NOS: a software suite to compute node overlap and segregation in ecological networks

Investigating the structure of ecological networks can help unravel the mechanisms promoting and maintaining biodiversity. Recently, Strona and Veech 2015 (A new measure of ecological network structure based on node overlap and segregation. – Methods Ecol. Evol. 6: 907–915) introduced a new metric (??, pronounced ‘nos’), that allows assessment of structural patterns in networks ranging from complete node segregation to perfect nestedness, and that also provides a visual and quantitative assessment of the degree of network modularity. The ?? metric permits testing of a wide range of hypotheses regarding the tendency for species to share interacting partners by taking into account ecologically plausible species interactions based on constraints such as trophic levels and habitat preference. Here we introduce NOS, a software suite (including a web interface freely accessible at  http://nos.alwaysdata.net , an executable program, and Python and R packages) that makes it possible to exploit the full potential of this method. Besides computing node overlap and segregation (??), the software provides different functions to automatically identify a set of possible resource–consumer interactions in food webs based on trophic levels. As an example of application, we analyzed two well‐resolved high‐latitude marine food webs, showing that an explicit a priori consideration of trophic levels is fundamental for a proper assessment of food web structure.     

Complex life cycles in a pond food web: effects of life stage structure and parasites on network properties,trophic positions and the fit of a probabilistic niche model

Most food webs use taxonomic or trophic species as building blocks, thereby collapsing variability in feeding linkages that occurs during the growth and development of individuals. This issue is particularly relevant to integrating parasites into food webs because parasites often undergo extreme ontogenetic niche shifts. Here, we used three versions of a freshwater pond food web with varying levels of node resolution (from taxonomic species to life stages) to examine how complex life cycles and parasites alter web properties, the perceived trophic position of organisms, and the fit of a probabilistic niche model. Consistent with prior studies, parasites increased most measures of web complexity in the taxonomic species web; however, when nodes were disaggregated into life stages, the effects of parasites on several network properties (e.g., connectance and nestedness) were reversed, due in part to the lower trophic generality of parasite life stages relative to free-living life stages. Disaggregation also reduced the trophic level of organisms with either complex or direct life cycles and was particularly useful when including predation on parasites, which can inflate trophic positions when life stages are collapsed. Contrary to predictions, disaggregation decreased network intervality and did not enhance the fit of a probabilistic niche model to the food webs with parasites. Although the most useful level of biological organization in food webs will vary with the questions of interest, our results suggest that disaggregating species-level nodes may refine our perception of how parasites and other complex life cycle organisms influence ecological networks.     

On the centrality and uniqueness of species from the network perspective

Identifying important species for maintaining ecosystem functions is a challenge in ecology. Since species are components of food webs, one way to conceptualize and quantify species importance is from a network perspective. The importance of a species can be quantified by measuring the centrality of its position in a food web, because a central node may have greater influence on others in the network. A species may also be important because it has a unique network position, such that its loss cannot be easily compensated. Therefore, for a food web to be robust, we hypothesize that central species must be functionally redundant in terms of their network position. In this paper, we test our hypothesis by analysing the Prince William Sound ecosystem. We found that species centrality and uniqueness are negatively correlated, and such an observation is also carried over to other food webs.     

Indirect Energy Flows in Niche Model Food Webs: Effects of Size and Connectance

Indirect interactions between species have long been of interest to ecologists. One such interaction type takes place when energy or materials flow via one or more intermediate species between two species with a direct predator-prey relationship. Previous work has shown that, although each such flow is small, their great number makes them important in ecosystems. A new network analysis method, dynamic environ approximation, was used to quantify the fraction of energy flowing from prey to predator over paths of length greater than 1 (flow indirectness or FI) in a commonly studied food web model. Web structure was created using the niche model and dynamics followed the Yodzis-Innes model. The effect of food web size (10 to 40 species) and connectance (0.1 to 0.48) on FI was examined. For each of 250 model realizations run for each pair of size and connectance values, the FI of every predator-prey interaction in the model was computed and then averaged over the whole network. A classification and regression tree (CART) analysis was then used to find the best predictors of FI. The mean FI of the model food webs is 0.092, with a standard deviation of 0.0279. It tends to increase with system size but peaks at intermediate connectance levels. Of 27 potential predictor variables, only five (mean path length, dominant eigenvalue of the adjacency matrix, connectance, mean trophic level and fraction of species belonging to intermediate trophic levels) were selected by the CART algorithm as best accounting for variation in the data; mean path length and the dominant eigenvalue of the adjacency matrix were dominant.     

