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Network analysis, a branch of discrete mathematics that quantifies the structure of links between a set of nodes, is emerging as a powerful methodology to approach complex ecological interactions.
There has been a rapidly increasing body of research targeting the topological description of trophic interactions. Here we categorize studies applying a topological approach to empirical trophic networks, with the aim of identifying recent trends and deficiencies in this approach to analyse trophic interactions.
There were biases in the taxonomic groups addressed and in the methodological approaches used for data collection and analyses. Studies on antagonistic interactions were generally focused on a single kind of bipartite interaction, and most studies compared network attributes across time, ecosystems or treatments.
We encourage a broader use of both interlinked and unipartite networks that would allow for describing indirect effects of trophic interactions, as well as time series of networks across seasons and phenological states of organisms. We also noted shortages of studies identifying interaction structures across levels of organization, on the correspondence between network structure and function, and particularly of studies on the behaviour of trophic networks in the face of environmental perturbations, which could provide guidance for preserving ecological interactions.
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Biodiversity was traditionally quantified by species richness and the evenness of species abundances (Wilson & Peter 1988; Magurran 2004). However, there is a growing awareness that the diversity of an ecosystem relies not only on the taxonomic richness of the organisms inhabiting it, but also on the diversity of the interactions between those organisms (Groves et al. 2002; Van der Putten et al. 2004; Reiss et al. 2009). Conservation biologists are subsequently moving their focus from preserving individual species into retaining ecosystem functions and services (Reiss et al. 2009; Caliman et al. 2010; Dalerum et al. 2012), which rely on the structure of the interactions between species (Jordán 2009; Montoya & Raffaelli 2010). Failure in preserving links between species may lead to the loss of one or several of the interacting species, which subsequently could permeate across the ecosystem causing unanticipated secondary extinctions (Solé & Montoya 2001; Dunne, Williams & Martinez 2002) or ecological state transitions (Scheffer et al. 2001).
The increased awareness of the importance of ecological interactions has been paralleled by dramatic improvements in our abilities to describe them. These improvements have emerged from the field of graph theory, a branch of discrete mathematics that describes the topological properties, that is, the continuity and connectivity of nodes and interaction links (Euler 1741). Although an old discipline (e.g. Euler 1741), network analysis has undergone a renaissance since the late 1990s, primarily caused by an increased focus on empirical networks that lead to the identification of small world (Watts & Strogatz 1998) and scale-free and self-organizing properties (Barabasi & Albert 1999). These theoretical breakthroughs were accompanied by the availability of more complete and consistent interaction data, more powerful computers and software, and subsequent development of more sophisticated topological indices (Batagelj & Mrvar 1998; Guimaraes & Guimaraes 2006; Newman, Barabasi & Watts 2006; Bascompte 2007; Dormann, Gruber & Jochen 2008). Under this approach, ecological interactions can be represented as graphs or networks, which are mathematical abstractions that describe relations between a set of nodes. In ecological applications, these nodes typically represent ecological entities which are connected by links that represent ecological interactions (Elton 1927; Harary 1961; Sugihara 1984).
Two approaches dominate the study of ecological networks. The community approach quantifies the topological architecture of trophic networks according to the occurrence and strength of interactions between ecological entities (Elton 1927; MacArthur 1955), whereas the ecosystem approach quantifies the strength of interactions, representing pathways of biomass flows (Lindeman 1942; Odum 1953), without an explicit focus on quantifying the network structure itself. In community studies, the different topological attributes characterize the structure of ecological networks (May 1973; McCann 2000; Tylianakis et al. 2010), which for instance can be used to predict network robustness against perturbations (May 1972). The central role of trophic interactions for ecosystem dynamics, coupled with the extraordinary applicability of network methodology to address such interactions (Memmott 2009; Hegland et al. 2010), has led to a very rapid expansion in the use of network analyses in trophic ecology (Ings et al. 2009).
In this study, we aim to characterize research trends in this rapidly expanding body of work, partly to synthesize current state of knowledge and partly to identify areas that have been underrepresented, which would allow for recommendations for further directions in research on trophic network structure and behaviour.
