resource types: leaves, flowers, seeds, wood, prey and carrion. By comparison to historical ATFWs and null ecological hypotheses, we show that our temperate forest web displays a potentially unique structure characterized by two properties: (i) a large fraction of carnivory interactions dominated by a small number of hyper-generalist, opportunistic bird and bat predators; and (ii) a smaller fraction of herbivory interactions dominated by a hyper-rich community of insects with variably sized but highly specific diets. We attribute our findings to the large-scale, even resolution of vertebrate, insect and plant guilds in our food web.This article is part of the theme issue 'Connected interactions: enriching food web research by spatial and social interactions'.

Ecological network structure in response to community assembly processes over evolutionary time

The dynamic structure of ecological communities results from interactions among taxa that change with shifts in species composition in space and time. However, our ability to study the interplay of ecological and evolutionary processes on community assembly remains relatively unexplored due to the difficulty of measuring community structure over long temporal scales. Here, we made use of a geological chronosequence across the Hawaiian Islands, representing 50 years to 4.15 million years of ecosystem development, to sample 11 communities of arthropods and their associated plant taxa using semiquantitative DNA metabarcoding. We then examined how ecological communities changed with community age by calculating quantitative network statistics for bipartite networks of arthropod-plant associations. The average number of interactions per species (linkage density), ratio of plant to arthropod species (vulnerability) and uniformity of energy flow (interaction evenness) increased significantly in concert with community age. The index of specializationH 2 ' has a curvilinear relationship with community age. Our analyses suggest that younger communities are characterized by fewer but stronger interactions, while biotic associations become more even and diverse as communities mature. These shifts in structure became especially prominent on East Maui (~0.5 million years old) and older volcanos, after enough time had elapsed for adaptation and specialization to act on populations in situ. Such natural progression of specialization during community assembly is probably impeded by the rapid infiltration of non-native species, with special risk to younger or more recently disturbed communities that are composed of fewer specialized relationships.

Pajda-De La O J, McCary MA. Pattern of seasonal variation in rates of predation between spider families is temporally stable in a food web with widespread intraguild predation

Intraguild predation (IGP)-predation between generalist predators (IGPredator and IGPrey) that potentially compete for a shared prey resource-is a common interaction module in terrestrial food webs. Understanding temporal variation in webs with widespread IGP is relevant to testing food web theory. We investigated temporal constancy in the structure of such a system: the spider-focused food web of the forest floor. Multiplex PCR was used to detect prey DNA in 3,300 adult spiders collected from the floor of a deciduous forest during spring, summer, and fall over four years. Because only spiders were defined as consumers, the web was tripartite, with 11 consumer nodes (spider families) and 22 resource nodes: 11 non-spider arthropod taxa (order- or family-level) and the 11 spider families. Most (99%) spider-spider predation was on spider IGPrey, and ~90% of these interactions were restricted to spider families within the same broadly defined foraging mode (cursorial or web-spinning spiders). Bootstrapped-derived confidence intervals (BCI's) for two indices of web structure, restricted connectance and interaction evenness, overlapped broadly across years and seasons. A third index, % IGPrey (% IGPrey among all prey of spiders), was similar across years (~50%) but varied seasonally, with a summer rate (65%) ~1.8x higher than spring and fall. This seasonal pattern was consistent across years. Our results suggest that extensive spider predation on spider IGPrey that exhibits consistent seasonal variation in frequency, and that occurs primarily within two broadly defined spider-spider interaction pathways, must be incorporated into models of the dynamics of forest-floor food webs.

Long-term changes as oil palm plantation age simplify the structure of host-parasitoid food webs