Examining the potential effects of species aggregation on the network structure of food webs

One of the key measures that have been used to describe the topological properties of complex networks is the “degree distribution”, which is a measure that describes the frequency distribution of number of links per node. Food webs are complex ecological networks that describe the trophic relationships among species in a community, and the topological properties of empirical food webs, including degree distributions, have been examined previously. Previously, the “niche model” has been shown to accurately predict degree distributions of empirical food webs, however, the niche model-generated food webs were referenced against empirical food webs that had their species grouped together based on their taxonomic and/or trophic relationships (aggregated food webs). Here, we explore the effects of species aggregation on the ability of the niche model to predict the total- (sum of prey and predator links per node), in- (number of predator links per node), and out- (number of prey links per node) degree distributions of empirical food webs by examining two food webs that can be aggregated at different levels of resolution. The results showed that (1) the cumulative total- and out-degree distributions were consistent with the niche model predictions when the species were aggregated, (2) when the species were disaggregated (i.e., higher resolution), there were mixed conclusions with regards to the niche model's ability to predict total- and out-degree distributions, (3) the model's ability to predict the in-degree distributions of the two food webs was generally inadequate. Although it has been argued that universal functional form based on the niche model could describe the degree distribution patterns of empirical food webs, we believe there are some limitations to the model's ability to accurately predict the structural properties of food webs.     

Complex networks: two ways to be robust?

Recent studies of biological networks have focused on the distribution of the number of links per node. However, the connectivity distribution does not uncover all the complexity of their topology. Here, we analyse the relation between the connectivity of a species and the average connectivity of its nearest neighbours in three of the most resolved community food webs. We compare the pattern arising with the one recently reported for protein networks and for a simple null model of a random network. Whereas two highly connected nodes are unlikely to be connected between each other in protein networks, the reverse happens in food webs. We discuss this difference in organization in relation to the robustness of biological networks to different types of perturbation.     

Exploring the evolutionary signature of food webs' backbones using functional traits

Increasing evidence suggests that an appropriate model for food webs, the network of feeding links in a community of species, should take into account the inherent variability of ecological interactions. Harnessing this variability, we will show that it is useful to interpret empirically observed food webs as realisations of a family of stochastic processes, namely random dot‐product graph models. These models provide an ideal extension of food‐web models beyond the limitations of current deterministic or partially probabilistic models. As an additional bene?t, our RDPG framework enables us to identify the pairwise distance structure given by species' functional food‐web traits: this allows for the natural emergence of ecologically meaningful species groups. Lastly, our results suggest the notion that the evolutionary signature in food webs is already detectable in their stochastic backbones, while the contribution of their ?ne wiring is arguable. Synthesis Food webs are influenced by many stochastic processes and are constantly evolving. Here, we treat observed food webs as realisations of random dot‐product graph models (RDPG), extending food‐web modelling beyond the limitations of current deterministic or partially probabilistic models. Our RDPG framework enables us to identify the pairwise‐distance structure given by species' functional food‐web traits, which in turn allows for the natural emergence of ecologically meaningful species groups. It also provides a way to measure the phylogenetic signal present in food webs, which we find is strongest in webs' low‐dimensional backbones.     

Environmentally‐induced noise dampens and reddens with increasing trophic level in a complex food web

Stochastic variability of key abiotic factors including temperature, precipitation and the availability of light and nutrients greatly influences species’ ecological function and evolutionary fate. Despite such influence, ecologists have typically ignored the effect of abiotic stochasticity on the structure and dynamics of ecological networks. Here we help to fill that gap by advancing the theory of how abiotic stochasticity, in the form of environmental noise, affects the population dynamics of species within food webs. We do this by analysing an allometric trophic network model of Lake Constance subjected to positive (red), negative (blue), and non‐autocorrelated (white) abiotic temporal variability (noise) introduced into the carrying capacity of basal species. We found that, irrespective of the colour of the introduced noise, the temporal variability of the species biomass within the network both reddens (i.e. its positive autocorrelation increases) and dampens (i.e. the magnitude of variation decreases) as the environmental noise is propagated through the food web by its feeding interactions from the bottom to the top. The reddening reflects a buffering of the noise‐induced population variability by complex food web dynamics such that non‐autocorrelated oscillations of noise‐free deterministic dynamics become positively autocorrelated. Our research helps explain frequently observed red variability of natural populations by suggesting that ecological processing of environmental noise through food webs with a range of species’ body sizes reddens population variability in nature.     

