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.     

Food webs robustness to biodiversity loss: the roles of connectance, expansibility and degree distribution

We analyse the robustness of food webs against species loss by considering the influence of several structural factors of the networks, such as connectance, degree distribution and expansibility. The last concept refers to the absence of structural bottlenecks in the food web, whose removal separate the network into large isolate clusters. In theory networks with identical connectance can display different expansibility characteristics. Using the spectral scaling method we studied 17 food networks and classified them as good expansion (GE) and not-GE networks. The combination of GE properties and degree distribution of species permitted the classification of food webs into six different classes. These classes characterize the differences in robustness of food webs to species loss. While the webs having uniform degree distributions and displaying GE properties are the most robust to species loss, the presence of bottlenecks and skewed distribution of the number of links per species make food webs very vulnerable to primary removal of species.     

Topological properties of food webs: from real data to community assembly models

We explore patterns of trophic connections between species in the largest and highest-quality empirical food webs to date, introducing a new topological property called the link distribution frequency (i.e. degree distribution), defined as the frequency of species S _L with L links. Non-trivial differences are shown in link distribution frequencies between species-rich and species-poor communities, which might have important consequences for the responses of ecosystems to disturbances. Coarse-grained topological properties observed, as species richness-connectance and number of links-species richness relationships, provide no support for the theory of links-species scaling law or constant connectance across empirical food webs investigated. We further explore these observations by means of simulated food webs resulting from multitrophic assembly models using different functional responses between species. Species richness-connectance and links-species richness relationships of empirical food webs are reproduced by our models, but degree distributions are not properly predicted, suggesting the need of new theoretical approximations to food web assembly. The best agreement between empirical and simulated webs occurs for low values of interaction strength between species, corroborating previous empirical and theoretical findings where weak interactions govern food web dynamics.     

Body sizes,cumulative and allometric degree distributions across natural food webs

The distributions of body masses and degrees (i.e. the number of trophic links) across species are key determinants of food‐web structure and dynamics. In particular, allometric degree distributions combining both aspects in the relationship between degrees and body masses are of critical importance for the stability of these complex ecological networks. They describe decreases in vulnerability (i.e. the number of predators) and increases in generality (i.e. the number of prey) with increasing species’ body masses. We used an entirely new global body‐mass database containing 94 food webs from four different ecosystem types (17 terrestrial, 7 marine, 54 lake, 16 stream ecosystems) to analyze (1) body mass distributions, (2) cumulative degree distributions (vulnerability, generality, linkedness), and (3) allometric degree distributions (e.g. generality – body mass relationships) for significant differences among ecosystem types. Our results demonstrate some general patterns across ecosystems: (1) the body masses are often roughly log‐normally (terrestrial and stream ecosystems) or multi‐modally (lake and marine ecosystems) distributed, and (2) most networks exhibit exponential cumulative degree distributions except stream networks that most often possess uniform degree distributions. Additionally, with increasing species body masses we found significant decreases in vulnerability in 70% of the food webs and significant increases in generality in 80% of the food webs. Surprisingly, the slopes of these allometric degree distributions were roughly three times steeper in streams than in the other ecosystem types, which implies that streams exhibit a more pronounced body mass structure. Overall, our analyses documented some striking generalities in the body‐mass (allometric degree distributions of generality and vulnerability) and degree structure (exponential degree distributions) across ecosystem types as well as surprising exceptions (uniform degree distributions in stream ecosystems). This suggests general constraints of body masses on the link structure of natural food webs irrespective of ecosystem characteristics.     

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.     

Food webs: Ordering species according to body size yields high degree of intervality

Food webs, the networks describing “who eats whom” in an ecosystem, are nearly interval, i.e. there is a way to order the species so that almost all the resources of each consumer are adjacent in the ordering. This feature has important consequences, as it means that the structure of food webs can be described using a single (or few) species' traits. Moreover, exploiting the quasi-intervality found in empirical webs can help build better models for food web structure. Here we investigate which species trait is a good proxy for ordering the species to produce quasi-interval orderings. We find that body size produces a significant degree of intervality in almost all food webs analyzed, although it does not match the maximum intervality for the networks. There is also a great variability between webs. Other orderings based on trophic levels produce a lower level of intervality. Finally, we extend the concept of intervality from predator-centered (in which resources are in intervals) to prey-centered (in which consumers are in intervals). In this case as well we find that body size yields a significant, but not maximal, level of intervality. These results show that body size is an important, although not perfect, trait that shapes species interactions in food webs. This has important implications for the formulation of simple models used to construct realistic representations of food webs.     