Understanding host-parasitoid food webs, as well as the factors affecting species interactions, is important for developing pest management strategies in an agroecosystem. This research aimed to study how the long-term change in oil palm plantations, specifically the tree age, affect the structure of host-parasitoid food webs. The field research was conducted on an oil palm plantation located in Central Kalimantan and Jambi Province, Indonesia. In Central Kalimantan, we conducted observations of lepidopteran larvae and parasitoid wasps at different tree ages, ranging from 3 to 18 years old. For tree ages from 3 to 10 years, observations of host-parasitoid food webs were conducted by collecting the lepidopteran larvae using a hand-collection method in each oil palm tree within a hundred trees and they were later reared in the laboratory for observing the emerging parasitoids. The fogging method was applied for trees aged 12 to 18 years because the tree height was too high, and hand-collection was difficult to perform. To compare host-parasitoid food webs between different regions, we also conducted a hand-collection method in Jambi, but only for trees aged 3 years old. The food-web structure that was analyzed included the species number of lepidopteran larvae and parasitoid wasps, linkage density, and interaction diversity. We found 32 species of lepidopteran pests and 16 species of associated parasitoids in Central Kalimantan and 12 species of lepidopteran pests, and 11 species of parasitoids in Jambi. Based on the GLM analysis, tree age had a negative relationship with the species number of lepidopteran larvae and parasitoids as well as linkage density and interaction diversity. Different geographical regions showed different host-parasitoid food web structures, especially the species number of lepidopteran larvae and interaction diversity, which were higher in Central Kalimantan than in Jambi. However, some parasitoids can be found across different tree ages. For example, Fornicia sp (Hymenoptera: Braconidae) was recorded in all ages of oil palm sampled. Results of the GLM analysis showed that the abundance of Fornicia sp and its host (lepidopteran larvae abundance) were not affected by the tree age of the oil palm. In conclusion, the long-term change in oil palm plantations simplifies the structure of host-parasitoid food webs. This highlights the importance of long-term studies across geographical regions for a better understanding of the consequences that wide monoculture oil palm plantations have on biological control services.

Gut microbiome responds compositionally and functionally to the seasonal diet variations in wild gibbons

Wild animals may encounter multiple challenges especially food shortage and altered diet composition in their suboptimal ranges. Yet, how the gut microbiome responds to dietary changes remains poorly understood. Prior studies on wild animal microbiomes have typically leaned upon relatively coarse dietary records and individually unresolved fecal samples. Here, we conducted a longitudinal study integrating 514 time-series individually recognized fecal samples with parallel fine-grained dietary data from two Skywalker hoolock gibbon (Hoolock tianxing) groups populating high-altitude mountainous forests in western Yunnan Province, China. 16S rRNA gene amplicon sequencing showed a remarkable seasonal fluctuation in the gibbons' gut microbial community structure both across individuals and between the social groups, especially driven by the relative abundances of Lanchnospiraceae and Oscillospiraceae associated with fluctuating consumption of leaf. Metagenomic functional profiling revealed that diverse metabolisms associated with cellulose degradation and short-chain fatty acids (SCFAs) production were enriched in the high-leaf periods possibly to compensate for energy intake. Genome-resolved metagenomics further enabled the resolving metabolic capacities associated with carbohydrate breakdown among community members which exhibited a high degree of functional redundancy. Our results highlight a taxonomically and functionally sensitive gut microbiome actively responding to the seasonally shifting diet, facilitating the survival and reproduction of the endangered gibbon species in their suboptimal habitats.

Stable pollination service in a generalist high Arctic community despite the warming climate

Insects provide key pollination services in most terrestrial biomes, but this service depends on a multistep interaction between insect and plant. An insect needs to visit a flower, receive pollen from the anthers, move to another conspecific flower, and finally deposit the pollen on a receptive stigma. Each of these steps may be affected by climate change, and focusing on only one of them (e.g., flower visitation) may miss important signals of change in service provision. In this study, we combine data on visitation, pollen transport, and single-visit pollen deposition to estimate functional outcomes in the high Arctic plant-pollinator network of Zackenberg, Northeast Greenland, a model system for global warming-associated impacts in pollination services. Over two decades of rapid climate warming, we sampled the network repeatedly: in 1996, 1997, 2010, 2011, and 2016. Although the flowering plant and insect communities and their interactions varied substantially between years, as expected based on highly variable Arctic weather, there was no detectable directional change in either the structure of flower-visitor networks or estimated pollen deposition. For flower-visitor networks compiled over a single week, species phenologies caused major within-year variation in network structure despite consistency across years. Weekly networks for the middle of the flowering season emerged as especially important because most pollination service can be expected to be provided by these large, highly nested networks. Our findings suggest that pollination ecosystem service in the high Arctic is remarkably resilient. This resilience may reflect the plasticity of Arctic biota as an adaptation to extreme and unpredictable weather. However, most pollination service was contributed by relatively few fly taxa (Diptera: Spilogona sanctipauli and Drymeia segnis [Muscidae] and species of Rhamphomyia [Empididae]). If these key pollinators are negatively affected by climate change, network structure and the pollination service that depends on it would be seriously compromised.