Materials and methods
Selection of studies
We focused our characterization on studies with a topological network approach to trophic interactions, that is, studies using a community (Elton 1927) rather than an ecosystem approach (Lindeman 1942). We constrained our selection to studies published since the upsurge of network analysis stimulated by the multidisciplinary interest on complex, nonrandom, real-world networks and by the development of new topological models (Watts & Strogatz 1998; Albert, Jeong & Barabási 1999; Barabasi & Albert 1999; Williams & Martínez 2000). Our search therefore includes publications from 1998, when this transition in network analysis arose, until April 2012 when the search was performed.
We did not restrict studies to traditional food webs (i.e. feeding interactions such as predator–prey or primary resource–consumer relationships, Lawton 1989), but also included studies on other trophic interactions such as pollination, seed dispersal mutualisms and parasitism (Lafferty, Dobson & Kuris 2006; Olff et al. 2009). Relevant studies were identified through ISI Web of Knowledge. In order to create an unbiased and representative sample to base our characterization of studies using a topological approach to trophic interactions on, we only included studies that stringently adhered to a priori-defined search criteria. Although such an approach may not capture all the relevant literature, including some of its key references, it is a necessary approach since it is the only way to guarantee an unbiased selection of studies to base the evaluation on (i.e. analogous to any statistical sampling process). Furthermore, the exclusion of individual studies was not critical, since we did not weight each included study by its scientific significance.
To guarantee an unbiased representation of the distribution of studies across different interaction types, we combined the search term ‘network analys*’ with the three terms that identify the main types of trophic interactions as searching terms: ‘food web*’; ‘mutualistic’; ‘host parasit*’. To also capture studies with a less well-defined language, we also combined the search term ‘network analys*’ to general search terms: ‘ecology’ and ‘trophic’. Finally, we also searched for the two general search terms ‘ecological network*’ and ‘trophic network*’. For studies that matched any of these search combinations, we applied three further criteria for inclusion into the data base. First, we only included studies that were published as articles in peer-reviewed journals. Secondly, we only included studies that were based on empirical data sets of trophic networks, that is, structures that are clearly arranged in stratified sets of ecological entities between which trophic links exist. Such trophic networks have a typical characteristic spanning tree shape (Caldarelli 2007). This criterion therefore excludes studies on cyclic food webs which are more congruent with the ecosystem network approach. Thirdly, we only included studies that analyse interaction matrices using the strictly structural approach of topological analysis that characterizes the community approach to ecological network analyses.
We first filtered studies by title to remove spurious hits and scanned the abstracts of the remaining studies to identify works meeting criteria 2 and 3. Whenever the information contained in title and abstract was not sufficient to clarify whether these criteria were met, the article was read to confirm its relevance. Although 1265 publications were identified by our search terms, only 108 matched our criteria for inclusion.
Categorization of studies and data analysis
We classed all selected studies according to two categorizations (Appendix S1, Supporting Information). First, by the nature of the described interactions, that is, antagonistic or mutualistic; and secondly, by the interaction type. For mutualistic interactions, this classification included plant–arbuscular mycorrhizal fungi interactions, plant–ant interactions, pollination and seed dispersal. For antagonistic interactions, it included plant–herbivore, prey–predator and host–parasite/parasitoid interactions.
We further conducted a more refined characterization on the 54 studies of antagonistic interactions, partly because this type of interaction provides more well-defined and therefore more interpretable classification criteria and partly because many of the most ecologically important trophic relationships are antagonistic (e.g. predator–prey or host–parasite relationships). We first categorized studies on antagonistic interactions using three biological study descriptors: general biome, the number of trophic levels included, and taxonomic categories of consumers and resources (Table 1). The taxonomic categories of consumers and resources were only recorded for bipartite networks, since nodes in multitrophic networks serve both as resources and as consumers (Table 1).