Biodiversity in model ecosystems, II: species assembly and food web structure

This is the second of two papers dedicated to the relationship between population models of competition and biodiversity. Here, we consider species assembly models where the population dynamics is kept far from fixed points through the continuous introduction of new species, and generalize to such models the coexistence condition derived for systems at the fixed point. The ecological overlap between species and shared preys, that we define here, provides a quantitative measure of the effective interspecies competition and of the trophic network topology. We obtain distributions of the overlap from simulations of a new model based both on immigration and speciation, and show that they are in good agreement with those measured for three large natural food webs. As discussed in the first paper, rapid environmental fluctuations, interacting with the condition for coexistence of competing species, limit the maximal biodiversity that a trophic level can host. This horizontal limitation to biodiversity is here combined with either dissipation of energy or growth of fluctuations, which in our model limit the length of food webs in the vertical direction. These ingredients yield an effective model of food webs that produce a biodiversity profile with a maximum at an intermediate trophic level, in agreement with field studies.     

Identifying compartments in ecological networks based on energy channels

It has been confirmed in many food webs that the interactions between species are divided into “compartments,” that is, subgroups of highly interacting taxa with few weak interactions between the subgroups. Many of the current methods for detecting compartments in food webs are borrowed from network theory, which do little to improve our understanding of the mechanisms underpinning them. Therefore, a method based on ecological context is needed. Here, we develop a new method for detecting compartments in food webs based on the reliance of each node on energy derived from basal resources (i.e., producers or decomposers). Additional Monte Carlo simulations were conducted to test the significance of the compartmentalization. Further, we applied a food web dynamics model to test whether the effects of permutation would be retained within a single compartment. The proposed method identified significant compartments in 23 of the 28 empirical food webs that were investigated. We further demonstrated that the effects of node removal were significantly higher within compartments than between compartments. Our methods and results emphasize the importance of energy channels in forming food web structures, which sheds light on the mechanisms of self‐organization within food webs.     

Food web structure in Mediterranean streams: exploring stabilizing forces in these ecosystems

We constructed the food webs of six Mediterranean streams in order to determine ecological generalities derived from analysis of their structure and to explore stabilizing forces within these ecosystems. Fish, macroinvertebrates, primary producers and detritus are the components of the studied food webs. Analysis focused on a suite of food web properties that describe species’ trophic habits, linkage complexity and food chains. A great structural similarity was found in analyzed food webs; we therefore suggest average values for the structural properties of Mediterranean stream food webs. Percentage of omnivorous species was positively correlated with connectance, and there was a predominance of intermediate trophic level species that had established simple links with detritus. In short, our results suggest that omnivory and the weak interactions of detritivores have a stabilizing role in these food webs.     

Emergence of non-random structure in local food webs generated from randomly structured regional webs

Previous studies have shown that high-resolution, empirical food webs possess a non-random network structure, typically characterized by uniform or exponential degree distributions. However, the empirical food webs that have been investigated for their structural properties represent local communities that are only a subset of a larger pool of regionally coexisting species. Here, we use a simple model to investigate the effects of regional food web structure on local food webs that are assembled by two simple processes: random immigration of species from a source web (regional food web), and random extinction of species within the local web. The model shows that local webs with non-random degree distributions can arise from randomly structured source webs. A comparison of local webs assembled from randomly structured source webs with local webs assembled from source webs generated by the niche model shows that the former have higher species richness at equilibrium, but have a nonlinear response to changing extinction rates. These results imply that the network structure of regional food webs can play a significant role in the assembly and dynamics of local webs in natural ecosystems. With natural landscapes becoming increasingly fragmented, understanding such structure may be a necessary key to understanding the maintenance and stability of local species diversity.     

Relevance of evolutionary history for food web structure

Explaining the structure of ecosystems is one of the great challenges of ecology. Simple models for food web structure aim at disentangling the complexity of ecological interaction networks and detect the main forces that are responsible for their shape. Trophic interactions are influenced by species traits, which in turn are largely determined by evolutionary history. Closely related species are more likely to share similar traits, such as body size, feeding mode and habitat preference than distant ones. Here, we present a theoretical framework for analysing whether evolutionary history--represented by taxonomic classification--provides valuable information on food web structure. In doing so, we measure which taxonomic ranks better explain species interactions. Our analysis is based on partitioning of the species into taxonomic units. For each partition, we compute the likelihood that a probabilistic model for food web structure reproduces the data using this information. We find that taxonomic partitions produce significantly higher likelihoods than expected at random. Marginal likelihoods (Bayes factors) are used to perform model selection among taxonomic ranks. We show that food webs are best explained by the coarser taxonomic ranks (kingdom to class). Our methods provide a way to explicitly include evolutionary history in models for food web structure.     