Human disturbances affect the topology of food webs

Networks describe nodes connected by links, with numbers of links per node, the degree, forming a range of distributions including random and scale-free. How network topologies emerge in natural systems still puzzles scientists. Based on previous theoretical simulations, we predict that scale-free food webs are favourably selected by random disturbances while random food webs are selected by targeted disturbances. We assume that lower human pressures are more likely associated with random disturbances, whereas higher pressures are associated with targeted ones. We examine these predictions using 351 empirical food webs, generally confirming our predictions. Should the topology of food webs respond to changes in the magnitude of disturbances in a predictable fashion, consistently across ecosystems and scales of organisation, it would provide a baseline expectation to understand and predict the consequences of human pressures on ecosystem dynamics.

Simultaneously estimating food web connectance and structure with uncertainty

Food web models explain and predict the trophic interactions in a food web, and they can infer missing interactions among the organisms. The allometric diet breadth model (ADBM) is a food web model based on the foraging theory. In the ADBM, the foraging parameters are allometrically scaled to body sizes of predators and prey. In Petchey et al. (Proceedings of the National Academy of Sciences, 2008; 105: 4191), the parameterization of the ADBM had two limitations: (a) the model parameters were point estimates and (b) food web connectance was not estimated.The novelty of our current approach is: (a) We consider multiple predictions from the ADBM by parameterizing it with approximate Bayesian computation, to estimate parameter distributions and not point estimates. (b) Connectance emerges from the parameterization, by measuring model fit using the true skill statistic, which takes into account prediction of both the presences and absences of links.We fit the ADBM using approximate Bayesian computation to 12 observed food webs from a wide variety of ecosystems. Estimated connectance was consistently greater than previously found. In some of the food webs, considerable variation in estimated parameter distributions occurred and resulted in considerable variation (i.e., uncertainty) in predicted food web structure.These results lend weight to the possibility that the observed food web data is missing some trophic links that do actually occur. It also seems likely that the ADBM likely predicts some links that do not exist. The latter could be addressed by accounting in the ADBM for additional traits other than body size. Further work could also address the significance of uncertainty in parameter estimates for predicted food web responses to environmental change.

Nest guarding behaviour of a temperate wrasse differs between sites off Mediterranean CO2 seeps

Organisms may respond to changing environmental conditions by adjusting their behaviour (i.e., behavioural plasticity). Ocean acidification (OA), resulting from anthropogenic emissions of carbon dioxide (CO₂), is predicted to impair sensory function and behaviour of fish. However, reproductive behaviours, and parental care in particular, and their role in mediating responses to OA are presently overlooked. Here, we assessed whether the nesting male ocellated wrasse Symphodus ocellatus from sites with different CO₂ concentrations showed different behaviours during their breeding season. We also investigated potential re-allocation of the time-budget towards different behavioural activities between sites. We measured the time period that the nesting male spent carrying out parental care, mating and exploring activities, as well as changes in the time allocation between sites at ambient (~400 μatm) and high CO₂ concentrations (~1000 μatm). Whilst the behavioural connectance (i.e., the number of linkages among different behaviours relative to the total amount of linkages) was unaffected, we observed a significant reduction in the time spent on parental care behaviour, and a significant decrease in the guarding activity of fish at the high CO₂ sites, with a proportional re-allocation of the time budget in favour of courting and wandering around, which however did not change between sites. This study shows behavioural differences in wild fish living off volcanic CO₂ seeps that could be linked to different OA levels, suggesting that behavioural plasticity may potentially act as a mechanism for buffering the effects of ongoing environmental change. A reallocation of the time budget between key behaviours may play a fundamental role in determining which marine organisms are thriving under projected OA.

A multi-site method to capture turnover in rare to common interactions in bipartite species networks

Ecological network structure is maintained by a generalist core of common species. However, rare species contribute substantially to both the species and functional diversity of networks. Capturing changes in species composition and interactions, measured as turnover, is central to understanding the contribution of rare and common species and their interactions. Due to a large contribution of rare interactions, the pairwise metrics used to quantify interaction turnover are, however, sensitive to compositional change in the interactions of, often rare, peripheral specialists rather than common generalists in the network. Here we expand on pairwise interaction turnover using a multi-site metric that enables quantifying turnover in rare to common interactions (in terms of occurrence of interactions). The metric further separates this turnover into interaction turnover due to species turnover and interaction rewiring. We demonstrate the application and value of this method using a host-parasitoid system sampled along gradients of environmental modification. In the study system, both the type and amount of habitat needed to maintain interaction composition depended on the properties of the interactions considered, that is, from rare to common. The analyses further revealed the potential of host switching to prevent or delay species loss, and thereby buffer the system from perturbation. Multi-site interaction turnover provides a comprehensive measure of network change that can, for example, detect ecological thresholds to habitat loss for rare to common interactions. Accurate description of turnover in common, in addition to rare, species and their interactions is particularly relevant for understanding how network structure and function can be maintained.