Table 1. Categories used in each of the classifications of the studies on antagonistic interactions
Unipartite network/bipartite network/network of networks/multitrophic network
Consumer taxonomic category (only in bipartite networks)
Ontogenic state/individual/species/taxonomic groups/trophic or functional groups
Link sampling method
Literature based (fully or partially)/collection in trap nests, parasite infestation in captured animals, emergence from collected samples, reared larvae/faecal or stomach contents/direct observations or visitation frequency in the field
Network structure characterization/node-specific or link-specific function within the network/network comparisons across time, space or treatments/comparisons across interaction types/factors affecting the interaction pattern observed/perturbations effect on network structure and stability/relationships between network indices/simulation of sequences of nodes or links loss
Topological indices measured
Network richness/connectivity/degree distribution/centrality/clustering/nestedness/specialization/niche overlap/intervality/robustness or extinction measures/topological importance and functionality
The observed configuration of a network can be highly affected by methodological aspects such as the sampling intensity (Winemiller 1989; Goldwasser & Roughgarden 1997), qualitative vs. quantitative link assessment (Cohen et al. 1993; Bersier, Banasek-Richter & Cattin 2002) or the way that taxa are aggregated (Sugihara, Schoenly & Trombla 1989; Martinez 1991). We therefore categorized studies according to network quality described as network resolution (i.e. the taxonomic or functional grouping level of each node in the network), network type (categorizing whether or not the links were binary or weighted by some measure of interaction strength) and link sampling method (categorizing the type of data acquisition; Table 1).
Finally, we categorized the purpose of the studies as level of the network analysis (i.e. whether the study focused on node or network properties), the questions addressed (the ecological relevance of each of the categorized questions are outlined in Table 2) and the topological indices measured (Table 1; for topological indices, see also Appendix S2, Supporting Information).
Table 2. Ecological relevance of questions addressed in network analysis studies
Network structure characterization
To describe the richness of ecological entities at different trophic levels, the diversity, strength and patterns of the trophic interactions between identities and their degree of dietary specialization/generalism
Node-specific or link-specific function within the network
To describe the roles of individual ecological entities and links and their contribution to the structure of trophic interactions
Network comparisons across time, space or treatments
To determine the differences and commonalities in the patterns of trophic interactions across seasons, sites or treatments
Network comparisons across interaction types
To determine the differences and commonalities in the patterns of trophic interactions when considering trophic relationships of different nature (e.g. predation, parasitism, herbivory, trophic mutualisms)
Factors affecting the interaction pattern observed
To identify the methodological factors or the morphologic, taxonomic, ecologic and functional traits of individual ecological entities that may affect the identity and strength of the trophic interactions held
Perturbations effect on network structure and stability
To analyse the resilience of the structure of trophic interactions against environmental perturbations
Relationships between network indices
To test the associations between the different topological descriptors of the structure of trophic interactions
Simulation of sequences of nodes or links loss
To predict the potential effect of the extinction of ecological entities or interaction mismatches on the original patterns of trophic interactions
We counted the number of studies that corresponded to each category. We allowed studies to be entered into more than one category within each categorization except for the categorization of network type and analyses level. A list of all studies on antagonistic interactions included in the study sample as well as their categorization is given in Appendix S3, Supporting Information.
We evaluated differences among number of studies conducted across and within categorizations using loglinear models. Analyses were performed using R version 2.15.1 for linux (R Development Core Team 2012).
There has been a drastic increase in the proportion of ecological studies that have used network approaches to trophic interactions during the past two decades (Fig. 1).
More studies dealt with mutualistic (65 studies, 55%) than with antagonistic networks (54 studies, 45%). Studies on mutualistic interactions deviated from equal distribution across the different interaction types (χ² = 77.20, d.f. = 2, P < 0.001), with studies on plant–pollinator interactions being the most dominant (Fig. 2a). Studies on antagonistic interactions, on the other hand, did not deviate from equal distribution across the three interaction types (χ² = 4.49, d.f. = 2, P = 0.11; Fig. 2b).
