Strong, long-term temporal dynamics of an ecological network

Nature is organized into complex, dynamical networks of species and their interactions, which may influence diversity and stability. However, network research is, generally, short-term and depict ecological networks as static structures only, devoid of any dynamics. This hampers our understanding of how nature responds to larger disturbances such as changes in climate. In order to remedy this we studied the long-term (12-yrs) dynamics of a flower-visitation network, consisting of flower-visiting butterflies and their nectar plants. Global network properties, i.e. numbers of species and links, as well as connectance, were temporally stable, whereas most species and links showed a strong temporal dynamics. However, species of butterflies and plants varied bimodally in their temporal persistance: Sporadic species, being present only 1-2(-5) years, and stable species, being present (9-)11-12 years, dominated the networks. Temporal persistence and linkage level of species, i.e. number of links to other species, made up two groups of species: Specialists with a highly variable temporal persistence, and temporally stable species with a highly variable linkage level. Turnover of links of specialists was driven by species turnover, whereas turnover of links among generalists took place through rewiring, i.e. by reshuffling existing interactions. However, in spite of this strong internal dynamics of species and links the network appeared overall stable. If this global stability-local instability phenomenon is general, it is a most astonishing feature of ecological networks.     

Nested structure is dependent on visitor sex in the flower‒visitor networks in Kyoto,Japan

The characteristics of flower‒visitor networks, comprised of multiple species interacting with each other, predict ecological and evolutionary processes. Intraspecific and interspecific variations in interaction patterns should affect network structures. Because female and male visitors usually differ in flower‐visiting patterns due to mating strategy, visitor sex should affect nestedness, in which specialist species interact with a subset of species that interact with generalist species. I hypothesized that a network of male visitors and flowering plants would be more nested than a female network because males are less picky about which flowers they visit. To examine the effect of visitor sex on nestedness, I used museum specimens of insects and built 11 flower–visitor species networks, each composed of female and male subnetworks, and compared the strength of nestedness and related network metrics between the subnetworks. I found that male subnetworks were significantly more nested than female ones, and species networks were less nested than male or female subnetworks. The result may be attributable to the by‐chance selection of flowers by males. Because a nested structure is predicted to promote community stability in mutualistic flower–visitor networks, the greater nestedness of male subnetworks may suggest a positive effect of male visitors on pollination community stability.     

Application of network theory to potential mycorrhizal networks

The concept of a common mycorrhizal network implies that the arrangement of plants and mycorrhizal fungi in a community shares properties with other networks. A network is a system of nodes connected by links. Here we apply network theory to mycorrhizas to determine whether the architecture of a potential common mycorrhizal network is random or scale-free. We analyzed mycorrhizal data from an oak woodland from two perspectives: the phytocentric view using trees as nodes and fungi as links and the mycocentric view using fungi as nodes and trees as links. From the phytocentric perspective, the distribution of potential mycorrhizal links, as measured by the number of ectomycorrhizal morphotypes on trees of Quercus garryana, was random with a short tail, implying that all the individuals of this species are more or less equal in linking to fungi in a potential network. From the mycocentric perspective, however, the distribution of plant links to fungi was scale-free, suggesting that certain fungus species may act as hubs with frequent connections to the network. Parallels exist between social networks and mycorrhizas that suggest future lines of study on mycorrhizal networks.     

The ‘night shift’: nocturnal pollen‐transport networks in a boreal pine forest

1. Diurnal plant–visitor networks are well studied, but the community‐level dimension of nocturnal visitation by insects has been largely overlooked. 2. This study focused on the role of moths as pollen vectors in a boreal pine forest in Scotland. Light traps were used to sample moths in 20 plots in two consecutive years. The pollen on moths' bodies was identified and pollen grains counted. This information was used to build a nocturnal pollen‐transport network for each year. These are the first networks to characterise a nocturnal plant–visitor community. 3. A total of 4162 moths belonging to 103 species were captured; 25 moth species were found to carry pollen of 12 plant taxa. Adding nocturnal data to diurnal networks increased number of plant taxa, insect species, and unique interactions in the network. 4. Despite differences in species composition, nocturnal networks exhibit similar properties to diurnal networks: significant nestedness, marked asymmetry of interactions, high dependence on a core of generalists, and high inter‐annual variation in species abundances and occurrence of interactions. 5. Traditional diurnal plant–visitor networks exclude a significant component of the community, i.e. nocturnal visitors. Exploring links across boundaries between networks (such as between diurnal and nocturnal networks) will provide a more accurate picture of ecosystem structure and function.     