Reinterpreting the relationship between number of species and number of links connects community structure and stability

For 50 years, ecologists have examined how the number of interactions (links) scales with the number of species in ecological networks. Here, we show that the way the number of links varies when species are sequentially removed from a community is fully defined by a single parameter identifiable from empirical data. We mathematically demonstrate that this parameter is network-specific and connects local stability and robustness, establishing a formal connection between community structure and two prime stability concepts. Importantly, this connection highlights a local stability-robustness trade-off, which is stronger in mutualistic than in trophic networks. Analysis of 435 empirical networks confirmed these results. We finally show how our network-specific approach relates to the classical across-network approach found in literature. Taken together, our results elucidate one of the intricate relationships between network structure and stability in community networks.

Finding missing links in interaction networks

Documenting which species interact within ecological communities is challenging and labor intensive. As a result, many interactions remain unrecorded, potentially distorting our understanding of network structure and dynamics. We test the utility of four structural models and a new coverage-deficit model for predicting missing links in both simulated and empirical bipartite networks. We find they can perform well, although the predictive power of structural models varies with the underlying network structure. The accuracy of predictions can be improved by ensembling multiple models. Augmenting observed networks with most-likely missing links improves estimates of qualitative network metrics. Tools to identify likely missing links can be simple to implement, allowing the prioritization of research effort and more robust assessment of network properties.

Simulated evolution assembles more realistic food webs with more functionally similar species than invasion

While natural communities are assembled by both ecological and evolutionary processes, ecological assembly processes have been studied much more and are rarely compared with evolutionary assembly processes. We address these disparities here by comparing community food webs assembled by simulating introductions of species from regional pools of species and from speciation events. Compared to introductions of trophically dissimilar species assumed to be more typical of invasions, introducing species trophically similar to native species assumed to be more typical of sympatric or parapatric speciation events caused fewer extinctions and assembled more empirically realistic networks by introducing more persistent species with higher trophic generality, vulnerability, and enduring similarity to native species. Such events also increased niche overlap and the persistence of both native and introduced species. Contrary to much competition theory, these findings suggest that evolutionary and other processes that more tightly pack ecological niches contribute more to ecosystem structure and function than previously thought.

Predation risk influences food-web structure by constraining species diet choice

The foraging behaviour of species determines their diet and, therefore, also emergent food-web structure. Optimal foraging theory (OFT) has previously been applied to understand the emergence of food-web structure through a consumer-centric consideration of diet choice. However, the resource-centric viewpoint, where species adjust their behaviour to reduce the risk of predation, has not been considered. We develop a mechanistic model that merges metabolic theory with OFT to incorporate the effect of predation risk on diet choice to assemble food webs. This 'predation-risk-compromise' (PR) model better captures the nestedness and modularity of empirical food webs relative to the classical optimal foraging model. Specifically, compared with optimal foraging alone, risk-mitigated foraging leads to more-nested but less-modular webs by broadening the diet of consumers at intermediate trophic levels. Thus, predation risk significantly affects food-web structure by constraining species' ability to forage optimally, and needs to be considered in future work.

The geographical variation of network structure is scale dependent: understanding the biotic specialization of host-parasitoid networks

Research on the structure of ecological networks suggests that a number of universal patterns exist. Historically, biotic specialization has been thought to increase towards the Equator. Yet, recent studies have challenged this view showing non-conclusive results. Most studies analysing the geographical variation in biotic specialization focus, however, only on the local scale. Little is known about how the geographical variation of network structure depends on the spatial scale of observation (i.e., from local to regional spatial scales). This should be remedied, as network structure changes as the spatial scale of observation changes, and the magnitude and shape of these changes can elucidate the mechanisms behind the geographical variation in biotic specialization. Here we analyse four facets of biotic specialization in host-parasitoid networks along gradients of climatic constancy, classifying the networks according to their spatial extension (local or regional). Namely, we analyse network connectance, consumer diet overlap, consumer diet breadth, and resource vulnerability at both local and regional scales along the gradients of both current climatic constancy and historical climatic change. While at the regional scale none of the climatic variables are associated to biotic specialization, at the local scale, network connectance, consumer diet overlap, and resource vulnerability decrease with current climatic constancy, whereas consumer generalism increases (i.e., broader diet breadths in tropical areas). Similar patterns are observed along the gradient of historical climatic change. We provide an explanation based on different beta-diversity for consumers and resources across the geographical gradients. Our results show that the geographical gradient of biotic specialization is not universal. It depends on both the facet of biotic specialization and the spatial scale of observation.