Exploring the temporal variability of a food web using long‐term biomonitoring data

Ecological communities are constantly being reshaped in the face of environmental change and anthropogenic pressures. Yet, how food webs change over time remains poorly understood. Food web science is characterized by a trade‐off between complexity (in terms of the number of species and feeding links) and dynamics. Topological analysis can use complex, highly resolved empirical food web models to explore the architecture of feeding interactions but is limited to a static view, whereas ecosystem models can be dynamic but use highly aggregated food webs. Here, we explore the temporal dynamics of a highly resolved empirical food web over a time period of 18 years, using the German Bight fish and benthic epifauna community as our case study. We relied on long‐term monitoring ecosystem surveys (from 1998 to 2015) to build a metaweb, i.e. the meta food web containing all species recorded over the time span of our study. We then combined time series of species abundances with topological network analysis to construct annual food web snapshots. We developed a new approach, ‘node‐weighted’ food web metrics by including species abundances to represent the temporal dynamics of food web structure, focusing on generality and vulnerability. Our results suggest that structural food web properties change through time; however, binary food web structural properties may not be as temporally variable as the underlying changes in species composition. Further, the node‐weighted metrics enabled us to detect that food web structure was influenced by changes in species composition during the first half of the time series and more strongly by changes in species dominance during the second half. Our results demonstrate how ecosystem surveys can be used to monitor temporal changes in food web structure, which are important ecosystem indicators for building marine management and conservation plans.     

The phylogenetic component of food web structure and intervality

Despite the exceptional complexity formed by species and their interactions in ecological networks, such as food webs, regularities in the network structures are repeatedly demonstrated. The interactions are determined by the characteristics of a species. The characteristics are in turn determined by the species’ phylogenetic relationships, but also by factors not related to evolutionary history. Here, we test whether species’ phylogenetic relationships provides a significant proxy for food web intervality. We thereafter quantify the degree to which different species traits remain valuable predictors of food web structure after the baseline effect of species’ relatedness has been removed. We find that the phylogenetic relationships provide a significant background from which to estimate food web intervality and thereby structure. However, we also find that there is an important, non-negligible part of some traits, e.g., body size, in food webs that is not accounted for by the phylogenetic relationships. Additionally, both these relationships differ depending if a predator or a prey perspective is adopted. Clearly, species’ evolutionary history as well as traits not determined by phylogenetic relationships shapes predator-prey interactions in food webs, and the underlying evolutionary processes take place on slightly different time scales depending on the direction of predator-prey adaptations.     

Who dominates whom in the ecosystem? Energy flow bottlenecks and cascading extinctions

In this paper, we investigate the problem of secondary extinction in food webs through the use of dominator trees, network topological structures that reduce food webs to linear pathways that are essential for energy delivery. Each species along these chains is responsible for passing energy to the taxa that follow it, and, as such, it is indispensable for their survival; because of this it is said to dominate them. The higher the number of species a node dominates, the greater the impact resulting from its removal. By computing dominator trees for 13 well-studied food webs we obtained for each of them the number of nodes dominated by a single species and the number of nodes that dominate each species. We illustrate the procedure for the Grassland Ecosystem showing the potential of this method for identifying species that play a major role in energy delivery and are likely to cause the greatest damage if removed. Finally, by means of two indices that measure error and attack sensitivity, we confirm a previous hypothesis that food webs are very robust to random loss of species but very fragile to the selective loss of the hubs.     

北京东灵山森林植物多样性的网络结构特征

一个群落可以看作是由物种相互连接的复杂系统,刻画其网络结构有助于深入揭示系统性质以及结构与功能之间的关系。在生态学中,复杂网络理论已被成功应用于食物网与互利网络的结构研究,但尚未检验其刻画生物多样性格局的能力。采用复杂网络理论研究了北京东灵山森林乔木层、灌木层、草本层植物关联关系的网络结构特征及其差异。结果表明,植物物种的共同出现是非随机的,并表现出一定的小世界模式;乔木层、灌木层、草本层植物共同出现的网络在结构特征上存在明显差异,草本层网络比乔木层和灌木层网络更松散且平均路径更长,灌木层和草本层网络的聚类系数高于乔木层且存在度的幂律分布。皆表明复杂网络理论具备反映不同层植物多样性格局差异的能力。     