Flower‐visitor networks only partially predict the function of pollen transport by bees

Mutualistic networks display distinct structural and organizational features such as nestedness, power‐law degree distribution and asymmetric dependencies. Attention is now focused on how these structural properties influence network function. Most plant‐pollinator networks are constructed using records of animals contacting flowers, which is based on the assumption that all visitors to flowers are pollinators; however, animals may visit flowers as nectar robbers, florivores, or to prey upon other visitors. To differentiate potential pollinator interactions from other interaction types, we examined individual bees that had visited flowers to detect if they carried pollen. Using these data, we constructed visitation and pollen‐transport networks for a spinifex‐dominated arid zone grassland. To determine how the structure of the visitation network reflects pollen transport, we compared the two networks using a null model approach to account for differences in network size. Differences in number of species, nestedness and connectance observed between the visitation and pollen‐transport networks were within expected ranges generated under the null model. The pollen‐transport network was more specialized, had lower interaction evenness, and fewer links compared to the visitation network. Almost half the number of species of the visitation network participated in the pollen‐transport network, and one‐third of unique visitation interactions resulted in pollen transport, highlighting that visitation does not always result in pollination. Floral visitor data indicate potential pollen transporters, but inferring pollination function from visitation networks needs to be performed cautiously as pollen transport resulted from both common and rare interactions, and depended on visitor identity. Although visitation and pollen‐transport networks are structurally similar, the function of all species cannot be predicted from the visitation network alone. Considering pollen transport in visitation networks is a simple first step towards determining pollinators from non‐pollinators. This is fundamental for understanding how network structure relates to network function.     

Comparing species interaction networks along environmental gradients

Knowledge of species composition and their interactions, in the form of interaction networks, is required to understand processes shaping their distribution over time and space. As such, comparing ecological networks along environmental gradients represents a promising new research avenue to understand the organization of life. Variation in the position and intensity of links within networks along environmental gradients may be driven by turnover in species composition, by variation in species abundances and by abiotic influences on species interactions. While investigating changes in species composition has a long tradition, so far only a limited number of studies have examined changes in species interactions between networks, often with differing approaches. Here, we review studies investigating variation in network structures along environmental gradients, highlighting how methodological decisions about standardization can influence their conclusions. Due to their complexity, variation among ecological networks is frequently studied using properties that summarize the distribution or topology of interactions such as number of links, connectance, or modularity. These properties can either be compared directly or using a procedure of standardization. While measures of network structure can be directly related to changes along environmental gradients, standardization is frequently used to facilitate interpretation of variation in network properties by controlling for some co‐variables, or via null models. Null models allow comparing the deviation of empirical networks from random expectations and are expected to provide a more mechanistic understanding of the factors shaping ecological networks when they are coupled with functional traits. As an illustration, we compare approaches to quantify the role of trait matching in driving the structure of plant–hummingbird mutualistic networks, i.e. a direct comparison, standardized by null models and hypothesis‐based metaweb. Overall, our analysis warns against a comparison of studies that rely on distinct forms of standardization, as they are likely to highlight different signals. Fostering a better understanding of the analytical tools available and the signal they detect will help produce deeper insights into how and why ecological networks vary along environmental gradients.     

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.     