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.

The effect of network size and sampling completeness in depauperate networks

The accurate estimation of interaction network structure is essential for understanding network stability and function. A growing number of studies evaluate under-sampling as the degree of sampling completeness (proportional richness observed). How the relationship between network structural metrics and sampling completeness varies across networks of different sizes remains unclear, but this relationship has implications for the within- and between-system comparability of network structure. Here, we test the combined effects of network size and sampling completeness on the structure of spatially distinct networks (i.e., subwebs) in a host-parasitoid model system to better understand the within-system variability in metric bias. Richness estimates were used to quantify a gradient of sampling completeness of species and interactions across randomly subsampled subwebs. The combined impacts of network size and sampling completeness on the estimated values of twelve unweighted and weighted network metrics were tested. The robustness of network metrics to under-sampling was strongly related to network size, and sampling completeness of interactions were generally a better predictor of metric bias than sampling completeness of species. Weighted metrics often performed better than unweighted metrics at low sampling completeness; however, this was mainly evident at large rather than small subweb size. These outcomes highlight the significance of under-sampling for the comparability of both unweighted and weighted network metrics when networks are small and vary in size. This has implications for within-system comparability of species-poor networks and, more generally, reveals problems with under-sampling ecological networks that may otherwise be difficult to detect in species-rich networks. To mitigate the impacts of under-sampling, more careful considerations of system-specific variation in metric bias are needed.

The origin of motif families in food webs

Food webs have been found to exhibit remarkable "motif profiles", patterns in the relative prevalences of all possible three-species subgraphs, and this has been related to ecosystem properties such as stability and robustness. Analysing 46 food webs of various kinds, we find that most food webs fall into one of two distinct motif families. The separation between the families is well predicted by a global measure of hierarchical order in directed networks-trophic coherence. We find that trophic coherence is also a good predictor for the extent of omnivory, defined as the tendency of species to feed on multiple trophic levels. We compare our results to a network assembly model that admits tunable trophic coherence via a single free parameter. The model is able to generate food webs in either of the two families by varying this parameter, and correctly classifies almost all the food webs in our database. This is in contrast with the two most popular food web models, the generalized cascade and niche models, which can only generate food webs within a single motif family. Our findings suggest the importance of trophic coherence in modelling local preying patterns in food webs.

Niche partitioning due to adaptive foraging reverses effects of nestedness and connectance on pollination network stability

Much research debates whether properties of ecological networks such as nestedness and connectance stabilise biological communities while ignoring key behavioural aspects of organisms within these networks. Here, we computationally assess how adaptive foraging (AF) behaviour interacts with network architecture to determine the stability of plant-pollinator networks. We find that AF reverses negative effects of nestedness and positive effects of connectance on the stability of the networks by partitioning the niches among species within guilds. This behaviour enables generalist pollinators to preferentially forage on the most specialised of their plant partners which increases the pollination services to specialist plants and cedes the resources of generalist plants to specialist pollinators. We corroborate these behavioural preferences with intensive field observations of bee foraging. Our results show that incorporating key organismal behaviours with well-known biological mechanisms such as consumer-resource interactions into the analysis of ecological networks may greatly improve our understanding of complex ecosystems.

Effects of genetically modified maize events expressing Cry34Ab1, Cry35Ab1, Cry1F, and CP4 EPSPS proteins on arthropod complex food webs

Four genetically modified (GM) maize (Zea mays L.) hybrids (coleopteran resistant, coleopteran and lepidopteran resistant, lepidopteran resistant and herbicide tolerant, coleopteran and herbicide tolerant) and its non-GM control maize stands were tested to compare the functional diversity of arthropods and to determine whether genetic modifications alter the structure of arthropods food webs. A total number of 399,239 arthropod individuals were used for analyses. The trophic groups' number and the links between them indicated that neither the higher magnitude of Bt toxins (included resistance against insect, and against both insects and glyphosate) nor the extra glyphosate treatment changed the structure of food webs. However, differences in the average trophic links/trophic groups were detected between GM and non-GM food webs for herbivore groups and plants. Also, differences in characteristic path lengths between GM and non-GM food webs for herbivores were observed. Food webs parameterized based on 2-year in-field assessments, and their properties can be considered a useful and simple tool to evaluate the effects of Bt toxins on non-target organisms.