Numerically dominant species drive patterns in resource use along a vertical gradient in tropical ant assemblages

Resource availability can influence the foraging strategy adopted by different ant species as they endeavor to meet nutrient demands of the colony. In tropical rain forests, environmental conditions including resource availability vary over a vertical gradient. Consequently, nitrogen is predicted to become more limiting than carbohydrates toward the canopy as food webs shift to become more reliant on plant-based resources. We used a “bait-choice” experiment in a tropical rain forest to examine differences in protein and carbohydrate use with height and determined whether there were differences in response between common (numerically dominant) and rare species. Additionally, we investigated the nutrient use at the species level. Using species co-occurrence analysis, we examined interspecific competition by testing the co-occurrence of ant species at the tree level. Over the 12 trees investigated, 124 morphospecies were identified with eight species comprising 90% of total ant abundance. Species richness and protein use increased with height of bait for all species pooled and for common species but not rare species. Correspondingly, relative carbohydrate use decreased with height. We found greater species richness of rare species on carbohydrate baits compared with protein baits. Ant species were randomly distributed among trees when all species were included in co-occurrence analysis. However, when only common species were considered, segregation between species was evident among trees providing evidence for the presence of ant mosaics. Our results suggest that nitrogen limitation in the canopy may not be true for the whole ant assemblage but rather for the few common species.     

Human impacts on minimum subsets of species critical for maintaining ecosystem structure

Humans have indirectly influenced species at lower trophic levels by driving losses of apex consumers. Furthermore, humans have indirectly influenced species at higher trophic levels by driving losses of primary producers. Beyond these broad classes of apex consumers and primary producers, it remains challenging to identify minimum subsets of species that are particularly important for maintaining ecosystem structure and functioning. Here we use a novel method at the intersection of control theory and network theory to identify a minimum set of driver node species upon which ecosystem structure strongly depends. Specifically, humans could unintentionally completely restructure ecosystems (i.e., change species abundances from any initial values to any final values, including zero) by altering the abundances of these few critical driver node species. We then quantify the proportion of these driver nodes that are influenced by humans, top predators, and primary producers in several marine food webs. We find that humans could unintentionally completely restructure marine food webs while only directly influencing less than one in four species. Additionally, humans directly influence: (1) most or all of the species necessary to completely restructure each network, (2) more driver nodes than top predators, and at least as many driver nodes as primary producers, and (3) an increasing proportion of driver nodes over time in the Adriatic Sea. We conclude that humans have potentially huge impacts on marine ecosystems while directly influencing only the relatively small subset of species that are currently fished. It may be possible to reduce unintentional and undesirable cascading human influences by decreasing human impacts on driver node species in these and other food webs.     

Predicting food‐web structure with metacommunity models

Synthesis Metacommunity theory aims to elucidate the relative influence of local and regional‐scale processes in generating diversity patterns across the landscape. Metacommunity research has focused largely on assemblages of competing organisms within a single trophic level. Here, we test the ability of metacommunity models to predict the network structure of the aquatic food web found in the leaves of the northern pitcher plant Sarracenia purpurea. The species‐sorting and patch‐dynamics models most accurately reproduced nine food web properties, suggesting that local‐scale interactions play an important role in structuring Sarracenia food webs. Our approach can be applied to any well‐resolved food web for which data are available from multiple locations. The metacommunity framework explores the relative influence of local and regional‐scale processes in generating diversity patterns across the landscape. Metacommunity models and empirical studies have focused mostly on assemblages of competing organisms within a single trophic level. Studies of multi‐trophic metacommunities are predominantly restricted to simplified trophic motifs and rarely consider entire food webs. We tested the ability of the patch‐dynamics, species‐sorting, mass‐effects, and neutral metacommunity models, as well as three hybrid models, to reproduce empirical patterns of food web structure and composition in the complex aquatic food web found in the northern pitcher plant Sarracenia purpurea. We used empirical data to determine regional species pools and estimate dispersal probabilities, simulated local food‐web dynamics, dispersed species from regional pools into local food webs at rates based on the assumptions of each metacommunity model, and tested their relative fits to empirical data on food‐web structure. The species‐sorting and patch‐dynamics models most accurately reproduced nine food web properties, suggesting that local‐scale interactions were important in structuring Sarracenia food webs. However, differences in dispersal abilities were also important in models that accurately reproduced empirical food web properties. Although the models were tested using pitcher‐plant food webs, the approach we have developed can be applied to any well‐resolved food web for which data are available from multiple locations.