Pattern of functional extinctions in ecological networks with a variety of interaction types

There is a strong trend of declining populations in many species of both animals and plants. Dwindling numbers of species can eventually lead to their functional extinction. Functional, or ecological, extinction occurs when a species becomes too rare to fulfill its ecological, interactive role in the ecosystem, leading to true (numerical) extinction of other depending species. Recent theoretical work on food webs suggests that the frequency of functional extinction might be surprisingly high. However, little is known about the risk of functional species extinctions in networks with other types of interactions than trophic ones. Here, we explore the frequency of functional extinctions in model ecological networks having different proportions of antagonistic and mutualistic links. Furthermore, we investigate the topological relationship between functionally and numerically extinct species. We find that (1) the frequency of functional extinctions is higher in networks containing a mixture of antagonistic and mutualistic interactions than in networks with only one type of interaction, (2) increased mortality rate of species having both mutualistic and antagonistic links is more likely to lead to extinction of another species than to extinction of the species itself compared to species having only mutualistic or antagonistic links, and (3) trophic distance (shortest path) between functionally and numerically extinct species is, on average, longer than one, indicating the importance of indirect effects. These results generalize the findings of an earlier study on food webs, demonstrating the potential importance of functional extinction in a variety of ecological network types.     

How structure determines correlations in neuronal networks

Networks are becoming a ubiquitous metaphor for the understanding of complex biological systems, spanning the range between molecular signalling pathways, neural networks in the brain, and interacting species in a food web. In many models, we face an intricate interplay between the topology of the network and the dynamics of the system, which is generally very hard to disentangle. A dynamical feature that has been subject of intense research in various fields are correlations between the noisy activity of nodes in a network. We consider a class of systems, where discrete signals are sent along the links of the network. Such systems are of particular relevance in neuroscience, because they provide models for networks of neurons that use action potentials for communication. We study correlations in dynamic networks with arbitrary topology, assuming linear pulse coupling. With our novel approach, we are able to understand in detail how specific structural motifs affect pairwise correlations. Based on a power series decomposition of the covariance matrix, we describe the conditions under which very indirect interactions will have a pronounced effect on correlations and population dynamics. In random networks, we find that indirect interactions may lead to a broad distribution of activation levels with low average but highly variable correlations. This phenomenon is even more pronounced in networks with distance dependent connectivity. In contrast, networks with highly connected hubs or patchy connections often exhibit strong average correlations. Our results are particularly relevant in view of new experimental techniques that enable the parallel recording of spiking activity from a large number of neurons, an appropriate interpretation of which is hampered by the currently limited understanding of structure-dynamics relations in complex networks.     

Effect of temporal data aggregation on the perceived structure of a quantitative plant–floral visitor network

Seasonal turnover in plant and floral visitor communities changes the structure of the network of interactions they are involved in. Despite the dynamic nature of plant–visitor networks, a usual procedure is to pool year‐round interaction data into a single network which may result in a biased depiction of the real structure of the interaction network. The annual temporal dynamics and the effect of merging monthly data have previously been described for qualitative data (i.e. describing the occurrence of interactions) alone, while its quantitative aspect (i.e. the actual frequency with which interactions occur) remain little explored. For this, we built a set of 12 monthly networks describing year‐round plant–floral visitor interactions in a 30‐hectare planted forest and its adjacent agricultural landscape at Bahauddin Zakariya University Multan, Pakistan. A total of 80 plant and 162 insect species, which engaged in 1573 unique interactions, were recorded. Most network properties (particularly the number of plants, visitors and unique interactions) varied markedly during the year. Data aggregation showed that while animal species, plant species, unique interaction, weighted nestedness, interaction diversity and robustness increased, connectance and specialization decreased. The only metric which seemed relatively unaffected by data pooling was interaction evenness. In general, quantitative metrics were relatively less affected by temporal data aggregation than qualitative ones. Avoiding data aggregation not only gives a more realistic depiction of the dynamic nature of plant–visitor community networks, but also avoids biasing network metrics and, consequently, their expected response to disturbances such as the loss of species.     

Cheaters in mutualism networks

Mutualism-network studies assume that all interacting species are mutualistic partners and consider that all links are of one kind. However, the influence of different types of links, such as cheating links, on network organization remains unexplored. We studied two flower-visitation networks (Malpighiaceae and Bignoniaceae and their flower visitors), and divide the types of link into cheaters (i.e. robbers and thieves of flower rewards) and effective pollinators. We investigated if there were topological differences among networks with and without cheaters, especially with respect to nestedness and modularity. The Malpighiaceae network was nested, but not modular, and it was dominated by pollinators and had much fewer cheater species than Bignoniaceae network (28% versus 75%). The Bignoniaceae network was mainly a plant–cheater network, being modular because of the presence of pollen robbers and showing no nestedness. In the Malpighiaceae network, removal of cheaters had no major consequences for topology. In contrast, removal of cheaters broke down the modularity of the Bignoniaceae network. As cheaters are ubiquitous in all mutualisms, the results presented here show that they have a strong impact upon network topology.     