Global synthesis suggests that food web connectance correlates to invasion resistance

Biological invasions are a key component of global change, and understanding the drivers of global invasion patterns will aid in assessing and mitigating the impact of invasive species. While invasive species are most often studied in the context of one or two trophic levels, in reality species invade communities comprised of complex food webs. The complexity and integrity of the native food web may be a more important determinant of invasion success than the strength of interactions between a small subset of species within a larger food web. Previous efforts to understand the relationship between food web properties and species invasions have been primarily theoretical and have yielded mixed results. Here, we present a synthesis of empirical information on food web connectance and species invasion success gathered from different sources (estimates of food web connectance from the primary literature and estimates of invasion success from the Global Invasive Species Database as well as the primary literature). Our results suggest that higher-connectance food webs tend to host fewer invaders and exert stronger biotic resistance compared to low-connectance webs. We argue that while these correlations cannot be used to infer a causal link between food web connectance and habitat invasibility, the promising findings beg for further empirical research that deliberately tests for relationships between food web connectance and invasion.

Exploring the "Middle Earth" of network spectra via a Gaussian matrix function

We study a Gaussian matrix function of the adjacency matrix of artificial and real-world networks. We motivate the use of this function on the basis of a dynamical process modeled by the time-dependent Schrödinger equation with a squared Hamiltonian. In particular, we study the Gaussian Estrada index-an index characterizing the importance of eigenvalues close to zero. This index accounts for the information contained in the eigenvalues close to zero in the spectra of networks. Such a method is a generalization of the so-called "Folded Spectrum Method" used in quantum molecular sciences. Here, we obtain bounds for this index in simple graphs, proving that it reaches its maximum for star graphs followed by complete bipartite graphs. We also obtain formulas for the Estrada Gaussian index of Erdős-Rényi random graphs and for the Barabási-Albert graphs. We also show that in real-world networks, this index is related to the existence of important structural patterns, such as complete bipartite subgraphs (bicliques). Such bicliques appear naturally in many real-world networks as a consequence of the evolutionary processes giving rise to them. In general, the Gaussian matrix function of the adjacency matrix of networks characterizes important structural information not described in previously used matrix functions of graphs.

Improved prediction of missing protein interactome links via anomaly detection

Interactomes such as Protein interaction networks have many undiscovered links between entities. Experimental verification of every link in these networks is prohibitively expensive, and therefore computational methods to direct the search for possible links are of great value. The problem of finding undiscovered links in a network is also referred to as the link prediction problem. A popular approach for link prediction has been to formulate it as a binary classification problem in which class labels indicate the existence or absence of a link (we refer to these as positive links or negative links respectively) between a pair of nodes in the network. Researchers have successfully applied such supervised classification techniques to determine the presence of links in protein interaction networks. However, it is quite common for protein-protein interaction (PPI) networks to have a large proportion of undiscovered links. Thus, a link prediction approach could incorrectly treat undiscovered positive links as negative links, thereby introducing a bias in the learning. In this paper, we propose to denoise the class of negative links in the training data via a Gaussian process anomaly detector. We show that this significantly reduces the noise due to mislabelled negative links and improves the resulting link prediction accuracy. We evaluate the approach by introducing synthetic noise into the PPI networks and measuring how accurately we can reconstruct the original PPI networks using classifiers trained on both noisy and denoised data. Experiments were performed with five different PPI network datasets and the results indicate a significant reduction in bias due to label noise, and more importantly, a significant improvement in the accuracy of detecting missing links via classification.