Biology,Methodology or Chance? The Degree Distributions of Bipartite Ecological Networks

The distribution of the number of links per species, or degree distribution, is widely used as a summary of the topology of complex networks. Degree distributions have been studied in a range of ecological networks, including both mutualistic bipartite networks of plants and pollinators or seed dispersers and antagonistic bipartite networks of plants and their consumers. The shape of a degree distribution, for example whether it follows an exponential or power-law form, is typically taken to be indicative of the processes structuring the network. The skewed degree distributions of bipartite mutualistic and antagonistic networks are usually assumed to show that ecological or co-evolutionary processes constrain the relative numbers of specialists and generalists in the network. I show that a simple null model based on the principle of maximum entropy cannot be rejected as a model for the degree distributions in most of the 115 bipartite ecological networks tested here. The model requires knowledge of the number of nodes and links in the network, but needs no other ecological information. The model cannot be rejected for 159 (69%) of the 230 degree distributions of the 115 networks tested. It performed equally well on the plant and animal degree distributions, and cannot be rejected for 81 (70%) of the 115 plant distributions and 78 (68%) of the animal distributions. There are consistent differences between the degree distributions of mutualistic and antagonistic networks, suggesting that different processes are constraining these two classes of networks. Fit to the MaxEnt null model is consistently poor among the largest mutualistic networks. Potential ecological and methodological explanations for deviations from the model suggest that spatial and temporal heterogeneity are important drivers of the structure of these large networks.     

Local stability properties of complex,species‐rich soil food webs with functional block structure

Ecologists have long debated the properties that confer stability to complex, species‐rich ecological networks. Species‐level soil food webs are large and structured networks of central importance to ecosystem functioning. Here, we conducted an analysis of the stability properties of an up‐to‐date set of theoretical soil food web models that account both for realistic levels of species richness and the most recent views on the topological structure (who is connected to whom) of these food webs. The stability of the network was best explained by two factors: strong correlations between interaction strengths and the blocked, nonrandom trophic structure of the web. These two factors could stabilize our model food webs even at the high levels of species richness that are typically found in soil, and that would make random systems very unstable. Also, the stability of our soil food webs is well‐approximated by the cascade model. This result suggests that stability could emerge from the hierarchical structure of the functional organization of the web. Our study shows that under the assumption of equilibrium and small perturbations, theoretical soil food webs possess a topological structure that allows them to be complex yet more locally stable than their random counterpart. In particular, results strongly support the general hypothesis that the stability of rich and complex soil food webs is mostly driven by correlations in interaction strength and the organization of the soil food web into functional groups. The implication is that in real‐world food web, any force disrupting the functional structure and distribution pattern of interaction strengths (i.e., energy fluxes) of the soil food webs will destabilize the dynamics of the system, leading to species extinction and major changes in the relative abundances of species.     

食物网结构与功能: 理论进展与展望

食物网刻画了物种间通过捕食而形成的复杂网络关系。阐明食物网结构与功能之间的关系, 既是生态学的基本理论问题, 也是预测全球变化背景下生态系统响应的重要依据。早期关于食物网结构与功能的研究往往是分离的, 或是基于食物链等的简单网络模型, 而近期研究基于复杂食物网模型取得了重要理论进展。本文综述了食物网研究的理论方法和近期进展, 特别介绍了复杂食物网中的结构、多样性和功能的度量指标、结构-多样性-功能之间的关系以及全球变化对食物网结构与功能的影响。本文最后对未来的一些研究方向进行了展望, 包括与功能性状和化学计量学的整合、食物网与其他网络类型的整合以及拓展食物网研究的空间和时间尺度。     