Volatility of network indices due to undersampling of intraspecific variation in plant–insect interactions

Appropriate sampling effort of interaction networks is necessary to extract robust indices describing the structure of species interactions. Here we show that time-invariant variation in the composition and diversity of interaction partners of plant individuals of the same species explains volatility in aggregate network statistics due to undersampling. Within a multi-species pollinator–plant interaction matrix, we replaced the interactions observed on multiple individuals of a single plant species (Sinapis arvensis, pooled interactions) with the plant–insect interactions observed on a single plant individual. In the resampling approach, we considered the interactions of 1 to 84 S. arvensis individuals in different combinations. For each resampled network, several commonly applied aggregated statistics were calculated to test how intraspecific variation affects the properties of a multi-species network. Our results showed that aggregate statistics are sensitive towards qualitative and quantitative intraspecific variation of flower–visitor interactions within a multi-species network, which may affect the ecological interpretation about the properties of a community. These findings challenge the robustness of commonly applied network indices, confirm the urge for a sufficient and representative sampling of interactions, and emphasize the significance of intraspecific variation in the context of communities and networks.     

Evaluating the Spatio-Temporal Factors that Structure Network Parameters of Plant-Herbivore Interactions

Despite the dynamic nature of ecological interactions, most studies on species networks offer static representations of their structure, constraining our understanding of the ecological mechanisms involved in their spatio-temporal stability. This is the first study to evaluate plant-herbivore interaction networks on a small spatio-temporal scale. Specifically, we simultaneously assessed the effect of host plant availability, habitat complexity and seasonality on the structure of plant-herbivore networks in a coastal tropical ecosystem. Our results revealed that changes in the host plant community resulting from seasonality and habitat structure are reflected not only in the herbivore community, but also in the emergent properties (network parameters) of the plant-herbivore interaction network such as connectance, selectiveness and modularity. Habitat conditions and periods that are most stressful favored the presence of less selective and susceptible herbivore species, resulting in increased connectance within networks. In contrast, the high degree of selectivennes (i.e. interaction specialization) and modularity of the networks under less stressful conditions was promoted by the diversification in resource use by herbivores. By analyzing networks at a small spatio-temporal scale we identified the ecological factors structuring this network such as habitat complexity and seasonality. Our research offers new evidence on the role of abiotic and biotic factors in the variation of the properties of species interaction networks.     

Design of a network with state stability

Designing a network with given functions or reconstruct a network based on its dynamical behavior is an important problem in the study of complex systems. In this paper, we put forward certain principles in constructing a network with state stability. We show that a necessary and sufficient condition to design networks with a global fixed point is that active nodes inhibit inactive nodes, while the latter activate the former directly or indirectly. We also designed networks based on basic modules, where each basic module consists a sub-network, they communicate through the inhibition link from each activator in lower module to the inhibitor of upper module. We found that long activation links, i.e. indirect activation links are important to the formation of convergence trajectory. We believe that these principles may help us to understand the topology of biological networks.     

An Adaptive Complex Network Model for Brain Functional Networks

Brain functional networks are graph representations of activity in the brain, where the vertices represent anatomical regions and the edges their functional connectivity. These networks present a robust small world topological structure, characterized by highly integrated modules connected sparsely by long range links. Recent studies showed that other topological properties such as the degree distribution and the presence (or absence) of a hierarchical structure are not robust, and show different intriguing behaviors. In order to understand the basic ingredients necessary for the emergence of these complex network structures we present an adaptive complex network model for human brain functional networks. The microscopic units of the model are dynamical nodes that represent active regions of the brain, whose interaction gives rise to complex network structures. The links between the nodes are chosen following an adaptive algorithm that establishes connections between dynamical elements with similar internal states. We show that the model is able to describe topological characteristics of human brain networks obtained from functional magnetic resonance imaging studies. In particular, when the dynamical rules of the model allow for integrated processing over the entire network scale-free non-hierarchical networks with well defined communities emerge. On the other hand, when the dynamical rules restrict the information to a local neighborhood, communities cluster together into larger ones, giving rise to a hierarchical structure, with a truncated power law degree distribution.     