Biological descriptors of studies on antagonistic trophic interactions
The 54 studies focusing on antagonistic trophic interactions did not deviate from even distribution across general biomes (χ² = 1.67, d.f. = 2, P = 0.43). There were, however, significant differences in the number of studies considering different trophic levels (χ² = 65.64, d.f. = 2, P < 0.001), with studies on multitrophic (30 studies, 56%) and bipartite approaches (25 studies, 46%) being the most common (Fig. 3a). Two studies (4%) interconnected bipartite networks, that is, the ‘network of networks’ approach (Pocock, Evans & Memmott 2012), but we found no studies projecting bipartite models into unipartite networks. Furthermore, the number of trophic levels considered varied between biomes (χ² = 14.23, d.f. = 4, P < 0.01), with the bipartite approach being dominant in the terrestrial systems and the multitrophic one in aquatic studies (Fig. 3a). Similarly, there were significant differences in the number of studies on different taxonomic categories, both at the resource (χ² = 47.72, d.f. = 11, P < 0.001) and consumer levels (χ² = 41.08, d.f. = 9, P < 0.001). However, the taxonomic categories did not vary across biomes neither for resources (χ² = 21.32, d.f. = 22, P = 0.50; Fig. 3b) nor for consumers (χ² = 15.79, d.f. = 18, P = 0.61; Fig. 3c).
Network quality of studies on antagonistic trophic interactions
There were significant differences in the number of studies conducted on networks of different resolution (χ² = 48.74, d.f. = 4 P < 0.001, Fig. 4a). More studies did design networks at the species or higher resolution (27 studies, 50%) than at broader taxonomic levels (13 studies, 24%) or at trophic and functional group levels (16 studies, 30%). Extremely highly resolved networks were found in only three studies (4%), in which consumer nodes were individuals of a population. We did not identify any study considering ontogenic states of a species as nodes.
There was a significant deviation from equal distribution of studies conducted on different network types (i.e. weighted, unweighted or both; χ² = 29.20, d.f. = 2, P < 0.001), but the number of studies of different network types did not differ between the different levels of network resolution (χ² = 2.73, d.f. = 8, P = 0.95). Most studies (36 studies, 67%) used unweighted networks while fewer (9 studies; 17%) quantified the interaction strengths in weighted approaches (Fig. 4a). An additional nine studies (17%) used a combination of weighted and unweighted forms of the same network to enable calculation of both weighted and unweighted indices or comparisons between the two network types.
Most of the studies were conducted on networks fully or partially drawn from the literature (46 studies, 85%; χ² = 69.77, d.f. = 3, P < 0.001; Fig. 4b). The studies that directly recorded empirical data to quantify species interactions identified species collected in trap nests, parasites infesting captured animals or reared collected larvae (five studies, 9%), identified species in faecal or stomach contents (seven studies, 13%) or used direct observations of interactions in the field (three studies, 6%), such as visitation frequencies of consumers to resources (Fig. 4b).
Purpose of studies on antagonistic trophic interactions
There were no significant differences in the number of studies conducted at different levels of network analysis (i.e. node vs. network level; χ² = 3.64, d.f. = 2, P = 0.16). However, there was a significant difference in the number of studies addressing the different questions (χ² = 23.49, d.f. = 7, P = 0.01). The predominant study questions addressed the comparison of network attributes across time, ecosystems or treatments (23 studies, 43%), and the factors that influence the interaction patterns observed (23 studies, 43%; Fig. 5a). There was no difference in the number of studies conducted at the different analysis levels across questions (χ² = 16.21, d.f. = 14, P = 0.30).
There was a significant deviation from equal utilization of different indices (χ² = 96.38, d.f. = 10, P < 0.001), with descriptive indices such as network connectivity (42 studies; 78%) and richness (18; 33%) being the most common, followed by those testing for clustered (17; 31%) and nested (15; 28%) patterns in the network (Fig. 5b). The least frequently used indices were robustness or extinction measures (5; 9%), intervality (2; 4%) and niche overlap (1; 2%).
Among the selected studies, we found a bias in the interaction types for mutualistic interactions, with plant–pollinator interactions being the most common, whereas we found equal distribution of studies across the three types of antagonistic interactions. Therefore, although we identified more studies on mutualistic than antagonistic interactions, there appears to be a poor representation of mutualistic interactions beyond plant–pollinator/seed disperser relationships. Among the studies on antagonistic interactions, we found no bias in the three main biomes (i.e. marine, freshwater and terrestrial).