Parasites in food webs: the ultimate missing links

Parasitism is the most common consumer strategy among organisms, yet only recently has there been a call for the inclusion of infectious disease agents in food webs. The value of this effort hinges on whether parasites affect food‐web properties. Increasing evidence suggests that parasites have the potential to uniquely alter food‐web topology in terms of chain length, connectance and robustness. In addition, parasites might affect food‐web stability, interaction strength and energy flow. Food‐web structure also affects infectious disease dynamics because parasites depend on the ecological networks in which they live. Empirically, incorporating parasites into food webs is straightforward. We may start with existing food webs and add parasites as nodes, or we may try to build food webs around systems for which we already have a good understanding of infectious processes. In the future, perhaps researchers will add parasites while they construct food webs. Less clear is how food‐web theory can accommodate parasites. This is a deep and central problem in theoretical biology and applied mathematics. For instance, is representing parasites with complex life cycles as a single node equivalent to representing other species with ontogenetic niche shifts as a single node? Can parasitism fit into fundamental frameworks such as the niche model? Can we integrate infectious disease models into the emerging field of dynamic food‐web modelling? Future progress will benefit from interdisciplinary collaborations between ecologists and infectious disease biologists.     

Phylogeny versus body size as determinants of food web structure

Food webs are the complex networks of trophic interactions that stoke the metabolic fires of life. To understand what structures these interactions in natural communities, ecologists have developed simple models to capture their main architectural features. However, apparently realistic food webs can be generated by models invoking either predator-prey body-size hierarchies or evolutionary constraints as structuring mechanisms. As a result, this approach has not conclusively revealed which factors are the most important. Here we cut to the heart of this debate by directly comparing the influence of phylogeny and body size on food web architecture. Using data from 13 food webs compiled by direct observation, we confirm the importance of both factors. Nevertheless, phylogeny dominates in most networks. Moreover, path analysis reveals that the size-independent direct effect of phylogeny on trophic structure typically outweighs the indirect effect that could be captured by considering body size alone. Furthermore, the phylogenetic signal is asymmetric: closely related species overlap in their set of consumers far more than in their set of resources. This is at odds with several food web models, which take only the view-point of consumers when assigning interactions. The echo of evolutionary history clearly resonates through current food webs, with implications for our theoretical models and conservation priorities.     

Node centrality indices in food webs: Rank orders versus distributions

Network analysis examines the role of species in ecological communities. The most common approach involves measurement of centrality of species or other groups of individuals based on their topological positions in food webs, followed by establishing the rank order of importance of these groups. However, ranking may differ considerably with indices of centrality and therefore comparison of rank orders is essential to obtain more meaningful results on species performance. Since ranking ignores absolute differences between centrality values, species orders may neglect important structural information in food webs. Consequently, simultaneous examination of the distribution of index values is inevitable. Hierarchical clustering and consensus generation revealed that rank orders of centrality exhibit a similar pattern over six example food webs, while distributions differ not only with indices because their relationships are largely inconsistent with food webs as well. Therefore, optimal analysis of networks and the selection of keystone species in any ecological study should rely upon both of these procedures. Similar conclusions are drawn from the detailed evaluation of a sample food web from the Florida Bay.     

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.     

Press perturbation experiments and the indeterminacy of ecological interactions: effects of taxonomic resolution and experimental duration

The outcomes of press perturbation experiments on community dynamics are difficult to predict because there is a high degree of indeterminacy in the strength and direction of ecological interactions. Ecologists need to quantify uncertainties in estimates of interaction strength, by determining all the possible values a given interaction strength could take and the relative likelihood of each value. In this study, we assess the degree to which fish effects on zooplankton and phytoplankton are indeterminate in direction using a combination of experimental data and Monte Carlo simulations. Based on probability distributions of interaction strength (i.e. effect magnitude), we estimated the probability of each fish interaction being negative, positive or undetermined in direction. We then investigated how interaction strength and its predictability might vary with experimental duration and the taxonomic resolution of food web data. Results show that most effects of fish on phyto- and zooplankton were indeed indeterminate, and that the effects of fish were more predictable in direction as the taxonomic resolution of food web data decreased and the experimental duration increased. Results also show that most distributions of interaction strength were not normal, suggesting that normal based statistical procedures for testing hypothesis about interaction strength may be misleading, as well as predictions of food web models assuming normal distributions of interaction strength. By considering the probability distributions and confidence intervals of interaction parameters, ecologists would better understand the outcomes of species interactions and make more realistic predictions about our perturbations in natural food webs.     

Do Food Web Models Reproduce the Structure of Mutualistic Networks?