Motifs in bipartite ecological networks: uncovering indirect interactions

Indirect interactions play an essential role in governing population, community and coevolutionary dynamics across a diverse range of ecological communities. Such communities are widely represented as bipartite networks: graphs depicting interactions between two groups of species, such as plants and pollinators or hosts and parasites. For over thirty years, studies have used indices, such as connectance and species degree, to characterise the structure of these networks and the roles of their constituent species. However, compressing a complex network into a single metric necessarily discards large amounts of information about indirect interactions. Given the large literature demonstrating the importance and ubiquity of indirect effects, many studies of network structure are likely missing a substantial piece of the ecological puzzle. Here we use the emerging concept of bipartite motifs to outline a new framework for bipartite networks that incorporates indirect interactions. While this framework is a significant departure from the current way of thinking about bipartite ecological networks, we show that this shift is supported by analyses of simulated and empirical data. We use simulations to show how consideration of indirect interactions can highlight differences missed by the current index paradigm that may be ecologically important. We extend this finding to empirical plant–pollinator communities, showing how two bee species, with similar direct interactions, differ in how specialised their competitors are. These examples underscore the need to not rely solely on network‐ and species‐level indices for characterising the structure of bipartite ecological networks.     

The smallest of all worlds: pollination networks

A pollination network may be either 2-mode, describing trophic and reproductive interactions between communities of flowering plants and pollinator species within a well-defined habitat, or 1-mode, describing interactions between either plants or pollinators. In a 1-mode pollinator network, two pollinator species are linked to each other if they both visit the same plant species, and vice versa for plants. Properties of 2-mode networks and their derived 1-mode networks are highly correlated and so are properties of 1-mode pollinator and 1-mode plant networks. Most network properties are scale-dependent, i.e. they are dependent upon network size. Pollination networks have the strongest small-world properties of any networks yet studied, i.e. all species are close to each other (short average path length) and species are highly clustered. Species in pollination networks are much more densely linked than species in traditional food webs, i.e. they have a higher density of links, a shorter distance between species, and species are more clustered.     

Rewiring and indirect effects underpin modularity reshuffling in a marine food web under environmental shifts

Species are characterized by physiological and behavioral plasticity, which is part of their response to environmental shifts. Nonetheless, the collective response of ecological communities to environmental shifts cannot be predicted from the simple sum of individual species responses, since co‐existing species are deeply entangled in interaction networks, such as food webs. For these reasons, the relation between environmental forcing and the structure of food webs is an open problem in ecology. To this respect, one of the main problems in community ecology is defining the role each species plays in shaping community structure, such as by promoting the subdivision of food webs in modules—that is, aggregates composed of species that more frequently interact—which are reported as community stabilizers. In this study, we investigated the relationship between species roles and network modularity under environmental shifts in a highly resolved food web, that is, a “weighted” ecological network reproducing carbon flows among marine planktonic species. Measuring network properties and estimating weighted modularity, we show that species have distinct roles, which differentially affect modularity and mediate structural modifications, such as modules reconfiguration, induced by environmental shifts. Specifically, short‐term environmental changes impact the abundance of planktonic primary producers; this affects their consumers’ behavior and cascades into the overall rearrangement of trophic links. Food web re‐adjustments are both direct, through the rewiring of trophic‐interaction networks, and indirect, with the reconfiguration of trophic cascades. Through such “systemic behavior,” that is, the way the food web acts as a whole, defined by the interactions among its parts, the planktonic food web undergoes a substantial rewiring while keeping almost the same global flow to upper trophic levels, and energetic hierarchy is maintained despite environmental shifts. This behavior suggests the potentially high resilience of plankton networks, such as food webs, to dramatic environmental changes, such as those provoked by global change.