Intervality and coherence in complex networks

Food webs-networks of predators and prey-have long been known to exhibit "intervality": species can generally be ordered along a single axis in such a way that the prey of any given predator tend to lie on unbroken compact intervals. Although the meaning of this axis-usually identified with a "niche" dimension-has remained a mystery, it is assumed to lie at the basis of the highly non-trivial structure of food webs. With this in mind, most trophic network modelling has for decades been based on assigning species a niche value by hand. However, we argue here that intervality should not be considered the cause but rather a consequence of food-web structure. First, analysing a set of 46 empirical food webs, we find that they also exhibit predator intervality: the predators of any given species are as likely to be contiguous as the prey are, but in a different ordering. Furthermore, this property is not exclusive of trophic networks: several networks of genes, neurons, metabolites, cellular machines, airports, and words are found to be approximately as interval as food webs. We go on to show that a simple model of food-web assembly which does not make use of a niche axis can nevertheless generate significant intervality. Therefore, the niche dimension (in the sense used for food-web modelling) could in fact be the consequence of other, more fundamental structural traits. We conclude that a new approach to food-web modelling is required for a deeper understanding of ecosystem assembly, structure, and function, and propose that certain topological features thought to be specific of food webs are in fact common to many complex networks.

How phylogeny shapes the taxonomic and functional structure of plant-insect networks

Phylogenetically related species share a common evolutionary history and may therefore have similar traits. In terms of interaction networks, where traits are a major determinant, related species should therefore interact with other species which are also related. However, this prediction is challenged by current evidence that there is a weak, albeit significant, phylogenetic signal in species' taxonomic niche, i.e., the identity of interacting species. We studied mutualistic and antagonistic plant-insect interaction networks in species-rich alpine meadows and show that there is instead a very strong phylogenetic signal in species' functional niches-i.e., the mean functional traits of their interactors. This pattern emerges because related species tend to interact with species bearing certain traits that allow biotic interactions (pollination, herbivory) but not necessarily with species from all the same evolutionary lineages. Those traits define a set of potential interactors and show clear patterns of phylogenetic clustering on several portions of plants and insect phylogenies. Thus, this emerging pattern of low phylogenetic signal in taxonomic niches but high phylogenetic signal in functional niches may be driven by the interplay between functional trait convergence across plants' and insects' phylogenies and random sampling of the potential interactors.

Communicability angles reveal critical edges for network consensus dynamics

We consider the question of determining how the topological structure influences a consensus dynamical processes taking place on a network. By considering a large data set of real-world networks we first determine that the removal of edges according to their communicability angle, an angle between position vectors of the nodes in an Euclidean communicability space, increases the average time of consensus by a factor of 5.68 in real-world networks. The edge betweenness centrality also identifies, in a smaller proportion, those critical edges for the consensus dynamics; i.e., its removal increases the time of consensus by a factor of 3.70. We justify theoretically these findings on the basis of the role played by the algebraic connectivity and the isoperimetric number of networks on the dynamical process studied and their connections with the properties mentioned before. Finally, we study the role played by global topological parameters of networks on the consensus dynamics. We determine that the network density and the average distance-sum, which is analogous of the node degree for shortest-path distances, account for more than 80% of the variance of the average time of consensus in the real-world networks studied.

Out-of-sample predictions from plant-insect food webs: robustness to missing and erroneous trophic interaction records

With increasing biotic introductions, there is a great need for predictive tools to anticipate which new trophic interactions will develop and which will not. Phylogenetic constraint of interactions in both native and novel food webs can make some novel interactions predictable. However, many food webs are sparsely sampled, or may include inaccurate interactions. In such cases, it is unclear whether modeling methods are still useful to anticipate novel interactions. We ran bootstrap simulations of host-use models on a Lepidoptera-plant data set to remove native trophic records or add erroneous records in order to observe the effect of missing or erroneous data on the prediction of interactions with novel plants. We found that the model was robust to a large amount of missing interaction records, but lost predictive power with the addition of relatively few erroneous interaction records. The loss of predictive power with missing records was due to inaccuracy in estimating phylogenetic distance between native and novel hosts. Removal of interaction records proportionally to their encounter frequency in the field had little effect on the loss of predictive power. Host-use models may have immediate value for predicting novel interactions from large, but sparsely sampled databases of trophic interactions.