Studies on antagonistic interactions in bipartite networks primarily addressed arthropods as consumers and plants as resources. We note that humans were rarely considered as an additional node in the network (de Visser, Freymann & Olff 2011), but were instead often incorporated in the form of perturbations affecting the network structure (e.g. Montoya et al. 2009; Laliberté & Tylianakis 2010). This suggests that the potential keystone role of humans as network connectors across space and time still remains to be quantified. We also note a general lack of inclusion of detritus as a resource in the sampled studies. The appropriateness of including detritivory (i.e. consumption of nonliving organic matter) as a trophic interaction has been argued (Jordán et al. 2006; Jordán & Osváth 2009), since it consists of a node that only passively receives matter from all other trophic levels. However, detritus has been shown to have a strong effect on the network structure in both aquatic and terrestrial ecosystems (Hagen et al. 2012) and is a central component of food webs (Abarca-Arenas et al. 2007). We therefore suggest that neglecting detritus could severely hamper our abilities to utilize network analyses to enhance our understanding of ecological relationships.
The studies were dominated by the use of multitrophic networks in freshwater and marine ecosystems and bipartite networks in terrestrial ones. Multitrophic approaches display information on trophic cascades (i.e. indirect vertical interactions between species belonging to nonconsecutive trophic levels) that is overlooked in bipartite networks (Montoya et al. 2009). Emerging evidence of trophic cascades in terrestrial environments (Pace et al. 1999), coupled with the accelerating human caused loss of biodiversity (Cardinale et al. 2012), prompts for more studies on multitrophic or interlinked bipartite networks in terrestrial biomes. In addition, we would welcome the use of unipartite projections of bipartite networks because of the strong ecological and evolutionary effects of intraguild processes such as competition or facilitation (Cohen 1977; Sugihara 1984). Furthermore, when interaction weights are available, unipartite projections can be performed in which information on interaction intensity of the original network is retained (Newman 2001; Opsahl 2009).
Analyses of networks that focus on one interaction type restrict species to only play a single ecological role. One option to overcome such biased interpretations of ecological relationships is to regard bipartite networks as representations of single interaction types that can be merged into a network of networks (Olff et al. 2009; Fontaine et al. 2011). However, the network of networks approach was only represented in two of the 54 studies, suggesting that there is great opportunity for expansion. This approach enables identification of species that display different trophic roles in multiple networks (Melián et al. 2009; Fontaine et al. 2011), such as an insect species preying on seeds in a herbivore–plant network while hosting a parasitoid in a separate parasitoid–host network (Pocock, Evans & Memmott 2012). The network of networks approach could permit not only to identify keystone nodes at the intranetwork level but to additionally identify keystone nodes coupling different networks. Hence, migrant or highly mobile species may connect nodes across space (Dobson 2009; McCann & Rooney 2009); for example, pollinators and herbivores involved in long migrations could link plants belonging to different patches, regions and continents through pollination and herbivory along their migratory routes. Similarly, long-lived species could be connecting short-lived species across time (Olesen et al. 2008).
Since 85% of the studies on antagonistic interactions relied on the literature for building their interaction networks, freely available online data repositories seem to play a crucial role for the advancement of this field. Parameters of network quality have been reported to affect the perception we have of the network structure. Thus, the level of node aggregation has been shown to affect our ability to predict the frequency distribution of the number of links per node (Sugihara, Schoenly & Trombla 1989; Martinez 1991). Also, a low sampling intensity of interactions may lead to a failure to observe links between less abundant species (Winemiller 1989; Goldwasser & Roughgarden 1997). Hence, ecologists using public sources of information could widely benefit from a reliable and standardized protocol with consistent data collection methodologies for network building, and details on data collection being reported to allow for across-network comparisons. According to our study, there appear to be a need for data that allow for incorporation of interaction strengths to be included in data repositories.
Although we identified a range of methods used for quantifying the presence and strength of the trophic interactions between nodes, we noted a general lack of the assessment of energy transfer between trophic entities as a measure to weight interaction strengths (but see Scotti & Jordán 2010). Topological networks that are built using energy or biomass transfers across ecologically relevant entities could provide a framework for integrating the function and structure of biodiversity (Thompson et al. 2012) and therefore reconciling the historically parallel community and ecosystem approaches. We therefore urge for more studies that use such metrics to quantify link strengths in topological networks.