Background

Simple models inspired by processes shaping consumer-resource interactions have helped to establish the primary processes underlying the organization of food webs, networks of trophic interactions among species. Because other ecological interactions such as mutualisms between plants and their pollinators and seed dispersers are inherently based in consumer-resource relationships we hypothesize that processes shaping food webs should organize mutualistic relationships as well.

Methodology/Principal Findings

We used a likelihood-based model selection approach to compare the performance of food web models and that of a model designed for mutualisms, in reproducing the structure of networks depicting mutualistic relationships. Our results show that these food web models are able to reproduce the structure of most of the mutualistic networks and even the simplest among the food web models, the cascade model, often reproduce overall structural properties of real mutualistic networks.

Conclusions/Significance

Based on our results we hypothesize that processes leading to feeding hierarchy, which is a characteristic shared by all food web models, might be a fundamental aspect in the assembly of mutualisms. These findings suggest that similar underlying ecological processes might be important in organizing different types of interactions.     

Fit, efficiency, and biology: some thoughts on judging food web models

Revealing the processes that determine who eats whom, and thereby the structure of food webs, is a long running challenge in ecological research. Recent advances include development of new methods for measuring fit of models to observed food web data, and thereby testing which are the ‘best’ food web models. The best model could be considered the most efficient with relatively few parameters and high explanatory power. Another recent advance involves adding some additional biology to food web models in the form of foraging theory based on maximisation of energy intake as the predictor of species' diets in food webs. While it is interesting to compare efficiency among food web models, we believe that such comparisons at least should be interpreted with caution, since they do not account for any differences in motivation, formulation, and potential that might also exist among models. Furthermore, we see an important but somewhat neglected role for experimental tests of models of food web structure.     

Current food web models cannot explain the overall topological structure of observed food webs

Topological food webs illustrating “who eats whom” in different systems exhibit similar, non‐random, structures suggesting that general rules govern food web structure. Current food web models correctly predict many measures of food web topology from knowledge of species richness and connectance (fraction of possible predator–prey links that actually occur), together with assumptions about the ecological rules governing “who eats whom”. However, current measures are relatively insensitive to small changes in topology. Improvement of, and discrimination among, current models requires development of new measures of food web structure. Here I examine whether current food web models (cascade, niche, and nested hierarchy models, plus a random null model) can predict a new measure of food web structure, structural stability. Structural stability complements other measures of food web topology because it is sensitive to changes in topology that other measures often miss. The cascade and null models respectively over‐ and underpredict structural stability for a set of 17 high‐quality food webs. While the niche and nested hierarchy models provide unbiased predictions on average, their 95% confidence intervals frequently fail to include the observed data. Observed structural stabilities for all models are overdispersed compared to model predictions, and predicted and observed structural stabilities are uncorrelated, indicating that important sources of variation in structural stability are not captured by the models. Crucially, poor model performance arises because observed variation in structural stability is unrelated to variation in species richness and connectance. In contrast, almost all other measures of food web topology vary with species richness and connectance in natural webs. No model that takes species richness and connectance as the only input parameters can reproduce observed variation in structural stability. Further progress in predicting and explaining food web topology will require fundamentally new models based on different input parameters.     

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.     

A landscape theory for food web architecture

Ecologists have long searched for structures and processes that impart stability in nature. In particular, food web ecology has held promise in tackling this issue. Empirical patterns in food webs have consistently shown that the distributions of species and interactions in nature are more likely to be stable than randomly constructed systems with the same number of species and interactions. Food web ecology still faces two fundamental challenges, however. First, the quantity and quality of food web data required to document both the species richness and the interaction strengths among all species within food webs is largely prohibitive. Second, where food webs have been well documented, spatial and temporal variation in food web structure has been ignored. Conversely, research that has addressed spatial and temporal variation in ecosystems has generally ignored the full complexity of food web architecture. Here, we incorporate empirical patterns, largely from macroecology and behavioural ecology, into a spatially implicit food web structure to construct a simple landscape theory of food web architecture. Such an approach both captures important architectural features of food webs and allows for an exploration of food web structure across a range of spatial scales. Finally, we demonstrated that food webs are hierarchically organized along the spatial and temporal niche axes of species and their utilization of food resources in ways that stabilize ecosystems.