Effects of spatial scale of sampling on food web structure

This study asks whether the spatial scale of sampling alters structural properties of food webs and whether any differences are attributable to changes in species richness and connectance with scale. Understanding how different aspects of sampling effort affect ecological network structure is important for both fundamental ecological knowledge and the application of network analysis in conservation and management. Using a highly resolved food web for the marine intertidal ecosystem of the Sanak Archipelago in the Eastern Aleutian Islands, Alaska, we assess how commonly studied properties of network structure differ for 281 versions of the food web sampled at five levels of spatial scale representing six orders of magnitude in area spread across the archipelago. Species (S) and link (L) richness both increased by approximately one order of magnitude across the five spatial scales. Links per species (L/S) more than doubled, while connectance (C) decreased by approximately two-thirds. Fourteen commonly studied properties of network structure varied systematically with spatial scale of sampling, some increasing and others decreasing. While ecological network properties varied systematically with sampling extent, analyses using the niche model and a power-law scaling relationship indicate that for many properties, this apparent sensitivity is attributable to the increasing S and decreasing C of webs with increasing spatial scale. As long as effects of S and C are accounted for, areal sampling bias does not have a special impact on our understanding of many aspects of network structure. However, attention does need be paid to some properties such as the fraction of species in loops, which increases more than expected with greater spatial scales of sampling.

What Can Interaction Webs Tell Us About Species Roles?

The group model is a useful tool to understand broad-scale patterns of interaction in a network, but it has previously been limited in use to food webs, which contain only predator-prey interactions. Natural populations interact with each other in a variety of ways and, although most published ecological networks only include information about a single interaction type (e.g., feeding, pollination), ecologists are beginning to consider networks which combine multiple interaction types. Here we extend the group model to signed directed networks such as ecological interaction webs. As a specific application of this method, we examine the effects of including or excluding specific interaction types on our understanding of species roles in ecological networks. We consider all three currently available interaction webs, two of which are extended plant-mutualist networks with herbivores and parasitoids added, and one of which is an extended intertidal food web with interactions of all possible sign structures (+/+, -/0, etc.). Species in the extended food web grouped similarly with all interactions, only trophic links, and only nontrophic links. However, removing mutualism or herbivory had a much larger effect in the extended plant-pollinator webs. Species removal even affected groups that were not directly connected to those that were removed, as we found by excluding a small number of parasitoids. These results suggest that including additional species in the network provides far more information than additional interactions for this aspect of network structure. Our methods provide a useful framework for simplifying networks to their essential structure, allowing us to identify generalities in network structure and better understand the roles species play in their communities.

The Ontogenetically Variable Trophic Niche of a Praying Mantid Revealed by Stable Isotope Analysis

Praying mantids have been shown to exert strong influences on arthropod community composition. However, they may not occupy the same trophic level throughout their lives. Trophic shifting over a life cycle could explain the documented variation in results from field studies, but specific interactions of predators within food webs have been difficult to determine simply by comparing control and treatment assemblages in field experiments. We examined the trophic position of the Chinese praying mantid, Tenodera aridifolia sinensis (Saussure), using stable isotope analysis (SIA). We measured the δ(13)C and δ(15)N of field-collected arthropods, and of laboratory groups of mantids fed known diets of these arthropods chosen from the most abundant trophic guilds: herbivores (sap feeders and plant chewers), and carnivores. We also collected mantids from the field over a growing season and compared their SIA values to those of the laboratory groups. Both δ(13)C and δ(15)N of mantids fed carnivorous prey (spiders or other mantids) were higher than those fed herbivores (grasshoppers). SIA values from field-collected mantids were highly variable, and indicated that they did not take prey from trophic guilds in proportion to their abundances, i.e., were not frequency-dependent predators. Further, δ(15)N decreased from a high at egg hatch to a low at the third instar as early nymphs fed mainly on lower trophic levels, and increased steadily thereafter as they shifted to feeding on higher levels. We suggest that the community impact of generalist predators can be strongly influenced by ontogenetic shifts in diet.

The impact of 850,000 years of climate changes on the structure and dynamics of mammal food webs

Most evidence of climate change impacts on food webs comes from modern studies and little is known about how ancient food webs have responded to climate changes in the past. Here, we integrate fossil evidence from 71 fossil sites, body-size relationships and actualism to reconstruct food webs for six large mammal communities that inhabited the Iberian Peninsula at different times during the Quaternary. We quantify the long-term dynamics of these food webs and study how their structure changed across the Quaternary, a period for which fossil data and climate changes are well known. Extinction, immigration and turnover rates were correlated with climate changes in the last 850 kyr. Yet, we find differences in the dynamics and structural properties of Pleistocene versus Holocene mammal communities that are not associated with glacial-interglacial cycles. Although all Quaternary mammal food webs were highly nested and robust to secondary extinctions, general food web properties changed in the Holocene. These results highlight the ability of communities to re-organize with the arrival of phylogenetically similar species without major structural changes, and the impact of climate change and super-generalist species (humans) on Iberian Holocene mammal communities.