One of the predominant study purposes was the comparison of network attributes across time, ecosystems or treatments (e.g. Dunne et al. 2008; Woodward et al. 2008; Laliberté & Tylianakis 2010). The implementation of such comparisons across gradients of species presence or perturbations could be extremely fruitful from an applied ecosystem management perspective and to complement simulations of extinction sequences. However, we note a lack of studies comparing networks across complete temporal series, for instance reproductive states (Jordán & Osváth 2009). This dynamic approach could yield detailed data on network flexibility according to resource quantity and quality and phenological states of consumers and resources.
We found several shortages of studies focusing on questions related to properties of individual nodes. First, none of the studies on antagonistic interactions examined whether network properties vary depending on the organizational level considered (i.e. from individuals up to ecosystem level, but see Dupont, Trojelsgaard & Olesen 2011 for mutualistic interactions). Classification of nodes using criteria such as individuals or sex–age classes could help identifying the network of functional interactions unrestricted from real or perceived taxonomic relationships (Wells & O'Hara 2013). Since resource use may vary both between and within individuals, for example between different ontogenic stages, such analyses could be imperative for evaluating functional properties of ecosystems and how these properties relate to taxonomic and phylogenetic diversity (Flynn et al. 2011). Furthermore, we could not identify any study evaluating interacting effects of species traits on the network attributes, for instance the effect of body size distributions on network structure depending on node abundances. Since node-specific traits have been shown to independently influence the interaction patterns observed (Woodward et al. 2005; Digel, Riede & Brose 2011), this is a potentially serious shortcoming.
Network clustering (degree of modularity) and nestedness (degree of asymmetry) both seem to provide information on evolutionary processes shaping network structure. Both indices are being increasingly applied (Kondoh, Kato & Sakato 2010; Meskens et al. 2011; Krasnov et al. 2012), and their formulas continuously improved (Almeida-Neto, Guimaraes & Lewinsohn 2007; Joppa & Williams 2011). Clustering and nestedness have additionally been suggested to potentially explain the network resilience against perturbations, with modular and nested patterns sometimes preventing the spread of perturbations across the network (Verdu & Valiente-Banuet 2008; Thébault & Fontaine 2010; Stouffer & Bascompte 2011). Indices at the whole network level may thus help uncovering the multispecific level at which evolution works resulting in perturbation-resistant network architectures. Few studies in our data base analysed the relationships between indices (e.g. Scotti, Podani & Jordán 2007; Fedor & Vasas 2009; Fortuna et al. 2010). Moreover, studies relating network indices to node performance (assessed as processes rates, for example productivity, fitness, population dynamics) or to ecosystem services (e.g. pollination rates) were absent from our sampled studies (but see Gómez & Perfectti 2012 for mutualistic interactions and Montoya, Rodríguez & Hawkings 2003 for an antagonistic network).
We identified some key issues related to recent work on trophic networks. First, there appears to be a poor representation of studies on mutualistic interactions beyond plant–pollinator/seed dispersal relationships. Our study also highlights that we systematically seem to avoid certain nodes such as detritus in trophic networks, despite their ecological significance. We therefore suggest that further theoretical development aimed at finding appropriate inclusion of such nodes in a topological framework is needed. We additionally need to increase the representation of anthropogenic processes in determining trophic network structure. We similarly need to tackle the challenge of developing integrated network of networks, since many ecological entities may link networks across space, time and interaction types. There is similarly a huge scope for integrating network patterns with specific node properties, such as fitness, ecosystem function and evolutionary history. For instance, functional groups based on trait similarity can be used as nodes instead of taxonomic units, or topological properties of nodes could be included as relevant functional traits for quantification of functional diversity. Finally, using energy or biomass transfer between ecologically relevant entities to build and weight topological networks could provide a possible avenue for unifying the community and ecosystem approaches to analyse ecological networks, but such an approach has so far seen very limited use.
The authors are grateful to Prof. J.M. Montoya and two anonymous reviewers who provided very useful comments and suggestions to a previous version of the manuscript. MM was supported by a free-standing postdoctoral fellowship cofunded by the National Research Foundation and the University of the Witwatersrand. FD was supported by a University of Pretoria Fellowship and by the National Research Foundation.